Sherpa 1.4.1 Manual

1. Introduction

Sherpa is a Monte Carlo event generator for the Simulation of High-Energy Reactions of PArticles in lepton-lepton, lepton-photon, photon-photon, lepton-hadron and hadron-hadron collisions. This document provides information to help users understand and apply Sherpa for their physics studies. The event generator is introduced, in broad terms, and the installation and running of the program are outlined. The various options and parameters specifying the program are compiled, and their meanings are explained. This document does not aim at giving a complete description of the physics content of Sherpa . To this end, the authors refer the reader to the original publication, [Gle08b] .

1.1 Introduction to Sherpa

Sherpa [Gle08b] is a Monte Carlo event generator that provides complete hadronic final states in simulations of high-energy particle collisions. The produced events may be passed into detector simulations used by the various experiments. The entire code has been written in C++, like its competitors Herwig++ [Bah08] and Pythia 8 [Sjo07] .

Sherpa simulations can be achieved for the following types of collisions:

• for lepton–lepton collisions, as explored by the CERN LEP experiments,
• for lepton–photon collisions,
• for photon–photon collisions with both photons either resolved or unresolved,
• for deep-inelastic lepton-hadron scattering, as investigated by the HERA experiments at DESY, and,
• in particular, for hadronic interactions as studied at the Fermilab Tevatron or the CERN LHC.

The list of physics processes that come with Sherpa covers particle production at tree level in the Standard Model and in models beyond the Standard Model: The complete set of Feynman rules for its Minimal Supersymmetric extension according to [Ros89] [Ros95] has been implemented, including general mixing matrices for inter-generational squark and slepton mixing. Among other interaction models the ADD model of Large Extra Dimensions has been made available, too [Gle03a] . Furthermore, anomalous gauge couplings [Hag86] , a model with an extended Higgs sector [Ded08] , and a version of the Two-Higgs Doublet Model are available. The Sherpa program owes this versatility to the inbuilt matrix-element generators, AMEGIC++ and Comix, and to it’s phase-space generator Phasic [Kra01] , which automatically calculate and integrate tree-level amplitudes for the implemented models. This feature enables Sherpa to be used as a cross-section integrator and parton-level event generator as well. This aspect has been extensively tested, see e.g. [Gle03b] ,[Hag05] .

As a second key feature of Sherpa the program provides an implementation of the merging approach of [Hoe09] . This algorithm yields improved descriptions of multijet production processes, which copiously appear at lepton-hadron colliders like HERA [Car09] , or hadron-hadron colliders like the Tevatron and the LHC, [Kra04] , [Kra05] ,[Gle05] ,[Hoe09a] . An older approach, implemented in previous versions of Sherpa and known as the CKKW technique [Cat01] ,[Kra02] , has been compared in great detail in [Alw07] with other approaches, such as the MLM merging prescription [Man01] as implemented in Alpgen [Man02] , Madevent [Ste94] ,[Mal02a] , or Helac [Kan00] ,[Pap05] and the CKKW-L prescription [Lon01] ,[Lav05] of Ariadne [Lon92] .

This manual contains all information necessary to get started with Sherpa as quickly as possible. By reading it, users should be enabled to setup the program according to their needs for studying various physics aspects. Therefore, all switches plus options that have been provided are listed. It is explained how to use them, how Sherpa can be run in different modes and how the results and output of Sherpa can be interpreted. For external code that can be linked, corresponding references are given and users are encouraged to cite them accordingly.

On the other hand, the physics of Sherpa and its underlying structure and coding principles are not detailed in this manual. For this, readers are encouraged to refer to original work of the authors. Also, whenever justified, Sherpa users are kindly asked to cite Sherpa ’s original publication [Gle08b] . Moreover the authors strongly recommend the study of the manuals and/or many excellent publications on different aspects of event generation and physics at collider experiments of the other event generator authors.

This manual is organized as follows: in Basic structure the modular structure intrinsic to Sherpa is introduced. Getting started contains information about and instructions for the installation of the package. There is also a description of the steps that are needed to run Sherpa and generate events. The Input structure is then discussed, and the ways in which Sherpa can be steered are explained. All parameters and options are discussed in Parameters. Advanced Tips and Tricks are detailed, and some options for Customization are outlined for those more familiar with Sherpa. There is also a short description of the different Examples provided with Sherpa.

It should be stressed that the construction of a Monte Carlo program requires a number of implicit assumptions, approximations and simplifications of complicated situations. Potential bugs and other shortcomings of the authors may also be included. The results of event generators, independent of their quality, should therefore always be verified and cross-checked with results obtained by the programs of other authors.

1.2 Basic structure

The construction of the Sherpa program has been pursued in a modular way. It fully reflects the paradigm of Monte Carlo event generation of factorizing the simulation into well defined phases. Accordingly, each module encapsulates a different aspect of event generation for high-energy particle reactions. It resides within its own namespace and is located in its own subdirectory of the same name. The main module called SHERPA steers the interplay of all modules – or phases – and the actual generation of the events. Altogether, the following modules are currently distributed with the Sherpa framework:

• ATOOLS

  This is the toolbox for all other modules. Since the Sherpa framework does not rely on CLHEP etc., the ATOOLS contain classes with mathematical tools like vectors and matrices, organization tools such as read-in or write-out devices, and physics tools like particle data or classes for the event record.

• METOOLS

  In this module some general methods for the evaluation of helicity amplitudes have been accumulated. They are used in AMEGIC++ , the EXTRA_XS module, and the new matrix-element generator Comix. This module also contains helicity amplitudes for some generic matrix elements, that are, e.g., used by HADRONS++ . Further, METOOLS also contains a simple library of tensor integrals which are used in the PHOTONS++ matrix element corrections.

• BEAM

  This module manages the treatment of the initial beam spectra for different colliders. The three options which are currently available include a monochromatic beam, which requires no extra treatment, photon emission in the Equivalent Photon Approximation (EPA) and - for the case of an electron collider - laser backscattering off the electrons, leading to photonic initial states.

• PDF

  The PDF module provides access to various parton density functions (PDFs) for the proton and the photon. In addition, it hosts an interface to the LHAPDF package, which makes a full wealth of PDFs available. An (analytical) electron structure function is supplied in the PDF module as well.

• MODEL

  This module is responsible for setting up the physics model for a simulation run. It comprises the initialization of particle properties, basic physics parameters (coupling constants, mixing angles, etc.) and the set of available interaction vertices (Feynman rules). By now, there exist explicit implementations of the Standard Model (SM), its Minimal Supersymmetric extension (MSSM), the ADD model of large extra dimensions, and a comprehensive set of operators parametrizing anomalous triple and quartic electroweak gauge boson couplings.

• EXTRA_XS

  In this module a (limited) collection of analytic expressions for simple 2->2 processes within the SM are provided together with classes embedding them into the Sherpa framework. This also includes methods used for the definition of the starting conditions for parton-shower evolution, such as colour connections and the hard scale of the process. The classes for phase-space integration are not included here, they are located in the module Phasic, since they are needed by AMEGIC++ and Comix as well.

• AMEGIC++

  AMEGIC++ [Kra01] is Sherpa ’s original matrix-element generator. It employs the method of helicity amplitudes [Kle85] ,[Bal92] and works as a generator, which generates generators: During the initialization run the matrix elements for a given set of processes, as well as their specific phase-space mappings are created by AMEGIC++. Corresponding C++ sourcecode is written to disk and compiled by the user using the makelibs script. The produced libraries are linked to the main program automatically in the next run and used to calculate cross sections and to generate weighted or unweighted events. AMEGIC++ has been tested for multi-particle production in the Standard Model [Gle03b] . Its MSSM implementation has been validated in [Hag05] .

• COMIX

  Comix is a multi-leg tree-level matrix element generator, based on the color dressed Berends-Giele recursive relations [Duh06] . It employs a new algorithm to recursively compute phase-space weights and can be run in multithreaded mode to make better use of multicore processors and multiprocessor machines [Gle08] , see also [Gle08a] . The module is a useful supplement to older matrix element generators like AMEGIC++ in the high multiplicity regime. Due to the usage of colour sampling it is particularly suited for an interface with parton shower simulations and can hence be easily employed for the ME-PS merging within Sherpa. It is Sherpa’s default large multiplicity matrix element generator for the Standard Model.

• PHASIC++

  All base classes dealing with the Monte Carlo phase-space integration are located in this module. For the evaluation of the initial-state (laser backscattering, initial-state radiation) and final-state integrals, the adaptive multi-channel method of [Kle94] ,[Ber94] is used by default together with a Vegas optimization [Lep80] of the single channels. In addition, final-state integration accomplished by Rambo [Kle85a] , Sarge [Dra00] and HAAG [Ham02] is supported.

• CSSHOWER++

  This is the module hosting Sherpa’s default parton shower, which was published in [Sch07a] . The corresponding shower model was originally proposed in [Nag05] , [Nag06] . It relies on the factorisation of real-emission matrix elements in the CS subtraction framework [Cat96b] , [Cat02] . There exist four general types of CS dipole terms that capture the complete infrared singularity structure of next-to-leading order QCD amplitudes. In the large-N_C limit, the corresponding splitter and spectator partons are always adjacent in colour space. The dipole functions for the various cases, taken in four dimensions and averaged over spins, are used as shower splitting kernels.

• AMISIC++

  AMISIC++ contains classes for the simulation of multiple parton interactions according to [Sjo87] . In Sherpa the treatment of multiple interactions has been extended by allowing for the simultaneous evolution of an independent parton shower in each of the subsequent (semi-)hard collisions. The beam–beam remnants are organized such that partons which are adjacent in colour space are also adjacent in momentum space. The corresponding classes for beam remnant handling reside in the PDF and SHERPA modules.

• AHADIC++

  AHADIC++ is Sherpa ’s hadronization package, for translating the partons (quarks and gluons) into primordial hadrons, to be further decayed in HADRONS++. The algorithm bases on the cluster fragmentation ideas presented in [Got82] ,[Got83] ,[Web83] ,[Got86] and implemented in the Herwig family of event generators. It should be noted, though, that the Sherpa version, based on [Win03] , indeed differs from the original versions.

• HADRONS++

  HADRONS++ is the module for simulating hadron and tau-lepton decays. The resulting decay products respect full spin correlations (if desired). Several matrix elements and form-factor models have been implemented, such as the Kühn-Santamaría model, form-factor parametrizations from Resonance Chiral Theory for the tau and form factors from heavy quark effective theory or light cone sum rules for hadron decays.

• PHOTONS++

  The PHOTONS++ module holds routines to add QED radiation to hadron and tau-lepton decays. This has been achieved by an implementation of the YFS algorithm [Yen61] . The structure of PHOTONS++ is such that the formalism can be extended to scattering processes and to a systematic improvement to higher orders of perturbation theory [Sch08] . The application of PHOTONS++ therefore accounts for corrections that usually are added by the application of PHOTOS [Bar93] to the final state.

• SHERPA

  Finally, SHERPA is the steering module that initializes, controls and evaluates the different phases during the entire process of event generation. All routines for the combination of truncated showers and matrix elements, which are independent of the specific matrix element and parton shower generator are found in this module.

The actual executable of the Sherpa generator can be found in the subdirectory <prefix>/bin/ and is called Sherpa . To run the program, input files have to be provided in the current working directory or elsewhere by specifying the corresponding path, see Input structure. All output files are then written to this directory as well.

2. Getting started

2.1 Installation

Sherpa is distributed as a tarred and gzipped file named Sherpa-<version>.tar.gz, and can be unpacked in the current working directory with

 tar -zxf Sherpa-<version>.tar.gz .

To guarantee successful installation, the following tools should have been made available on the system: make, autoconf, automake and libtool. Furthermore, a C++ and FORTRAN compiler must be provided. Compilation and installation proceed through the following commands

 ./configure

 make install

If not specified differently, the directory structure after installation is organized as follows

$(prefix)/bin

Sherpa executeable and scripts

$(prefix)/include

headers for process library compilation

$(prefix)/lib

basic libraries

$(prefix)/share

PDFs, Decaydata, fallback run cards

The installation directory $(prefix) can be specified by using the ./configure --prefix /path/to/installation/target directive and defaults to the current working directory.

If Sherpa has to be moved to a different directory after the installation, one has to set the following environment variables for each run:

• SHERPA_INCLUDE_PATH=$newprefix/include/SHERPA-MC
• SHERPA_SHARE_PATH=$newprefix/share/SHERPA-MC
• SHERPA_LIBRARY_PATH=$newprefix/lib/SHERPA-MC
• LD_LIBRARY_PATH=$SHERPA_LIBRARY_PATH:$LD_LIBRARY_PATH

Sherpa can be interfaced with various external packages, e.g. HepMC, for event output, or LHAPDF, for PDFs. For this to work, the user has to pass the appropriate commands to the configure step. This is achieved as shown below:

./configure --enable-hepmc2=/path/to/hepmc2 --enable-lhapdf=/path/to/lhapdf

Here, the paths have to point to the top level installation directories of the external packages, i.e. the ones containing the lib/, share/, ... subdirectories.

For a complete list of possible configuration options run ‘./configure --help’.

The Sherpa package has successfully been compiled, installed and tested on SuSE, RedHat / Scientific Linux and Debian / Ubuntu Linux systems using the GNU C++ compiler versions 3.2, 3.3, 3.4, 4.0, 4.1, 4.2, 4.3 and 4.4 as well as on Mac OS X 10 using the GNU C++ compiler version 4.0. In all cases the GNU FORTRAN compiler g77 or gfortran has been employed. Note that GCC version 2.96 is not supported.

If you have multiple compilers installed on your system, you can use shell environment variables to specify which of these are to be used. A list of the available variables is printed with

./configure --help

in the Sherpa top level directory and looking at the last lines. Depending on the shell you are using, you can set these variables e.g. with export (bash) or setenv (csh). Examples:

export CXX=g++-3.4
export CC=gcc-3.4
export CPP=cpp-3.4

MacOS Installation

Installation on MacOS is supported at least in all Sherpa versions > 1.1.2. Before that, there might have been problems on the newer MacOS versions or architectures (10.5, Intel). The following issues have come up on Mac installations before, so please be aware of them:

• On 10.4 and 10.5 only gfortran is supported, and you will have to install it e.g. from HPC
• If you want to reconfigure, i.e. run the command autoreconf or (g)libtoolize, you have to make sure that you have a recent version of GNU libtool (>=1.5.22 has been tested). Don’t confuse this with the native non-GNU libtool which is installed in /usr/bin/libtool and of no use! Also make sure that your autools (autoconf >= 2.61, automake >= 1.10 have been tested) are of recent versions. All this should not be necessary though, if you only run configure.
• Make sure that you don’t have two versions of g++ and libstdc++ installed and being used inconsistently. This appeared e.g. when the gcc suite was installed through Fink to get gfortran. This caused Sherpa to use the native MacOS compilers but link the libstdc++ from Fink (which is located in /sw/lib). You can find out which libraries are used by Sherpa by running otool -L bin/Sherpa

2.2 Running Sherpa

The Sherpa executable resides in the directory <prefix>/bin/ where <prefix> denotes the path to the Sherpa installation directory. The way a particular simulation will be accomplished is defined by several parameters, which can all be listed in a common file, or data card (Parameters can be alternatively specified on the command line; more details are given in Input structure). This steering file is called Run.dat and some example setups (i.e. Run.dat files) are distributed with the current version of Sherpa. They can be found in the directory <prefix>/share/SHERPA-MC/Examples/, and descriptions of some of their key features can be found in the section Examples.

Please note: It is not in general possible to reuse run cards from previous Sherpa versions. Often there are small changes in the parameter syntax of the run cards from one version to the next. These changes are documented in our manuals. In addition, always use the newer Hadron.dat and Decaydata directories (and reapply any changes which you might have applied to the old ones), see HADRONS++.

The very first step in running Sherpa is therefore to adjust all parameters to the needs of the desired simulation. The details for properly doing this are given in Parameters. In this section, the focus is on the main issues for a successful operation of Sherpa. This is illustrated by discussing and referring to the parameter settings that come in the run card ./Examples/Tevatron_WJets/Run.dat. This is a simple run card created to show the basics of how to operate Sherpa. It should be stressed that this run-card relies on many of Sherpa’s default settings, and, as such, the user should understand those settings before using it to look at physics. For more information on the settings and parameters in Sherpa, see Parameters, and for more examples see the Examples section.

2.2.1 Process selection and initialization

Central to any Monte Carlo simulation is the choice of the hard processes that initiate the events. These hard processes are described by matrix elements. In Sherpa, the selection of processes happens in the (processes) part of the steering file. Only a few 2->2 reactions have been hard-coded. They are available in the EXTRA_XS module. The more usual way to compute matrix elements is to employ one of Sherpa’s automatic tree-level generators, AMEGIC++ and Comix, see Basic structure. If no matrix-element generator is selected, using the ME_SIGNAL_GENERATOR tag, then Sherpa will use whichever generator is capable of calculating the process, checking EXTRA_XS first, then Comix and then AMEGIC++. Therefore, for some processes, several of the options are used. In this example, EXTRA_XS calculates the 2->2 part of the process, and Comix calculates the 2->3,4 parts.

To begin with the example, the Sherpa run has to be started by changing into the <prefix>/share/SHERPA-MC/Examples/Tevatron_WJets/ directory and executing

<prefix>/bin/Sherpa 

The user may also run from an arbitrary directory, employing <prefix>/bin/Sherpa PATH=<prefix>/share/SHERPA-MC/Examples/Tevatron_WJets. In the example, the keyword PATH is specified by an absolute path. It may also be specified relative to the current working directory. If it is not specified at all or it is omitted, the current working directory is understood.

For good book-keeping, it is highly recommended to reserve different subdirectories for different simulations as is demonstrated with the example setups.

If AMEGIC++ is used, Sherpa requires an initialization run, where libraries are written out, then the libraries must be compiled and linked by running a makelibs script in the working directory, and then Sherpa is run again for the actual cross section integrations and event generation. For an example of how to run Sherpa using AMEGIC++, see Running Sherpa with AMEGIC++.

If the Internal hard-coded cross sections or Comix are used, and AMEGIC++ is not, an initialization run is not needed, and Sherpa will calculate the cross sections and generate events during the first run.

As the cross sections are integrated, the integration over phase space is optimized to arrive at an efficient event generation. Subsequently events are generated if EVENTS was specified either at the command line or added to the Run.dat file in the (run) section.

The generated events are not stored into a file by default; for details on how to store the events see Event output formats. Note that the computational effort to go through this procedure of generating, compiling and integrating the matrix elements of the hard processes depends on the complexity of the parton-level final states. For low multiplicities ( 2->2,3,4 ), of course, it can be followed instantly.

Usually more than one generation run is wanted. As long as the parameters that affect the matrix-element integration are not changed, it is advantageous to store the cross sections obtained during the generation run for later use. This saves CPU time especially for large final-state multiplicities of the matrix elements. To store the integration results, a <result> directory has to be created in Tevatron_WJets (Alternatively, the command line option ‘-g’ can be invoked, see Command line options). Then utilizing an extended command line reading

<prefix>/bin/Sherpa RESULT_DIRECTORY=<result>/

a generation run can be started and the results of the integration will be stored in <result>, see RESULT_DIRECTORY. The next time this command line is used, Sherpa will look for the integration results in <result> and read them in. Of course, if corresponding parameters do change, the cross sections have to be re-evaluated for a valid new generation run. The new results have to be stored in a new directory or the <result> directory may be re-used once it has been emptied. Basically, most of the parameters listed in the (model), (me) and (selector) part of Run.dat determine the calculation of cross sections. Standard examples are changing the magnitude of couplings, renormalization or factorization scales, changing the PDF or centre-of-mass energy, or, applying different cuts at the parton level. If unsure whether a re-integration is required, a simple test is to remove the RESULT_DIRECTORY option from the run command and check whether the new integration numbers (statistically) comply with the stored ones.

One more remark (or maybe warning) concerning the validity of the process libraries is in order here: it is absolutely mandatory to generate new library files, whenever the physics model is altered, i.e. particles are added or removed and hence new or existing diagrams may or may not anymore contribute to the same final states. Also, when particle masses are switched on or off new library files must be generated (however, masses may be changed between non-zero values keeping the same process libraries). Old library files cannot account for such changes, since once generated their functional structure is fixed. The best thing is to create a new and separate setup directory. Otherwise the Process and Result directories have to be erased:

rm -rf Process/     and     rm -rf Result/

In either case one has to start over with the whole initialization procedure to prepare for the generation of events again.

2.2.2 The example set-up: W+Jets at Tevatron

The setup (or the Run.dat file) provided in ./Examples/Tevatron_WJets/ can be considered as a standard example to illustrate the generation of fully hadronized events in Sherpa. Such events will include effects from parton showering, hadronization into primary hadrons and their subsequent decays into stable hadrons. Moreover, the example chosen here nicely demonstrates how Sherpa is used in the context of merging matrix elements and parton showers [Hoe09] . In addition to the aforementioned corrections, this simulation of inclusive W production (with the W decaying into electron and anti-electron-neutrino ) will then include higher-order jet corrections at the tree level. As a result the transverse-momentum distribution of the W boson as measured by the D0 and CDF collaborations at Tevatron Run I can be well described, see also [Kra04] ,[Kra05] ,[Gle05] .

Before event generation, the initialization procedure as described in Process selection and initialization has to be completed. The matrix-element processes included in the setup are the following:

  proton anti-proton -> parton parton -> electron anti-electron-neutrino + up to two partons

In the (processes) part of the steering file this translates into

  Process 93 93 -> 11 -12 93{2}
  Order_EW 2;
  CKKW sqr(30/E_CMS)
  End process;

The physics model for these processes is the Standard Model (‘SM’) which is the default setting of the parameter MODEL, in the (model) part of Run.dat. Fixing the order of electroweak couplings to ‘2’, matrix elements of all partonic subprocesses for W production without any and with up to two extra QCD parton emissions will be generated. Proton–antiproton collisions are considered at beam energies of 900 GeV; under the (beam) part of the Run.dat file, one therefore has BEAM_1=2212, BEAM_2=-2212 and BEAM_ENERGY_{1,2}=980.0. The default PDF used by Sherpa is CTEQ66. Model parameters and couplings can be set in the Run.dat section (model), and the way couplings are treated can be defined under the (me) category. The QCD radiation matrix elements have to be regularized to obtain meaningful cross sections. This is achieved by specifying ‘CKKW sqr(30/E_CMS)’ in the (processes) part of Run.dat. Simultaneously, this tag initiates the ME-PS merging procedure. To eventually obtain fully hadronized events, the FRAGMENTATION tag has been left on it’s default setting ‘Ahadic’, which will run Sherpa’s cluster hadronization, and the tag DECAYMODEL has it’s default setting ‘Hadrons’, which will run Sherpa’s hadron decays. Additionally corrections owing to photon emissions are taken into account.

To run this example set-up, use the

<prefix>/bin/Sherpa 

command as descibed in Running Sherpa. Sherpa displays some output as it runs. At the start of the run, Sherpa initializes the relevant model, and displays a table of particles, with their PDG codes and some properties. It also displays the Particle containers, and their contents. The other relevant parts of Sherpa are initialized, including the matrix element generator(s). The Sherpa output will look like:

Initialized the beams Monochromatic*Monochromatic
CTEQ6_Fortran_Interface::CTEQ6_Fortran_Interface(): Init member 400.
PDF set 'cteq6.6m' loaded from 'libCTEQ6Sherpa' for beam 1 (P+).
CTEQ6_Fortran_Interface::CTEQ6_Fortran_Interface(): Init member 400.
PDF set 'cteq6.6m' loaded from 'libCTEQ6Sherpa' for beam 2 (P+b).
Initialized the ISR: (SF)*(SF)
CTEQ6_Fortran_Interface::CTEQ6_Fortran_Interface(): Init member 400.
CTEQ6_Fortran_Interface::CTEQ6_Fortran_Interface(): Init member 400.
Initialize the Standard Model from  / Model.dat
Running_AlphaS::Running_AlphaS() {
  Setting \alpha_s according to PDF
  perturbative order 1
  \alpha_s(M_Z) = 0.118
}
Initialized the Beam_Remnant_Handler.
Initialized the Shower_Handler.
Initialized the Fragmentation_Handler.
+----------------------------------+
|                                  |
|      CCC  OOO  M   M I X   X     |
|     C    O   O MM MM I  X X      |
|     C    O   O M M M I   X       |
|     C    O   O M   M I  X X      |
|      CCC  OOO  M   M I X   X     |
|                                  |
+==================================+
|  Color dressed  Matrix Elements  |
|     http://comix.freacafe.de     |
|   please cite  JHEP12(2008)039   |
+----------------------------------+
Matrix_Element_Handler::BuildProcesses(): Looking for processes . done ( 23252 kB, 0s ).
Matrix_Element_Handler::InitializeProcesses(): Performing tests . done ( 23252 kB, 0s ).
Initialized the Matrix_Element_Handler for the hard processes.
Initialized the Soft_Photon_Handler.

Then Sherpa will start to integrate the cross sections. The output will look like:

Process_Group::CalculateTotalXSec(): Calculate xs for '2_2__j__j__e-__nu_eb' (Comix)
Starting the calculation. Lean back and enjoy ... .
1019.05 pb +- ( 52.4212 pb = 5.14411 % ) 5000 ( 5013 -> 99.7 % )
full optimization:  ( 0s elapsed / 15s left )
...

The first line here displays the process which is being calculated. In this example, the integration is for the 2->2 process, parton, parton -> electron, neutrino. The matrix element generator used is displayed after the process. As the integration progresses, summary lines are displayed, like the one shown above. The current estimate of the cross section is displayed, along with its statistical error estimate. The number of phase space points calculated is displayed after this (‘5000’ in this example), and the efficiency is displayed after that. On the line below, the time elapsed is shown, and an estimate of the total time till the optimization is complete.

When the integration is complete, the output will look like:

...
1098.97 pb +- ( 0.373022 pb = 0.0339428 % ) 300000 ( 300020 -> 100 % )
integration time:  ( 13s elapsed / 0s left )
1098.86 pb +- ( 0.366442 pb = 0.0333475 % ) 310000 ( 310020 -> 100 % )
integration time:  ( 13s elapsed / 0s left )
2_2__j__j__e-__nu_eb : 1098.86 pb +- ( 0.366442 pb = 0.0333475 % )  exp. eff: 27.3833 %
  reduce max for 2_2__j__j__e-__nu_eb to 0.518502 ( eps = 0.001 )

with the final cross section result and its statistical error displayed.

Sherpa will then move on to integrate the other processes specified in the run card.

When the integration is complete, the event generation will start. As the events are being generated, Sherpa will display a summary line stating how many events have been generated, and an estimate of how long it will take. When the event generation is complete, Sherpa’s output looks like:

...
  Event 10000 ( 122 s total )
In Event_Handler::Finish : Summarizing the run may take some time.
+-----------------------------------------------------+
|                                                     |
|  Total XS is 1139.05 pb +- ( 11.1111 pb = 0.97 % )  |
|                                                     |
+-----------------------------------------------------+

A summary of the number of events generated is displayed, with the total cross section for the processes.

The generated events are not stored into a file by default; for details on how to store the events see Event output formats.

