Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

Abstract

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 support Mathematica’s arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica’s Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FeynCalc and LoopTools. New version program summaryProgram title: Package-XProgram files doi:http://dx.doi.org/10.17632/yfkwrd4d5t.1Licensing provisions: CC by 4.0Programming language: Mathematica (Wolfram Language)Journal reference of previous version: H. H. Patel, Comput. Phys. Commun 197, 276 (2015)Does the new version supersede the previous version?: YesSummary of revisions: Extension to four point one-loop integrals with higher powers of denominator factors, separate extraction of UV and IR divergent parts, testing for power IR divergences, construction of Taylor series expansions of one-loop integrals, numerical evaluation with arbitrary precision arithmetic, manipulation of fermion chains, improved tensor algebraic routines, and much expanded documentation.Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory.Solution method: Passarino–Veltman reduction formula, Denner–Dittmaier reduction formulae, and additional algorithms described in the manuscript.Restrictions: One-loop integrals are limited to those involving no more than four denominator factors.