golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs

We present a program for the numerical evaluation of form factors entering the calculation of one-loop amplitudes with up to six external legs. The program is written in Fortran95 and performs the reduction to a certain set of basis integrals numerically, using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with massless internal particles in a fast and numerically stable way.

[1]  Z. Kunszt,et al.  Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes , 2006, hep-ph/0612277.

[2]  G. Duplančić,et al.  Reduction method for dimensionally regulatedone-loop N-point Feynman integrals , 2003, hep-ph/0303184.

[3]  William H. Press,et al.  Numerical recipes , 1990 .

[4]  L. Dixon,et al.  Dimensionally-regulated pentagon integrals☆ , 1993, hep-ph/9306240.

[5]  A. I. Davydychev.  A simple formula for reducing Feynman diagrams to scalar integrals , 1991 .

[6]  D. Soper,et al.  Numerical integration of one-loop Feynman diagrams for N-photon amplitudes , 2006, hep-ph/0610028.

[7]  Rikkert Frederix,et al.  MadDipole: automation of the dipole subtraction method in MadGraph/MadEvent , 2008, 0808.2128.

[8]  G. Zanderighi,et al.  Scalar one-loop integrals for QCD , 2007, 0712.1851.

[9]  Z. Kunszt,et al.  Full one-loop amplitudes from tree amplitudes , 2008, 0801.2237.

[10]  T. Binoth,et al.  Reduction formalism for dimensionally regulated one loop N point integrals , 1999, hep-ph/9911342.

[11]  Ansgar Denner,et al.  Feyn Calc―computer-algebraic calculation of Feynman amplitudes , 1991 .

[12]  N.,et al.  Automatic Computation of Cross Sections in HEP ∗ Status of GRACE System , 1999 .

[13]  Giovanni Ossola,et al.  Reducing full one-loop amplitudes to scalar integrals at the integrand level , 2006, hep-ph/0609007.

[14]  A. Denner,et al.  Electroweak corrections to charged-current e+ e- ---> 4 fermion processes: Technical details and further results , 2005, hep-ph/0505042.

[15]  Costas G. Papadopoulos,et al.  CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes , 2007, 0711.3596.

[16]  Bo Feng,et al.  Polynomial Structures in One-Loop Amplitudes , 2008, 0803.3147.

[17]  T. Hahn,et al.  Generating Feynman Diagrams and Amplitudes with FeynArts 3 , 2001 .

[18]  J. Guillet,et al.  Algebraic evaluation of rational polynomials in one-loop amplitudes , 2006, hep-ph/0609054.

[19]  F. Krauss,et al.  From multileg loops to trees (by-passing Feynman's Tree Theorem) , 2008, 0807.0531.

[20]  R. Pittau,et al.  The NLO multileg working group: summary report , 2008, 0803.0494.

[21]  Michael H. Seymour,et al.  TeVJet: A general framework for the calculation of jet observables in NLO QCD , 2008, 0803.2231.

[22]  German Rodrigo,et al.  From Loops to Trees By-passing Feynman's Theorem , 2008, 0804.3170.

[23]  Bo Feng,et al.  Complete One-Loop Amplitudes With Massless Propagators , 2008 .

[24]  Z. Kunszt,et al.  Masses, fermions and generalized D-dimensional unitarity , 2008, 0806.3467.

[25]  Z. Bern,et al.  Dimensionally regulated one-loop integrals , 1993 .

[26]  Connection between Feynman integrals having different values of the space-time dimension. , 1996, Physical review. D, Particles and fields.

[27]  T. Hahn,et al.  Automatized One-Loop Calculations in 4 and D dimensions , 1998 .

[28]  L. Dixon,et al.  On-shell methods in perturbative QCD , 2007, 0704.2798.

[29]  T. Binoth,et al.  A numerical evaluation of the scalar hexagon integral in the physical region , 2003 .

[30]  A. Denner,et al.  Reduction schemes for one-loop tensor integrals , 2005, hep-ph/0509141.

[31]  J. Vermaseren,et al.  New algorithms for one-loop integrals , 1990 .

[32]  Paul Roman,et al.  The Analytic S-Matrix , 1967 .

[33]  W. Kilgore.  One-loop Integral Coefficients from Generalized Unitarity , 2007, 0711.5015.

[34]  Z. Kunszt,et al.  A numerical unitarity formalism for evaluating one-loop amplitudes , 2007, 0708.2398.

[35]  D. Maitre,et al.  An Automated Implementation of On-shell Methods for One-Loop Amplitudes , 2008, 0803.4180.

[36]  T. Hahn,et al.  Excursions into FeynArts and FormCalc , 2006, hep-ph/0607049.

[37]  C. Schubert,et al.  An algebraic/numerical formalism for one-loop multi-leg amplitudes , 2005 .

[38]  J. Guillet,et al.  Six-Photon Amplitudes in Scalar QED , 2007, 0711.4713.

[39]  S. D. Ellis,et al.  A New Monte Carlo Treatment of Multiparticle Phase Space at High-energies , 1986 .

[40]  G.Zanderighi.  Semi-numerical evaluation of one-loop corrections , 2005, hep-ph/0511350.

[41]  Yoshimitsu Shimizu,et al.  Automatic Computation of Cross Sections in HEP , 2000 .

[42]  Ciaran Williams,et al.  One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case , 2008, 0804.4149.

[43]  P. Mastrolia,et al.  Closed-form decomposition of one-loop massive amplitudes , 2008, 0803.1989.

[44]  G. Zanderighi,et al.  On the numerical evaluation of one-loop amplitudes: the gluonic case , 2008, 0805.2152.

[45]  S. Moch,et al.  Automating dipole subtraction , 2008, 0807.3701.

[46]  T. Hahn,et al.  News from FormCalc and LoopTools , 2006, hep-ph/0601248.

[47]  Tanju Gleisberg,et al.  Automating dipole subtraction for QCD NLO calculations , 2007, 0709.2881.

[48]  R. Pittau,et al.  Optimizing the Reduction of One-Loop Amplitudes , 2008, 0803.3964.