2.2.3 Parton-level event generation with Sherpa

Sherpa has its own tree-level matrix-element generators called AMEGIC++ and Comix. Furthermore, with the module PHASIC++, sophisticated and robust tools for phase-space integration are provided. Therefore Sherpa obviously can be used as a cross-section integrator. Because of the way Monte Carlo integration is accomplished, this immediately allows for parton-level event generation. Taking the Tevatron_WJets setup, users have to modify just a few settings in Run.dat and would arrive at a parton-level generation for the process gluon down-quark to electron antineutrino and up-quark, to name an example. When, for instance, the options “EVENTS=0 OUTPUT=2” are added to the command line, a pure cross-section integration for that process would be obtained with the results plus integration errors written to the screen.

For the example, the (processes) section alters to

  Process : 21 1 -> 11 -12 2
  Order_EW 2
  End process

and under the assumption to start afresh, the initialization procedure has to be followed as before. Picking the same collider environment as in the previous example there are only two more changes before the Run.dat file is ready for the calculation of the hadronic cross section of the process g d to e- nu_e-bar u at Tevatron Run I and subsequent parton-level event generation with Sherpa . These changes read SHOWER_GENERATOR=None, to switch off parton showering, and, FRAGMENTATION=Off, to do so for the hadronization effects.

3. Cross section

To determine the total cross section, in particular in the context of running CKKW merging with Sherpa, the final output of the event generation run should be used, e.g.

+-----------------------------------------------------+
|                                                     |
|  Total XS is 1612.17 pb +- ( 8.48908 pb = 0.52 % )  |
|                                                     |
+-----------------------------------------------------+

Note that the Monte Carlo error quoted for the total cross section is determined during event generation. It, therefore, might differ substantially from the errors quoted during the integration step.

In contrast to plain leading order results, Sherpa’s total cross section is composed of values from various leading order processes, namely those which are combined by applying the ME-PS merging, see ME-PS merging. In this context, it is important to note that

The exclusive higher order tree-level cross sections determined during the integration step are meaningless by themselves, only the inclusive cross section printed at the end of the event generation run is to be used.

In principle, this value has the same formal accuracy as a leading order result, but it might still differ by a significant amount. Depending on jet definitions, process etc., the merged cross section may be either larger or smaller than the leading order cross section.

Concerning a comparison with NLO calculations: It is known that for, e.g., inclusive Z production the NLO-LO K-factor is larger than one. In some setups the Sherpa cross section is smaller than the LO one, and therefore further from the NLO. Therefore, the Sherpa total cross section should not be thought of as an “improved leading order result”, which would suggest that it is always closer to the NLO than the LO cross section.

Sherpa total cross sections have leading order accuracy.

Broadly speaking, Sherpa’s ME-PS merging is adequate for capturing the information from (resummed) logarithmic corrections to the leading order (as is the parton shower). On the contrary, NLO cross sections are typically dominated by finite terms, as they are often quite inclusive and there are no large logarithms in this case. Sherpa’s merging algorithm has no way to calculate these finite terms, and this is why Sherpa’s cross section is not a better approximation to the NLO cross section. On the other hand, shape observables (especially jet transverse momenta and the like) are typically dominated by logarithmic corrections. If they are concerned, Sherpa can be expected to perform reasonably well.

4. Command line options

The available command line options for Sherpa.

‘-f <file>’

Read input from file ‘<file>’.

‘-p <path>’

Read input file from path ‘<path>’.

‘-L <path>’

Set Sherpa library path to ‘<path>’, see SHERPA_CPP_PATH.

‘-e <events>’

Set number of events to generate ‘<events>’, see EVENTS.

‘-r <results>’

Set the result directory to ‘<results>’, see RESULT_DIRECTORY.

‘-R <seed>’

Set the seed of the random number generator to ‘<seed>’, see RANDOM_SEED.

‘-m <generators>’

Set the matrix element generator list to ‘<generators>’, see ME_SIGNAL_GENERATOR.

‘-w <mode>’

Set the event generation mode to ‘<mode>’, see EVENT_GENERATION_MODE.

‘-s <generator>’

Set the parton shower generator to ‘<generator>’, see SHOWER_GENERATOR.

‘-F <module>’

Set the fragmentation module to ‘<module>’, see Fragmentation.

‘-D <module>’

Set the decay module to ‘<module>’, see Fragmentation.

‘-a <analyses>’

Set the analysis handler list to ‘<analyses>’, see ANALYSIS.

‘-A <path>’

Set the analysis output path to ‘<path>’, see ANALYSIS_OUTPUT.

‘-O <level>’

Set general output level ‘<level>’, see OUTPUT.

‘-o <level>’

Set output level for event generation ‘<level>’, see OUTPUT.

‘-l <logfile>’

Set log file name ‘<logfile>’, see LOG_FILE.

‘-j <threads>’

Set number of threads ‘<threads>’, see Multi-threading.

‘-g’

Do not create result directory, see RESULT_DIRECTORY.

‘-b’

Switch to non-batch mode, see BATCH_MODE.

‘-v, --version’

Print versioning information.

‘-h, --help’

Print a help message.

‘PARAMETER=VALUE’

Set the value of a parameter, see Parameters.

‘TAG:=VALUE’

Set the value of a tag, see Tags.

5. Input structure

A Sherpa setup is steered by various parameters, associated with the different components of event generation.

These have to be specified in a run-card which by default is named “Run.dat” in the current working directory. If you want to use a different setup directory for your Sherpa run, you have to specify it on the command line as ‘-p <dir>’ or ‘PATH=<dir>’. To read parameters from a run-card with a different name, you may specify ‘-f <file>’ or ‘RUNDATA=<file>’.

Sherpa’s parameters are grouped according to the different aspects of event generation, e.g. the beam parameters in the group ‘(beam)’ and the fragmentation parameters in the group ‘(fragmentation)’. In the run-card this looks like:

  (beam){
    BEAM_ENERGY_1 = 7000.
    ...
  }(beam)

Each of these groups is described in detail in another chapter of this manual, see Parameters.

If such a section or file does not exist in the setup directory, a Sherpa-wide fallback mechanism is employed, searching the file in various locations in the following order (where $SHERPA_DAT_PATH is an optionally set environment variable):

• ‘$SHERPA_DAT_PATH/<PATH>/’
• ‘$SHERPA_DAT_PATH/’
• ‘$prefix/share/SHERPA-MC/<PATH>/’
• ‘$prefix/share/SHERPA-MC/’

All parameters can be overwritten on the command line, i.e. command-line input has the highest priority. The syntax is

  <prefix>/bin/Sherpa  KEYWORD1=value1 KEYWORD2=value2 ...

To change, e.g., the default number of events, the corresponding command line reads

  <prefix>/bin/Sherpa  EVENTS=10000

All over Sherpa, particles are defined by the particle code proposed by the PDG. These codes and the particle properties will be listed during each run with ‘OUTPUT=2’ for the elementary particles and ‘OUTPUT=4’ for the hadrons. In both cases, antiparticles are characterized by a minus sign in front of their code, e.g. a mu- has code ‘13’, while a mu+ has ‘-13’.

All quantities have to be specified in units of GeV and millimeter. The same units apply to all numbers in the event output (momenta, vertex positions). Scattering cross sections are denoted in pico-barn in the output.

There are a few extra features for an easier handling of the parameter file(s), namely global tag replacement, see Tags, and algebra interpretation, see Interpreter.

5.1 Interpreter

Sherpa has a built-in interpreter for algebraic expressions, like ‘cos(5/180*M_PI)’. This interpreter is employed when reading integer and floating point numbers from input files, such that certain parameters can be written in a more convenient fashion. For example it is possible to specify the factorisation scale as ‘sqr(91.188)’.
There are predefined tags to alleviate the handling

‘M_PI’

Ludolph’s Number to a precision of 12 digits.

‘M_C’

The speed of light in the vacuum.

‘E_CMS’

The total centre of mass energy of the collision.

The expression syntax is in general C-like, except for the extra function ‘sqr’, which gives the square of its argument. Operator precedence is the same as in C. The interpreter can handle functions with an arbitrary list of parameters, such as ‘min’ and ‘max’.
The interpreter can be employed to construct arbitrary variables from four momenta, like e.g. in the context of a parton level selector, see Selectors. The corresponding functions are

‘Mass(v)’

The invariant mass of v in GeV.

‘Abs2(v)’

The invariant mass squared of v in GeV^2.

‘PPerp(v)’

The transverse momentum of v in GeV.

‘PPerp2(v)’

The transverse momentum squared of v in GeV^2.

‘MPerp(v)’

The transverse mass of v in GeV.

‘MPerp2(v)’

The transverse mass squared of v in GeV^2.

‘Theta(v)’

The polar angle of v in radians.

‘Eta(v)’

The pseudorapidity of v.

‘Phi(v)’

The azimuthal angle of v in radians.

‘Comp(v,i)’

The i’th component of the vector v.

‘PPerpR(v1,v2)’

The relative transverse momentum between v1 and v2 in GeV.

‘ThetaR(v1,v2)’

The relative angle between v1 and v2 in radians.

‘DEta(v1,v2)’

The rapidity difference between v1 and v2.

‘DPhi(v1,v2)’

The relative polar angle between v1 and v2 in radians.

5.2 Tags

Tag replacement in Sherpa is performed through the data reading routines, which means that it can be performed for virtually all inputs. Specifying a tag on the command line using the syntax ‘<Tag>:=<Value>’ will replace every occurrence of ‘<Tag>’ in all files during read-in. An example tag definition could read

  <prefix>/bin/Sherpa QCUT:=20 NJET:=3

and then be used in the (me) and (processes) sections like

  (me){
    RESULT_DIRECTORY = Result_QCUT/
  }(me)
  (processes){
    Process 93 93 -> 11 -11 93{NJET}
    Order_EW 2;
    CKKW sqr(QCUT/E_CMS)
    End process;
  }(processes)

6. Parameters

A Sherpa setup is steered by various parameters, associated with the different components of event generation. These are set in Sherpa’s run-card, see Input structure for more details. Tag replacements may be performed in all inputs, see Tags.

6.1 Run Parameters

The following parameters describe general run information. They may be set in the (run) section of the run-card, see Input structure.

6.1.1 EVENTS

This parameter specifies the number of events to be generated.
It can alternatively be set on the command line through option ‘-e’, see Command line options.

6.1.2 OUTPUT

This parameter specifies the output level (verbosity) of the program.
It can alternatively be set on the command line through option ‘-O’, see Command line options. A different output level can be specified for the event generation step through ‘EVT_OUTPUT’ or command line option ‘-o’, see Command line options

The value can be any sum of the following:

• 0: Error messages (-> always displayed).
• 1: Event display.
• 2: Informational messages during the run.
• 4: Tracking messages (lots of output).
• 8: Debugging messages (even more output).

E.g. OUTPUT=3 would display information, events and errors.

6.1.3 LOG_FILE

This parameter specifies the log file. If set, the standard output from Sherpa is written to the specified file, but output from child processes is not redirected. This option is particularly useful to produce clean log files when running the code in MPI mode, see MPI parallelization. A file name can alternatively be specified on the command line through option ‘-l’, see Command line options.

6.1.4 RANDOM_SEED

SHERPA uses a random-number generator as described in [Florida State University Report FSU-SCRI-87-50]. The two independent integer-valued seeds are specified by the option “RANDOM_SEED=A B”. The seeds A and B may range from 0 to 31328 and from 0 to 30081, respectively. They can also directly be set using “RANDOM_SEED1=A” and “RANDOM_SEED2=B” If RANDOM_SEED is not specified at all or only by one integer number, the old random-number generator (SHERPA 1.0.6 and older) will be used. This value can also be set using the command line option ‘-R’, see Command line options.

6.1.5 ANALYSIS

Analysis routines can be switched on or off by setting the ANALYSIS flag. The default is no analysis, corresponding to option ‘0’. This parameter can also be specified on the command line using option ‘-a’, see Command line options.

The following analysis handlers are currently available

‘Internal’

Sherpa’s internal analysis handler.
To use this option, the package must be configured with option ‘--enable-analysis’.
An output directory can be specified using ANALYSIS_OUTPUT.

‘Rivet’

The Rivet package, see Rivet Website.
To enable it, Rivet and HepMC have to be installed and Sherpa must be configured as described in Rivet analyses.

Multiple options can be combined using a comma, e.g. ‘ANALYSIS=Internal,Rivet’.

6.1.6 ANALYSIS_OUTPUT

Name of the directory for histogram files when using the internal analysis and name of the Aida file when using Rivet, see ANALYSIS. The directory / file will be created w.r.t. the working directory. The default value is ‘Analysis/’. This parameter can also be specified on the command line using option ‘-A’, see Command line options.

6.1.7 TIMEOUT

A run time limitation can be given in user CPU seconds through TIMEOUT. This option is of some relevance when running SHERPA on a batch system. Since in many cases jobs are just terminated, this allows to interrupt a run, to store all relevant information and to restart it without any loss. This is particularly useful when carrying out long integrations. Alternatively, setting the TIMEOUT variable to -1, which is the default setting, translates into having no run time limitation at all.

6.1.8 BATCH_MODE

Whether or not to run Sherpa in batch mode. The default is ‘1’, meaning Sherpa does not attempt to save runtime information when catching a signal or an exception. On the contrary, if option ‘0’ is used, Sherpa will store potential integration information and analysis results, once the run is terminated abnormally.

Note that when running the code on a cluster or in a grid environment, BATCH_MODE should never be different from 1.

The command line option ‘-b’ should therefore not be used in this case, see Command line options.

6.1.9 SPIN_CORRELATIONS

The algorithm used to transfer spin-correlation information from AMEGIC++ to HADRONS++ is switched off (=0) by default. It can be switched on via SPIN CORRELATIONS=1. Process libraries have to be re-created in this case.

6.1.10 NUM_ACCURACY

The targeted numerical accuracy can be specified through NUM ACCURACY, e.g. for comparing two numbers. This might have to be reduced if gauge tests fail for numerical reasons.

6.1.11 SHERPA_CPP_PATH

The path in which Sherpa will eventually store dynamically created C++ source code. If not specified otherwise, sets ‘SHERPA_LIB_PATH’ to ‘$SHERPA_CPP_PATH/Process/lib’. This value can also be set using the command line option ‘-L’, see Command line options.

6.1.12 SHERPA_LIB_PATH

The path in which Sherpa looks for dynamically linked libraries from previously created C++ source code, cf. SHERPA_CPP_PATH.

6.1.13 Event output formats

Sherpa provides the possibility to output events in its native and two other output formats: The HepEVT common block structure or the HepMC format. The authors of Sherpa assume that the user is sufficiently acquainted with these formats when selecting them.

If the events are to be written to file, the following parameters have to be specified:

‘SHERPA_OUTPUT=<filename>’

Filename for output in Sherpa format

‘HEPMC2_GENEVENT_OUTPUT=<filename>’

Filename for output in HepMC::IO_GenEvent format.

‘HEPMC2_SHORT_OUTPUT=<filename>’

Filename for output in HepMC::IO_GenEvent format. Only incoming beams and outgoing particles are stored. Intermediate and decayed particles are not listed.

‘HEPEVT_OUTPUT=<filename>’

Filename for output in HepEvt format.

‘ROOTNTUPLE_OUTPUT=<filename>’

Filename for output in ROOT ntuple format for NLO event generation. For details on ntuple format, see Structure of ROOT NTuple Output. This output option is only available if Sherpa was linked to ROOT during installation by using the configure option --enable-root=/path/to/root.

With these keywords the filename’s root can be specified, i.e. HEPEVT_OUTPUT=<filename> will create files named <filename>.#.hepevt, where the hash mark numerates the files if events are split into multiple files. The output can be further steered with the following options:

‘FILE_SIZE’

Number of events per file (default: 1000).

‘EVT_FILE_PATH’

Directory where the files will be stored.

‘OUTPUT_PRECISION’

Steers the precision of all numbers written to file.

To write events directly to gzipped files instead of plain text, the option ‘--enable-gzip’ has to be specified during the installation.

There is also the option to change the format of the event output printed to screen (if any) with the switch EVENT_MODE:

‘EVENT_MODE=Sherpa’

Blob list output (default)

‘EVENT_MODE=HepMC’

GenEvent print method

‘EVENT_MODE=HepMC_Short’

GenEvent print method of shortend event record

‘EVENT_MODE=HepEvt’

HepEvt common block

6.1.14 MPI parallelization

MPI parallelization in Sherpa can be enabled using the configuration option ‘--enable-mpi’. Sherpa supports OpenMPI and MPICH2 . For detailed instructions on how to run a parallel program, please refer to the documentation of your local cluster resources or the many excellent introductions on the internet. MPI parallelization is mainly intended to speed up the integration process, as event generation can be parallelized trivially by starting multiple instances of Sherpa with different random seed, cf. RANDOM_SEED. However, both the internal analysis module and the Root NTuple writeout can be used with MPI. Note that these require substantial data transfer. We only recommend to use them in MPI mode if your local cluster has sufficient ethernet bandwidth.

When compiled with MPI support, Sherpa implements an automatic load balancing to make optimal use of potentially different types of cluster nodes. If you do not wish Sherpa to take control, this option can be disabled by setting ‘PSI_ADJUST_POINTS=0’.

6.1.15 Multi-threading

Multi-threaded integration in Sherpa can be enabled using the configuration option ‘--enable-multithread’. Subsequently the computation of amplitudes for large groups of processes is split into a number of threads which is limited from above by the parameter ‘PG_THREADS’. This parameter can also be specified using the command line option ‘-j’, see Command line options. Additionally, matrix-element calculation and phase-space evaluation for a single process with Comix can be distributed to different threads according to [Gle08] . The number of threads is then specified using the parameters ‘COMIX_ME_THREADS’ and ‘COMIX_PS_THREADS’, respectively.

6.2 Beam Parameters

The setup of the colliding beams is covered by the (beam) section of the steering file or the beam data file Beam.dat, respectively, see Input structure. The mandatory settings to be made are

• The initial beam particles specified through ‘BEAM_1’ and ‘BEAM_2’, given by their PDG particle number. For (anti)protons and (positrons) electrons, for example, these are given by (-)2212 or (-)11, respectively. The code for photons is 22.
• The energies of both incoming beams, defined through ‘BEAM_ENERGY_1’ and ‘BEAM_ENERGY_2’, given in units of GeV.

More options related to beamstrahlung and intrinsic transverse momentum can be found in the following subsections.

6.2.1 Beam Spectra

If desired, you can also specify spectra for beamstrahlung through BEAM_SPECTRUM_1 and BEAM_SPECTRUM_2. The possible values are Possible values are

‘Monochromatic’

The beam energy is unaltered and the beam particles remain unchanged. That is the default and corresponds to ordinary hadron-hadron or lepton-lepton collisions.

‘Laser_Backscattering’

This can be used to describe the backscattering of a laser beam off initial leptons. The energy distribution of the emerging photon beams is modelled by the CompAZ parametrization, see [Zar02] Note that this parametrization is valid only for the proposed TESLA photon collider, as various assumptions about the laser parameters and the initial lepton beam energy have been made.

‘Simple_Compton’

This corresponds to a simple light backscattering off the initial lepton beam and produces initial-state photons with a corresponding energy spectrum.

‘EPA’

This enables the equivalent photon approximation for colliding protons, see [Arc08] . The resulting beam particles are photons that follow a dipole form factor parametrization, cf. [Bud74] . The authors would like to thank T. Pierzchala for his help in implementing and testing the corresponding code.

‘Spectrum_Reader’

A user defined spectrum is used to describe the energy spectrum of the assumed new beam particles. The name of the corresponding spectrum file needs to be given through the keywords SPECTRUM_FILE_1 and SPECTRUM_FILE_2.

The BEAM_SMIN and BEAM_SMAX parameters may be used to specify the minimum/maximum fraction of cms energy squared after Beamstrahlung. The reference value is the total centre of mass energy squared of the collision, not the centre of mass energy after eventual Beamstrahlung.
The parameter can be specified using the internal interpreter, see Interpreter, e.g. as ‘BEAM_SMIN sqr(20/E_CMS)’.

6.2.2 Intrinsic Transverse Momentum

‘K_PERP_MEAN_1’

This parameter specifies the mean intrinsic transverse momentum for the first (left) beam in case of hadronic beams, such as protons.
The default value for protons is 0.8 GeV.

‘K_PERP_MEAN_2’

This parameter specifies the mean intrinsic transverse momentum for the second (right) beam in case of hadronic beams, such as protons.
The default value for protons is 0.8 GeV.

‘K_PERP_SIGMA_1’

This parameter specifies the width of the Gaussian distribution of intrinsic transverse momentum for the first (left) beam in case of hadronic beams, such as protons.
The default value for protons is 0.8 GeV.

‘K_PERP_SIGMA_2’

This parameter specifies the width of the Gaussian distribution of intrinsic transverse momentum for the first (left) beam in case of hadronic beams, such as protons.
The default value for protons is 0.8 GeV.

If the option ‘BEAM_REMNANTS=0’ is specified, pure parton-level events are simulated, i.e. no beam remnants are generated. Accordingly, partons entering the hard scattering process do not acquire primordial transverse momentum.

6.3 ISR Parameters

The following parameters are used to steer the setup of beam substructure and initial state radiation (ISR). They may be set in the (isr) section of the run-card, see Input structure.

BUNCH_1/BUNCH_2

Specify the PDG ID of the first (left) and second (right) bunch particle, i.e. the particle after eventual Beamstrahlung specified through the beam parameters, see Beam Parameters. Per default these are taken to be identical to the parameters BEAM_1/BEAM_2, assuming the default beam spectrum is Monochromatic. In case the Simple Compton or Laser Backscattering spectra are enabled the bunch particles would have to be set to 22, the PDG code of the photon.

ISR_SMIN/ISR_SMAX

This parameter specifies the minimum fraction of cms energy squared after ISR. The reference value is the total centre of mass energy squared of the collision, not the centre of mass energy after eventual Beamstrahlung.
The parameter can be specified using the internal interpreter, see Interpreter, e.g. as ‘ISR_SMIN=sqr(20/E_CMS)’.

Sherpa provides access to a variety of structure functions. They can be configured with the following parameters.

PDF_LIBRARY

Switches between different interfaces to PDFs. If the two colliding beams are of different type, e.g. protons and electrons or photons and electrons, it is possible to specify two different PDF libraries using ‘PDF_LIBRARY_1’ and ‘PDF_LIBRARY_2’. The following options are distributed with Sherpa:

LHAPDFSherpa

Use PDF’s from LHAPDF [Wha05] . The interface is only available if Sherpa has been compiled with support for LHAPDF, see Installation.

CTEQ6Sherpa

Built-in library for some PDF sets from the CTEQ collaboration, cf. [Nad08] . This is the default, if Sherpa has not been compiled with LHAPDF support.

MSTW08Sherpa

Built-in library for PDF sets from the MSTW group, cf. [Mar09] .

MRST04QEDSherpa

Built-in library for photon PDF sets from the MRST group, cf. [Mar04] .

MRST01LOSherpa

Built-in library for the 2001 leading-order PDF set from the MRST group, cf. [Mar01] .

MRST99Sherpa

Built-in library for the 1999 PDF sets from the MRST group, cf. [Mar99] .

GRVSherpa

Built-in library for the GRV photon PDF [Glu91a] , [Glu91]

PDFESherpa

Built-in library for the electron structure function. The perturbative order of the fine structure constant can be set using the parameter ISR_E_ORDER (default: 1). The switch ISR_E_SCHEME allows to set the scheme of respecting non-leading terms. Possible options are 0 ("mixed choice"), 1 ("eta choice"), or 2 ("beta choice", default).

Furthermore it is simple to build an external interface to an arbitrary PDF and load that dynamically in the Sherpa run. See External PDF for instructions.

PDF_SET

Specifies the PDF set for hadronic bunch particles. All sets available in the chosen PDF_LIBRARY can be figured by running Sherpa with the parameter SHOW_PDF_SETS=1, e.g.:

  Sherpa PDF_LIBRARY=CTEQ6Sherpa SHOW_PDF_SETS=1

If the two colliding beams are of different type, e.g. protons and electrons or photons and electrons, it is possible to specify two different PDF sets using ‘PDF_SET_1’ and ‘PDF_SET_2’.

PDF_SET_VERSION

This parameter allows to eventually select a specific version (member) within the chosen PDF set. Specifying a negative value, e.g.

  PDF_LIBRARY LHAPDFSherpa;
  PDF_SET NNPDF12_100.LHgrid; PDF_SET_VERSION -100;

results in Sherpa sampling all sets 1..100, which can be used to obtain the averaging required when employing PDF’s from the NNPDF collaboration [Bal08] , [Bal09] .

6.4 Model Parameters

The interaction model setup is covered by the (model) section of the steering file or the model data file Model.dat, respectively.

The main switch here is called MODEL and sets the model that Sherpa uses throughout the simulation run. The default is ‘SM’, for the Standard Model. For a complete list of available models, run Sherpa with SHOW_MODEL_SYNTAX=1 on the command line. This will display not only the available models, but also the parameters for those models.

The chosen model also defines the list of particles and their default properties. With the following switches it is possible to change the properties of all fundamental particles:

MASS[<id>]

Sets the mass (in GeV) of the particle with PDG id ‘<id>’.
Masses of particles and corresponding anti-particles are always set simultaneously.

MASSIVE[<id>]

Specifies whether the finite mass of particle with PDG id ‘<id>’ is to be considered in matrix-element calculations or not.

WIDTH[<id>]

Sets the width (in GeV) of the particle with PDG id ‘<id>’.

ACTIVE[<id>]

Enables/disables the particle with PDG id ‘<id>’.

STABLE[<id>]

Sets the particle with PDG id ‘<id>’ either stable or unstable according to the following options:

‘0’

Particle and anti-particle are unstable

‘1’

Particle and anti-particle are stable

‘2’

Particle is stable, anti-particle is unstable

‘3’

Particle is unstable, anti-particle is stable

At present this affects only the simulation of tau decays, dealt with by the HADRONS++ package. Decays of other particles have to be specified in the process setup (see Processes) and are not treated automatically.

Note: To set properties of hadrons, you can use the same switches (except for MASSIVE) in the fragmentation section, see Fragmentation.

6.4.1 Standard Model

The SM inputs for the electroweak sector can be given in four different schemes, that correspond to different choices of which SM physics parameters are considered fixed and which are derived from the given quantities. The input schemes are selected through the EW_SCHEME parameter, whose default is ‘0’. The following options are provided:

• Case 0:

  all EW parameters are explicitly given. Here the W, Z and Higgs masses are taken as inputs, and the parameters 1/ALPHAQED(default), SIN2THETAW, VEV and LAMBDA have to be specified as well. While 1/ALPHAQED(default) corresponds to the fine structure constant, (which by default is not running), the parameters SIN2THETAW, VEV, and LAMBDA thereby specify the weak mixing angle, the Higgs field vacuum expectation value, and the Higgs quartic coupling respectively.

• Case 1:

  all EW parameters are calculated out of the W, Z and Higgs masses and 1/ALPHAQED(default) using tree-level relations.

• Case 2:

  all EW parameters are calculated out of 1/ALPHAQED(default), SIN2THETAW, VEV and the Higgs mass using tree-level relations.

• Case 3:

  this choice corresponds to the G_mu-scheme. The EW parameters are calculated out of the weak gauge boson masses M_W, M_Z, the Higgs boson mass M_H and the Fermi constant GF using tree-level relations.

The electro-weak coupling is by default not running. If its running has been enabled (cf. COUPLINGS), one can specify its value at zero momentum transfer as input value by 1/ALPHAQED(0).

