Package-X is hosted by Hepforge, IPPP Durham

Hiren H. Patel


Package-X is a Mathematica package to obtain compact analytic expressions for one-loop integrals in higher order calculations of relativistic quantum field theory in 4 spacetime dimensions.

               Technical features
  • Compute one-loop integrals with up to three propagators
  • Obtain analytic expressions for UV-divergent, IR-divergent and finite parts of one-loop dimensionally regulated integrals
  • Get results for any kinematic configuration (at zero external momentum, at physical threshold, etc.) with real masses and external invariants.
  • Numerical evaluations always consistent with the + prescription
  • Works for arbitrarily high-rank tensor integrals
  • Calculates traces of products of Dirac matrices in d dimensions
               User interface features
  • Complete set of help pages (accessed via the Documentation Center inside Mathematica)
  • Readable and intuitive input
  • Output easily manipulatable (copy/paste friendly) and readily evaluated numerically

Featured code snippets

Compute a rank-1 tensor integral:

Compute the trace over gamma matrices:

Calculate the Higgs to two gluons decay amplitude


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


Package-X is closed source and distributed under the standard CPC license agreement.

Latest release

v1.0.4: (October 12, 2015) Download
  • Scalar C function pvC[0,0,0,0,m^2,0,m,0,0] now reduces to the correct analytic expression by LoopRefine (thanks, Benjamin Lillard).
  • Simplify and FullSimplify no longer tries to bring the divergent and finite parts of LoopRefine output under a common denominator proportional to ϵ.
v1.0.3: (September 5, 2015, second release September 20, 2015) Download
  • Fixed bug in LoopIntegrate that lead to excessive evaluation times for integrands that used Projector due to uncontracted Lorentz four-vectors. (thanks, Shanmuka Shivashankara).
  • Various under-the-hood improvements.
  • (Second release) Fixed typos in Wolfram documentation help pages for LoopIntegrate and ϵ, and tutorial (thanks, Gregory Ovanesyan and Nicholas Rodd).
v1.0.2: (June 23, 2015) Download
  • Added option Organization to LoopRefine. Results can now be organized by tensor structures.
  • Improved performance of LoopRefine; (e.g. LoopRefine no longer sometimes hangs when the option ExplicitC0 -> All is set).
  • Transverse and Longitudinal no longer throw errors when three arguments are passed to them (Transverse and Longitudinal are no longer Listable).
  • Fixed typos / clarified certain points in Wolfram documentation help pages.
v1.0.1: (March 24, 2015) Download
  • Scalar C function pvC[0,0,0,0,0,s,0,0,m0] now reduces to the correct analytic expression by LoopRefine (thanks, Vladyslav Shtabovenko).
  • FrontEndObject::notavail warnings are no longer issued when Package-X is loaded without a front end.
v1.0.0: (March 6, 2015) Download


Any computer running Mathematica 8.0.4 or higher.

Installation Instructions

Uncompress downloaded file, and copy the Package-X folder (/X) with all its contents to the folder $UserBaseDirectory/Applications/. See the tutorial for details.


Get started with the tutorial (September 20, 2015).