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.
User interface 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 +iε prescription
- Works for arbitrarily high-rank tensor integrals
- Calculates traces of products of Dirac matrices in d dimensions
- 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),
Package-X is closed source and distributed under the standard CPC license agreement.
v1.0.4: (October 12, 2015) Download
v1.0.3: (September 5, 2015, second release September 20, 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).
FullSimplify no longer tries to bring the divergent and finite parts of
LoopRefine output under a common denominator proportional to
v1.0.2: (June 23, 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
ϵ, and tutorial (thanks, Gregory Ovanesyan and Nicholas Rodd).
v1.0.1: (March 24, 2015) Download
- Added option
LoopRefine. Results can now be organized by tensor structures.
- Improved performance of
LoopRefine no longer sometimes hangs when the option
ExplicitC0 -> All is set).
Longitudinal no longer throw errors when three arguments are passed to them (
Longitudinal are no longer
- Fixed typos / clarified certain points in Wolfram documentation help pages.
v1.0.0: (March 6, 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.
Any computer running Mathematica 8.0.4 or higher.
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).