Numerical evaluation of multi-gluon amplitudes for High Energy Factorization ?
We present a program to evaluate tree-level multi-gluon amplitudes with up to two of them off-shell. Furthermore, it evaluates squared amplitudes summed over colors and helicities for up to six external gluons. It employs both analytic expressions, obtained via BCFW recursion, and numerical BCFW recursion. It has been validated numerically with the help of an independent program employing numerical DysonSchwinger recursion. Program title: AMP4HEF Catalogue identifier: AEXF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXF_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 26563 No. of bytes in distributed program, including test data, etc.: 467441 Distribution format: tar.gz Programming language: Fortran 2003, implemented at least as far as in gfortran- 4.6. Computer: Any computer with the required Fortran compiler. Operating system: Any operating system with the required Fortran compiler. RAM: Negligible Classification: 11.1. Nature of problem: The numerical evaluation of matrix elements applicable in factorization prescriptions for the cross section calculation of hadron scattering processes that require off-shell partonic initial states. Solution method: The generalization of the recursive method of Britto, Cachazo, Feng and Witten [1] to amplitudes with off-shell gluons [2] is applied, both to obtain expressions which are hard-coded in the program, and numerically. Restrictions: Matrix element summed over color and spin can be evaluated for up to 6 external gluons with up to 2 of them off-shell. Color-ordered amplitudes can be evaluated essentially for an arbitrary number of external gluons, with up to 2 of them off-shell. Running time: The evaluation of the matrix element for a single phase space point summed over colors and helicities takes 0.005ms for 4 gluons with 2 of them off-shell, 0.1ms for 5 gluons with 2 of them off-shell, and 2.7ms for 6 gluons with 2 of them off-shell. This is on a single 2.30 GHz Intel Core i7, without any compiler optimization. References: R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in YangMills theory, Phys. Rev. Lett. 94 (2005) 181602, [hep-th/0501052]. A. van Hameren, BCFW recursion for off-shell gluons, JHEP 1407 (2014) 138, [1404.7818].
amplitudes off-shell qcd