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anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models. (English) Zbl 1344.81008

Summary: We provide three programs which evaluate the QCD analytic (holomorphic) couplings \(\mathcal{A}_\nu(Q^2)\) for complex or real squared momenta \(Q^2\). These couplings are holomorphic analogs of the powers \(a(Q^2)^\nu\) of the underlying perturbative QCD (pQCD) coupling \(a(Q^2) \equiv \alpha_s(Q^2) / \pi\), in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2\(\delta\)anQCD), and Massive Perturbation Theory (MPT). The index \(\nu\) can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously [“anQCD: a mathematica package for calculations in general analytic QCD models”, Comput. Phys. Commun. 190, 182–199 (2015; doi:10.1016/j.cpc.2014.12.024)], but are now written in Fortran.

MSC:

81-04 Software, source code, etc. for problems pertaining to quantum theory
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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References:

[1] Bakulev, A. P.; Mikhailov, S. V.; Stefanis, N. G., QCD analytic perturbation theory: From integer powers to any power of the running coupling, Phys. Rev. D. Phys. Rev. D, Phys. Rev. D. Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, Phys. Rev. D. Phys. Rev. D. Phys. Rev. D, Phys. Rev. D. Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, Phys. Rev. D, J. High Energy Phys., 1006, 085 (2010), arXiv:1004.4125 [hep-ph] · Zbl 1288.81139
[2] Ayala, C.; Contreras, C.; Cvetič, G., Extended analytic QCD model with perturbative QCD behavior at high momenta, Phys. Rev. D, 85, Article 114043 pp. (2012), arXiv:1203.6897 [hep-ph]
[3] Ayala, C.; Cvetič, G., anQCD: a mathematica package for calculations in general analytic QCD models, Comput. Phys. Comm., 190, 182 (2015), arXiv:1408.6868 [hep-ph]
[4] Cvetič, G.; Villavicencio, C., Operator product expansion with analytic QCD in tau decay physics, Phys. Rev. D, 86, Article 116001 pp. (2012), arXiv:1209.2953 [hep-ph]
[5] Shirkov, D. V., ‘Massive’ Perturbative QCD, regular in the IR limit, Phys. Part. Nucl. Lett., 10, 186 (2013), arXiv:1208.2103 [hep-th]
[6] Simonov, Yu. A., Perturbative theory in the nonperturbative QCD vacuum, Phys. Atom. Nucl.. Phys. Atom. Nucl., Yad. Fiz., 58, 113 (1995), arXiv:hep-ph/9311247 Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism, arXiv:1011.5386 [hep-ph]
[7] Badalian, A. M., Strong coupling constant in coordinate space, Phys. Atom. Nucl.. Phys. Atom. Nucl., Yad. Fiz., 63, 2269 (2000)
[8] Ayala, C.; Cvetič, G., Mathematica and Fortran programs for various analytic QCD couplings, J. Phys. Conf. Ser., 608, 1, 012064 (2015), arXiv:1411.1581 [hep-ph]
[9] Solovtsov, I. L.; Shirkov, D. V., Analytic approach to perturbative QCD and renormalization scheme dependence, Phys. Lett. B, 442, 344-348 (1998) · Zbl 1118.81075
[10] Nesterenko, A. V., Adler function in the analytic approach to QCD, eConf C. eConf C, Nucl. Phys. Proc. Suppl., 186, 207 (2009), arXiv:0808.2043 [hep-ph]
[11] Nesterenko, A. V.; Simolo, C., \(QCDMAPT_F\): Fortran version of QCDMAPT package, Comput. Phys. Comm., 182, 2303 (2011), arXiv:1107.1045 [hep-ph]
[12] Nesterenko, A. V.; Simolo, C., QCDMAPT: Program package for Analytic approach to QCD, Comput. Phys. Comm., 181, 1769 (2010), arXiv:1001.0901 [hep-ph] · Zbl 1219.81246
[13] Bakulev, A. P.; Khandramai, V. L., FAPT: a Mathematica package for calculations in QCD fractional analytic perturbation theory, Comput. Phys. Comm., 184, 1, 183 (2013) · Zbl 1296.81123
[14] Kotikov, A. V.; Krivokhizhin, V. G.; Shaikhatdenov, B. G., Analytic and ‘frozen’ QCD coupling constants up to NNLO from DIS data, Phys. Atom. Nucl., 75, 507 (2012), arXiv:1008.0545 [hep-ph]
[16] Ayala, C.; Mikhailov, S. V., How to perform a QCD analysis of DIS in Analytic Perturbation Theory, Phys. Rev. D, 92, 1, Article 014028 pp. (2015), arXiv:1503.00541 [hep-ph]
[17] Chetyrkin, K. G.; Kniehl, B. A.; Steinhauser, M., Strong coupling constant with flavor thresholds at four loops in the \(\overline{MS}\) scheme, Phys. Rev. Lett.. Phys. Rev. Lett., Nuclear Phys. B, 510, 61 (1998)
[18] Cvetič, G.; Kotikov, A. V., Analogs of noninteger powers in general analytic QCD, J. Phys. G, 39, Article 065005 pp. (2012), arXiv:1106.4275 [hep-ph]
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