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

TL;DR

Package-X is a Mathematica tool that automates the analytic calculation of one-loop integrals, providing compact, readable expressions for divergent and finite parts, enhancing speed and usability for research and education.

Contribution

It introduces a comprehensive Mathematica package capable of computing high-rank tensor integrals with up to three propagators, including divergent parts, with a focus on speed and user-friendliness.

Findings

Efficient computation of tensor integrals with up to three propagators.

Provides compact expressions for divergent and finite parts of integrals.

Includes tools for Dirac matrix traces and fermion form factor projectors.

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.