
Hiren H. Patel
hhpatelumass.edu
Overview
Package‑X is a Mathematica package for the analytic calculation and symbolic manipulation of oneloop Feynman integrals in relativistic quantum field theory.
Technical features
 Computes dimensionally regulated oneloop integrals with up to four distinct propagators of arbitrarily high rank.
 Calculates traces of Dirac matrices in d dimensions for closed fermion loops, or carries out Dirac algebra for open fermion lines
 Generates analytic results for any kinematic configuration (e.g. at zero external momentum, at physical threshold, etc.) for real masses and external invariants.
 Provides analytic expressions for UVdivergent, IRdivergent and finite parts either separately or all together.
 Computes discontinuities across cuts of oneloop integrals.
 Constructs Taylor series expansions for oneloop integrals.
 Evaluates with either machine precision or arbitrary precision arithmetic, and is always consistent with the +iε prescription.
User interface features
 Complete documentation available online and within the Wolfram Documentation Center which includes
 over 350 basic usage examples with detailed information for every symbol defined by Package‑X,
 4 projectscale tutorials,
 and instructions on linking Package‑X to FeynCalc, LoopTools, and the COLLIER library.
 Readable and intuitive input
 Output easily manipulatable and readily numerically evaluatable
 Commandline friendly
Reference and Source
Package‑X was developed after several long years of tedious work. Please include the following citation if Package‑X was useful for your publication.
Hiren H. Patel, Comput. Phys. Commun. 197, 276 (2015), ePrint: arXiv:1503.01469
Esentially all algorithms and formulae used by Package‑X can be viewed in handwritten form at hhpatel.net/notes (Vol II, §1 and §5, and Vol V).
Bug report and feature request
Please report any bugs to hhpatelumass.edu.
Any comments and suggestions for improvements, including feature requests, are welcome.
Latest Program Files, License, and Release Notes
Package‑X 2.1 is closed source and distributed under the CC by 4.0 license agreement.
v2.1.0: (September 7, 2017) Download  Primer  Documentation
 Numerous symbols have been renamed to make Package‑X commandline friendly (more info).
 Added option
Dimensions>4 to LoopIntegrate , LoopRefine , and LoopRefineSeries to facilitate the calculation of loop integrals in spacetime dimensions other than 4.
 Option
Part to LoopRefine can now take the setting Discontinuity[s] to calculate discontinuities across normal threshold cuts of oneloop integrals.
 The precision of output of special functions (
ScalarC0 , ScalarD0 , etc) evaluated with arbitrary precision arithmetic now tracks the precision of input. It is no longer necessary to experimentally adjust the input precision to achieve the desired precision.

X`Utilities`EnableFancyInput and X`Utilities`DisableFancyInput have been renamed to X`Utilities`EnableFancyIO and X`Utilities`DisableFancyIO , respectively.

LoopIntegrate and Projector no longer support v1.0 syntax.

PVC no longer automatically reorganizes its arguments.
 Added tutorial "TreeLevel e^{+}e^{−}→γγ Cross Secion by The Optical Theorem".
 Added tutorial "Linking PackageX to COLLIER".
 Fixed a bug affecting
FermionLineExpand and LoopIntegrate that occasionally caused FermionLineProduct to be expanded incorrectly.
 Fixed a bug where
D0Expand would fail to return an analytic expression when trying to expand ScalarD0IR16 in certain cases (thanks, Christoph Bobeth).
Requirements
Any computer running Mathematica 8.0.4 or higher.
Recommended: Mathematica 10.1.0 or higher.
Note A bug was introduced in Mathematica 10.4.0 (fixed in 11.0.0) causing the numerical evaluation of Package‑X special functions compiled to the Wolfram Virtual Machine (e.g. ScalarC0 , ScalarD0 , ...) to take an excessive amount of time.
Installation Instructions
Uncompress downloaded file, and copy the Package‑X folder (/X) with all its contents to the folder $UserBaseDirectory/Applications/. See the primer for details.
Expansion Packs
CollierLink 1.0.0 
Interface to the COLLIER library for rapid numerical evaluation of PassarinoVeltman functions 
GPLv3 
Download  Documentation 
8.0+ 
TensorD (beta) 
Compute vector derivatives (gradients) of loop integrals 
CC by 4.0 
(by request) 
10.1+ 
PVReduce (beta) 
Reduce PassarinoVeltman functions to scalar functions without limiting to 4 dimensions, and without inserting explicit formulae 
CC by 4.0 
(by request) 
8.0+ 
To install an expansion pack, uncompress the downloaded file, and copy the directory with all its contents to the folder $UserBaseDirectory/Applications/ (but not inside the Package‑X directory itself).