To account for quark mixing the CKM matrix elements have to be assigned. For this purpose the Wolfenstein parametrization [Wol83] is employed. The order of expansion in the lambda parameter is defined through CKMORDER, with default ‘0’ corresponding to a unit matrix. The parameter convention for higher expansion terms reads:

• CKMORDER = 1, the CABIBBO parameter has to be set, it parametrizes lambda and has the default value ‘0.2272’.
• CKMORDER = 2, in addition the value of A has to be set, its default is ‘0.818’.
• CKMORDER = 3, the order lambda^3 expansion, ETA and RHO have to be specified. Their default values are ‘0.349’ and ‘0.227’, respectively.

The remaining parameter to fully specify the Standard Model is the strong coupling constant at the Z-pole, given through ALPHAS(MZ). Its default value is ‘0.118’. If the setup at hand involves hadron collisions and thus PDFs, the value of the strong coupling constant is automatically set consistent with the PDF fit and can not be changed by the user. For this fine structure constant there is also the option to provide a fixed value that can be used in calculations of matrix elements in case running of the coupling is disabled (cf. COUPLINGS). The keyword is ALPHAS(default). When using a running strong coupling, the order of the perturbative expansion used can be set through ORDER_ALPHAS, where the default ‘0’ corresponds to one-loop running and 1,2,3 to 2,3,4-loops, respectively.

6.4.2 Minimal Supersymmetric Standard Model

To use the MSSM within Sherpa (cf. [Hag05] ) the MODEL switch has to be set to ‘MSSM’. Further, the parameter spectrum has to be fed in. To achieve this files that conform to the SUSY-Les-Houches-Accord [Ska03] are used. The actual SLHA file name has to be specified by SLHA_INPUT and has to reside in the current run directory, i.e. PATH. From this file the full low-scale MSSM spectrum is read, including sparticle masses, mixing angles etc. In addition information provided on the total particle’s widths is read from the input file. Note that the setting of masses and widths through the SLHA input is superior to setting through MASS[<id>] and WIDTH[<id>].

6.4.3 ADD Model of Large Extra Dimensions

In order to use the ADD model within Sherpa the switch MODEL = ADD has to be set. The parameters of the ADD model can be set as follows:

The variable N_ED specifies the number of extra dimensions. The value of the Newtonian constant can be specified in natural units using the keyword G_NEWTON. The size of the string scale M_S can be defined by the parameter M_S. Setting the value of KK_CONVENTION allows to change between three widely used conventions for the definition of M_S and the way of summing internal Kaluza-Klein propagators. The switch M_CUT one restricts the c.m. energy of the hard process to be below this specified scale.

The masses, widths, etc. of both additional particles can set in the same way as for the Standard Model particles using the MASS[<id>] and WIDTH[<id>] keywords. The ids of the graviton and graviscalar are 39 and 40.

For details of the implementation, the reader is referred to [Gle03a] .

6.4.4 Anomalous Gauge Couplings

Sherpa includes a number of effective Lagrangians describing anomalous gauge interactions:

• WWV interactions: The general coupling between two charged vector bosons and a neutral one is given by [Hag86] The parameters for the individual coupling terms can be specified through the switches G1_GAMMA, KAPPA_GAMMA, LAMBDA_GAMMA, G4_GAMMA, G5_GAMMA, KAPPAT_GAMMA, LAMBDAT_GAMMA, G1_Z, KAPPA_Z, LAMBDA_Z, G4_Z, G5_Z, KAPPAT_Z and LAMBDAT_Z. As a default the Standard Model limit is used (G1_GAMMA/Z=KAPPA_GAMMA/Z=1, all other =0).
• Quadrupole interactions: The SU(2) custodial symmetry conserving interactions are implemented as in [Gan99] Here, the parameters can be specified through ALPHA_4_G_4 and ALPHA_5.
• Anomalous interactions between photons and Z bosons: The general anomalous coupling of two on-shell neutral gauge bosons to an off-shell boson has been given in [Hag86] .

  The coupling parameters are specified through F4_GAMMA, F5_GAMMA, H1_GAMMA, H2_GAMMA, H3_GAMMA, H4_GAMMA, F4_Z, F5_Z, H1_Z, H2_Z, H3_Z and H4_Z, all equal zero by default. It should be noted that the most general anomalous coupling between three off-shell neutral gauge bosons allows for more coupling terms [Gou00] which are not implemented in the current version. Outside the on-shell limit of two of the vector bosons a symmetrized version of the above vertex is used.

Due to the effective nature of the anomalous couplings unitarity might be violated for coupling parameters other than the SM values. For very large momentum transfers, such as probed at the LHC, this will lead to unphysical results. As discussed in Ref. [Bau88] this can be avoided introducing form factors to be applied on the deviation of coupling parameters from their Standard Model values, The corresponding switches are UNITARIZATION_SCALE and UNITARIZATION_N. By default the form factor is switched off

6.4.5 Two Higgs Doublet Model

The THDM is incorporated as a subset of the MSSM Lagrangian. It is defined as the extension of the SM by a second SU(2) doublet of Higgs fields. Besides the particle content of the SM it contains interactions of five physical Higgs bosons: a light and a heavy scalar, a pseudo-scalar and two charged ones. Besides the SM inputs the model is defined through the masses and widths of the Higgs particles, MASS[PDG] and WIDTH[PDG], where PDG = [25,35,36,37] for h^0, H^0, A^0 and H^+, respectively. The inputs are complete, when TAN(BETA), the ratio of the two Higgs vacuum expectation values, and ALPHA, the Higgs mixing angle, are specified.

The model is invoked by specifying MODEL = THDM in the (model) section of the steering file or the model data file Model.dat, respectively.

6.4.6 Effective Higgs Couplings

The EHC describes the effective coupling of gluons and photons to Higgs bosons via a top-quark loop, and a W-boson loop in case of photons. This supplement to the Standard Model can be invoked by specifying MODEL = SM+EHC in the (model) section of the steering file or the model data file Model.dat, respectively.

The effective coupling of gluons to the Higgs boson, g_ggH, can be calculated either for a finite top-quark mass or in the limit of an infinitely heavy top using the switch FINITE_TOP_MASS=[1,0]. Similarily, the photon-photon-Higgs coupling, g_ppH, can be calculated both for finite top and/or W masses or in the infinite mass limit using the switches FINITE_TOP_MASS=[1,0] and FINITE_W_MASS=[1,0]. The default choice for both is the infinite mass limit in either case.

Either one of these couplings can be switched off using the DEACTIVATE_GGH=[1,0] and DEACTIVATE_PPH=[1,0] switches. Both default to 0.

6.4.7 Fourth Generation

The 4thGen model adds a fourth family of quarks and leptons to the Standard Model. It is invoked by specifying MODEL = SM+4thGen in the ’(model)’ section of the steering file or the model data file ‘Model.dat’, respectively.

The masses and widths of the additional particles are defined via the usual MASS[PDG] and WIDTH[PDG] switches, where PDG = [7,8,17,18] for the fourth generation down and up quarks, the charged lepton and the neutrino, respectively. A general mixing is implemented for both leptons and quarks, parametrised through three additional mixing angles and two additional phases, as described in [Hou87a] : A_14, A_24, A_34, PHI_2 and PHI_3 for quarks, THETA_L14, THETA_L24, THETA_L34, PHI_L2 and PHI_L3 for leptons. Both 4x4 mixing matrices expand upon their 3x3 Standard Model counter parts: the CKM matrix for quarks and the unit matrix for leptons. Both mixing matrices can be printed on screen with OUTPUT_MIXING = 1.

Per default, all particles are set unstable and have to be decayed into Standard Model particles within the matrix element or set stable via STABLE[PDG] = 1.

6.4.8 FeynRules model

To use a model generated using the FeynRules package, cf. Refs. [Chr08] and [Chr09] , the MODEL switch has to be set to ‘FeynRules’ and ME_SIGNAL_GENERATOR has to be set to ‘Amegic’. Note, in order to obtain the FeynRules model output in a format readable by Sherpa the FeynRules subroutine ’WriteSHOutput[ L ]’ needs to be called for the desired model Lagrangian ’L’. This results in a set of ASCII files that represent the considered model through its particle data, model parameters and interaction vertices. Note also that Sherpa/Amegic can only deal with Feynman rules in unitary gauge.

The FeynRules output files need to be copied to the current working directory or have tto reside in the directory referred to by the PATH variable, cf. Input structure. There exists an agreed default naming convention for the FeynRules output files to be read by Sherpa. However, the explicite names of the input files can be changed. They are referred to by the variables

• FR_PARTICLES = <file name>: File containing the particle data, default value Particle.dat.
• FR_IDENTFILE = <file name>: File hosting declaration of all external model parameters, default value ident_card.dat.
• FR_PARAMCARD = <file name>: List of numerical values of all elementary parameters, masses and decay widths, default param_card.
• FR_PARAMDEF = <file name>: Input file where all derived parameters get defined, default value param_definition.dat.
• FR_INTERACTIONS = <file name>: File where all interaction vertices are defined, default value Interactions.dat.

For more details on the Sherpa interface to FeynRules please consult [Chr09] .

6.5 Matrix Elements

The setup of matrix elements is covered by the ‘(me)’ section of the steering file or the ME data file ‘ME.dat’, respectively. There are no mandatory settings to be made.

The following parameters are used to steer the matrix element setup.

6.5.1 ME_SIGNAL_GENERATOR

The list of matrix element generators to be employed during the run. When setting up hard processes from the ‘(processes)’ section of the input file (see Processes), Sherpa calls these generators in order to check whether either one is capable of generating the corresponding matrix element. This parameter can also be set on the command line using option ‘-m’, see Command line options.

The built-in generators are

‘Internal’

Simple matrix element library, implementing a variety of 2->2 processes.

‘Amegic’

The AMEGIC++ generator published under [Kra01]

‘Comix’

The Comix generator published under [Gle08]

It is possible to employ an external matrix element generator within Sherpa. For advice on this topic please contact the authors, Authors.

6.5.2 RESULT_DIRECTORY

This parameter specifies the name of the directory which is used by Sherpa to store integration results and phasespace mappings. The default is ‘Results/’. It can also be set using the command line parameter ‘-r’, see Command line options. The directory will be created automatically, unless the option ‘GENERATE_RESULT_DIRECTORY=0’ is specified. Its location is relative to a potentially specified input path, see Command line options.

6.5.3 EVENT_GENERATION_MODE

This parameter specifies the event generation mode. It can also be set on the command line using option ‘-w’, see Command line options. The three possible options are ‘Weighted’ (shortcut ‘W’), ‘Unweighted’ (shortcut ‘U’) and ‘PartiallyUnweighted’ (shortcut ‘P’). For partially unweighted events, the weight is allowed to exceed a given maximum, which is lower than the true maximum weight. In such cases the event weight will exceed the otherwise constant value.

6.5.4 SCALES

This parameter specifies how to compute the renormalization and factorization scale and potential additional scales.

Sherpa provides several built-in scale schemes. The options which are currently available are

‘VAR’

Scales are specified by additional parameters in a form which is understood by the internal interpreter, see Interpreter. If, for example the invariant mass of the lepton pair in Drell-Yan production is the desired scale, the corresponding setup reads

SCALES VAR{Abs2(p[2]+p[3])}

Note: the square of the desired scale must be given.

Renormalization and factorization scales can be chosen differently. For example in Drell-Yan + jet production one could set

SCALES VAR{Abs2(p[2]+p[3])}{MPerp2(p[2]+p[3])}

In this case the factorization scale must be specified first. More than two scales can be set as well to be subsequently used, e.g. by different couplings, see COUPLINGS.

‘FASTJET’

If FastJet is enabled, this tag can be used to set a scale based on jet, rather than parton momenta. Such a scale must be specified in the process block, see Scales. The jets can be defined in all possible ways allowed by FastJet with the arguments given as follows

Scales FASTJET[A=antikt,PT=10,ET=0,R=0.4,M=1]{...}

Thereby, A defines the jet algorithm, R sets the cone size, and PT / ET define the minimum transverse momentum/energy of the jets. The additional argument M (default 1) sets the averaging mode. After jet finding, the jet momenta are ordered as in FastJet. Non-QCD partons are unaffected by this procedure, i.e. their momentum indices remain the same. The additional tags MU_22 .. MU_n2, with n the number of strongly interacting final state particles, hold the nodal values of the jet clustering and the transverse momenta of the final state jets in descending order.

‘QCD’

The matrix element is clustered onto a core 2->2 configuration using a k_T-type algorithm with recombination into on-shell partons. Scales are defined as the minimum of the largest transverse momentum during clustering and the lowest invariant mass in the core process.

‘METS’

The matrix element is clustered onto a core 2->2 configuration using a k_T-type algorithm with recombination into on-shell particles. Their corresponding flavours are determined using run-time information from the matrix element generator. Scales are defined as the lowest invariant mass or negative virtuality in the core process. For core interactions which are pure QCD processes scales are set to the maximum transverse mass squared of the outgoing particles.
This is the default scale scheme in Sherpa, since it is employed for truncated shower merging, see ME-PS merging. However, it might be subject to changes to enable further classes of processes for merging in the future and should therefore be seen with care. Integration results might change slightly between different Sherpa versions.
Occasionally, users might encounter the warning message

METS_Scale_Setter::CalculateScale(): No CSS history for '<process name>' in <percentage>% of calls. Set \hat{s}.

As long as the percentage quoted here is not too high, this does not pose a serious problem. The warning occurs when - based on the current colour configuration and matrix element information - no suitable clustering is found by the algorithm. In such cases the scale is set to the invariant mass of the partonic process.

It is possible to implement a dedicated scale scheme within Sherpa. For advice on this topic please contact the authors, Authors.

6.5.4.1 Scale schemes for NLO calculations

For next-to-leading order calculations it must be guaranteed that the scale is calculated separately for the real correction and the subtraction terms, such that within the subtraction procedure the same amount is subtracted and added back. Starting from version 1.2.2 this is the case for all scale setters in Sherpa. Also, the definition of the scale must be infrared safe w.r.t. to the radiation of an extra parton. Infrared safe (for QCD-NLO calculations) are:

• any function of momenta of NOT strongly interacting particles
• sum of transverse quantities of all partons (e.g. H_T2)
• any quantity refering to jets, constructed by an IR safe jet algorithm (not implemented yet)

Not infrared safe are

• any function of momenta of specific partons
• for processes with hadrons in the initial state: any quantity that depends on parton momenta along the beam axis, including the initial state partons itself

Since the total number of partons is different for different pieces of the NLO calculation any explicit reference to a parton momentum will lead to an inconsistent result.

6.5.4.2 Simple scale variations

Simple scale variations can be done using the following parameters:

• ‘FACTORIZATION_SCALE_FACTOR’ specifies a global factor which the squared factorisation scale (as specified above) is to be multiplied with when evaluating PDFs.

  Note: Shower starting scales are not affected by this factor, change the ‘SCALES’ parameter to achieve that.

• ‘RENORMALIZATION_SCALE_FACTOR’ specifies a global factor which the squared renormalisation scale (as specified above) is to be multiplied with when evaluating running couplings.

  Note: This affects also the running coupling used in the parton shower evolution.

6.5.5 COUPLINGS

Within Sherpa, strong and electroweak couplings can be computed at any scale specified by a scale setter (cf. SCALES). The ‘COUPLINGS’ tag links the argument of a running coupling to one of the respective scales. This is better seen in an example. Assuming the following input

SCALES    VAR{...}{PPerp2(p[2])}{Abs2(p[2]+p[3])}
COUPLINGS Alpha_QCD 1, Alpha_QED 2

Sherpa will compute any strong couplings at scale one, i.e. ‘PPerp2(p[2])’ and electroweak couplings at scale two, i.e. ‘Abs2(p[2]+p[3])’. Note that counting starts at zero.

6.5.6 KFACTOR

This parameter specifies how to evaluate potential K-factors in the hard process. This is equivalent to the ‘COUPLINGS’ specification of Sherpa versions prior to 1.2.2. Currently available options are

‘NO’

No reweighting

‘VAR’

Couplings specified by an additional parameter in a form which is understood by the internal interpreter, see Interpreter. The tags Alpha_QCD and Alpha_QED serve as links to the built-in running coupling implementation.

If for example the process ‘g g -> h g’ in effective theory is computed, one could think of evaluating two powers of the strong coupling at the Higgs mass scale and one power at the transverse momentum squared of the gluon. Assuming the Higgs mass to be 120 GeV, the corresponding reweighting would read

SCALES    VAR{...}{PPerp2(p[3])}
COUPLINGS Alpha_QCD 1
KFACTOR   VAR{sqr(Alpha_QCD(sqr(120))/Alpha_QCD(MU_12))}

As can be seen from this example, scales are referred to as MU_<i>2, where <i> is replaced with the appropriate number. Note that counting starts at zero.

It is possible to implement a dedicated K-factor scheme within Sherpa. For advice on this topic please contact the authors, Authors.

6.5.7 YUKAWA_MASSES

This parameter specifies whether the Yukawa couplings are evaluated using running or fixed quark masses: YUKAWA_MASSES=Running is the default since version 1.2.2 while YUKAWA_MASSES=Fixed was the default until 1.2.1.

6.5.8 Dipole subtraction

This list of parameters can be used to optimize the performance when employing the Catani-Seymour dipole subtraction [Cat96b] as implemented in Amegic [Gle07] .

‘`DIPOLE_ALPHA'’

Specifies a dipole cutoff in the nonsingular region [Nag03] . Changing this parameter shifts contributions from the subtracted real correction piece (RS) to the piece including integrated dipole terms (I), while their sum remains constant. This parameter can be used to optimize the integration performance of the individual pieces. Also the average calculation time for the subtracted real correction is reduced with smaller choices of ‘DIPOLE_ALPHA’ due to the (on average) reduced number of contributing dipole terms. For most processes a reasonable choice is between 0.01 and 1 (default). See also Choosing DIPOLE_ALPHA

‘`DIPOLE_AMIN'’

Specifies the cutoff of real correction terms in the infrared reagion to avoid numerical problems with the subtraction. The default is 1.e-8.

‘`DIPOLE_NF_GSPLIT'’

Specifies the number of quark flavours that are produced from gluon splittings. This number must be at least the number of massless flavours (default). If this number is larger than the number of massless quarks the massive dipole subtraction [Cat02] is employed.

‘`DIPOLE_KAPPA'’

Specifies the kappa-parameter in the massive dipole subtraction formalism [Cat02] .

6.6 Processes

The process setup is covered by the ‘(processes)’ section of the steering file or the process data file ‘Processes.dat’, respectively.

The following parameters are used to steer the process setup.

6.6.1 Process

This tag starts the setup of a process or a set of processes with common properties. It must be followed by the specification of the (core) process itself. The setup is completed by the ‘End process’ tag, see End process. The initial and final state particles are specified by their PDG codes, or by particle containers, see Particle containers. Examples are

Process 93 93 -> 11 -11

Sets up a Drell-Yan process group with light quarks in the initial state.

Process 11 -11 -> 93 93 93{3}

Sets up jet production in e+e- collisions with up to three additional jets.

The syntax for specifying processes is explained in the following sections:

6.6.1.1 PDG codes

Initial and final state particles are specified using their PDG codes (cf. PDG). A list of particles with their codes, and some of their properties, is printed at the start of each Sherpa run, when the OUTPUT is set at level ‘2’.

6.6.1.2 Particle containers

Sherpa contains a set of containers that collect particles with similar properties, namely

• lepton (carrying number 90),
• neutrino (carrying number 91),
• fermion (carrying number 92),
• jet (carrying number 93),
• quark (carrying number 94).

These containers hold all massless particles and anti-particles of the denoted type and allow for a more efficient definition of initial and final states to be considered. The jet container consists of the gluon and all massless quarks (as set by MASS[..]=0.0 or MASSIVE[..]=0). A list of particle containers is printed at the start of each Sherpa run, when the OUTPUT is set at level ‘2’.

It is also possible to define a custom particle container using the keyword PARTICLE_CONTAINER either on the command line or in the (model) section of the input file. The container must be given an unassigned particle ID (kf-code) and its name and content must be specified. An example would be the collection of all down-type quarks, which could be declared as

  PARTICLE_CONTAINER 98 downs 1 3 5;

6.6.1.3 Curly brackets

The curly bracket notation when specifying a process allows up to a certain number of jets to be included in the final state. This is easily seen from an example,

Process 11 -11 -> 93 93 93{3}

Sets up jet production in e+e- collisions. The matix element final state may be 2, 3, 4 or 5 light partons or gluons.

6.6.2 Decay

Specifies the exclusive decay of a particle produced in the matrix element. The virtuality of the decaying particle is sampled according to a Breit-Wigner distribution. An example would be

Process 11 -11 -> 6[a] -6[b]
Decay 6[a] -> 5 24[c]
Decay -6[b] -> -5 -24[d]
Decay 24[c] -> -13 14
Decay -24[d] -> 94 94

6.6.3 Onshell_Decay

Specifies the exclusive decay of a particle produced in the matrix element. The decaying particle is on mass-shell, i.e. a strict narrow-width approximation is used. This tag can be specified alternatively as ‘DecayOS’. An example would be

Process 11 -11 -> 6[a] -6[b]
DecayOS 6[a] -> 5 24[c]
DecayOS -6[b] -> -5 -24[d]
DecayOS 24[c] -> -13 14
DecayOS -24[d] -> 94 94

6.6.4 No_Decay

Remove all diagrams associated with the decay of the given flavours. Serves to avoid resonant contributions in processes like W-associated single-top production. Note that this method breaks gauge invariance! At the moment this flag can only be set for Comix. An example would be

Process 93 93 -> 6[a] -24[b] 93{1}
Decay 6[a] -> 5 24[c]
DecayOS 24[c] -> -13 14
DecayOS -24[b] -> 11 -12
No_Decay -6

6.6.5 Scales

Sets a process-specific scale. For the corresponding syntax see SCALES.

6.6.6 Couplings

Sets process-specific couplings. For the corresponding syntax see COUPLINGS.

6.6.7 CKKW

Sets up multijet merging according to [Hoe09] . The additional argument specifies the separation cut in the form (Q_{cut}/E_{cms})^2. It can be given in any form which is understood by the internal interpreter, see Interpreter. Examples are

• CKKW pow(10,-2.5)
• CKKW sqr(20/E_CMS)

6.6.8 Selector_File

Sets a process-specific selector file name.

6.6.9 Order_EW

Sets a process-specific electroweak order. The given number is exclusive, i.e. only matrix elements with exactly the given order in the electroweak coupling are generated.

Note that for decay chains with Amegic this setting applies to the core process only, while with Comix it applies to the full process, see Decay and DecayOS.

6.6.10 Max_Order_EW

Sets a process-specific maximum electroweak order. The given number is inclusive, i.e. matrix elements with up to the given order in the electroweak coupling are generated.

Note that for decay chains with Amegic this setting applies to the core process only, while with Comix it applies to the full process, see Decay and DecayOS.

6.6.11 Order_QCD

Sets a process-specific QCD order. The given number is exclusive, i.e. only matrix elements with exactly the given order in the strong coupling are generated.

Note that for decay chains with Amegic this setting applies to the core process only, while with Comix it applies to the full process, see Decay and DecayOS.

6.6.12 Max_Order_QCD

Sets a process-specific maximum QCD order. The given number is inclusive, i.e. matrix elements with up to the given order in the strong coupling are generated.

Note that for decay chains with Amegic this setting applies to the core process only, while with Comix it applies to the full process, see Decay and DecayOS.

6.6.13 Min_N_Quarks

Limits the minimum number of quarks in the process to the given value.

6.6.14 Max_N_Quarks

Limits the maximum number of quarks in the process to the given value.

6.6.15 Min_N_TChannels

Limits the minimum number of t-channel propagators in the process to the given value.

6.6.16 Print_Graphs

Writes out Feynman graphs in LaTeX format.

• When using Comix, the parameter specifies the directory name in which the diagram information is stored. This directory is created automatically by Sherpa.
• When using AMEGIC++, the parameter must be set to ‘1’, and the diagram information is stored in the directory Process/P<n>_<m>, where n is the number of incoming and m the number of outgoing particles of the process it has generated.

After Sherpa has run, there will be a .tex-file located in the diagram information directory with the name <process>.tex. This has to be compiled by using latex <process>.tex, which produces a .mp-file. Enter mpost *.mp and again latex <process>.tex in order to produce the .dvi-file <process>.dvi containing the Feynman diagrams.

6.6.17 Integration_Error

Sets a process-specific relative integration error target.

For multijet processes, this parameter can be specified per final state multiplicity. An example would be

Process 93 93 -> 93 93 93{2}
Integration_Error 0.02 {3,4}

Here, the integration error target is set to 2% for 2->3 and 2->4 processes.

6.6.18 Max_Epsilon

Sets epsilon for maximum weight reduction. The key idea is to allow weights larger than the maximum during event generation, as long as the fraction of the cross section represented by corresponding events is at most the epsilon factor times the total cross section. In other words, the relative contribution of overweighted events to the inclusive cross section is at most epsilon.

6.6.19 Enhance_Factor

Sets a process specific enhance factor.

For multijet processes, this parameter can be specified per final state multiplicity. An example would be

Process 93 93 -> 93 93 93{2}
Enhance_Factor 4 {3}
Enhance_Factor 16 {4}

Here, 3-jet processes are enhanced by a factor of 4, 4-jet processes by a factor of 16.

6.6.20 Enhance_Function

Sets a process specific enhance function.

This feature can only be used when generating weighted events.

For multijet processes, the parameter can be specified per final state multiplicity. An example would be

Process 93 93 -> 11 -11 93{1}
Enhance_Function VAR{PPerp2(p[4])} {3}

Here, the 1-jet process is enhanced with the transverse momentum squared of the jet.

Note that the convergence of the Monte Carlo integration can be worse if enhance functions are employed and therefore the integration can take significantly longer. The reason is that the default phase space mapping, which is constructed according to diagrammatic information from hard matrix elements, is not suited for event generation including enhancement. It must first be adapted, which, depending on the enhance function and the final state multiplicity, can be an intricate task.

If Sherpa cannot achieve an integration error target due to the use of enhance functions, it might be appropriate to locally redefine this error target, see Integration_Error.

6.6.21 Enhance_Observable

Allows for the specification of a ME-level observable in which the event generation should be flattened. Of course, this induces an appropriate weight for each event. This option is available for both weighted and unweighted event generation, but for the latter as mentioned above the weight stemming from the enhancement is introduced. For multijet processes, the parameter can be specified per final state multiplicity.

An example would be

Process 93 93 -> 11 -11 93{1}
Enhance_Observable VAR{log10(PPerp(p[2]+p[3]))}|1|3 {3}

Here, the 1-jet process is flattened with respect to the logarithmic transverse momentum of the lepton pair in the limits 1.0 (10 GeV) to 3.0 (1 TeV). For the calculation of the observable one can use any function available in the algebra interpreter (see Interpreter).

Note that the convergence of the Monte Carlo integration can be worse if enhance observables are employed and therefore the integration can take significantly longer. The reason is that the default phase space mapping, which is constructed according to diagrammatic information from hard matrix elements, is not suited for event generation including enhancement. It must first be adapted, which, depending on the enhance function and the final state multiplicity, can be an intricate task.

If Sherpa cannot achieve an integration error target due to the use of enhance functions, it might be appropriate to locally redefine this error target, see Integration_Error.

