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

TL;DR

Package-X 2.0 is a comprehensive Mathematica tool that automates the analytic calculation of complex one-loop integrals, supporting high-rank tensor integrals, arbitrary kinematic points, and enhanced tensor algebra routines.

Contribution

It introduces new features for high-rank tensor integrals, arbitrary dimensional regularization, and improved tensor algebra support, significantly advancing automated one-loop integral calculations.

Findings

Supports arbitrarily high rank tensor integrals with multiple propagators.

Generates multivariable Taylor series expansions around non-singular points.

Enhanced stability with arbitrary precision evaluation in Mathematica.

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 supports 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.