AnQCD: A Mathematica package for calculations in general analytic QCD models (new version announcement)

Abstract

A previously submitted Mathematica package (Ayala and Cvetič, 2015), which evaluates the QCD couplings in several analytic (holomorphic) versions of QCD, has been adjusted (anQCDv2.m) so that it now works in the newest version of Mathematica (version 11) as well. New version program summaryProgram Title: anQCDv2.m; and the supplementary packages s0r.m and Li__nu.mProgram Files doi:http://dx.doi.org/10.17632/vsnjr4bhr9.1Licensing provisions: GPLv3Programming language: Mathematica, versions 9, 10 and 11Supplementary material: file READMEanQCDv2Journal reference of previous version: Comput. Phys. Commun. 190 (2015) 182–199Does the new version supersede the previous version? For the use with Mathematica 11, yes.Reasons for the new version: The previous version (anQCD.m) does not work in Mathematica version 11.Summary of revisions: When calling the previous version (anQCD.m) with Mathematica 11, the message SystemException[“MemoryAllocationFailure”] appears, because version 11 of Mathematica apparently cannot deal efficiently with numerical dispersion integrals where the integration is over semiinfinite interval and is slowly converging. Therefore, in the new version, in the integrals J0[Nf] for the Two-delta analytic QCD model the upper integration bound is changed from ‘Infinity’ to $wmaxJ=108.5. This modification does not change the precision of evaluations in any significant manner.Nature of problem: Evaluation of spacelike physical QCD quantities D(Q2) (Q2≡−q2 nonnegative) in terms of a truncated perturbation series of the perturbative QCD coupling a(Q2)≡αs(Q2)∕π gives us a quantity which has singularities at low positive Q2, because a(Q2) has such singularities. This is incompatible with the holomorphic (analytic) properties of D(Q2) as required by the general principles of Quantum Field Theories. Further, for low |Q2| such evaluations give very unreliable results dominated by the vicinity of the mentioned (unphysical) singularities. However, if using instead a coupling A(Q2) which respects the mentioned analyticity properties in the complex Q2-plane, then such problems do not appear.Solution method: anQCDv2.m package evaluates the coupling A(Q2) and the analogs Aν(Q2) of the powers a(Q2)ν, for three versions of QCD with couplings with aforementioned analytic properties: Analytic Perturbation Theory (APT); Two-delta analytic QCD (2δanQCD); and Massive Perturbation Theory (MPT). The couplings are evaluated by numerical evaluation of the corresponding dispersion integrals.Reference:C. Ayala and G. Cvetič, anQCD: a Mathematica package for calculations in general analytic QCD models, Comput. Phys. Commun. 190 (2015) 182–199 [arXiv:1408.6868 [hep-ph]].