6.6.22 NLO_QCD_Part

Specifies which pieces of a QCD NLO calculation are computed. Possible choices are

• B ... born term
• RS ... real correction, regularized using Catani-Seymour subtraction terms
• I ... integrated subtraction terms
• V ... virtual (one-loop) correction
• P ... check cancelation of epsilon poles between ’I’ and ’V’

Different pieces can be combined in the processes setup. Only pieces with the same number of final state particles and the same order in alpha_S can be treated as one process, otherwise they will be automatically split up.

Note that Sherpa includes only a very limited selection of one-loop corrections. For processes not included external codes can be interfaced, see External one-loop ME

6.6.23 NLO_EW_Part

6.6.24 ME_Generator

Set a process specific nametag for the desired tree-ME generator, see ME_SIGNAL_GENERATOR.

6.6.25 Loop_Generator

Set a process specific nametag for the desired loop-ME generator. The only Sherpa-native option is Internal with a few hard coded loop matrix elements, e.g. NLO_W.

6.6.25.1 BlackHat Interface

Another source for loop matrix elements is BlackHat. To use this Sherpa has to be linked to BlackHat during installation by using the configure option --enable-blackhat=/path/to/blackhat.

6.6.26 End process

Completes the setup of a process or a list of processes with common properties.

6.7 Selectors

The setup of cuts at the matrix element level is covered by the ‘(selector)’ section of the steering file or the selector data file ‘Selector.dat’, respectively.

Sherpa provides the following selectors

6.7.1 One particle selectors

The selectors listed here implement cuts on the matrix element level, based on single particle kinematics. The corresponding syntax in ‘Selector.dat’ is

<keyword> <flavour code> <min value> <max value>

‘<min value>’ and ‘<max value>’ are floating point numbers, which can also be given in a form that is understood by the internal algebra interpreter, see Interpreter. The selectors act on all possible particles with the given flavour. Their respective keywords are

‘Energy’

energy cut

‘ET’

transverse energy cut

‘PT’

transverse momentum cut

‘Rapidity’

rapidity cut

‘PseudoRapidity’

pseudorapidity cut

6.7.2 Two particle selectors

The selectors listed here implement cuts on the matrix element level, based on two particle kinematics. The corresponding syntax in ‘Selector.dat’ is

<keyword> <flavour1 code> <flavour2 code> <min value> <max value>

‘<min value>’ and ‘<max value>’ are floating point numbers, which can also be given in a form that is understood by the internal algebra interpreter, see Interpreter. The selectors act on all possible particles with the given flavour. Their respective keywords are

‘Mass’

invariant mass

‘Angle’

angular separation (rad)

‘BeamAngle’

angular separation w.r.t. beam

(‘<flavour2 code>’ is 0 or 1, referring to beam 1 or 2)

‘DeltaEta’

pseudorapidity separation

‘DeltaPhi’

azimuthal angle separation (rad)

‘DeltaR’

R separation

6.7.3 Jet finders

There are three different types of jet finders

‘JetFinder’

k_T-algorithm

‘ConeFinder’

cone-algorithm

‘NJetFinder’

k_T-type algorithm to select on a given number of jets

Their respective syntax is

JetFinder  <ycut>[<ycut decay 1>[<ycut decay 11>...]...]... <D parameter>
ConeFinder <min R> 
NJetFinder <n> <ptmin> <etmin> <D parameter> [<exponent>] [<eta max>] [<mass max>]

For ‘JetFinder’, it is possible to give different values of ycut in individual subprocesses of a production-decay chain. The square brackets are then used to denote the decays. In case only one uniform set of ycut is to be used, the square brackets are left out.

‘<ycut>’, ‘<min R>’ and ‘<D parameter>’ are floating point numbers, which can also be given in a form that is understood by the internal algebra interpreter, see Interpreter.

The ‘NJetFinder’ allows to select for kinematic configurations with at least ‘<n>’ jets that satisfy both, the ‘<ptmin>’ and the ‘<etmin>’ minimum requirements and that are in a PseudoRapidity region |eta|<‘<eta max>’. The ‘<exponent>’ allows to apply a kt-algorithm (1) or an anti-kt algorithm (-1). As only massless partons are clustered by default, the ‘<mass max>’ allows to also include partons with a mass up to the specified values. This is useful e.g. in calculations with massive b-quarks which shall nonetheless satisfy jet criteria.

6.7.4 Universal selector

The universal selector is intended to implement non-standard cuts on the matrix element level. Its syntax is

"<variable>" <kf1>,..,<kfn> <min1>,<max1>:..:<minn>,<maxn> [<order1>,...,<orderm>]

No additional white spaces are allowed

The first word has to be double-quoted, and contains the name of the variable to cut on. The keywords for available predefined <variable>s can be figured by running Sherpa ‘SHOW_VARIABLE_SYNTAX=1’. Or alternatively, an arbitrary cut variable can be constructed using the internal interpreter, see Interpreter. This is invoked with the command ‘Calc(...)’. In the formula specified there you have to use place holders for the momenta of the particles: ‘p[0]’ ... ‘p[n]’ hold the momenta of the respective particles ‘kf1’ ... ‘kfn’. A list of available vector functions and operators can be found here Interpreter.

‘<kf1>,..,<kfn>’ specify the PDG codes of the particles the variable has to be calculated from. In case this choice is not unique in the final state, you have to specify multiple cut ranges (‘<min1>,<max1>:..:<minn>,<maxn>’) for all (combinations of) particles you want to cut on, separated by semicolons.

If no fourth argument is given, the order of cuts is determined internally, according to Sherpa’s process classification scheme. This then has to be matched if you want to have different cuts on certain different particles in the matrix element. To do this, you should put enough (for the possible number of combinations of your particles) arbitrary ranges at first and run Sherpa with debugging output for the universal selector: ‘Sherpa OUTPUT=2[Variable_Selector::Trigger|15]’. This will start to produce lots of output during integration, at which point you can interrupt the run (Ctrl-c). In the ‘Variable_Selector::Trigger(): {...}’ output you can see, which particle combinations have been found and which cut range your selector has held for them (vs. the arbitrary range you specified). From that you should get an idea, in which order the cuts have to be specified.

If the fourth argument is given, particles are ordered before the cut is applied. Possible orderings are ‘PT_UP’, ‘ET_UP’, ‘E_UP’ and ‘ETA_UP’, (increasing p_T, E_T, E, eta). They have to be specified for each of the particles, separated by commas.

Examples

Two-body transverse mass

"mT" 11,-12 50,E_CMS

Cut on the pT of only the hardest lepton in the event

"PT" 90 50.0,E_CMS [PT_UP]

Using bool operations to restrict eta of the electron to |eta| < 1.1 or 1.5 < |eta| < 2.5

"Calc(abs(Eta(p[0]))<1.1||(abs(Eta(p[0]))>1.5&&abs(Eta(p[0]))<2.5))" 11 1,1

Note the range 1,1 meaning true for bool operations.

Requesting opposite side tag jets in VBF would for example need a setup like this

"Calc(Eta(p[0])*Eta(p[1]))" 93,93 -100,0 [PT_UP,PT_UP]

Restricting electron+photon mass to be outside of [87.0,97.0]:

"Calc(Mass(p[0]+p[1])<87.0||Mass(p[0]+p[1])>97.0)" 11,22 1,1

In ‘Z[lepton lepton] Z[lepton lepton]’, cut on mass of lepton-pairs produced from Z’s:

"m" 90,90 80,100:0,E_CMS:0,E_CMS:0,E_CMS:0,E_CMS:80,100

Here we use knowledge about the internal ordering to cut only on the correct lepton pairs.

6.7.5 Minimum selector

This selector can combine several selectors to pass an event if either those passes the event. It is mainly designed to generate more inclusive samples that, for instance, include several jet finders and that allows a specification later. The syntax is

MinSelector {
  Selector 1
  Selector 2
  ...
} 

6.7.6 NLO selectors

Phase-space cuts that are applied on next-to-leading order calculations must be defined in a infrared safe way. Technically there is also a special treatment for the real (subtracted) correction required. Currently only the following selectors meet this requirement:

QCD parton cuts

NJetFinder <n> <ptmin> <etmin> <D parameter> [<exponent>] [<eta max>] [<mass max>]

(see Jet finders)

Cuts on not strongly interacting particles

One particle selectors

PTNLO <flavour code> <min value> <max value>
RapidityNLO <flavour code> <min value> <max value>
PseudoRapidityNLO <flavour code> <min value> <max value>

Two particle selectors

PT2NLO <flavour1 code> <flavour2 code> <min value> <max value>
Mass <flavour1 code> <flavour2 code> <min value> <max value>

The Minimum selector can be used if constructed with other selectors mentioned in this section

6.8 Integration

The integration setup is covered by the ‘(integration)’ section of the steering file or the integration data file ‘Integration.dat’, respectively.

The following parameters are used to steer the integration.

6.8.1 ERROR

Specifies the relative integration error target.

6.8.2 INTEGRATOR

Specifies the integrator. The possible integrator types depend on the matrix element generator. In general users should rely on the default value and otherwise seek the help of the authors, see Authors. However, there are a few generator independent choices which have been designed for specific processes and might be more efficient there:

• ‘1’: is an integrator for a final state of a weak boson, decaying into two particles plus two or more jets. When this integrator is used the keyword VHAAG_RES_KF specifies the kf-code of the weak boson, the default is W (24). VHAAG_RES_D1 and VHAAG_RES_D2 define the positions of the Boson decay products within the internal naming scheme, where 2 is the position of the first outgoing particle. The defaults are VHAAG_RES_D1=2 and VHAAG_RES_D2=3, which is the correct choice for all processes where the decay products are the only not strongly interacting final state particles.
• ‘2’: is an integrator designed for pure QCD final states. It is based on the HAAG algorithm [Ham02] .

6.8.3 VEGAS

Specifies whether or not to employ Vegas for adaptive integration. The two possible values are ‘On’ and ‘Off’, the default being ‘On’.

6.8.4 FINISH_OPTIMIZATION

Specifies whether the full Vegas optimization is to be carried out. The two possible options are ‘On’ and ‘Off’, the default being ‘On’.

6.8.5 PSI_NMAX

The maximum number of points before cuts to be generated during integration. This parameter acts on a process-by-process basis.

6.9 Shower Parameters

The shower setup is covered by the ‘(shower)’ section of the steering file or the shower data file ‘Shower.dat’, respectively.

The following parameters are used to steer the shower setup.

6.9.1 SHOWER_GENERATOR

The only shower option currently available in Sherpa is ‘CSS’, and this is the default for this tag. See the module summaries in Basic structure for details about this shower.

Different shower modules are in principle supported and more choices will be provided by Sherpa in the near future. To list all available shower modules, the tag SHOW_SHOWER_GENERATORS=1 can be specified on the command line.

SHOWER_GENERATOR=None switches parton showering off completely. However, even in the case of strict fixed order calculations, this might not be the desired behaviour as, for example, then neither the METS scale setter, cf. SCALES, nor Sudakov rejection weights can be employed. To circumvent when using the CS Shower see CS Shower options.

6.9.2 CS Shower options

Sherpa’s default shower module is based on [Sch07a] . A new ordering parameter for initial state splitters was introduced in [Hoe09] and a novel recoil strategy for initial state splittings was proposed in [Hoe09a] . While the ordering variable is fixed, the recoil strategy for dipoles with initial-state emitter and final-state spectator can be changed for systematics studies. Setting ‘CSS_KIN_SCHEME=0’ (default) corresponds to using the recoil scheme proposed in [Hoe09a] , while ‘CSS_KIN_SCHEME=1’ enables the original recoil strategy. Note that the latter is more suitable for parton evolution in deep-inelastic lepton nucleon scattering, see HERA_DIS [Car09] . The lower cutoff of the shower evolution can be set via ‘CSS_PT2MIN’. Note that this value is specified in GeV^2.

By default, only QCD splitting functions are enabled in the shower. If you also want to allow for photon splittings, you can enable them by using ‘CSS_EW_MODE=1’. Note, that if you have leptons in your matrix-element final state, they are by default treated by a soft photon resummation as explained in QED Corrections. To avoid double counting, this has to be disabled as explained in that section.

The CS Shower can be forced not to emit any partons setting ‘CSS_NOEM=1’. Sudakov rejection weights for merged samples are calculated nontheless. Setting ‘CSS_MAXEM=<N>’, on the other hand, forces the CS Shower to truncate its evolution at the Nth emission. This setting, however does not necessarily compute all Sudakov weights correctly. Both settings still enable the CS Shower to be used in the METS scale setter, cf. SCALES.

6.10 MPI Parameters

The multiple parton interaction (MPI) setup is covered by the ‘(mi)’ section of the steering file or the MPI data file ‘MI.dat’, respectively. The basic MPI model is described in [Sjo87] while Sherpa’s implementation details are discussed in [Ale05]

The following parameters are used to steer the MPI setup.

6.10.1 MI_HANDLER

Specifies the MPI handler. The two possible values at the moment are ‘None’ and ‘Amisic’.

6.10.2 SCALE_MIN

Specifies the transverse momentum integration cutoff in GeV.

6.10.3 PROFILE_FUNCTION

Specifies the hadron profile function. The possible values are ‘Exponential’, ‘Gaussian’ and ‘Double_Gaussian’. For the double gaussian profile, the relative core size and relative matter fraction can be set using PROFILE_PARAMETERS.

6.10.4 PROFILE_PARAMETERS

The potential parameters for hadron profile functions, see PROFILE_FUNCTION. For double gaussian profiles there are two parameters, corresponding to the relative core size and relative matter fraction.

6.10.5 REFERENCE_SCALE

Specifies the centre-of-mass energy at which the transverse momentum integration cutoff is used as is, see SCALE_MIN. This parameter should not be changed by the user. The default is ‘1800’, corresponding to Tevatron Run I energies.

6.10.6 RESCALE_EXPONENT

Specifies the rescaling exponent for fixing the transverse momentum integration cutoff at centre-of-mass energies different from the reference scale, see SCALE_MIN, REFERENCE_SCALE.

6.11 Fragmentation

The hadronization setup is covered by the ‘(fragmentation)’ section of the steering file or the fragmentation data file ‘Fragmentation.dat’, respectively.

There are, broadly speaking, two options of how Sherpa handles the transition of quarks and gluons into primordial hadrons (hadronization) and their decay:

• In previous versions the only way of dealing with this was to invoke corresponding routines of Pythia, invoking the Lund model of string fragmentation and Pythia’s native hadron decay routines. Although now the ‘Lund’ option is disfavoured, it will still be kept in Sherpa for backward compatibility and for some consistency checks.
• From version 1.1 on, the default choice will be to rely entirely on two internal modules, AHADIC++ and HADRONS++ for hadronization and hadron decays.

6.11.1 Hadronization parameters

The FRAGMENTATION parameter sets the fragmentation module to be employed during event generation. The default is ‘Ahadic’. This parameter steers whether the fragmentation is switched on and performed by the internal cluster fragmentation module AHADIC++, by an interface to the corresponding routines of the Lund string hadronization of Pythia [Sjo03] ), indicated by ‘Lund’), or whether the fragmentation is completely switched (‘Off’).

The treatment of hadron and tau decays is specified by DECAYMODEL. Its allowed values are either the default choice ‘Hadrons’, which renders the HADRONS++ module responsible for performing the decays, or as alternative, the interface to Pythia can be invoked by setting this parameter to ‘Lund’. For the former option, the reader is referred to HADRONS++ for a more detailed discussion.

Please note that it is absolutely not advisable to use one fragmentation model with another model for the hadron decays, since there is quite an intimate relation between two - for instance, AHADIC++ knows and allows for many more primordial hadrons than Pythia does, which would obviously lead to problems, if they were created in AHADIC++ and left to Pythia for decays.

6.11.1.1 Using the Pythia routines

The Pythia routines have been made available through an interface to the corresponding Fortran code, with the option to steer Pythia parameters through Sherpa. The Lund parameters can be collected in a file set by the parameter LUND_FILE (default is Lund.dat), if ‘Lund’ is chosen as the method of choice for both fragmentation and hadron decays. Driven in this option, Sherpa is more or less ignorant about hadron decays, with the exception of tau-decays, which have been supplemented early in the development of the Sherpa event generator.

The coarse features of the string breakup in the Lund model are characterized by three parameters, Lund-a through PARJ(41), Lund-b through PARJ(42), and Lund-sigma through PARJ(21). If the data-file parameters are not set, Sherpa employs the default values in Pythia.

More Pythia parameters can be added to the Lund.dat file using the Pythia nomenclature in the common-blocks, e.g. MSTJ(11) for changing the fragmentation function for heavy quarks. Please note that particle decays cannot directly be disabled there. Instead, the stable flag for the corresponding hadron needs to be used.

6.11.2 AHADIC++

TODO.

6.11.3 HADRONS++

HADRONS++ is the module within the Sherpa framework which is responsible for treating hadron and tau decays. It contains decay tables with branching ratios for approximately 2500 decay channels, of which many have their kinematics modelled according to a matrix element with corresponding form factors. Especially decays of the tau lepton and heavy mesons have form factor models similar to dedicated codes like Tauola [Jad93] and EvtGen [Lan01] .

Some general switches which relate to hadron decays can be adjusted in the (fragmentation) section:

• DECAYPATH The path to the parameter files for the hadron and tau decays (default: Decaydata/). It is important to note that the path has to be given relative to the current working directory. If it doesn’t exist, the default Decaydata directory (\$prefix/share/SHERPA-MC/Decaydata) will be used.
• Hadron properties like mass, width, stable/unstable and active can be set in the (fragmentation) section in full analogy to the settings for fundamental particles in the (model) section (cf. Model Parameters).
• MASS_SMEARING = [0,1,2] (default: 1) Determines whether particles entering the hadron decay event phase should be put off-shell according to their mass distribution. It is taken care that no decay mode is suppressed by a potentially too low mass. While HADRONS++ determines this dynamically from the chosen decay channel, for Pythia as hadron decay handler its w-cut parameter is employed. Choosing option 2 instead of 1 will only set unstable (decayed) particles off-shell, but leave stable particles on-shell.
• MAX_PROPER_LIFETIME = [mm] Parameter for maximum proper lifetime (in mm) up to which particles are considered unstable. If specified, this will make long-living particles stable, even if they are set unstable by default or by the user.

Many aspects of the above mentioned “Decaydata” can be adjusted. There exist three levels of data files, which are explained in the following sections. As with all other setup files, the user can either employ the default “Decaydata” in <prefix>/share/SHERPA-MC/Decaydata, or overwrite it (also selectively) by creating the appropriate files in the directory specified by DECAYPATH.

6.11.3.1 HadronDecays.dat

HadronDecays.dat consists of a table of particles that are to be decayed by HADRONS++. Note: Even if decay tables exist for the other particles, only those particles decay that are set unstable, either by default, or in the model/fragmentation settings. It has the following structure, where each line adds one decaying particle:

It is possible to specify different decay tables for the particle (positive kf-code) and anti-particle (negative kf-code). If only one is specified, it will be used for both particle and anti-particle.

If more than one decay table is specified for the same kf-code, these tables will be used in the specified sequence during one event. The first matching particle appearing in the event is decayed according to the first table, and so on until the last table is reached, which will be used for the remaining particles of this kf-code.

Additionally, this file may contain the keyword CREATE_BOOKLET on a separate line, which will cause HADRONS++ to write a LaTeX document containing all decay tables.

6.11.3.2 Decay table files

The decay table contains information about outgoing particles for each channel, its branching ratio and eventually the name of the file that stores parameters for a specific channel. If the latter is not specified HADRONS++ will produce it and modify the decay table file accordingly.

Additionally to the branching ratio, one may specify the error associated with it, and its source. Every hadron is supposed to have its own decay table in its own subdirectory. The structure of a decay table is

It should be stressed here that the branching ratio which is explicitly given for any individual channel in this file is always used regardless of any matrix-element value.

6.11.3.3 Decay channel files

A decay channel file contains various information about that specific decay channel. There are different sections, some of which are optional:

• <Options>
      AlwaysIntegrate = 0
      CPAsymmetryC = 0.0
      CPAsymmetryS = 0.0
  </Options>
  

  • AlwaysIntegrate = [0,1] For each decay channel, one needs an integration result for unweighting the kinematics (see below). This result is stored in the decay channel file, such that the integration is not needed for each run. The AlwaysIntegrate option allows to bypass the stored integration result, and do the integration nonetheless (same effect as deleting the integration result).
  • CPAsymmetryC/CPAsymmetryS If one wants to include time dependent CP asymmetries through interference between mixing and decay one can set the coefficients of the cos and sin terms respectively. HADRONS++ will then respect these asymmetries between particle and anti-particle in the choice of decay channels.

• <Phasespace>
    1.0 MyIntegrator1
    0.5 MyIntegrator2
  </Phasespace>
  

  Specifies the phase-space mappings and their weight.

• <ME>
    1.0 0.0 my_matrix_element[X,X,X,X,X,...]
    1.0 0.0 my_current1[X,X,...] my_current2[X,X,X,...]
  </ME>
  

  Specifies the matrix elements or currents used for the kinematics, their respective weights, and the order in which the particles (momenta) enter them. For more details, the reader is referred to [Kra10] .

• <my_matrix_element[X,X,X,X,X,...]>
    parameter1 = value1
    parameter2 = value2
    ...
  </my_matrix_element[X,X,X,X,X,...]>
  

  Each matrix element or current may have an additional section where one can specify needed parameters, e.g. which form factor model to choose. Each parameter has to be specified on a new line as shown above. Available parameters are listed in [Kra10] . Parameters not specified get a default value, which might not make sense in specific decay channels. One may also specify often needed parameters in HadronConstants.dat, but they will get overwritten by channel specific parameters, should these exist.

• <Result>
    3.554e-11 6.956e-14 1.388e-09;
  </Result>
  

  These last three lines have quite an important meaning. If they are missing, HADRONS++ integrates this channel during the initialization and adds the result lines. If this section exists though, and AlwaysIntegrate is off (the default value, see above) then HADRONS++ reads in the maximum for the kinematics unweighting.

  Consequently, if some parameters are changed (also masses of incoming and outgoing particles) the maximum might change such that a new integration is needed in order to obtain correct kinematical distributions. There are two ways to enforce the integration: either by deleting the last three lines or by setting AlwaysIntegrate to 1. When a channel is re-integrated, HADRONS++ copies the old decay channel file into .<filename>.dat.old.

6.11.3.4 HadronConstants.dat

HadronConstants.dat may contain some globally needed parameters (e.g. for neutral meson mixing, see [Kra10] ) and also fall-back values for all matrix-element parameters which one specifies in decay channel files. Here, the Interference_X = 1 switch would enable rate asymmetries due to CP violation in the interference between mixing and decay (cf. Decay channel files), and setting Mixing_X = 1 enables explicit mixing in the event record according to the time evolution of the flavour states. By default, all mixing effects are turned off.

• Mixing parameters with some example values

  x_K = 0.946
  y_K = -0.9965
  qoverp2_K = 1.0
  Interference_K = 0
  Mixing_K = 0
  
  x_D = 0.0
  y_D = 0.0
  qoverp2_D = 1.0
  Interference_D = 0
  Mixing_D = 0
  
  x_B = 0.776
  y_B = 0.0
  qoverp2_B = 1.0
  Interference_B = 1
  Mixing_B = 0
  
  x_B(s) = 30.0
  y_B(s) = 0.155
  qoverp2_B(s) = 1.0
  Interference_B(s) = 0
  Mixing_B(s) = 0
  

6.11.3.5 Further remarks

Spin correlations: the spin correlation algorithm is implemented, also for decays of tau’s produced in the signal process. It can be switched on through the keyword SPIN_CORRELATIONS in the (run) section, see Run Parameters for more details.

Adding new channels: if new channels are added to HADRONS++ (choosing isotropic decay kinematics) a new decay table must be defined and the corresponding hadron must be added to HadronDecays.dat. The decay table merely needs to consist of the outgoing particles and branching ratios, i.e. the last column (the one with the decay channel file name) can safely be dropped. By running Sherpa it will automatically produce the decay channel files and write their names in the decay table.

Some details on tau decays: $\tau$ decays are treated within the HADRONS++ framework, even though the $\tau$ is not a hadron. As for many hadron decays, the hadronic tau decays have form factor models implemented, for details the reader is referred to [Kra10] .

6.12 QED Corrections

Higher order QED corrections are effected both on hard interaction and, upon their formation, on each hadron’s subsequent decay. The Photons [Sch08] module is called in both cases for this task. It employes a YFS-type resummation [Yen61] of all infrared singular terms to all orders and is equipped with complete first order corrections for the most relevant cases (all other ones receive approximate real emission corrections built up by Catani-Seymour splitting kernels).

6.12.1 General Switches

The relevant switches to steer the higher order QED corrections reside in the ‘(fragmentation)’ section of the steering file or the fragmentation data file ‘Fragmentation.dat’, respectively.

6.12.1.1 YFS_MODE

The keyword YFS_MODE = [0,1,2] determines the mode of operation of Photons. YFS_MODE = 0 switches Photons off. Consequently, neither the hard interaction nor any hadron decay will be corrected for soft or hard photon emission. YFS_MODE = 1 sets the mode to "soft only", meaning soft emissions will be treated correctly to all orders but no hard emission corrections will be included. With YFS_MODE = 2 these hard emission corrections will also be included up to first order in alpha_QED. This is the default setting.

6.12.1.2 YFS_USE_ME

The switch YFS_USE_ME = [0,1] tells Photons how to correct hard emissions to first order in alpha_QED. If YFS_USE_ME = 0, then Photons will use collinearly approximated real emission matrix elements. Virtual emission matrix elements of order alpha_QED are ignored. If, however, YFS_USE_ME=1, then exact real and/or virtual emission matrix elements are used wherever possible. These are presently available for V->FF, V->SS, S->FF, S->SS, S->Slnu, S->Vlnu type decays, Z->FF decays and leptonic tau and W decays. For all other decay types general collinearly approximated matrix elements are used. In both approaches all hadrons are treated as point-like objects. The default setting is YFS_USE_ME = 1. This switch is only effective if YFS_MODE = 2.

6.12.1.3 YFS_IR_CUTOFF

YFS_IR_CUTOFF sets the infrared cut-off dividing the real emission in two regions, one containing the infrared divergence, the other the "hard" emissions. This cut-off is currently applied in the rest frame of the multipole of the respective decay. It also serves as a minimum photon energy in this frame for explicit photon generation for the event record. In contrast, all photons below with energy less than this cut-off will be assumed to have negligible impact on the final-state momentum distributions. The default is YFS_IR_CUTOFF = 1E-3 (GeV). Of course, this switch is only effective if Photons is switched on, i.e. YFS_MODE = [1,2].

6.12.2 QED Corrections to the Hard Interaction

The switch to steer QED corrections to the hard scatter resides in the ’(me)’ section of the steering file or the matrix element data file ‘ME.dat’, respectively.

6.12.2.1 ME_QED

ME_QED = On/Off turns the higher order QED corrections to the matrix element on or off, respectively. The default is ‘On’. Switching QED corrections to the matrix element off has no effect on QED Corrections to Hadron Decays. The QED corrections to the matrix element will only be effected on final state not strongly interacting particles. If a resonant production subprocess for an unambiguous subset of all such particles is specified via the process declaration (cf. Processes) this can be taken into account and dedicated higher order matrix elements can be used (if YFS_MODE = 2 and YFS_USE_ME = 1).

