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QFT Diagram generators/evaluators:

  • DIANA is a DIagram ANAlyser, designed for automation of Feynman diagram evaluation. I haven't tried it yet but it looks neato.
  • COMPHEP does tree-level generation of feynman diagrams and evaluation in C. It squares the amplitude and then evaluates, so is \mathcal{O}(N^2) in the number of diagrams, but has flexible input so that new models can be defined. Files are available for the MSSM, for instance.
  • FF A fortran library for evaluating one-loop integrals (1 to 6-point scalar functions with real masses).
  • GRACE creates and evaluates all 1PI diagrams for processes in the SM and MSSM using the helicity amplitude technique.
  • LoopTools is a package for evaluation of scalar and tensor one-loop integrals based on the FF package by G.J. van Oldenborgh. It features an easy Fortran, C++, and Mathematica interface to the scalar one-loop functions of FF and in addition provides the 2-, 3-, and 4-point tensor coefficient functions.
  • MadGraph Generates tree-level SM feynman diagrams as postscript given a process, and outputs the amplitude as fortran. Uses HELAS (Helicity Amplitudes) so is \mathcal{O}(N) in the number of diagrams. As such it is especially good for large numbers of external particles.
  • Xloops is a Maple program that evalates loop diagrams. Development has stopped in favor of a GiNaC?-based version.
  • AMEGIC++ is A Matrix Element Generator in C++. It is downloadable inside the SHERPA Monte Carlo package
  • HELAC is a fortran code which generates cross sections using the Schwinger-Dyson equations, leading to a growth in computational complexity for n external particles that is 3^n, rather than n! as is usual from a feynman diagram expansion.

Monte Carlo:

  • HERWIG simulates hadron emission in e^+ e^- interactions, including interfering gluons. A new version based on C++ is also available: HERWIG++
  • Pythia (and JETSET) (6.206 manual in pdf)
  • Geant is a toolkit for the simulation of the passage of particles through matter.
  • SHERPA is an event generator in C++ that uses AMEGIC++. (Simulation for High-Energy Reactions of PArticles) It is maintained by the HEP group at Dresden and can be downloaded here
  • Pluto++ is a ROOT and C++-based monte carlo framework for hadronic physics, by the HADES collaboration.
  • EvtGen handles simulation of B decays for BaBar and CLEO.
  • Whizard by Wolfgang Kilian calls O'Mega, MadGraph?, or CompHEP? for matrix elements.
  • Alpgen handles multi-parton processes in hadronic collisions, optionally with extra jets from QCD radiation.

Data Analysis:

  • PAW is part of cernlib and is fortran-based
  • ROOT is C++ and is the successor to PAW

High Energy Physics Libraries:

  • CERNLIB contains a vast array of useful functions in fortran.
  • CLHEP is a Class Library for High-Energy Physics and contains the basics like LorentzVector
  • DVEGAS uses CORBA to distribute a VEGAS integration over many machines.
  • Kinematics is Nikolas Kauer's implementation of kinematics for hadron colliders.
  • GSL is the GNU Scientific Library, and contains a vast array of useful functions in C. It also has bindings to most scripting languages and wrappers for C++.
  • MTL is the Matrix Template Library, the fastest way to do matrices in C++. It also has BLAS/LAPACK interfaces.

Feynman Diagrams:

  • JaxoDraw New! The best so far! Java point-and click!
  • FeynArts is a Mathematica package for the generation and visualization of Feynman diagrams and amplitudes.
  • FeynmanGraphs is a maple package that will draw feynman diagrams. (No calculation, only draws)
  • FeynDiagram lets you write a small C++ program that will generate a .ps file with your diagram.
  • AxoDraw by J.A.M. Vermaseren (same author as FORM) lets you use LaTeX primives to draw diagrams. (J.A.M. Vermaseren: "Axodraw", Comp. Phys. Comm. 83:45-58, 1994)
  • Xfey is a little clicky program that will draw Feynman Diagrams, but it is difficult to obtain the source and I am unable to get it to compile. frown

Phase Space/Multidimensional Integration:

  • BASES/SPRING (source code) part of the Grace package.
  • CUBA
  • VEGAS (in the GNU Scientific Library) (PVEGAS parallelized C version by Kreckel)
  • MISER (in the GNU Scientific Library)
  • HIntLib High-Dimensional Integration Library (under development -- many fancy techniques)

NLO Tools:

  • AIR Automatic Integral Reduction. A Maple program for the reduction of loop integrals to master integrals.
  • TSIL Two-loop Self-energy Integral Library

NLO Codes for specific processes:

  • hprod (Djouadi) e^+ e^- \rightarrow H_i H_j (MSSM)
  • HDECAY (SM, MSSM Higgs decays)
  • NMHDECAY (NMSSM Higgs spectrum and LEP constraints)
  • HIGLU (gg \rightarrow H,A)
  • VV2H (WW,ZZ \rightarrow H)
  • PROSPINO (SUSY particle production)
  • micrOMEGAs computes the relic density in the MSSM and mSUGRA
  • FEHiP Fully Exclusive Higgs Production (NNLO gg \rightarrow h in the m_t \rightarrow \infty limit).
  • TAUOLA accurately simulates \tau lepton decays, including \mathcal{O}(\alpha) QED corrections. It can ---++be interfaced to Pythia and Herwig. (download the 1/27/04 version...)
  • PHOTOS is a universal library for QED radiative corrections (used, for instance, by TAUOLA).

Symbolic Algebra:

  • A Critique of the Mathematical Abilities of CA Systems from 1999 including Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD?, and Reduce
  • The Rosetta Stone for Computer Algebra Systems
  • Maple is the tool I use the most, though I advocate and participate in the development of free alternatives. Math is a cooperative human adventure, not a profit-making enterprise. o Feynman is a Maple package for drawing Feynman diagrams by Marvin Weinstein of SLAC. (No calculation, only draws) The author calls it FeynmanGraphs o SPUR is a Maple package by Andrea Siver to compute the trace of Dirac gamma matrices. o QFT is the evolution of the partials and Grassmann packages and has been written having in mind computations in Physics, from simple applications to more complex quantum field theory. The package implements - by default - many of the standard objects used in Physics, as for instance the Kronecker symbol, the metrics g, the Pauli and Dirac matrices, the indexed differentiation operator, the d'Alembertian, an n-dimensional Dirac delta function, etc. The QFT package makes use of the (Einstein) sum rule for repeated indices. o Maple Pet Peeves
  • Axiom is a mature symbolic algebra program originally developed at IBM, and released as free software on August 27, 2003. Extensive documentation is available in a 1142 page PDF book. It has a TeXmacs? interface. o An Introduction To Programming In Axiom o My notes on Axiom in Particle Physics
  • GiNaC is a symbolic algebra program using C++. The authors are the same as those of xloops, and aim to eventually replace xloops with a GiNaC?-based loop package.
  • gTybalt is an interactive symbolic algebra system using GiNaC?, TeXmacs? and Root
  • FORM is a symbolic algebra program that is good for doing tensor manipulations, and anything with very large polynomials (it is very efficent)
  • Maxima is the most mature free symbolic algebra program out there. It is written in Common Lisp and is GPL'd. Packages are available for doing traces of gamma matrices and tensors though the tensor package is apparently broken. o Imaxima is an emacs mode for maxima. o Symaxx2 is a Perl/Tk frontend to Maxima. o TeXmacs is a WYSIWYG TeX? editor that also supports Maxima sessions.
  • REDUCE is another commonly used package. It is not free.
  • Mathematica You know it, it's the expensive one that requires a notary and your CPU's serial number to obtain. I refuse to use it. o DiracReduce o LoopTools o FeynCalc o FormCalc? o FeynArts?
  • LanHEP is a specific tool to take a lagrangian as input, and generate model files with feynman rules for CompHEP? or micrOmega, or latex.


  • TopDrawer is a popular plotting program among physicists.
  • The Intel Fortran Compiler speaks fortran 90 and generates fast code, and is free for noncommercial use. (Click the "free evaluation download" on the RHS of that page)
  • SUSY Les Houches Accord is a specification of conventions for input/output for SUSY extensions of the Standard Model.

-- DenisPerretGallix - 16 Apr 2005

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