QCDMAPT_F: Fortran version of QCDMAPT package

arXiv:1107.1045v1 [hep-ph] 6 Jul 2011 QCDMAPT F: Fortran version of QCDMAPT package A.V. Nesterenkoa,∗, C. Simolob aBLTPh, Joint Institute for Nuclear Research, Dubna, 141980, Russian Federation bISAC–CNR, I–40129, Bologna, Italy Abstract The QCDMAPT program package facilitates computations in the framework of dispersive approach to Quantum Chromodynamics. The QCDMAPT F version of this package enables one to perform such computations with For- tran, whereas the previous version was developed for use with Maple system. The QCDMAPT F package possesses the same basic features as its previous version. Namely, it embodies the calculated explicit expressions for relevant spectral functions up to the four–loop level and the subroutines for necessary integrals. NEW VERSION PROGRAM SUMMARY Manuscript Title: QCDMAPT F: Fortran version of QCDMAPT package Authors: A.V. Nesterenko and C. Simolo Program Title: QCDMAPT F Journal Reference: Comput. Phys. Comm. 182 (2011) 2303–2304 Catalogue identifier: AEGP v2 0 Programming language: Fortran 77 and higher Computer: Any which supports Fortran 77 Operating system: Any which supports Fortran 77 Keywords: Nonperturbative QCD; Dispersion relations Classification: 11.1, 11.5, 11.6 External routines/libraries: MATHLIB routine RADAPT (D102) from CERNLIB Program Library [1]. Catalogue identifier of previous version: AEGP v1 0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1769– 1775 ∗Corresponding author. E-mail address: nesterav@theor.jinr.ru Does the new version supersede the previous version?: No Nature of problem: A central object of the dispersive (or “analytic”) approach to Quantum Chromodynamics [2, 3] is the so–called spectral function, which can be calculated by making use of the strong running coupling. At the one–loop level the latter has a quite simple form and the relevant spectral function can easily be calculated. However, at the higher loop levels the strong running coupling has a rather cumbersome structure. Here, the explicit calculation of corresponding spec- tral functions represents a somewhat complicated task (see Sect. 3 and App. B of Ref. [4]), whereas their numerical evaluation requires a lot of computational re- sources and essentially slows down the overall computation process. Solution method: The developed package includes the calculated explicit expres- sions for relevant spectral functions up to the four–loop level and the subroutines for necessary integrals. Reasons for the new version: The previous version of the package (Ref. [4]) was developed for use with Maple system. The new version is developed for Fortran programming language. Summary of revisions: The QCDMAPT F package consists of the main program (QCDMAPT F.f) and two samples of the file containing the values of input pa- rameters (QCDMAPT F.i1 and QCDMAPT F.i2). The main program includes the definitions of relevant spectral functions and subroutines for necessary inte- grals. The main program also provides an example of computation of the values of (M)APT spacelike/timelike expansion functions for the specified set of input parameters and (as an option) generates the output data files with values of these functions over the given kinematic intervals. Additional comments: For the proper functioning of QCDMAPT F package, the “MATHLIB” CERNLIB library [1] has to be installed. Running time: The running time of the main program with sample set of in- put parameters specified in the file QCDMAPT F.i2 is about a minute (depends on CPU). References [1] Subroutine D102 of the “MATHLIB” CERNLIB library, URL addresses: http://cernlib.web.cern.ch/cernlib/mathlib.html http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/d102/top.html [2] D.V. Shirkov and I.L. Solovtsov, Phys. Rev. Lett. 79 (1997) 1209; K.A. Milton and I.L. Solovtsov, Phys. Rev. D 55 (1997) 5295; K.A. Milton and I.L. Solovtsov, Phys. Rev. D 59 (1999) 107701; 2 I.L. Solovtsov and D.V. Shirkov, Theor. Math. Phys. 120 (1999) 1220; D.V. Shirkov and I.L. Solovtsov, Theor. Math. Phys. 150 (2007) 132. [3] A.V. Nesterenko, Phys. Rev. D 62 (2000) 094028; A.V. Nesterenko, Phys. Rev. D 64 (2001) 116009; A.V. Nesterenko, Int. J. Mod. Phys. A 18 (2003) 5475; A.V. Nesterenko, Nucl. Phys. B (Proc. Suppl.) 133 (2004) 59; A.V. Nesterenko and J. Papavassiliou, J. Phys. G 32 (2006) 1025; A.V. Nesterenko, Nucl. Phys. B (Proc. Suppl.) 186 (2009) 207; A.V. Nesterenko, arXiv:1106.4006 [hep-ph]. [4] A.V. Nesterenko and C. Simolo, Comput. Phys. Commun. 181 (2010) 1769. 3

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