6.12.3 QED Corrections to Hadron Decays

If the Photons module is switched on, all hadron decays are corrected for higher order QED effects.

7. ME-PS merging

For a large fraction of LHC final states, the application of reconstruction algorithms will lead to the identification of several hard jets. A major task is to distinguish whether such events are signals for new physics or just manifestations of SM physics. Related calculations therefore need to describe as accurately as possible both the full matrix element for the underlying hard processes as well as the subsequent evolution and conversion of the hard partons into jets of hadrons. Several scales therefore determine the thorough development of the event. This makes it difficult to unambiguously disentangle the components, which belong to the hard process from those of the hard-parton evolution. Given an n-jet event of well separated partons, its jet structure is retained when emitting a further collinear or soft parton. An additional hard, large-angle emission however gives rise to an extra jet changing the n to an n+1 final state. The merging scheme has to define, on an event-by-event basis, which possibility has to be followed. Its primary goals are therefore to avoid double counting by preventing events to appear twice, i.e. once for each possibility, as well as dead regions by generating each configuration only once and using the appropriate path.

Various such merging schemes have been proposed. The currently most advanced treatment at tree-level is detailed in [Hoe09] . It relies on a strict separation of the phasespace for additional QCD radiation into a matrix-element and a parton-shower domain. Truncated showers are then needed to account for potential radiation in the parton-shower domain, if radiation in the matrix-element domain has already occured. This technique has been applied to the simulation of final states containing hard photons [Hoe09a] and has been extended to multi-scale processes where the leading order is dominated by very low scales [Car09] . A merging approach similar to [Hoe09] was presented in [Ham09] for the special case of angular-ordered parton showers. Several older approaches exist. The CKKW scheme as a procedure similar to the truncated shower merging was introduced in [Cat01] . Its extension to hadronic processes has been discussed in [Kra02] , and the approach has been validated for several cases [Sch05] , [Kra05a] , [Kra04] , [Kra05] , [Gle05] . A reformulation of CKKW to a merging procedure in conjunction with a dipole shower (CKKW-L) has been presented in [Lon01] . The MLM scheme has been developed using a geometric analysis of the unconstrained radiation pattern in terms of cone jets to generate the inclusive samples [Man01] ,[Man06] . In a number of works, all these different algorithms have been implemented in different variations on different levels of sophistication in conjunction with various matrix-element generators or already in full-fledged event generators. Their respective results have been compared e.g. in [Hoc06] , [Alw07] . Common to all schemes is that sequences of tree-level multileg matrix elements with increasing final-state multiplicity are merged with parton showers to yield a fully inclusive sample with no double counting. Their connection with truncated shower merging is outlined in [Hoe09] .

7.1 The algorithm implemented in Sherpa

In Sherpa the merging of matrix elements and parton showers is accomplished as follows, cf. [Hoe09] :

1. All cross sections sigma_k for processes with k=0,1,...,N extra partons are calculated with the constraint that the matrix-element final states pass the jet criteria. They are determined by the jet measure shown below, and the minimal distance is set by the actual merging scale Q_cut. The measure used for jet identification can be written as

   Q_ij^2 = 2p_i.p_j min{2/(Cijk+Cjik)}

   where the minimum is taken over the colour-connected partons k (k different from i and j), and where, for final state partons i and j,

   Cijk = p_i.p_k/((p_i+p_k).p_j) - m_i^2/(2p_i.p_j)      if j=g, Cijk = 1                                               else.

2. Processes of fixed parton multiplicity are chosen with probability sigma_k/(sum of all sigma_k). The event’s hard process is picked from the list of partonic processes having the desired multiplicity and according to their particular cross-section contributions. All particle momenta are distributed respecting the correlations encoded in the matrix elements. Merged samples therefore fully include lepton-jet and jet–jet correlations up to N extra jets.
3. The parton configuration of the matrix element has to be analysed to eventually accomplish the reweighting. Matrix elements are interpreted in the large N_c limit. The partons are clustered backwards according to the shower measure and inverted shower kinematics. The clustering is guided by physically allowed parton combinations, restricting the shower histories to those which correspond to a Feynman diagram. It is stopped after a 2->2 configuration (a core process) has been identified.
4. The reweighting proceeds according to the reconstructed shower history. The event is accepted or rejected according to a kinematics-dependent weight, which corresponds to evaluating strong couplings in the parton shower scheme.
5. The parton-shower evolution is started with suitably defined scales for intermediate and final-state particles.
6. Intermediate partons undergo truncated shower evolution. This allows parton-shower emissions between the scales of one matrix element branching and the next. This leads to a situation where, due to additional partons originating from these branchings, the kinematics of the next matrix-element branching needs to be redefined. If for any reason (e.g. energy-momentum conservation) the matrix element branching cannot be reconstructed after a truncated shower branching, this shower branching must be vetoed.
7. In all circumstances parton-shower radiation is subject to the condition that no extra jet is produced. If any emission turns out to be harder than the separation cut Q_cut, the event is vetoed. This effectively implements a Sudakov rejection and reduces the individual inclusive cross section to exclusive ones. The exception to this veto – called highest-multiplicity treatment – is for matrix-element configurations with the maximal number N of extra partons. These cases require the parton shower to cover the phase space for more jets than those produced by the matrix elements. To obtain an inclusive N-jet prediction, the veto therefore is on parton emissions at scales harder than the softest parton-shower scale, which can produce allowed emissions harder than the separation scale Q_cut. Of course, correlations including the N+1th jet are only approximately taken into account.

7.2 Generation of merged samples

The generation of inclusive event samples, i.e. the combination of matrix elements for different parton multiplicities with parton showers and hadronization, is completely automatized within Sherpa. To obtain consistent results, certain parameters related to the matrix-element calculation and the parton showers have to be set accordingly. In the following the basic parameter settings for generating “merged” samples are summarised. Potential pitfalls are pointed out.

1. Process setup

   The starting point is the definition of a basic core (lowest-order) process with respect to which the impact of additional QCD radiation shall be studied. As an illustrative example, consider Drell–Yan lepton-pair production in proton–proton collisions. The lowest-order process reads pp -> l-bar l, mediated through Z/photon exchange. Additional QCD radiation will then manifest itself through additional QCD partons in the final state, i.e. pp -> l\bar l + n jets with n=1,...,N. To initialise the calculation of all the different matrix elements (for pp -> l\bar l+0,1,...,N QCD partons) in a single generator run, besides selecting the basic core process, the maximal number N of additional final-state QCD partons has to be specified in the (processes) section of the steering file. For the above example, assuming N=3, this reads:

       Process 93 93 -> 90 90 93{3}
       Order_EW 2
   

   N is given in the curly brackets belonging to the 93, the code for QCD partons. Note, that it is mandatory to fix the order of electroweak couplings to the corresponding order of the basic core process, here pp -> l-bar l or 93 93 -> 90 90, as only QCD corrections to this process can be considered and further electroweak corrections are not treated by Sherpa’s ME-PS merging implementation.

2. Setting the merging scale

   The most important parameter to be specified when generating merged samples with Sherpa is the actual value of the jet resolution that separates the subsamples of different parton multiplicities, the merging scale.

   The jet criterion is explained in The algorithm implemented in Sherpa. The separation cut, Q_cut, must be specified. It is set using the CKKW tag, usually in the form (Q_cut/E_cms)^2. For example, a valid setting reads

       CKKW sqr(20/E_CMS)
   

   and must be included in the process specification, before the End process line. More sophisticated and more flexible settings of Q_cut are possible, as is exemplified in HERA_DIS. As mentioned before, all extra QCD parton radiation is regularised by satisfying the jet criterion. However, divergences of the basic core process, such as vanishing invariant masses of lepton pairs, need to be regularised by imposing additional cuts, see Selectors.

3. Parton showering

   It always should be ensured that the parton showers are switched on.

Further remarks

Although the merging of different multiplicity matrix-element samples with parton showers attached is fully automatized in Sherpa, some care has to be taken to ensure physical meaningful results. Some of the most prominent mistakes are listed here:

• The jet criterion specified by the CKKW parameter defines which phase-space regions are populated by matrix elements and which ones by parton showers. In order to guarantee functioning of Sherpa’s ME-PS merging implementation, no further phase-space cuts on the additional QCD parton emissions need/should be applied while generating the samples.
• When jets are included in the core process, like in the Tevatron_QCD example, a jet criterion must be specified for the core jets. This can be done using the NJetFinder parameter, which applies it’s jet criterion to only the specified number of jets. See the Examples section for an example of the usage.
• In Getting started it has been pointed out that the cross-section results of the matrix-element integration can be stored and hence re-used in later runs. The same applies to the cross sections sigma_k (cf. the first item in The algorithm implemented in Sherpa) of the various matrix-element multiplicities. For the merging algorithm to work correctly, the re-evaluation of these cross sections is however mandatory and stored integration results of former runs will not be valid whenever related parameters are changed. This includes all parameters given in the (selector) part of the steering file, or the merging scale set by CKKW. Furthermore, changing the centre-of-mass energy, the choice of the PDF or the running of alpha_s requires to integrate and possibly store afresh.
• The total inclusive cross section of a merged Sherpa prediction does not correspond to the sum of the sigma_k. Because of reweighting with Sudakov form factors on an event-by-event basis, all these fixed-multiplicity cross sections are modified (scaled down) by the ME-PS merging procedure. The sum of the modified values determines Sherpa’s total inclusive cross section, which is given in the final output after event generation, see Running Sherpa.
• The ME-PS merging implemented in Sherpa is not yet enabled for processes involving coloured supersymmetric particles.

Finally, a few more useful comments related to Sherpa’s merging are stated below:

• Factors can be given to vary the default choices for the renormalization and factorization scales used in Sherpa simulations. The corresponding keywords are RENORMALIZATION_SCALE_FACTOR and FACTORIZATION_SCALE_FACTOR, and they are multiplied to the default mu_R^2 and mu_F^2 scales used for alpha_s and PDF evaluations, respectively. By varying them in a certain range around 1 (like [1/4,4]), an estimate for the uncertainty of Sherpa merged predictions can be obtained conveniently. Note that the application of the factors requires to re-integrate the matrix elements.
• The generation of merged event samples for the production and decay of heavy particles in association with jets has a few particularities, which are best explained by means of an example. The reader is therefore referred to Examples for some applications of merged matrix elements and parton showers.

8. Tips and Tricks

8.1 Bash completion

Sherpa will install a file named ‘$prefix/share/SHERPA-MC/sherpa-completion’ which contains tab completion functionality for the bash shell. You simply have to source it in your active shell session by running

  .  $prefix/share/SHERPA-MC/sherpa-completion

and you will be able to tab-complete any parameters on a Sherpa command line.

To permanently enable this feature in your bash shell, you’ll have to add the source command above to your ~/.bashrc.

8.2 Rivet analyses

Sherpa is equipped with an interface to the analysis tool Rivet. To enable it, Rivet and HepMC have to be installed (e.g. using the Rivet bootstrap script) and your Sherpa compilation has to be configured with the following options:

  ./configure --enable-hepmc2=/path/to/hepmc2 --enable-rivet=/path/to/rivet

(Note: Both paths are equal if you used the Rivet bootstrap script.)

To use the interface, specify the switch

  Sherpa ANALYSIS=Rivet

and create an analysis section in Run.dat that reads as follows:

  (analysis){
    BEGIN_RIVET {
      -a D0_2008_S7662670 CDF_2007_S7057202 D0_2004_S5992206 CDF_2008_S7828950
    } END_RIVET
  }(analysis)

The line starting with -a specifies which Rivet analyses to run and the histogram output file can be changed with the normal ANALYSIS_OUTPUT switch.

You can also use rivet-mkhtml (distributed with Rivet) to create plot webpages from Rivet’s output files:

  source /path/to/rivetenv.sh   # see below
  rivet-mkhtml -o output/ file1.aida [file2.aida, ...]
  firefox output/index.html &

If your Rivet installation is not in a standard location, the bootstrap script should have created a rivetenv.sh which you have to source before running the rivet-mkhtml script.

8.3 HZTool analyses

Sherpa is equipped with an interface to the analysis tool HZTool. To enable it, HZTool and CERNLIB have to be installed and your Sherpa compilation has to be configured with the following options:

  ./configure --enable-hztool=/path/to/hztool --enable-cernlib=/path/to/cernlib --enable-hepevtsize=4000

To use the interface, specify the switch

  Sherpa ANALYSIS=HZTool

and create an analysis section in Run.dat that reads as follows:

  (analysis){
    BEGIN_HZTOOL {
      HISTO_NAME output.hbook;
      HZ_ENABLE hz00145 hz01073 hz02079 hz03160;
    } END_HZTOOL;
  }(analysis)

The line starting with HZ_ENABLE specifies which HZTool analyses to run. The histogram output directory can be changed using the ANALYSIS_OUTPUT switch, while HISTO_NAME specifies the hbook output file.

8.4 PGS interface

Sherpa is equipped with an interface to StdHEP, which can be used to pass events to PGS. To enable the interface, PGS must be installed and your Sherpa compilation has to be configured with the following options:

  ./configure --enable-pgs=/path/to/pgs --enable-hepevtsize=4000

To use the interface, run Sherpa with

  Sherpa ANALYSIS=PGS

or specify ANALYSIS PGS; in the ‘(run)’ section of your input file.

and create an analysis section in Run.dat that reads as follows:

  (analysis){
    BEGIN_PGS {
      FILE_NAME events.lhe;
      WRITE_MODE 4;
    } END_PGS;
  }(analysis)

The line starting with FILE_NAME specifies the name of the StdHEP output file, while WRITE_MODE controls the content of the file. It should be set to 4 for weighted events, and can be 1 or 4 for unweighted. If set to 4, the event weight may be located in the HEPEV4 common block as EVENTWEIGHTLH. Please refer to the StdHEP documentation for more details.

Please refer to the PGS documentation for how to pass StdHEP event files on to PGS. If you are using the LHC olympics executeable, this can be achieved with

  ./olympics --stdhep events.lhe <other options>

8.5 MCFM interface

Sherpa is equipped with an interface to the NLO library of MCFM for decdicated processes. To enable it, MCFM has to be installed and compiled into a single library, libMCFM.a, and your Sherpa compilation has to be configured with the following options:

  ./configure --enable-mcfm=/path/to/mcfm

To use the interface, specify

  Loop_Generator MCFM;

in the process section of the run card and add it to the list of generators in ME_SIGNAL_GENERATOR. For an example, see LHC_HWW_POWHEG. Of course, MCFM’s process.DAT file has to be copied to the current run directory.

8.6 Debugging a crashing/stalled event

8.6.1 Crashing events

If an event crashes, Sherpa tries to obtain all the information needed to reproduce that event and writes it out into a directory named

  Status__<date>_<time>

If you are a Sherpa user and want to report this crash to the Sherpa team, please attach a tarball of this directory to your email. This allows us to reproduce your crashed event and debug it.

To debug it yourself, you can follow these steps (Only do this if you are a Sherpa developer, or want to debug a problem in an addon library created by yourself):

• Copy the random seed out of the status directory into your run path:

    cp  Status__<date>_<time>/random.dat  ./
  

• Run your normal Sherpa commandline with an additional parameter:

    Sherpa [...] STATUS_PATH=./
  

  Sherpa will then read in your random seed from “./random.dat” and generate events from it.

• Ideally, the first event will lead to the crash you saw earlier, and you can now turn on debugging output to find out more about the details of that event and test code changes to fix it:

    Sherpa [...] OUTPUT=15 STATUS_PATH=./
  

8.6.2 Stalled events

If event generation seems to stall, you first have to find out the number of the current event. For that you would terminate the stalled Sherpa process (using Ctrl-c) and check in its final output for the number of generated events. Now you can request Sherpa to write out the random seed for the event before the stalled one:

  Sherpa [...] EVENTS=[#events - 1] SAVE_STATUS=Status/

(Replace [#events - 1] using the number you figured out earlier)

The created status directory can either be sent to the Sherpa developers, or be used in the same steps as above to reproduce that event and debug it.

8.7 Versioned installation

If you want to install different Sherpa versions into the same prefix (e.g. /usr/local), you have to enable versioning of the installed directories by using the configure option ‘--enable-versioning’. Optionally you can even pass an argument to this parameter of what you want the version tag to look like.

8.8 NLO calculations

8.8.1 Choosing DIPOLE_ALPHA

A variation of the parameter DIPOLE_ALPHA (see Dipole subtraction) changes the contribution from the real (subtracted) piece (RS) and the integrated subtraction terms (I), keeping their sum constant. Varying this parameter provides a nice check of the consistency of the subtraction procedure and it allows to optimize the integration performance of the real correction. This piece has the most complicated momentum phase space and is often the most time consuming part of the NLO calculation. The optimal choice depends on the specific setup and can be determined best by trial.

Hints to find a good value:

• The smaller DIPOLE_ALPHA is the less dipole term have to be calculated, thus the less time the evaluation/phase space point takes.
• Too small choices lead to large cancelations between the RS and the I parts and thus to large statisical errors.
• For very simple processes (with only a total of two partons in the iniatial and the final state of the born process) the best choice is typically DIPOLE_ALPHA=1. The more complicated a process is the smaller DIPOLE_ALPHA should be (e.g. with 5 partons the best choice is typically around 0.01).
• A good choice is typically such that the cross section from the RS piece is significantly positive but not much larger than the born cross section.

8.8.2 Integrating complicated Loop-ME

For complicated processes the evaluation of one-loop matrix elements can be very time consuming. The generation time of a fully optimized integration grid can become prohibitively long. Rather than using a poorly optimized grid in this case it is more advisable to use a grid optimized with the born matrix elements, since the distibution in the phase space is rather similar.

This can be done as follows:

1. Run the born piece with a specified (and existing) RESULT_DIRECTORY and adding the parameter RESULT_OMIT_NLO_SUFFIX=1.
2. Run the loop piece using the same RESULT_DIRECTORY and also with RESULT_OMIT_NLO_SUFFIX=1.
3. Note: while running the total cross section of the born piece is displayed. This is not an error, the weighted event generation will produce the correct (one-loop) cross section.

Note: this will not work for the RS piece!

8.8.3 Structure of HepMC Output

The generated events can be written out in the HepMC format to be passed through an independent analysis. For this purpose a shortened event structure is used containing only a single vertex. Correlated real and subtraction events are labeled with the same event number such that their possible cancelations can be taken into account properly.

To use this output option Sherpa has to be compiled with HepMC support. cf. Installation. The HEPMC2_SHORT_OUTPUT=<filename> has to used, cf. Event output formats.

Using this HepMC output format the internal Rivet interface (Rivet analyses) can be used to pass the events through Rivet. It has to be stressed, however, that Rivet currently cannot take the correlations between real and subtraction events into account properly. The Monte-Carlo error is thus overestimated. Nonetheless, the mean is unaffected.

As above, the Rivet interface has to be instructed to use the shortened HepMC event structure:

  (analysis){
    BEGIN_RIVET {
      USE_HEPMC_SHORT 1
      -a ...
    } END_RIVET
  }(analysis)

8.8.4 Structure of ROOT NTuple Output

The generated events can be stored in a ROOT NTuple file, see Event output formats. The internal ROOT Tree has the following Branches:

‘id’

Event ID to identify correlated real sub-events.

‘nparticle’

Number of outgoing partons.

‘E/px/py/pz’

Momentum components of the partons.

‘kf’

Parton PDG code.

‘weight’

Event weight, if sub-event is treated independently.

‘weight2’

Event weight, if correlated sub-events are treated as single event.

‘me_wgt’

ME weight (w/o PDF), corresponds to ’weight’.

‘me_wgt2’

ME weight (w/o PDF), corresponds to ’weight2’.

‘id1’

PDG code of incoming parton 1.

‘id2’

PDG code of incoming parton 2.

‘fac_scale’

Factorisation scale.

‘ren_scale’

Renormalisation scale.

‘x1’

Bjorken-x of incoming parton 1.

‘x2’

Bjorken-x of incoming parton 2.

‘x1p’

x’ for I-piece of incoming parton 1.

‘x2p’

x’ for I-piece of incoming parton 2.

‘nuwgt’

Number of additional ME weights for loops and integrated subtraction terms.

‘usr_wgt[nuwgt]’

Additional ME weights for loops and integrated subtraction terms.

8.8.4.1 Computing (differential) cross sections of real correction events with statistical errors

Real correction events and their counter-events from subtraction terms are highly correlated with exhibit large cancellations. Although a treatment of sub-events as independent events leads to the correct cross section the statistical error would be greatly overestimated. In order to get a realistic statistical error sub-events belonging to the same event must be combined before added to the total cross section or a histogram bin of a differential cross section. Since in general each sub-event comes with it’s own set of four momenta the following treatment becomes necessary:

1. An event here refers to a full real correction event that may contain several sub-events. All entries with the same id belong to the same event. Step 2 has to be repeated for each event.
2. Each sub-event must be checked separately whether it passes possible phase space cuts. Then for each observable add up weight2 of all sub-events that go into the same histogram bin. These sums x_id are the quantities to enter the actual histogram.
3. To compute statistical errors each bin must store the sum over all x_id and the sum over all x_id^2. The cross section in the bin is given by <x> = 1/N \sum x_id, where N is the number of events (not sub-events). The 1-\sigma statistical error for the bin is \sqrt{ (<x^2>-<x>^2)/(N-1) }

Note: The main difference between weight and weight2 is that they refer to a different counting of events. While weight corresponds to each event entry (sub-event) counted separately, weight2 counts events as defined in step 1 of the above procedure. For NLO pieces other than the real correction weight and weight2 are identical.

8.8.4.2 Computation of cross sections with new PDF’s

Born and real pieces:

Notation:

f_a(x_a) = PDF 1 applied on parton a,

F_b(x_b) = PDF 2 applied on parton b.

The total cross section weight is given by

weight = me_wgt f_a(x_a)F_b(x_b).

Loop piece and integrated subtraction terms:

The weights here have an explicit dependence on the renormalization and factorization scales.

To take care of the renormalization scale dependence (other than via alpha_S) the weight w_0 is defined as

w_0 = me_wgt + usr_wgts[0] log((\mu_R^new)^2/(\mu_R^old)^2) + usr_wgts[1] 1/2 [log((\mu_R^new)^2/(\mu_R^old)^2)]^2.

To address the factorization scale dependence the weights w_1,...,w_8 are given by

w_i = usr_wgts[i+1] + usr_wgts[i+9] log((\mu_F^new)^2/(\mu_F^old)^2).

The full cross section weight can be calculated as

weight = w_0 f_a(x_a)F_b(x_b) + (f_a^1 w_1 + f_a^2 w_2 + f_a^3 w_3 + f_a^4 w_4) F_b(x_b) + (F_b^1 w_5 + F_b^2 w_6 + F_b^3 w_7 + F_b^4 w_8) f_a(x_a)

where

f_a^1 = f_a(x_a) (a=quark), \sum_q f_q(x_a) (a=gluon),

f_a^2 = f_a(x_a/x'_a)/x'_a (a=quark), \sum_q f_q(x_a/x'_a)x'_a (a=gluon),

f_a^3 = f_g(x_a),

f_a^4 = f_g(x_a/x'_a)/x'_a.

9. Customization

Customizing Sherpa according to your needs.

Sherpa can be easily extended with certain user defined tools. To this extent, a corresponding class must be written, equipped with a corresponding getter function and compiled into an external library which can be linked to Sherpa at runtime. Several specific examples are listed in the following sections.

9.1 External RNG

To use an external Random Number Generator (RNG) in Sherpa, you need to provide an interface to your RNG in an external dynamic library. This library is then loaded at runtime and Sherpa replaces the internal RNG with the one provided.

In this case Sherpa will not attempt to set, save, read or restore the RNG

The corresponding code for the RNG interface is

#include "ATOOLS/Math/Random.H"

using namespace ATOOLS;

class Example_RNG: public External_RNG {
public:
  double Get() 
  { 
    // your code goes here ... 
  }
};// end of class Example_RNG

// this makes Example_RNG loadable in Sherpa
DECLARE_GETTER(Example_RNG_Getter,"Example_RNG",External_RNG,RNG_Key);
External_RNG *Example_RNG_Getter::operator()(const RNG_Key &arg) const
{ return new Example_RNG(); }
// this eventually prints a help message
void Example_RNG_Getter::PrintInfo(std::ostream &str,const size_t width) const
{ str<<"example RNG interface"; }

If the code is compiled into a library called libExampleRNG.so, then this library is loaded dynamically in Sherpa using the command ‘SHERPA_LDADD=ExampleRNG’ either on the command line or in ‘Run.dat’. If the library is bound at compile time, like e.g. in cmt, you may skip this step.

Finally Sherpa is instructed to retrieve the external RNG by specifying ‘EXTERNAL_RNG=Example_RNG’ on the command line or in ‘Run.dat’.

9.2 External PDF

To use an external PDF (not included in LHAPDF) in Sherpa, you need to provide an interface to your PDF in an external dynamic library. This library is then loaded at runtime and it is possible within Sherpa to access all PDFs included.

The simplest C++ code to implement your interface looks as follows

#include "PDF/Main/PDF_Base.H"

using namespace PDF;

class Example_PDF: public PDF_Base {
public:
  void Calculate(double x,double Q2)
  {
    // calculate values x f_a(x,Q2) for all a
  }
  double GetXPDF(const ATOOLS::Flavour a)
  {
    // return x f_a(x,Q2)
  }
  virtual PDF_Base *GetCopy()
  {
    return new Example_PDF();
  }
};// end of class Example_PDF

// this makes Example_PDF loadable in Sherpa
DECLARE_PDF_GETTER(Example_PDF_Getter);
PDF_Base *Example_PDF_Getter::operator()(const Parameter_Type &args) const
{ return new Example_PDF(); }
// this eventually prints a help message
void Example_PDF_Getter::PrintInfo
(std::ostream &str,const size_t width) const
{ str<<"example PDF"; }
// this lets Sherpa initialize and unload the library
Example_PDF_Getter *p_get=NULL;
extern "C" void InitPDFLib()
{ p_get = new Example_PDF_Getter("ExamplePDF"); }
extern "C" void ExitPDFLib() { delete p_get; }

If the code is compiled into a library called libExamplePDFSherpa.so, then this library is loaded dynamically in Sherpa using ‘PDF_LIBRARY=ExamplePDFSherpa’ either on the command line, in ‘Run.dat’ or in ‘ISR.dat’. If the library is bound at compile time, like e.g. in cmt, you may skip this step. It is now possible to list all accessible PDF sets by specifying ‘SHOW_PDF_SETS=1’ on the command line.

Finally Sherpa is instructed to retrieve the external PDF by specifying ‘PDF_SET=ExamplePDF’ on the command line, in ‘Run.dat’ or in ‘ISR.dat’.

9.3 Exotic physics

It is possible to add your own models to Sherpa in a straightforward way. To illustrate, a simple example has been included in the directory ./AddOns/ExampleModel, showing how to add a Z-prime boson to the Standard Model.

The important features of this example include:

• The SM_Zprime.C file.

  This file contains the initialisation of the Z-prime boson. The properties of the Z-prime are set here, such as mass, width, electromagnetic charge, spin etc.

• The Interaction_Model_SM_Zprime.C file.

  This file contains the definition of the Z-prime boson’s interactions. The right- and left-handed couplings to each of the fermions are set here.

• An example Makefile.

  This shows how to compile the sources above into a shared library.

