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Manuscript Title: QCDMAPT F: Fortran version of QCDMAPT package
Authors: A.V. Nesterenko, C. Simolo
Program title: QCDMAPT F
Catalogue identifier: AEGP_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)2303
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: MATHLIB routine RADAPT (D102) from CERNLIB Program Library [1].

Does the new version supersede the previous version?: No. This version provides an alternative to the previous, Maple, version.

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 spectral functions represents a somewhat complicated task (see Sect. 3 and App. B of Ref. [4]), whereas their numerical evaluation requires a lot of computational resources and essentially slows down the overall computation process.

Solution method:
The developed package includes the calculated explicit expressions for relevant spectral functions up to the four-loop level and the subroutines for necessary integrals.

Reasons for 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 parameters (QCDMAPT_F.i1 and QCDMAPT_F.i2). The main program includes the definitions of relevant spectral functions and subroutines for necessary integrals. 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 input 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;
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 and J. Papavassiliou, J. Phys. G 32 (2006) 1025;
A.V. Nesterenko, Nucl. Phys. B (Proc. Suppl.) 186 (2009) 207.
[4] A.V. Nesterenko and C. Simolo, Comput. Phys. Commun. 181 (2010) 1769.