|Compute the transverse part of the QED vacuum polarization tensor:|
|Its series expansion near q2 = 0:|
|Compute the QED vertex function:|
|Compute the UV-divergent part of the QCD vacuum polarization function in general covariant Rξ gauges:|
|Compute the massless one loop scalar four-point integral in 6 dimensions:|
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),
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).
Serieswould occasionally incorrectly expand
DiscBat zero external momentum (thanks, Camilo Garcia Cely).
LoopRefineSerieswould not convert its input to analytic expressions when the input was independent of the expansion parameter (thanks, Prasenjit Sanyal).
General::optberror messages to be generated at initialization in earlier versions of Mathematica (thanks, Prasenjit Sanyal).
Transverseno longer have
HoldFirstattribute, since it used to interfere with simplification routines of other tensor algebraic functions like
LoopIntegratenow correctly applies Sirlin identities to
FermionLineProductinvolving massive spinors (thanks, Matteo Fael).
FermionLineExpandno longer avoids applying spinor equations of motion when downvalues to scalar products are assigned.
FermionLineExpandmore completely simplifies
LoopRefineno longer gives
FermionLineExpandand other tensor manipulation routines would drop the quadruply contracted Levi-Civita symbol (thanks, Matthew Kirk).
FermionLineProductwould fail to automatically expand over deeply nested sums over
Serieswould incorrectly expand
DiscBaround normal threshold.
pvC0IR6are now named
ScalarC0IR6, respectively, consistent with the naming convention of capitalizing the first letter of pre-defined symbols.
LoopIntegratenow normalizes its integration measure so that e-γ ϵ is factored out instead of rΓ. This is to prepare Package-X for computing two loop integrals in the future. This only changes the output of
LoopRefinefor integrals exhibiting 1/ϵ2 poles, arising from overlapping soft and collinear divergences, by an amount proportional to ~π2/12 to the finite part.
pvC0) has been changed to match that of FeynCalc, LoopTools, and essentially all other authors in the literature (Sorry to v1.0 users who struggled to match against literature!). The relations are
PVC[r,n1,n2,s1,s12,s2,m0,m1,m2] = pvC[r,n1,n2,s1,s2,s12,m2,m1,m0]and
ScalarC0[s1,s12,s2,m0,m1,m2] = pvC0[s1,s2,s12,m2,m1,m0]
ScalarC0is now a function defined manifestly in four dimensions, and will return
ComplexInfinityfor cases that are IR divergent. The related function
PVC[0,0,0, args]lives in d dimensions, and will yield 1/ϵ poles by
LoopRefinefor IR divergent cases.
X`OneLoop`are deprecated; all package symbols now belong to a common context
pvbis now obsolete, and is covered by higher weight
μRis now denoted with
\[Micro]), and entered with the keyboard alias
PVD, and the three-point functions
ScalarC0are generated with the updated ordering for their arguments.
LoopRefinegenerates expressions with
µdenoting the dimensional regularization scale, and with the updated normalization affecting integrals with overlapping soft and collinear IR divergences. Since legacy syntax of
LoopIntegrateis still possible and the syntax of
LoopRefineis unchanged, rerunning code with v2.0 in notebooks that used v1.0 should update expressions reflecting the changes. You may download v1.0.4 here, but it is no longer supported.