• The line SHERPA_LDADD = SMZprime in the (run) section of the run-card.

  This line tells Sherpa to load the extra libraries created from the *.C files above.

• The line MODEL = SM+Zprime in the (model) section of the run-card.

  This line tells Sherpa which model to use for the run.

• The lines MASS[32] = 1000. and WIDTH[32] = 50. in the (model) section of the run-card.

  These lines show how you can overrule the choices you made for the properties of the new particle in the SM_Zprime.C file. For more information on changing parameters in Sherpa, see Input structure and Parameters.

To use this model, create the libraries for Sherpa to use by running

make

in this directory. Then run Sherpa as normal:

../../bin/Sherpa

To implement your own model, copy these example files anywhere and modify them according to your needs.

Note: You don’t have to modify or recompile any part of Sherpa to use your model. As long as the SHERPA_LDADD parameter is specified as above, Sherpa will pick up your model automatically.

Furthermore note: New physics models with an existing implementation in FeynRules, cf. [Chr08] and [Chr09] , can directly be invoked using Sherpa’s interface to FeynRules, see FeynRules model.

9.4 External one-loop ME

Sherpa includes only a very limited selection of one-loop matrix elements. To make full use of the implemented automated dipole subtraction it is possible to link external one-loop codes to Sherpa in order to perform full calculations at QCD next-to-leading order.

In general Sherpa can take care of any piece of the calculation except one-loop matrix elements, i.e. the born ME, the real correction, the real and integrated subtraction terms as well as the phase space integration and PDF weights for hadron collisions. Sherpa will provide sets of four-momenta and request for a specific parton level process the helicity and colour summed one-loop matrix element (more specific: the coefficients of the Laurent series in the dimensional regularization parameter epsilon up to the order epsilon^0).

An example setup for interfacing such an external one-loop code, following the Binoth Les Houches interface proposal [Bin10a] of the 2009 Les Houches workshop, is provided in LHC_WJet_LHOLE. To use the LH-OLE interface, Sherpa has to be configured with --enable-lhole.

The interface:

• During an initialization run Sherpa stores setup information (schemes, model information etc.) and requests a list of parton-level one-loop processes that are needed for the NLO calculation. This information is stored in a file, by default called OLE_order.lh. The external one-loop code (OLE) should confirm these settings/requests and write out a file OLE_contract.lh. For the syntax and details see [Bin10a] .

  For Sherpa the output/input of the order/contract file is handled in LH_OLE_Communicator.[CH]. The actual interface is contained in LH_OLE_Interface.C. The parameters to be exchanged with the OLE are defined in the latter file via

    lhfile.AddParameter(...);
  

  and might require an update for specific OLE or processes.

• At runtime the communication is performed via function calls. To allow Sherpa to call the external code the functions

    void OLP_Start(const char * filename);
    void OLP_EvalSubProcess(int,double*,double,double,double*);
  

  which are defined and called in LH_OLE_Interface.C must be specified. For keywords and possible data fields passed with this functions see [Bin10a] .

  The function OLP_Start(...) is called once when Sherpa is starting. The function OLP_EvalSubProcess(...) will be called many times for different subprocesses and momentum configurations.

The setup:

• The setup example includes three different files for the born Run_B.dat, the virtual Run_I.dat and the real correction piece Run_R.dat. While for a full NLO calculation all three must be employed (and their results combined) only the virtual piece requires the interface.
• The line Loop_Generator LHOLE tells the code to use the interface for computing one-loop matrix elements.
• The switch SHERPA_LDADD present in Run_I.dat has to be set to the appropriate library name (and path) of the one-loop generator, see LHC_WJet_LHOLE.
• Sherpa’s internal analysis package can be used to generate a few histograms. Thus, then when installing Sherpa the option --enable-analysis must be include on the command line when Sherpa is configured, see ANALYSIS.

9.5 My own interface

It is possible to pass Sherpa output to an external Fortran or C++ framework on-the-flight. To illustrate this option, a simple, yet functional example is included in the directory ./AddOns/HEPEVTInterface, showing how to fill the HEPEVT common from Sherpa output. It also exemplifies how to retrieve the weight of weighted events and how to access information about the total cross section of the event sample at the end of the run.

Note that only the event converter is included in the sources, you will still need to implement the calling function and an initialize and finalize method, see below. However, these are rather simple.

The important features of this example include:

• Your part of the interface (The rest is handled in HEPEVT_Interface.C)

  #include "SHERPA/Main/Sherpa.H"
  
  class My_Sherpa {
  private:
    SHERPA::Sherpa m_sherpa;
  public:
    void init(int argc,char *argv[])
    {
      // initialize the generator
      m_sherpa.InitializeTheRun(argc,argv);
      // set it up for event generation
      m_sherpa.InitializeTheEventHandler();
    }
    bool one_event()
    {
      // generate event and return status
      if (!m_sherpa.GenerateOneEvent()) return false;
      // now the HEPEVT common is filled and you can use it
      return true;
    }
    void finish()
    {
      // clean up and store total cross section
      m_sherpa.SummarizeRun();
    }
  };// end of class My_Sherpa
  

• The source file HEPEVT_Interface.C.

  This file defines a pseudo-analysis, which implements the conversion to HEPEVT.

• An example Makefile.

  This shows how to compile the source into a shared library called libSherpaHEPEVT.so. The library can either be copied into the directory <prefix>/lib/SHERPA-MC, or it can be placed in the run path.

• The line SHERPA_LDADD = SherpaHEPEVT in the (run) section of the run-card.

  This line tells Sherpa to load the extra library created from the *.C file above.

• The line ANALYSIS = HEPEVT in the (run) section of the run-card.

  This line tells Sherpa to run the pseudo-analysis implementing your HEPEVT interface.

To use this interface, create the additional library for Sherpa by running

make SHERPA_PREFIX=/path/to/sherpa

in the directory AddOns/HEPEVTInterface. After copying the library, run Sherpa from your interface.

Note: You don’t have to modify or recompile any part of Sherpa to use this interface. As long as the SHERPA_LDADD parameter is specified as above, Sherpa will pick up the HEPEVT converter automatically.

10. Examples

Some example set-ups are included in Sherpa, in the <prefix>/share/SHERPA-MC/Examples/ directory. These may be useful to new users to practice with, or as templates for creating your own Sherpa run-cards. In this section, we will look at some of the main features of these examples.

10.1 LHC_ZJets

This example is for an LHC set-up, with a proton–proton collision at centre of mass energy 14TeV. The final state is an electron–positron pair and up to 4 partons from the matrix element.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 7000;
  BEAM_2 = 2212; BEAM_ENERGY_2 = 7000;
}(beam)

(processes){
  Process 93 93 -> 11 -11 93{4}
  Order_EW 2;
  CKKW sqr(30/E_CMS)
  Integration_Error 0.02 {6};
  End process;
}(processes)

(selector){
  Mass 11 -11 66 116
}(selector)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• the number of events generated is set in the (run) section. If this parameter is not set, 100 events will be generated.
• the beam particles are specified in the (beam) section, using PDG codes, see PDG codes. The beam energy must also be specified in GeV.
• the process is specified in the (processes) section, using PDG codes again. ‘93’ is a particle container for light quarks and gluons, see Particle containers. The ‘4’ in curly brackets after the final state ‘93’ means that the matrix element will be generated with up to 4 extra partons in the final state, see Curly brackets.
• the multi-jet merging parameter CKKW is set using an algebraic expression. For more information on algrebraic expressions recognised by Sherpa, see Interpreter. For more information on the CKKW parameter and the Sherpa method for merging matrix elements and parton showers, see ME-PS merging.
• the Integration_Error is set separately for some of the final state multiplicities. The higher multiplicity cross sections are smaller, so to get the same order of magnitude for the absolute error in the cross section integrations, the relative error can be higher.
• there is a selector cut on the invariant mass of the lepton pair. This cut shields the IR singularity as the invariant mass tends to zero, and focuses on the area around the Z-peak, from 66Gev to 116GeV.
• the matrix element signal generators have been chosen to be the Internal hard coded ones in module EXTRA_XS, and Comix.
• multiple interactions have been switched off.

10.2 Tevatron_ZJets

This set-up is very similar to the one above, for LHC_ZJets, but with proton–anti-proton collisions at Tevatron energies.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 =  2212; BEAM_ENERGY_1 = 980;
  BEAM_2 = -2212; BEAM_ENERGY_2 = 980;
}(beam)

(processes){
  Process 93 93 -> 11 -11 93{4}
  Order_EW 2;
  CKKW sqr(30/E_CMS)
  Integration_Error 0.02 {6};
  End process;
}(processes)

(selector){
  Mass 11 -11 66 116
}(selector)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• the PDG code for an anti-proton ‘-2212’ is minus the PDG code for a proton ‘2212’.

10.3 Tevatron_WJets

The Tevatron W+jets set-up is very similar to the Z+jets example. The only differences are in the final state leptons, and the invariant mass cuts on the lepton pairs.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 =  2212; BEAM_ENERGY_1 = 980;
  BEAM_2 = -2212; BEAM_ENERGY_2 = 980;
}(beam)

(processes){
  Process 93 93 -> 11 -12 93{2}
  Order_EW 2
  CKKW sqr(30/E_CMS)
  End process;

  Process 93 93 -> -11 12 93{2}
  Order_EW 2
  CKKW sqr(30/E_CMS)
  End process;
}(processes)

(selector){
  Mass -11 12 1.7 E_CMS
  Mass 11 -12 1.7 E_CMS
}(selector)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• the invariant mass cut is necessary to avoid evaluating the PDF outside its valid range of the factorisation scale Q^2 (which in this process is typically given by the boson mass).

10.4 Tevatron_QCD

This example generates QCD events at the Tevatron, with 2, 3 or 4 final state partons in the matrix element.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 =  2212; BEAM_ENERGY_1 = 980;
  BEAM_2 = -2212; BEAM_ENERGY_2 = 980;
}(beam)

(processes){
  Process 93 93 -> 93 93 93{2};
  Order_EW 0; Max_N_Quarks 4;
  CKKW sqr(20/E_CMS);
  Selector_File *|(coresel){|}(coresel) {2};
  Integration_Error 0.02 {4};
  End process;
}(processes)

(coresel){
  NJetFinder  2  10.0  0.0  1.0
}(coresel)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• Order_EW is set to ‘0’. This ensures that all final state jets are produced via the strong interaction.
• an NJetFinder selector is used to set a resolution criterion for the two jets of the core process. This is necessary because the ‘CKKW’ tag does not apply any cuts to the core process, but only to the extra-jet matrix elements, see ME-PS merging. This cut is applied only to the 2->2 process using the {2} specification, since the higher-order matrix elements should only be cut by the ME+PS separation criterion.

10.5 Tevatron_Photons

We have studied prompt photon production in [Hoe09a] and this section serves as a practical guide to the features necessary for these studies. Its main emphasis lies on how to generate samples which include both the direct and fragmentation component and how to apply ME+PS merging.

Traditionally, the direct and fragmentation component are well separated in a parton-shower Monte-Carlo, e.g. for single photon production: The direct component is produced by using the 2->2 matrix element with a photon and a parton in the final state, and the fragmentation component can be generated by using the 2->2 matrix element with two partons in the final state. On top of the LO matrix elements the parton shower would then produce interleaved QCD+QED emissions, where the QED shower emissions from the dijet sample will create the fragmentation component.

Note, that the generation of the fragmentation component in this way is very inefficient, because the shower will only very rarely produce hard isolated photons. To be able to compare to this method at all in [Hoe09a] , we have implemented an enhancement of the QED splitting functions in the parton shower which is of course corrected for by giving the events appropriate weights, cf. the appendix of that paper.

But the main feature of [Hoe09a] is the consistent treatment of photons in the context of ME+PS merging. This effectively means that one can split the fragmentation component into two parts by phase space slicing. Hard isolated photons are produced from the exact higher-order tree-level matrix element (e.g. pp -> photon + 2, 3, ... partons) while collinear photons are produced by the parton-shower, taking into account the correct resummation of the quark-photon singularities.

This is not only advisable to become less dependent on uncertain parton-shower approximations in the non-collinear region, but will also help to generate the fragmentation component more efficiently: If the phase space slicing criterion in the ME+PS merging is sufficiently similar (or loose) compared to the photon isolation criterion used in the analysis, one can expect that the second, painful, part of the fragmentation component, i.e. the one from the parton shower, becomes irrelevant for the analysis.

So in the following we describe how to generate single photons and diphotons making use of the default photon slicing criterion which looks like:

$\min(p_\perp^2(\gamma), p_\perp^2(parton)) (\DeltaR(\gamma, parton)/D)^2 > Q^2_cut$

where D=0.3 by default and Q_cut is the merging parameter specified in the CKKW line of the processes section. It might be sufficient to adapt these two parameters, e.g. in the following run cards set

  CKKW sqr(10.0/E_CMS)|0.2

for Q_cut=10.0 and D=0.2. If you notice that your photon isolation criterion is not sufficiently similar (the shower sample does contribute to your analysis or your ME sample still produces many photons which aren’t isolated according to your criterion) one could still manually adapt the slicing criterion in Sherpa. Please contact us for assistance in that case.

In the following sections we show and discuss run cards for single- and diphoton production. They have been separated into a matrix-element part (i.e. direct and fragmentation-from-ME component) and a parton-shower part (i.e. fragmentation from the shower) as described above. In all analyses which we have compared to so far we found the contribution of the second part negligible. Please note, that these run cards will generate weighted events with ME enhancements in phase space regions which would otherwise not be filled very efficiently.

10.5.1 Single photon production

10.5.1.1 Photons from ME

(run){
  EVENTS = 1000000
}(run)

(processes){
  Process 93 93 -> 22 93 93{2}
  Order_EW 1
  CKKW sqr(10.0/E_CMS)
  Selector_File *|(coresel){|}(coresel) {2};
  Enhance_Function VAR{PPerp2(p[2])} {2}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]))} {3}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]))} {4}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]),PPerp2(p[6]))} {5}
  Integration_Error 0.05 {4}
  End process
}(processes)

(coresel){
  NJetFinder  2  10.0  0.0  1.0
}(coresel)

(shower){
  CSS_EW_MODE = 1
}(shower)  

(me){
  EVENT_GENERATION_MODE = Weighted
  ME_QED = Off
}(me)

(fragmentation){
  FRAGMENTATION = Off
  DECAYMODEL = Off
}(fragmentation)

(mi){
  MI_HANDLER = None
}(mi)

(beam){
  BEAM_1 = 2212
  BEAM_ENERGY_1 = 980.0
  BEAM_2 = -2212
  BEAM_ENERGY_2 = 980.0
}(beam)

• In the processes section, matrix elements for pp(bar) -> photon + 1, 2, 3 partons are requested. Only Feynman diagrams with exactly one electroweak coupling are allowed.

  The merging criterion is set to Q_cut=10.0 GeV.

  Enhance_Function’s (cf. Enhance_Function) are introduced to produce more hard partons/photons than the steeply falling cross section would imply (appropriately weighted).

• The higher-order matrix elements will be regularised by the ME+PS automatically, but here the Born process also has a divergence which has to be regularised. By applying a Selector_File setting specifically for the 2->2 process, we demand two jets/photons with pT > 10.0 GeV, cf. Jet finders.
• Electro-weak splitting functions in the shower are activated in the shower section.
• The me section enables weighted event generation and switches off the emission of additional soft photons from the hard scattering.
• To generate only prompt photons, the hadronisation, hadron decays and underlying event are turned off. These steps of the simulation can be enabled as described in Hadronization parameters and MI_HANDLER.
• The beam section specifies Tevatron Run 2 conditions in this example but can simply be changed.

10.5.1.2 Photons from Shower

(which will ideally be irrelevant for the analysis)

(run){
  EVENTS = 1000000
}(run)

(processes){
  Process 93 93 -> 93 93 93{2}
  Order_EW 0
  CKKW sqr(10.0/E_CMS)
  Selector_File *|(coresel){|}(coresel) {2};
  Enhance_Function VAR{PPerp2(p[2])} {2}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]))} {3}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]))} {4}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]),PPerp2(p[6]))} {5}
  Integration_Error 0.05 {4}
  End process
}(processes)

(coresel){
  NJetFinder  2  10.0  0.0  1.0
}(coresel)

(shower){
  CSS_EW_MODE = 1
}(shower)  

(me){
  EVENT_GENERATION_MODE = Weighted
  ME_QED = Off
}(me)

(fragmentation){
  FRAGMENTATION = Off
  DECAYMODEL = Off
}(fragmentation)

(mi){
  MI_HANDLER = None
}(mi)

(beam){
  BEAM_1 = 2212
  BEAM_ENERGY_1 = 980.0
  BEAM_2 = -2212
  BEAM_ENERGY_2 = 980.0
}(beam)

Here only the differences with respect to above are explained:

• In the processes section, matrix elements for pp(bar) -> dijet + 0, 1, 2 partons are requested. Only Feynman diagrams without electroweak couplings are allowed (for efficiency reasons).

10.5.2 Diphoton production

10.5.2.1 Photons from ME

(run){
  EVENTS = 1000000
}(run)

(processes){
  Process 21 21 -> 22 22
  Scales VAR{Abs2(p[2]+p[3])}
  Loop_Generator gg_yy
  End process;

  Process 93 93 -> 22 22 93{2}
  Order_EW 2
  CKKW sqr(10.0/E_CMS)
  Selector_File *|(coresel){|}(coresel) {2};
  Enhance_Function VAR{PPerp2(p[2])} {2}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]))} {3}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]))} {4}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]),PPerp2(p[6]))} {5}
  Integration_Error 0.05 {4}
  End process
}(processes)

(coresel){
  NJetFinder  2  10.0  0.0  1.0
}(coresel)

(shower){
  CSS_EW_MODE = 1
}(shower)  

(me){
  EVENT_GENERATION_MODE = Weighted
  ME_QED = Off
}(me)

(fragmentation){
  FRAGMENTATION = Off
  DECAYMODEL = Off
}(fragmentation)

(mi){
  MI_HANDLER = None
}(mi)

(beam){
  BEAM_1 = 2212
  BEAM_ENERGY_1 = 980.0
  BEAM_2 = -2212
  BEAM_ENERGY_2 = 980.0
}(beam)

Here only the differences with respect to the single photon example are explained:

• In the processes section, tree-level matrix elements for pp(bar) -> photon photon + 0, 1, 2 partons are requested. Only Feynman diagrams with exactly two electroweak couplings are allowed (for efficiency reasons).

  In addition, the loop-induced matrix element for the process gg -> photon photon is enabled.

10.5.2.2 Photons from Shower

(which will ideally be irrelevant for the analysis)

The shower can produce di-photon events either from single-photon events or from di-jet events by producing one or two photons respectively. Here these two contributions are generated in one run, but of course they could be separated as well.

(run){
  EVENTS = 1000000
}(run)

(processes){
  Process 93 93 -> 22 93 93{2}
  Order_EW 1
  CKKW sqr(10.0/E_CMS)
  Selector_File *|(coresel){|}(coresel) {2};
  Enhance_Function VAR{PPerp2(p[2])} {2}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]))} {3}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]))} {4}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]),PPerp2(p[6]))} {5}
  Integration_Error 0.05 {4}
  End process

  Process 93 93 -> 93 93 93{2}
  Order_EW 0
  CKKW sqr(10.0/E_CMS)
  Selector_File *|(coresel){|}(coresel) {2};
  Enhance_Function VAR{PPerp2(p[2])} {2}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]))} {3}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]))} {4}
  Enhance_Function VAR{max(PPerp2(p[2]),PPerp2(p[3]),PPerp2(p[4]),PPerp2(p[5]),PPerp2(p[6]))} {5}
  Integration_Error 0.05 {4}
  End process
}(processes)

(coresel){
  NJetFinder  2  10.0  0.0  1.0
}(coresel)

(shower){
  CSS_EW_MODE = 1
}(shower)  

(me){
  EVENT_GENERATION_MODE = Weighted
  ME_QED = Off
}(me)

(fragmentation){
  FRAGMENTATION = Off
  DECAYMODEL = Off
}(fragmentation)

(mi){
  MI_HANDLER = None
}(mi)

(beam){
  BEAM_1 = 2212
  BEAM_ENERGY_1 = 980.0
  BEAM_2 = -2212
  BEAM_ENERGY_2 = 980.0
}(beam)

Here only the differences with respect to above are explained:

• In the processes section, matrix elements for pp(bar) -> dijet + 0, 1, 2 partons and pp(bar) -> photon + 1, 2, 3 partons are requested. Only Feynman diagrams with 0 or 1 electroweak couplings respectively are allowed (for efficiency reasons).

10.6 LEP91

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 =  11; BEAM_ENERGY_1 = 45.6;
  BEAM_2 = -11; BEAM_ENERGY_2 = 45.6;
}(beam)

(isr){
  PDF_SET PDFe;
}(isr)

(processes){
  Process 11 -11 -> 93 93 93{1};
  CKKW pow(10,-2.25);
  Order_EW 2;
  End process;

  Process 11 -11 -> 5 -5 93{1};
  CKKW pow(10,-2.25);
  Order_EW 2;
  End process;
}(processes)

(model){
  MASSIVE[5] = 1
}(model)

This example shows a LEP set up, with electrons and positrons colliding at a centre of mass energy of 91.25GeV. Two processes have been specified, one final state with two or three light quarks and gluons being produced, and one with a b b-bar pair and possibly an extra light parton.

Things to notice:

• the b-quark mass has been enabled for the matrix element calculation (the default is massless) because it is not negligible for LEP energies
• the b b-bar process is specified separately because the ‘93’ particle container contains only partons set massless in the matrix element calculation, see Particle containers.
• some model parameters have been set. In the (model) section of the run-card, parameters relating to the model can be set. In this example, the running of alpha_s is set to leading order and the value of alpha_s at the Z-mass is set.

10.7 HERA_DIS

This is an example of a setup for hadronic final states in deep-inelastic lepton-nucleon scattering at a centre-of-mass energy of 300 GeV. Corresponding measurements were carried out by the H1 and ZEUS collaborations at the HERA collider at DESY Hamburg.

(run){
  OUTPUT 2; EVENTS 10000000;
  NJET:=4; QCUT:=5; SDIS:=0.6;
  CDXS_ITMAX 5000; CSS_AS_FAC 2.5;
  COUPLING_SCHEME Running;
}(run);

(beam){
  BEAM_1  -11; BEAM_ENERGY_1 27.6;
  BEAM_2 2212; BEAM_ENERGY_2  820; 
}(beam);

(processes){
  Process -11 93 -> -11 93 93{NJET};
  Order_EW 2; Max_N_Quarks 6;
  CKKW sqr(QCUT/E_CMS)/(1.0+sqr(QCUT/SDIS)/Abs2(p[2]-p[0]));
  Scales METS{MU_F2}{MU_R2}{Abs2(p[2]-p[0])};
  Couplings Alpha_QCD 1, Alpha_QED 2;
  Integration_Error 0.02 {6};
  Max_Epsilon 1e-1 {5,6};
  End process;
}(processes);

(selector){
  Q2 -11 -11 4 1e12
  PT -11 1 E_CMS
}(selector)

Things to notice:

• the beams are asymmetric with the positrons at an energy of 27.6 GeV, while the protons carry 820 GeV of energy.
• the multi-jet merging cut is set dynamically for each event, depending on the photon virtuality, see [Car09] .
• there is a selector cut on the photon virtuality. This cut implements the experimental requirements for idenitfying the deep-inelastic scattering process.

10.8 LHC_SingleTop

This set-up illustrates the possibility of removing a resonant contribution from the signal process.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 7000;
  BEAM_2 = 2212; BEAM_ENERGY_2 = 7000;
}(beam)

(processes){
  Process 93 93 -> 6[a] 93 93{2};
    Decay 6[a] -> 5 24[c];
      Decay 24[c] -> 90 91;
  Order_EW 4; CKKW sqr(20/E_CMS);
  End process;
  Process 93 93 -> 6[a] -24[b] 93{1};
    Decay 6[a] -> 24[c] 5;
      Decay 24[c] -> 90 91;
    Decay -24[b] -> 94 94;
    No_Decay -6;
  Order_EW 4; CKKW sqr(20/E_CMS);
  End process;
}(processes);

(selector){
  DecayMass 6 150 200;
  DecayMass 24 50 110;
}(selector);

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

The process generated is the production of a single top quark in association with up to three light partons in the final state. The top quark decays into a bottom quark and a W-boson. The resonant production of a top-antitop final state in the Wt-mode is excluded by diagram removal.

Things to notice:

• the tag No_Decay is used to specify the resonances to be avoided, see No_Decay. In this example, the contribution from s-channel antitop quark propagators is excluded.
• the decaying particles have labels. In order to specify a decay, the decaying particle must be given an identifier, eg ‘6[a]’, ‘24[c]’ etc. Each identifier must be unique within any given process, and must be included when specifying the particle’s production, and it’s decay.
• the particle containers for charged leptons (‘90’), neutrinos (‘91’), quarks (‘94’) and massless partons (‘93’) are all used in this example. See Particle containers.

10.9 LHC_TTH

This set-up illustrates the possibility of specifying a particular decay chain for the particles in the signal process.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 7000;
  BEAM_2 = 2212; BEAM_ENERGY_2 = 7000;
}(beam)

(processes){
  Process 93 93 -> 6[a] -6[b] 25[h];
    DecayOS 6[a] -> 5 24[c];
      DecayOS 24[c] -> 90 91;
    DecayOS -6[b] -> -5 -24[d];
      DecayOS -24[d] -> 94 94;
    DecayOS 25[h] -> 5 -5;
  End process;
}(processes)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

The process generated is the production of a Higgs boson in association with a top quark pair from two light partons in the initial state. The Higgs boson decays into a bottom-antibottom pair, while each top quark decays into (anti-)bottom quark and W-boson. The W+ boson in turn decays leptonically, and the W- boson decays to quarks.

Things to notice:

• the tag DecayOS is used to specify the decays. See DecayOS.
• the decaying particles have labels. In order to specify a decay, the decaying particle must be given an identifier, eg ‘6[a]’, ‘24[c]’ etc. Each identifier must be unique within any given process, and must be included when specifying the particle’s production, and it’s decay.
• the particle containers for charged leptons (‘90’), neutrinos (‘91’), quarks (‘94’) and massless partons (‘93’) are all used in this example. See Particle containers.

10.10 Tevatron_TopPair

This set-up is very similar to the LHC_TTH example above. There are three notable differences. Firstly, the colliding beams are changed to proton anti-proton at Tevatron energies. Secondly, there is no Higgs boson produced in the core process, but there are two allowed decay channels of the top quark pair. Third, Matrix-Element Parton-Shower merging is enabled using the CKKW tag.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 2212; BEAM_ENERGY_1 980;
  BEAM_2 -2212; BEAM_ENERGY_2 980;
}(beam)

(processes){
  Process 93 93 -> 6[a] -6[b] 93{1};
    DecayOS 6[a] -> 5 24[c];
      DecayOS 24[c] -> 90 91;
    DecayOS -6[b] -> -5 -24[d];
      DecayOS -24[d] -> 94 94;
  Order_EW 4; CKKW sqr(20/E_CMS);
  End process;

  Process 93 93 -> 6[a] -6[b] 93{1};
    DecayOS 6[a] -> 5 24[c];
      DecayOS 24[c] -> 94 94;
    DecayOS -6[b] -> -5 -24[d];
      DecayOS -24[d] -> 90 91;
  Order_EW 4; CKKW sqr(20/E_CMS);
  End process;
}(processes)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

The process generated is the production of a top pair from two light quarks, with possibly an extra final-state parton. Each top then decays into (anti-)bottom quark and W+(-) boson. One of the W-bosons then decays leptonically, and the other decays to quarks. This time we include processes with either of the two W-bosons decaying leptonically, not just the W-, as in the LHC_TTH example above.

