Package-X: A Mathematica package for the analytic calculation of one-loop integrals

Abstract

Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-in Mathematica functions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool. Program summaryProgram title: Package-XCatalogue identifier: AEXT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXT_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 63912No. of bytes in distributed program, including test data, etc.: 1224562Distribution format: tar.gzProgramming language: Mathematica (Wolfram Language).Computer: Any, which supports Mathematica.Operating system: Windows, Mac OS X, Linux (or any system supporting Mathematica 8.0 or higher).RAM: 10 MB, depending on size of computationClassification: 4.4, 11.1.Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory for arbitrarily high-rank tensor integrals and any kinematic configuration of real-valued external invariants and internal masses.Solution method: Passarino–Veltman reduction formula, Denner–Dittmaier reduction formulae, and two new reduction algorithms described in the manuscript.Restrictions: One-loop integrals are limited to those involving no more than three propagator factors.Unusual features: Includes rudimentary routines for tensor algebraic operations and for performing traces over Dirac gamma matrices.Running time: 5 ms to 10 s for integrals typically occurring in practical computations; longer for higher rank tensor integrals.