Things to notice:

• there are two separate processes defined. Every different decay route must have it’s own process. It is not possible to group the different W- decays into one top-production process.

10.11 Tevatron_UE

In this example, the underlying event has been switched on. The parameters controlling the simulation of multiple interactions can be set in the (mi) section of the run card. For a full list of the available settings, see MPI Parameters.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 900;
  BEAM_2 = -2212; BEAM_ENERGY_2 = 900;
}(beam)

(processes){
  Process 93 93 -> 93 93
  Order_EW 0
  End process
}(processes)

(selector){
  # To be as inclusive as possible, the pT cut has been lowered to the
  # same value as in the multiple parton interactions.
  # Note that this pT cut has to be adjusted if E_CMS is changed,
  # such that it is never lower then SCALE_MIN*pow((E_CMS/1800),RESCALE_EXPONENT)
  # in the multiple parton interactions.
  NJetFinder  2  2.63  0.0  1.0
}(selector)

(mi){
  MI_HANDLER = Amisic
}(mi)

Things to notice:

• multiple interactions have been turned on, by setting MI_HANDLER to ‘Amisic’.
• the transverse momentum cut-off SCALE_MIN has been set to 2.5GeV.

10.12 Tevatron_DiBoson

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1 =  2212; BEAM_ENERGY_1 = 980;
  BEAM_2 = -2212; BEAM_ENERGY_2 = 980;
}(beam)

(processes){
  Process : 93 93 ->  12 -11 13 -14 93{2}
  Order_EW : 4
  CKKW sqr(30/E_CMS)
  End process
}(processes)

(selector){
  Mass -11 12 10 E_CMS
  Mass 13 -14 10 E_CMS
}(selector)

(model){
  ACTIVE[6] = 0
  ACTIVE[25] = 0
}(model)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

This is a Tevatron set-up with two W bosons produced, and both decaying leptonically. Up to two jets are also included in the matrix element.

Things to notice:

• in the (model) section, the top quark and Higgs have been turned off, using the ACTIVE[PDG] switches.

10.13 EGamma

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1          = 11;
  BEAM_ENERGY_1   = 250.
  BEAM_SPECTRUM_1 = Laser_Backscattering

  BEAM_2          = 11
  BEAM_ENERGY_2   = 250.
  BEAM_SPECTRUM_2 = Monochromatic

  BEAM_SMIN       = 0.3
  BEAM_SMAX       = 1.0

  E_LASER_1          = 1.17e-9      ! Laser energy in GeV
  P_LASER_1          = 0.           ! Laser polarization +-1
  LASER_MODE         = 0            ! 0 = all, 1,2,3 = individual components
  LASER_ANGLES       = Off          ! On/Off
  LASER_NONLINEARITY = On           ! On/Off
}(beam)

(processes){
  Process : 22 11 -> 11 1 -1
  End process
}(processes)

(selector){
  NJetFinder  2  0.  1. .4
  ET         11       1.   10000.
  ET          1       1.   10000.
  ET         -1       1.   10000.
  BeamAngle   1  0   -0.9      0.9
  BeamAngle  -1  0   -0.9      0.9
  BeamAngle  11  0   -0.9      0.9
}(selector)

(isr){
  PDF_SET = None
  BUNCH_1         = 22
  BUNCH_2         = 11
}(isr)

Things to notice:

• the incoming beams are both electrons. Accordingly, in the (beam) section of the data card, the beams are set as electrons by BEAM_{1,2}=11.
• the photon is produced through laser backscattering off one of the incoming electrons. BEAM_SPECTRUM_1=Laser_Backscattering and BEAM_SPECTRUM_2=Monochromatic have been specified.

10.14 PEPII_BaBar

(run){
  EVENTS = 10000;
  ANALYSIS = 0;
}(run)

(beam){
  BEAM_1 = 11
  BEAM_ENERGY_1 = 9.0
  BEAM_2 = -11
  BEAM_ENERGY_2 = 3.109
}(beam)

(processes){
  #
  # electron positron -> Y(4S) -> B+ B-
  #
  Process 11 -11 -> 300553[a];
  Decay 300553[a] -> 521 -521;
  End process;
  #
  # electron positron -> Y(4S) -> B0 B0bar
  #
  Process 11 -11 -> 300553[a];
  Decay 300553[a] -> 511 -511;
  End process;
}(processes)

(isr){
  BUNCH_1         = 11
  BUNCH_2         = -11

  PDF_LIBRARY PDFESherpa
  PDF_SET PDFe;

  ISR_SMIN        = 0.01
  ISR_SMAX        = 1.0

  ISR_E_ORDER     = 1   ! Perturbative order of electron structure function
  ISR_E_SCHEME    = 2   ! Beta-scheme : 0,1,2 , default = 2
}(isr)

(analysis){
  BEGIN_ANALYSIS {
    LEVEL  Hadrons

      Multi -0.5 50.5 51 LinErr FinalState

      MultiEmin  22 0.01 -0.5 20.5 21 LinErr FinalState
      MultiEmin 211 0.   -0.5 10.5 11 LinErr FinalState
      MultiEmin 321 0.   -0.5 10.5 11 LinErr FinalState

  } END_ANALYSIS
}(analysis)

This example shows a set up for the BaBar experiment at the PEPII collider, with electrons and positrons colliding at a centre of mass energy of 10.58 GeV. It also serves as an example for a setup with asymmetric beams. Two processes have been specified, the production of a B+ B- pair and the production of B0 B0bar pair. Hence, both processes will be mixed according to their respective cross sections into an inclusive sample.

Things to notice:

• as PEPII is an asymmetric collider, both beams are set to different energies: the electron beam is set to 9.0 GeV, the positron beam to 3.109 GeV.
• the processes specified are the production of a B+ B- pair and a B0 B0bar pair, both produced via a Y(4S) resonance.
• the PDF has been set to an internal electron PDF for both beams, such that both beams may undergo initial state radiation (ISR). For the ISR scheme definitions for electrons, see ISR Parameters.
• a simple analysis histogramming certain final state multiplicities has been added, using Sherpa’s internal analysis package. To use this Analysis package, when Sherpa is installed, the option --enable-analysis must be include on the command line when Sherpa is configured, see ANALYSIS. Further, it has to be switched on by setting ANALYSIS = Internal. To display the analysis package syntax, run Sherpa with SHOW_ANALYSIS_SYNTAX=1 on the command line.

10.15 LHC_4thGen

This example shows a beyond the Standard Model set-up. In this example, a 4th generation of particles is included, as well as the Standard Model particles. This is one of Sherpa’s built-in BSM options, see Models available in Sherpa. For more information on using your own BSM models with Sherpa, see Exotic physics.

(run){
  EVENTS = 2000;
  ANALYSIS = 0;
}(run)

(beam){
  BEAM_1          = 2212
  BEAM_ENERGY_1   = 7000.

  BEAM_2          = 2212
  BEAM_ENERGY_2   = 7000.
}(beam)

(processes){
  #
  # jet jet -> tau'[-> nutau e- nueb] nutaub'[-> tau+ mu- numub]
  #
  Process 93 93 -> 17[a] -18[b]
    Decay   17[a] ->  16 11 -12
    Decay  -18[b] -> -15 13 -14
  Print_Graphs : Process;
  End process
}(processes)

(selector){
}(selector)

(model){
  MODEL         = SM+4thGen

  ## full description of all parameters with
  ## Sherpa SHOW_MODEL_SYNTAX=1

  ## masses and widths of 4th gen leptons
  MASS[17] = 200;  WIDTH[17] = 3.0;
  MASS[18] = 150;  WIDTH[18] = 2.0;

  ## mixing angle to other generations
  THETA_L14 = 0.; PHI_L2 = 0.;
  THETA_L24 = 0.; PHI_L3 = 0.;
  THETA_L34 = 0.1;

  OUTPUT_MIXING = 1
}(model)

(me){
  SCALES = VAR{Abs2(p[0]+p[1])}
}(me)

(fragmentation){
  FRAGMENTATION=Off;
}(fragmentation)

(analysis){
  BEGIN_ANALYSIS {
    LEVEL  MEs Showers

    PT3    16  11 -12    0. 300.  75  LinErr FinalState
    PT3   -15  13 -14    0. 300.  75  LinErr FinalState
    3Mass  16  11 -12  150. 250.  50  LinErr FinalState
    3Mass -15  13 -14  100. 200.  50  LinErr FinalState

    PT6    11 -12 13 -14 -15 16  0. 2000. 100 LinErr FinalState
    6Mass  11 -12 13 -14 -15 16  0. 2000. 100 LinErr FinalState

  } END_ANALYSIS
}(analysis)

Things to notice:

• the matrix element generator AMEGIC++ is used for this set-up. Running Sherpa with AMEGIC++ is decribed below.
• the model is chosen in the (model) section of the run card, using the parameter MODEL, see Model Parameters. The default is the SM.
• for a full description of all parameters in any chosen model, use the tag SHOW_MODEL_SYNTAX=1 on the command line when running Sherpa.
• the properties of the 4th generation fermions, such as MASS[<id>] and WIDTH[<id>], may be set in the runcard, or on the command line, in exactly the same way as the SM particle properties. In the above example, only the fourth generation lepton masses and widths have been set. The corresponding parameters of the fourth generation quarks were left at their default values since they do not play a role in this process.
• the 3x3 mixing matrices for quarks (CKM matrix) and leptons (unit matrix) are supplemented with three additional mixing angles and two additional phases according to [Hou87a] . Note that in the above example only small mixing of the 4th and the 3rd generation of leptons is allowed. For all relevant switches and their defaults see Fourth Generation. Again, the corresponding parameters for the quark sector were left at their default values since they do not play a role here.
• the switch OUTPUT_MIXING is used to print the 4x4 mixing matrices for leptons and quarks on screen at the beginning of each run, just before the particle content of the model.
• the analysis has been switched off, but to use it, switch ANALYSIS to ‘Internal’.
• the analysis in this example uses Sherpa’s in-built analysis package. To use this Analysis package, when Sherpa is installed, the option --enable-analysis must be include on the command line when Sherpa is configured, see ANALYSIS. To display the Analysis package syntax, run Sherpa with SHOW_ANALYSIS_SYNTAX=1 on the command line.

10.15.1 Running Sherpa with AMEGIC++

When Sherpa is run using the matrix element generator AMEGIC++, it is necessary to run it twice. During the first run (the initialization run) Feynman diagrams for the hard processes are constructed and translated into helicity amplitudes. Furthermore suitable phase-space mappings are produced. The amplitudes and corresponding integration channels are written to disk as C++ sourcecode, placed in a subdirectory of LHC_4thGen, which is called Process. The initialization run is started using the standard Sherpa executable, as decribed in Running Sherpa. The relevant command is

<prefix>/bin/Sherpa 

The initialization run apparently stops with an error message, which is nothing but the request to carry out the compilation and linking procedure for the generated matrix-element libraries. The makelibs script, provided for this purpose and created in the working directory, must be invoked by the user:

./makelibs

Afterwards Sherpa can be restarted using the same command as before. In this run (the generation run) the cross sections of the hard processes are evaluated. Simultaneously the integration over phase space is optimized to arrive at an efficient event generation.

10.16 LHC_AGC

Another built-in BSM model in Sherpa allows the inclusion of anomalous gauge couplings. An example with an anomalous Z-gamma-gamma coupling is given here.

(run){
  EVENTS = 10000
}(run)

(beam){
  BEAM_1          = 2212
  BEAM_ENERGY_1   = 7000.

  BEAM_2          = 2212
  BEAM_ENERGY_2   = 7000.
}(beam)

(processes){
  Process : 93 93 -> 11 -11 22
  Print_Graphs : Process
  Integration_Error : 0.02
  End process
}(processes)

(selector){
  Mass 11 -11 66.0 116.0
  PT  22  100.0  7000.0
}(selector)

(model){
  MODEL         = SM+AGC

  ## Z gamma gamma coupling
  H1_GAMMA = 1.e-4
  H2_GAMMA = 1.e-4
  H3_GAMMA = 1.e-4
  H4_GAMMA = 1.e-4

  UNITARIZATION_N  = 2
  UNITARIZATION_N3 = 2
  UNITARIZATION_N4 = 3
  UNITARIZATION_SCALE  = 5000.
  UNITARIZATION_SCALE3 = 5000.
  UNITARIZATION_SCALE4 = 10000.
}(model)

Things to notice:

• the AGC model is chosen using the MODEL parameter, see Models available in Sherpa.
• parameters from the model are set in the (model) section. For more information on available parameters, and their meanings, run Sherpa with SHOW_MODEL_SYNTAX=1 on the command line, or see Anomalous Gauge Couplings.
• Print_Graphs is included in the (processes) section. When Sherpa is run with this option enabled, the valid Feynman graphs for the process are drawn, and they are stored in tex format, in the specified directory. In this example, the graphs will be found in the Process directory, after Sherpa is run.
• the matrix element generator AMEGIC++ is used for this set-up, see Running Sherpa with AMEGIC++.

10.17 LHC_EPA

This example demonstrates the usage of beam spectra based on the equivalent photon approximation (EPA) in Sherpa. The corresponding setup is discussed in detail in [Arc08] .

(run){
  EVENTS = 10000;
  PDF_SET = None
}(run);

(beam){
  BEAM_1 2212; BEAM_ENERGY_1 7000;
  BEAM_2 2212; BEAM_ENERGY_2 7000;
  BEAM_SPECTRUM_1 EPA; BEAM_SPECTRUM_2 EPA;
}(beam);

(processes){
  Process 22 22 -> 24[a] -24[b];
  Decay 24[a] -> 90 91;
  Decay -24[b] -> 90 91;
  Scales VAR{Abs2(p[0]+p[1])};
  End process;
}(processes);

(selector){
  PT 90 10 1e12;
  Rapidity 90 -2.5 2.5;
  DeltaR 90 90 0.2 1e12;
}(selector);

Things to notice:

• EPA beam spectra are enabled using the BEAM_SPECTRUM_<i> parameter, see Beam Parameters.

10.18 LHC_ADD

This example shows a set-up for the ADD model. This is one of Sherpa’s built-in BSM options. For more information on using your own BSM models with Sherpa, see Exotic physics.

(run){
  EVENTS = 2000;
  ANALYSIS = 0;
}(run)

(beam){
  BEAM_1          = 2212
  BEAM_ENERGY_1   = 7000.

  BEAM_2          = 2212
  BEAM_ENERGY_2   = 7000.
}(beam)

(processes){
  #
  # jet jet -> jet graviton
  #
  Process 93 93 -> 93 39;
  Print_Graphs : Process;
  End process;
}(processes)

(selector){
  PT 93 150 14000
}(selector)

(model){
  MODEL = ADD

  N_ED  = 2
  M_S   = 2000
  M_CUT = 2000
  KK_CONVENTION = 5

  MASS[39] = 100.
  MASS[40] = 100.
}(model)

(fragmentation){
  FRAGMENTATION=Off;
}(fragmentation)

(analysis){
  BEGIN_ANALYSIS {
    LEVEL  MEs Showers

    PT    39  0. 2000. 100 LinErr FinalState

  } END_ANALYSIS
}(analysis)

Things to notice:

• the matrix element generator AMEGIC++ is used for this set-up, see Running Sherpa with AMEGIC++.
• the model is chosen in the (model) section of the run card, using the parameter MODEL, see Model Parameters. The default is the SM.
• for a full description of all parameters in any chosen model, use the tag SHOW_MODEL_SYNTAX=1 on the command line when running Sherpa.
• the properties of the graviton (<id> = 39) and graviscalar (<id> = 40), such as e.g. MASS[<id>] and WIDTH[<id>], may be set in the runcard, or on the command line, in exactly the same way as the SM particle properties.
• the number of extra dimensions is fixed to N_ED = 2. Further the cut-off scale and the ADD scale M_S have been set equal to a rather low value (2 TeV).
• the analysis has been switched off, but to use it, switch ANALYSIS to ‘Internal’.
• the analysis in this example uses Sherpa’s in-built analysis package. To use this Analysis package, when Sherpa is installed, the option --enable-analysis must be include on the command line when Sherpa is configured, see ANALYSIS. To display the Analysis package syntax, run Sherpa with SHOW_ANALYSIS_SYNTAX=1 on the command line.

10.19 LHC_SUSY

This example shows a beyond the Standard Model set-up, namely a setup for the Minimal Supersymmetric Standard Model (MSSM). This is one of Sherpa’s built-in BSM options, see Models available in Sherpa. For more information on using your own BSM models with Sherpa, see Exotic physics.

(run){
  EVENTS = 10000;
  FRAGMENTATION = Off;
}(run);

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 7000;
  BEAM_2 = 2212; BEAM_ENERGY_2 = 7000;
}(beam);

(processes){
  #
  # jet jet -> snu_2[-> chi0_1 numu] smuon_L[-> chi0_1 mu+] + 0-1 jets
  # 
  Process 93 93 -> 1000014[a] -1000013[b] 93{1};
    DecayOS 1000014[a] -> 1000022 14;
    DecayOS -1000013[b] -> 1000022 -13;
  Order_EW 2;
  CKKW sqr(30/E_CMS);
  Print_Graphs : Process;
  End process;
}(processes);

(model){
  MODEL = MSSM;
  # SUSY spectrum input file
  SLHA_INPUT = LesHouches_SPS1A.dat;
}(model);

Things to notice:

• the model is chosen in the (model) section of the run card, using the parameter MODEL, see Model Parameters. The default is the SM.
• the necessary SUSY Les Houches Accord input file containing all parameters is set by SLHA_INPUT, see Minimal Supersymmetric Standard Model.
• the process is specified with up to one extra parton in the production subprocess, see Curly brackets.
• the multi-jet merging parameter CKKW is set using an algebraic expression, see ME-PS merging.
• the tag DecayOS is used to specify the decays. See DecayOS.
• the matrix element generator AMEGIC++ is used for this set-up, see Running Sherpa with AMEGIC++.

10.20 NLO_W

This example computes the next-to-leading W-production cross section at Tevatron Run II energies.

(run){
  EVENTS 1000000; ANALYSIS_WRITEOUT_INTERVAL 0.1;
  ANALYSIS Internal;
  BATCH_MODE 0; OUTPUT 2;
}(run);
(processes){
  Process 93 93 -> 11 -12;
  NLO_QCD_Part BIV;
  Loop_Generator Internal;
  Order_EW 2;
  End process;
  #
  Process 93 93 -> 11 -12;
  NLO_QCD_Part RS;
  Order_EW 2;
  Enhance_Factor 10;
  End process;
}(processes);
(selector){
  Mass 11 -12 10 E_CMS;
}(selector)
(me){
  ME_SIGNAL_GENERATOR Amegic;
  EVENT_GENERATION_MODE Weighted;
  NLO_Mode 1;
  SCALES VAR{Abs2(p[2]+p[3])};
}(me);
(beam){
  BEAM_1  2212; BEAM_ENERGY_1 980;
  BEAM_2  -2212; BEAM_ENERGY_2 980;
  K_PERP_MEAN_1 0.; K_PERP_SIGMA_1 0.;
  K_PERP_MEAN_2 0.; K_PERP_SIGMA_2 0.;
}(beam);
(integration){
  INTEGRATOR 7; ERROR 0.1;
  FINISH_OPTIMIZATION On;
}(integration);
(shower){
  SHOWER_GENERATOR None;
  FSR_SHOWER 0; ISR_SHOWER 0;
}(shower);
(fragmentation){
  FRAGMENTATION Off;
}(fragmentation);
(analysis){
    BEGIN_ANALYSIS {
        LEVEL MENLO
                
        PT        11  0. 500. 100   LinErr FinalState
        PT        -12  0. 500. 100  LinErr FinalState
        Y2        11 -12 -5. 5. 50  LinErr FinalState
    } END_ANALYSIS;
}(analysis)

Things to notice:

• The results are generated exactly up to order alpha_S^1. It is not possible to attach parton showers or a hadronization consistently to these pure NLO matrix elements. To perform a parton shower matched NLO calculation one of the following examples has to be invoked: LHC_WJets_MENLOPS, Tevatron_ZJets_MENLOPS, LHC_HWW_POWHEG, LHC_HZZ_POWHEG, LHC_HPP_POWHEG.
• This setup will generate 1e6 weighted events and and put them into histograms for a few observables, reproducing the NLO data in Fig. 8 of [Gle07] .
• The process setup has been explicitly split into pieces with born-like and with real-correction-like kinematics. It is possible to run the setup without this, however, usually the phase space integration for the real correction is more complicated and thus less efficient. To cope with this an Enhance_Factor has been added, see Processes.
• Sherpa’s internal analysis package is used. Therefore, when installing Sherpa the option --enable-analysis must be include on the command line when Sherpa is configured, see ANALYSIS.
• In order to correctly treat real correction contributions within the internal analysis it must be set up with LEVEL MENLO.
• For more information on how to use the implemeted automated dipole subtraction for NLO calculations see Parameters, NLO calculations and External one-loop ME.

10.21 LHC_WJet_LHOLE

This example computes the next-to-leading W+jet-production cross section at current LHC energies using the Binoth Les Houches interface proposal for an external one-loop generator [Bin10a] .

Run_B.dat :
(run){
  EVENTS 100000;
}(run);
(processes){
  Process 93 93 -> 11 -12 93;
  Order_EW 2;
  End process;
}(processes);
(selector){
  NJetFinder 1 50. 0. 1.
}(selector);
(me){
  ME_SIGNAL_GENERATOR Amegic;
  EVENT_GENERATION_MODE Weighted;
  SCALES VAR{MPerp2(p[2]+p[3])}{MPerp2(p[2]+p[3])};
}(me);
(beam){
  BEAM_1  2212; BEAM_ENERGY_1 3500;
  BEAM_2  2212; BEAM_ENERGY_2 3500;
  K_PERP_MEAN_1 0.; K_PERP_SIGMA_1 0.;
  K_PERP_MEAN_2 0.; K_PERP_SIGMA_2 0.;
}(beam);
(integration){
  INTEGRATOR 7; ERROR 0.05;
  FINISH_OPTIMIZATION On;
}(integration);
(shower){
  SHOWER_GENERATOR None;
}(shower);
(fragmentation){
  FRAGMENTATION Off;
}(fragmentation);

Run_I.dat :
(run){
  EVENTS 100000;
  SHERPA_LDADD OLE
}(run);
(processes){
  Process 93 93 -> 11 -12 93;
  NLO_QCD_Part VI;
  Loop_Generator LHOLE;
  Order_EW 2;
  End process;
}(processes);
(selector){
  NJetFinder 1 50. 0. 1.
}(selector);
(me){
  ME_SIGNAL_GENERATOR Amegic LHOLE;
  EVENT_GENERATION_MODE Weighted;
  SCALES VAR{MPerp2(p[2]+p[3])}{MPerp2(p[2]+p[3])};
}(me);
(beam){
  BEAM_1  2212; BEAM_ENERGY_1 3500;
  BEAM_2  2212; BEAM_ENERGY_2 3500;
  K_PERP_MEAN_1 0.; K_PERP_SIGMA_1 0.;
  K_PERP_MEAN_2 0.; K_PERP_SIGMA_2 0.;
}(beam);
(integration){
  INTEGRATOR 7; ERROR 0.05;
  FINISH_OPTIMIZATION On;
}(integration);
(shower){
  SHOWER_GENERATOR None;
}(shower);
(fragmentation){
  FRAGMENTATION Off;
}(fragmentation);

Run_R.dat :
(run){
  EVENTS 1000000;
}(run);
(processes){
  Process 93 93 -> 11 -12 93;
  NLO_QCD_Part RS;
  Order_EW 2;
  End process;
}(processes);
(selector){
  NJetFinder 1 50. 0. 1.
}(selector);
(me){
  ME_SIGNAL_GENERATOR Amegic;
  EVENT_GENERATION_MODE Weighted;
  SCALES VAR{MPerp2(p[2]+p[3])}{MPerp2(p[2]+p[3])};
}(me);
(beam){
  BEAM_1  2212; BEAM_ENERGY_1 3500;
  BEAM_2  2212; BEAM_ENERGY_2 3500;
  K_PERP_MEAN_1 0.; K_PERP_SIGMA_1 0.;
  K_PERP_MEAN_2 0.; K_PERP_SIGMA_2 0.;
}(beam);
(integration){
  INTEGRATOR 7; ERROR 0.1;
  FINISH_OPTIMIZATION On;
}(integration);
(shower){
  SHOWER_GENERATOR None;
}(shower);
(fragmentation){
  FRAGMENTATION Off;
}(fragmentation);

Things to notice:

• this setup includes three run cards, separating the three different contributions to an NLO calculation: Run_B.dat contains the Born contribution, Run_I.dat the virtual and integrated subtraction terms, and Run_R.dat the real and real-subtraction terms.
• the setup including the virtual bit sets LHOLE as the loop generator. It also need to be added to the ME_SIGNAL_GENERATOR list. For additional information see External one-loop ME.
• The switch SHERPA_LDADD present in Run_I.dat has to be set to the appropriate library name (and path) of the one-loop generator. In the above example, the corresponding library to be loaded would be called libOLE.so.
• both the factorisation and renormalisation scales are set to the transverse mass of the electron-neutrino pair.

10.22 Tevatron_ZJets_MENLOPS

This setup implements the MENLOPS method, combining both POWHEG-style NLO matrix element parton shower matching and CKKW-style multijet merging, cf. [Hoe10a] , [Ham10] . Its result, after switching on both the hadronisation and underlying event modules, can then be directly compared to experimental data.

(run){
  EVENTS 10000000
  FRAGMENTATION Off
  MASSIVE[15]=1
}(run)

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 980.;
  BEAM_2 = -2212; BEAM_ENERGY_2 = 980.;
}(beam)

(processes){
  Process 93 93 -> 90 -90 93{3};
  NLO_QCD_Part BVIRS {2};
  Loop_Generator Internal;
  Order_EW 2;
  CKKW sqr(20./E_CMS);
  Scales VAR{MPerp2(p[2]+p[3])} {2};
  Enhance_Function VAR{PPerp2(p[2]+p[3])} {3,4,5};
  Integration_Error 0.02 {3,4,5};
  End process;
}(processes)

(selector){
  Mass 90 -90 66. 116.
}(selector)

(me){
  ME_SIGNAL_GENERATOR Amegic Internal;
  EVENT_GENERATION_MODE Weighted;
  NLO_Mode 2;
}(me)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• This is a Tevatron Run II setup for inclusive Drell-Yan production, using the MENLOPS method.
• The core process is calculated at NLO accuracy. The NLO part of setup is therefore similar to LHC_WJets_MENLOPS. Its scale is set to the transverse mass of the lepton pair.
• Up to three additional jets are described by leading order matrix elements.
• An internal hard-coded matrix element is used for the virtual term of the Drell-Yan core process. For more information on how to interface External one-loop MEs see the linked section. Higher order emissions are only described at tree-level.
• Enhance_Function have been added to raise statistics on hard jet emissions (cf. Enhance_Function).
• Neither hadronisation nor underlying event corrections are taken into account. Both can be switched on by setting the relevant Parameters accordingly.

10.23 LHC_WJets_MENLOPS

This setup implements the MENLOPS method, combining both POWHEG-style NLO matrix element parton shower matching and CKKW-style multijet merging, cf. [Hoe10a] , [Ham10] . Its result, after switching on both the hadronisation and underlying event modules, can then be directly compared to experimental data.

(run){
  EVENTS 1000000
  FRAGMENTATION Off
  MASSIVE[15]=1
  PH_CSS_KT_RESOLUTION=8;
}(run)

(beam){
  BEAM_1 = 2212; BEAM_ENERGY_1 = 3500.;
  BEAM_2 = 2212; BEAM_ENERGY_2 = 3500.;
}(beam)

(processes){
  Process 93 93 -> 90 91 93{3};
  NLO_QCD_Part BVIRS {2};
  Loop_Generator Internal;
  ME_Generator Amegic {2,3};
  Order_EW 2;
  CKKW sqr(20./E_CMS);
  Enhance_Function VAR{PPerp2(p[2]+p[3])} {3,4,5,6,7,8};
  Integration_Error 0.02 {3,4};
  End process;
}(processes)

(selector){
  Mass  11 -12 10. E_CMS
  Mass  13 -14 10. E_CMS
  Mass -11  12 10. E_CMS
  Mass -13  14 10. E_CMS
}(selector)

(me){
  ME_SIGNAL_GENERATOR Comix Amegic Internal;
  EVENT_GENERATION_MODE Weighted;
  NLO_Mode 2;
}(me)

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• This is a LHC setup for inclusive W boson production, using the MENLOPS method.
• The automated dipole subtraction implemented in the matrix element generator Amegic [Gle07] is used.
• An internal hard-coded matrix element is used for the virtual term. For more information on how to interface External one-loop MEs see the linked section.
• Further, Amegic is invoked for all matrix elements with final state multiplicities 2 and 3, while Comix is used for all other.
• The kt-resolution parameter determining the splitting between singular and regular real contributions is set to 8.
• Neither hadronisation nor underlying event corrections are taken into account. Both can be switched on by setting the relevant Parameters accordingly.

10.24 LHC_HWW_POWHEG

This setup implements a matching of NLO matrix elements with the parton shower using the POWHEG method, cf. [Hoe10] , [Nas04] , [Fri07] . Its result, after switching on both the hadronisation and underlying event modules, can then be directly compared to experimental data.

(run){
  EVENTS 1000000;
  OUTPUT 2;
  MASS[25]=145.
  MASSIVE[15]=1
  YUKAWA_B=0.;
  FRAGMENTATION Off;
}(run);

(model){
  MODEL=SM+EHC;
}(model);

(processes){
  Process 93 93 -> 25[a]
    Decay   25[a] -> 90 90 91 91;
  NLO_QCD_Part BVIRS;
  Loop_Generator Internal;
  Print_Graphs 1;
  Order_EW 1;
  End process;
}(processes);

(selector){
  "Calc(Mass(p[0]+p[1]+p[2]+p[3]))" 90,90,91,91 10.,E_CMS [PT_UP,PT_UP,PT_UP,PT_UP]
}(selector)

(me){
  ME_SIGNAL_GENERATOR Amegic Internal;
  EVENT_GENERATION_MODE Weighted;
  NLO_Mode 2;
  SCALES VAR{MPerp2(p[2]+p[3]+p[4]+p[5])};
}(me);

(beam){
  BEAM_1  2212; BEAM_ENERGY_1 3500;
  BEAM_2  2212; BEAM_ENERGY_2 3500;
}(beam);

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• This is a LHC setup at 7 TeV for a parton shower matched NLO simulation, using the POWHEG method.
• The model has been set to the Standard Model supplemented with effective Higgs couplings, cf. Effective Higgs Couplings.
• The explicite generation of an s-channel Higgs-resonance decaying into two leptons and two neutrinos, is enforced. Width effects, interferences and spin-correlations are accounted for.
• The renormalisation and factorisation scales are set to the transverse mass of the leptonic final state.
• The automated dipole subtraction implemented in matrix element generator Amegic [Gle07] is used.
• An internal hardcoded one-loop matrix element is used for the virtual term.
• Neither hadronisation nor underlying event corrections are taken into account. Both can be switched on by setting the relevant Parameters accordingly.

10.25 LHC_HZZ_POWHEG

This setup implements a matching of NLO matrix elements with the parton shower using the POWHEG method, cf. [Hoe10] , [Nas04] , [Fri07] . Its result, after switching on both the hadronisation and underlying event modules, can then be directly compared to experimental data.

(run){
  EVENTS 1000000;
  OUTPUT 2;
  MASS[25]=145.
  MASSIVE[15]=1;
  YUKAWA_B=0.;
  FRAGMENTATION Off;
}(run);

(model){
  MODEL=SM+EHC;
}(model);

(processes){
  Process 93 93 -> 25[a]
    Decay  25[a] -> 90 90 90 90;
  NLO_QCD_Part BVIRS;
  Loop_Generator Internal;
  Print_Graphs 1;
  Order_EW 1;
  End process;
}(processes);

(selector){
  "Calc(Mass(p[0]+p[1]+p[2]+p[3]))" 90,90,90,90 10.,E_CMS [PT_UP,PT_UP,PT_UP,PT_UP]
}(selector)

(me){
  ME_SIGNAL_GENERATOR Amegic Internal;
  EVENT_GENERATION_MODE Weighted;
  NLO_Mode 2;
  SCALES VAR{MPerp2(p[2]+p[3]+p[4]+p[5])};
}(me);

(beam){
  BEAM_1  2212; BEAM_ENERGY_1 3500;
  BEAM_2  2212; BEAM_ENERGY_2 3500;
}(beam);

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• This is a LHC setup at 7 TeV for a parton shower matched NLO simulation, using the POWHEG method.
• The model has been set to the Standard Model supplemented with effective Higgs couplings, cf. Effective Higgs Couplings.
• A Higgs boson is produced via gluon fusion and decays into four charged lepton. Width effects, interferences and spin-correlations are accounted for.
• The renormalisation and factorisation scales are set to the transverse mass of the leptonic final state.
• The automated dipole subtraction implemented in matrix element generator Amegic [Gle07] is used.
• An internal hardcoded one-loop matrix element is used for the virtual term.
• Neither hadronisation nor underlying event corrections are taken into account. Both can be switched on by setting the relevant Parameters accordingly.

10.26 LHC_HPP_POWHEG

This setup implements a matching of NLO matrix elements with the parton shower using the POWHEG method, cf. [Hoe10] , [Nas04] , [Fri07] . Its result, after switching on both the hadronisation and underlying event modules, can then be directly compared to experimental data.

(run){
  EVENTS 1000000;
  OUTPUT 2;
  MASS[25]=115.
  YUKAWA_B=0.;
  FRAGMENTATION Off;
}(run);

(model){
  MODEL=SM+EHC;
  FINITE_TOP_MASS=1;
  FINITE_W_MASS=1
}(model);

(processes){
  Process 93 93 -> 25[a]
    Decay   25[a] -> 22 22;
  NLO_QCD_Part BVIRS;
  Loop_Generator Internal;
  Print_Graphs 1;
  Order_EW 1;
  End process;
}(processes);

(selector){
  Mass 22 22 20. E_CMS
}(selector)

(me){
  ME_SIGNAL_GENERATOR Amegic Internal;
  EVENT_GENERATION_MODE Weighted;
  NLO_Mode 2;
  SCALES VAR{MPerp2(p[2]+p[3])};
}(me);

(beam){
  BEAM_1  2212; BEAM_ENERGY_1 3500;
  BEAM_2  2212; BEAM_ENERGY_2 3500;
}(beam);

(mi){
  MI_HANDLER = None  # None or Amisic
}(mi)

Things to notice:

• This is a LHC setup at 7 TeV for a parton shower matched NLO simulation, using the POWHEG method.
• The model has been set to the Standard Model supplemented with effective Higgs couplings, cf. Effective Higgs Couplings. Top mass effects in the effective gluon-gluon-Higgs vertex and both top mass and W mass effects in the effective photon-photon-Higgs vertex are taken into account.
• The explicite generation of an s-channel Higgs-resonance decaying into a pair of prompt photons is enforced. Width effects and spin-correlations are accounted for.
• The renormalisation and factorisation scales are set to the transverse mass of the photon pair.
• The automated dipole subtraction implemented in matrix element generator Amegic [Gle07] is used.
• An internal hard-coded matrix element is used for the virtual term. For more information on how to interface External one-loop MEs see the linked section.
• Neither hadronisation nor underlying event corrections are taken into account. Both can be switched on by setting the relevant Parameters accordingly.

11. Getting help

If Sherpa exits abnormally, first check the Sherpa output for hints on the reason of program abort, and try to figure out what has gone wrong with the help of the Manual. Note that Sherpa throwing a ‘normal_exit’ exception does not imply any abnormal program termination! When using AMEGIC++ Sherpa will exit with the message:

   New libraries created. Please compile.

In this case, follow the instructions given in Running Sherpa with AMEGIC++.

If this does not help, contact the Sherpa team (see the Sherpa Team section of the website http://www.sherpa-mc.de), providing all information on your setup. Please include

1. A complete tarred and gzipped set of the ‘.dat’ files leading to the crash. Use the status recovery directory Status__<date of crash> produced before the program abort.
2. The command line (including possible parameters) you used to start Sherpa.
3. The installation log file, if available.

12. Authors

Sherpa was written by the Sherpa Team, see http://www.sherpa-mc.de.

13. Copying

Sherpa is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation. You should have received a copy of the GNU General Public License along with the source for Sherpa; see the file COPYING. If not, write to the Free Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.

Sherpa is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

Sherpa was created during the Marie Curie RTN’s HEPTOOLS and MCnet. The MCnet Guidelines apply, see the file GUIDELINES and http://www.montecarlonet.org/index.php?p=Publications/Guidelines.

A. References

• [Ale05] S. Alekhin and others, HERA and the LHC - A workshop on the implications of HERA for LHC physics: Proceedings Part A, hep-ph/0601012.
  
  
• [Alw07] J. Alwall and others, Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions, Eur. Phys. J. C53 (2008) 473-500 [arXiv:0706.2569].
  
  
• [Arc08] J. Archibald and T. Gleisberg and S. Hoche and F. Krauss and M. Schonherr and S. Schumann and F. Siegert and J. C. Winter, Simulation of photon-photon interactions in hadron collisions with Sherpa, Nucl. Phys. 179 (2008) 218-225 .
  
  
• [Bah08] M. Bahr and others, Herwig++ Physics and Manual, Eur. Phys. J. C58 (2008) 639-707 [arXiv:0803.0883].
  
  
• [Bal08] R. D. Ball and others, A determination of parton distributions with faithful uncertainty estimation, Nucl. Phys. B809 (2009) 1-63 [arXiv:0808.1231].
  
  
• [Bal09] R. D. Ball and others, Precision determination of electroweak parameters and the strange content of the proton from neutrino deep-inelastic scattering, Nucl. Phys. B823 (2009) 195-233 [arXiv:0906.1958].
  
  
• [Bal92] A. Ballestrero and E. Maina and S. Moretti, Heavy quarks and leptons at e^+e^- colliders, Nucl. Phys. B415 (1994) 265-292 [hep-ph/9212246].
  
  
• [Bar93] E. Barberio and Z. Wc as, PHOTOS - a universal monte carlo for QED radiative corrections: version 2.0, Comput. Phys. Commun. 79 (1994) 291-308 .
  
  
• [Bau88] U. Baur and D. Zeppenfeld, Probing the WWgamma vertex at future hadron colliders, Nucl. Phys. B308 (1988) 127 .
  
  
• [Ber94] F. A. Berends and R. Pittau and R. Kleiss, All electroweak four-fermion processes in electron-positron collisions, Nucl. Phys. B424 (1994) 308 [hep-ph/9404313].
  
  
• [Bin10a] T. Binoth and others, A proposal for a standard interface between Monte Carlo tools and one-loop programs, arXiv:1001.1307.
  
  
• [Bud74] V. M. Budnev and I. F. Ginzburg and G. V. Meledin and V. G. Serbo, The two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation, Phys. Rept. 15 (1974) 181-281 .
  
  
• [Car09] T. Carli and T. Gehrmann and S. Hoche, Hadronic final states in deep-inelastic scattering with Sherpa, Eur. Phys. J. C67 (2010) 73 [arXiv:0912.3715].
  
  
• [Cat01] S. Catani and F. Krauss and R. Kuhn and B. R. Webber, QCD matrix elements + parton showers, JHEP 11 (2001) 063 [hep-ph/0109231].
  
  
• [Cat02] S. Catani and S. Dittmaier and M. H. Seymour and Z. Trocsanyi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B627 (2002) 189-265 [hep-ph/0201036].
  
  
• [Cat96b] S. Catani and M. H. Seymour, A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys. B485 (1997) 291-419 [hep-ph/9605323].
  
  
• [Chr08] N. D. Christensen and C. Duhr, FeynRules - Feynman rules made easy, Comput. Phys. Commun. 180 (2009) 1614-1641 [arXiv:0806.4194].
  
  
• [Chr09] N. D. Christensen and others, A comprehensive approach to new physics simulations, arXiv:0906.2474.
  
  
• [Ded08] A. Dedes and T. Figy and S. Hoche and F. Krauss and T. E. J. Underwood, Searching for Nambu-Goldstone Bosons at the LHC, JHEP 11 (2008) 036 [arXiv:0807.4666].
  
  
• [Dra00] P. D. Draggiotis and A. van Hameren and R. Kleiss, SARGE: An algorithm for generating QCD-antennas, Phys. Lett. B483 (2000) 124-130 [hep-ph/0004047].
  
  
• [Duh06] C. Duhr and S. Hoche and F. Maltoni, Color-dressed recursive relations for multi-parton amplitudes, JHEP 08 (2006) 062 [hep-ph/0607057].
  
  
• [Fri07] S. Frixione and P. Nason and C. Oleari, Matching NLO QCD computations with parton shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092].
  
  
• [Gan99] F. Gangemi and G. Montagna and M. Moretti and O. Nicrosini and F. Piccinini, Electroweak physics in six-fermion final states at future e^+ e^- colliders, hep-ph/0001065.
  
  
• [Gle03a] T. Gleisberg and F. Krauss and K. T. Matchev and A. S. and S. Schumann and G. Soff, Helicity formalism for spin-2 particles, JHEP 09 (2003) 001 [hep-ph/0306182].
  
  
• [Gle03b] T. Gleisberg and F. Krauss and C. G. Papadopoulos and A. Schalicke and S. Schumann, Cross sections for multi-particle final states at a linear collider, Eur. Phys. J. C34 (2004) 173-180 [hep-ph/0311273].
  
  
• [Gle05] T. Gleisberg and F. Krauss and A. Schalicke and S. Schumann and J. C. Winter, Studying W^+ W^- production at the Fermilab Tevatron with Sherpa, Phys. Rev. D72 (2005) 034028 [hep-ph/0504032].
  
  
• [Gle07] T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J. C53 (2008) 501-523 [arXiv:0709.2881].
  
  
• [Gle08] T. Gleisberg and S. Hoche, Comix a new matrix element generator, JHEP 12 (2008) 039 [arXiv:0808.3674].
  
  
• [Gle08a] T. Gleisberg and S. Hoche and F. Krauss and R. law Matyskiewicz, How to calculate colourful cross sections efficiently, arXiv:0808.3672.
  
  
• [Gle08b] T. Gleisberg and S. Hoche and F. Krauss and M. Schonherr and S. Schumann and F Siegert and J. Winter, Event generation with Sherpa 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622].
  
  
• [Glu91] M. Gluck and E. Reya and A. Vogt, Parton structure of the photon beyond the leading order, Phys. Rev. D45 (1992) 3986-3994 .
  
  
• [Glu91a] M. Gluck and E. Reya and A. Vogt, Photonic parton distributions, Phys. Rev. D46 (1992) 1973-1979 .
  
  
• [Got82] T. D. Gottschalk, A realistic model for e^+e^- annihilation including parton bremsstrahlung effects, Nucl. Phys. B214 (1983) 201 .
  
  
• [Got83] T. D. Gottschalk, An improved description of hadronization in the QCD cluster model for e^+e^- annihilation, Nucl. Phys. B239 (1984) 349 .
  
  
• [Got86] T. D. Gottschalk and D. A. Morris, A new model for hadronization and e^+e^- annihilation, Nucl. Phys. B288 (1987) 729 .
  
  
• [Gou00] G. J. Gounaris and J. Layssac and F. M. Renard, Off-shell structure of the anomalous Z and gamma self- couplings, Phys. Rev. D62 (2000) 073012 [hep-ph/0005269].
  
  
• [Hag05] K. Hagiwara and others, Supersymmetry simulations with off-shell effects for the CERN LHC and an ILC, Phys. Rev. D73 (2006) 055005 [hep-ph/0512260].
  
  
• [Hag86] K. Hagiwara and R. D. Peccei and D. Zeppenfeld and K. Hikasa, Probing the weak boson sector in e^+e^-to W^+W^-, Nucl. Phys. B282 (1987) 253 .
  
  
• [Ham02] A. van Hameren and C. G. Papadopoulos, A hierarchical phase space generator for QCD antenna structures, Eur. Phys. J. C25 (2002) 563-574 [hep-ph/0204055].
  
  
• [Ham09] K. Hamilton and P. Richardson and J. Tully, A modified CKKW matrix element merging approach to angular-ordered parton showers, JHEP 11 (2009) 038 [arXiv:0905.3072].
  
  
• [Ham10] K. Hamilton and P.Nason, Improving NLO-parton shower matched simulations with higher order matrix elements, JHEP 06 (2010) 039 [arXiv:1004.1764].
  
  
• [Hoc06] S. Hoche and others, Matching Parton Showers and Matrix Elements, hep-ph/0602031.
  
  
• [Hoe09] S. Hoche and F. Krauss and S. Schumann and F. Siegert, QCD matrix elements and truncated showers, JHEP 05 (2009) 053 [arXiv:0903.1219].
  
  
• [Hoe09a] S. Hoche and S. Schumann and F. Siegert, Hard photon production and matrix-element parton-shower merging, Phys. Rev. D81 (2010) 034026 [arXiv:0912.3501].
  
  
• [Hoe10] S. Hoche and F. Krauss and M. Schonherr and F. Siegert, Automating the POWHEG method in Sherpa, [arXiv:1008.5399].
  
  
• [Hoe10a] S. Hoche and F. Krauss and M. Schonherr and F. Siegert, NLO matrix elements and truncated showers, [arXiv:1009.1127].
  
  
• [Hou87a] W. S. Hou and A. Soni and H. Steger, Charmless Decays of Bottom Mesons and a Fourth Generation, Phys. Rev. Lett. 59 (1987) 1521 .
  
  
• [Jad93] S. Jadach and Z. Was and R. Decker and J. H. Kuhn, The tau decay library TAUOLA: Version 2.4, Comput. Phys. Commun. 76 (1993) 361-380 .
  
  
• [Kan00] A. Kanaki and C. G. Papadopoulos, HELAC: A package to compute electroweak helicity amplitudes, Comput. Phys. Commun. 132 (2000) 306-315 [hep-ph/0002082].
  
  
• [Kle85] R. Kleiss and W. J. Stirling, Spinor techniques for calculating pbarpto W^pm/Z^0+jets, Nucl. Phys. B262 (1985) 235-262 .
  
  
• [Kle85a] R. Kleiss and W. J. Stirling and S. D. Ellis, A new Monte Carlo treatment of multiparticle phase space at high energies, Comput. Phys. Commun. 40 (1986) 359 .
  
  
• [Kle94] R. Kleiss and R. Pittau, Weight optimization in multichannel Monte Carlo, Comput. Phys. Commun. 83 (1994) 141-146 [hep-ph/9405257].
  
  
• [Kra01] F. Krauss and R. Kuhn and G. Soff, AMEGIC++ 1.0: A Matrix Element Generator In C++, JHEP 02 (2002) 044 [hep-ph/0109036].
  
  
• [Kra02] F. Krauss, Matrix elements and parton showers in hadronic interactions, JHEP 0208 (2002) 015 [hep-ph/0205283].
  
  
• [Kra04] F. Krauss and A. Schalicke and S. Schumann and G. Soff, Simulating W / Z + jets production at the Tevatron, Phys. Rev. D70 (2004) 114009 [hep-ph/0409106].
  
  
• [Kra05] F. Krauss and A. Schalicke and S. Schumann and G. Soff, Simulating W/Z + jets production at the CERN LHC, Phys. Rev. D72 (2005) 054017 [hep-ph/0503280].
  
  
• [Kra05a] F. Krauss and A. Schalicke and G. Soff, APACIC++ 2.0: A PArton Cascade In C++, Comput. Phys. Commun. 174 (2006) 876-902 [hep-ph/0503087].
  
  
• [Kra10] F. Krauss and T. Laubrich and F. Siegert, Simulation of hadron decays in Sherpa, .
  
  
• [Lan01] D. J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462 (2001) 152-155 .
  
  
• [Lav05] N. Lavesson and L. Lonnblad, W+jets matrix elements and the dipole cascade, JHEP 07 (2005) 054 [hep-ph/0503293].
  
  
• [Lep80] G. P. Lepage, VEGAS - An Adaptive Multi-dimensional Integration Program, .
  
  
• [Lon01] L. Lonnblad, Correcting the colour-dipole cascade model with fixed order matrix elements, JHEP 05 (2002) 046 [hep-ph/0112284].
  
  
• [Lon92] L. Lonnblad, Ariadne version 4: A program for simulation of QCD cascades implementing the colour dipole model, Comput. Phys. Commun. 71 (1992) 15-31 .
  
  
• [Mal02a] F. Maltoni and T. Stelzer, MadEvent: automatic event generation with MadGraph, JHEP 02 (2003) 027 [hep-ph/0208156].
  
  
• [Man01] M. L. Mangano and M. Moretti and R. Pittau, Multijet matrix elements and shower evolution in hadronic collisions: W bbarb+n-jets as a case study, Nucl. Phys. B632 (2002) 343-362 [hep-ph/0108069].
  
  
• [Man02] M. L. Mangano and M. Moretti and F. Piccinini and R. Pittau and A. D. Polosa, ALPGEN a generator for hard multiparton processes in hadronic collisions, JHEP 07 (2003) 001 [hep-ph/0206293].
  
  
• [Man06] M. L. Mangano and M. Moretti and F. Piccinini and M. Treccani, Matching matrix elements and shower evolution for top-pair production in hadronic collisions, JHEP 01 (2007) 013 [hep-ph/0611129].
  
  
• [Mar01] A. D. Martin and R. G. Roberts and W. J. Stirling and R. S. Thorne, MRST2001: Partons and alpha_s from precise deep inelastic scattering and Tevatron jet data, Eur. Phys. J. C23 (2002) 73-87 [hep-ph/0110215].
  
  
• [Mar04] A. D. Martin and R. G. Roberts and W. J. Stirling and R. S. Thorne, Parton distributions incorporating QED contributions, Eur. Phys. J. C39 (2005) 155-161 [hep-ph/0411040].
  
  
• [Mar09] A. D. Martin and W. J. Stirling and R. S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C63 (2009) 189-295 [arXiv:0901.0002].
  
  
• [Mar99] A. D. Martin and R. G. Roberts and W. J. Stirling and R. S. Thorne, Parton distributions and the LHC: W and Z production, Eur. Phys. J. C14 (2000) 133-145 [hep-ph/9907231].
  
  
• [Nad08] P. M. Nadolsky and others, Implications of CTEQ global analysis for collider observables, Phys. Rev. D78 (2008) 013004 [arXiv:0802.0007].
  
  
• [Nag03] Z. Nagy, Next-to-leading order calculation of three-jet observables in hadron-hadron collisions, Phys. Rev. D68 (2003) 094002 [hep-ph/0307268].
  
  
• [Nag05] Z. Nagy and D. E. Soper, Matching parton showers to NLO computations, JHEP 10 (2005) 024 [hep-ph/0503053].
  
  
• [Nag06] Z. Nagy and D. E. Soper, A new parton shower algorithm: Shower evolution matching at leading and next-to-leading order level, hep-ph/0601021.
  
  
• [Nas04] P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146].
  
  
• [Pap05] C. G. Papadopoulos and M. Worek, Multi-parton cross sections at hadron colliders, Eur. Phys. J. C50 (2007) 843-856 [hep-ph/0512150].
  
  
• [Ros89] J. Rosiek, Complete set of Feynman rules for the minimal supersymmetric extension of the standard model, Phys. Rev. D41 (1990) 3464 .
  
  
• [Ros95] J. Rosiek, Complete set of Feynman rules for the MSSM – ERRATUM, hep-ph/9511250.
  
  
• [Sch05] A. Schalicke and F. Krauss, Implementing the ME+PS merging algorithm, JHEP 07 (2005) 018 [hep-ph/0503281].
  
  
• [Sch07a] S. Schumann and F. Krauss, A parton shower algorithm based on Catani-Seymour dipole factorisation, JHEP 03 (2008) 038 [arXiv:0709.1027].
  
  
• [Sch08] M. Schonherr and F. Krauss, Soft photon radiation in particle decays in Sherpa, JHEP 12 (2008) 018 [arXiv:0810.5071].
  
  
• [Sjo03] T. Sjostrand and L. Lonnblad and S. M. and P. Skands, PYTHIA 6.3 Physics and Manual, hep-ph/0308153.
  
  
• [Sjo07] T. Sjostrand and S. Mrenna and P. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852-867 [arXiv:0710.3820].
  
  
• [Sjo87] T. Sjostrand and M. van Zijl, A multiple-interaction model for the event structure in hadron collisions, Phys. Rev. D36 (1987) 2019 .
  
  
• [Ska03] P. Skands and others, SUSY Les Houches accord: interfacing SUSY spectrum calculators decay packages and event generators, JHEP 07 (2004) 036 [hep-ph/0311123].
  
  
• [Ste94] T. Stelzer and W. F. Long, Automatic generation of tree level helicity amplitudes, Comput. Phys. Commun. 81 (1994) 357-371 [hep-ph/9401258].
  
  
• [Web83] B. R. Webber, A QCD model for jet fragmentation including soft gluon interference, Nucl. Phys. B238 (1984) 492 .
  
  
• [Wha05] M. R. Whalley and D. Bourilkov and R. C. Group, The Les Houches Accord PDFs (LHAPDF) and LHAGLUE, hep-ph/0508110.
  
  
• [Win03] J. C. Winter and F. Krauss and G. Soff, A modified cluster-hadronisation model, Eur. Phys. J. C36 (2004) 381-395 [hep-ph/0311085].
  
  
• [Wol83] L. Wolfenstein, Parametrization of the Kobayashi-Maskawa Matrix, Phys. Rev. Lett. 51 (1983) 1945 .
  
  
• [Yen61] D. R. Yennie and S. C. Frautschi and H. Suura, The Infrared Divergence Phenomena and High-Energy Processes, Ann. Phys. 13 (1961) 379-452 .
  
  
• [Zar02] A. F. Zarnecki, CompAZ: Parametrization of the luminosity spectra for the photon collider, Acta Phys. Polon. B34 (2003) 2741-2758 [hep-ex/0207021].
  
  

B. Index

Table of Contents

This document was generated by Frank Siegert on July 25, 2012 using texi2html 1.82.