anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models

详细信息    查看全文

• 作者：Cé ; sar Ayala^a ; ^{c.ayala86@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Gorazd Cvetič^b ; ^{gorazd.cvetic@usm.cl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Analytic (holomorphic) QCD coupling ; Fractional Analytic Perturbation Theory ; Two-delta analytic QCD model ; Massive Perturbation Theory ; Perturbative QCD ; Renormalization group evolution
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：199
• 期：Complete
• 页码：114-117
• 全文大小：373 K

文摘

We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings A_ν(Q²)${\mathcal{A}}_{\nu }\left(Q^2\right)$ for complex or real squared momenta Q²$Q^2$. These couplings are holomorphic analogs of the powers a(Q²)^ν$a{\left(Q^2\right)}^{\nu }$ of the underlying perturbative QCD (pQCD) coupling a(Q²)≡α_s(Q²)/π$a\left(Q^2\right)\equiv {\alpha }_s\left(Q^2\right)/\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2δ$\delta$anQCD), and Massive Perturbation Theory (MPT). The index ν$\nu$ can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran.

Program summary

Program title: AanQCDext

Catalogue identifier: AEYK_v1_0

Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYK_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 12105

No. of bytes in distributed program, including test data, etc.: 98822

Distribution format: tar.gz

Programming language: Fortran.

Computer: Any work-station or PC where Fortran 95/2003/2008 (gfortran) is running.

Operating system: Operating system Linux (Ubuntu and Scientific Linux), Windows (in all cases using gfortran).

Classification: 11.1, 11.5.

Nature of problem:   Calculation of values of the running analytic couplings A_ν(Q²;N_f)${\mathcal{A}}_{\nu }(Q^2;N_f)$ for general complex squared momenta Q²≡−q²$Q^2\equiv -q^2$, in three analytic QCD models, where A_ν(Q²;N_f)${\mathcal{A}}_{\nu }(Q^2;N_f)$ is the analytic (holomorphic) analog of the power (α_s(Q²;N_f)/π)^ν${({\alpha }_s(Q^2;N_f)/\pi )}^{\nu }$. Here, A_ν(Q²;N_f)${\mathcal{A}}_{\nu }(Q^2;N_f)$ is a holomorphic function in the Q²$Q^2$ complex plane, with the exception of the negative semiaxis $(-\infty ,-M_{\mathrm{thr}}^2]$, reflecting the analyticity properties of the spacelike renormalization invariant quantities D(Q²)$D\left(Q^2\right)$ in QCD. In contrast, the perturbative QCD power (α_s(Q²;N_f)/π)^ν${({\alpha }_s(Q^2;N_f)/\pi )}^{\nu }$ has singularities even outside the negative semiaxis (Landau ghosts). The three considered models are: Analytic Perturbation theory (APT); Two-delta analytic QCD (2δ$\delta$anQCD); Massive Perturbation Theory (MPT). We refer to Ref. [1] for more details and literature.

Solution method:   The Fortran programs for FAPT and 2δ$\delta$anQCD models contain routines and functions needed to perform two-dimensional numerical integrations involving the spectral function, in order to evaluate A_ν(Q²)${\mathcal{A}}_{\nu }\left(Q^2\right)$ couplings. In MPT model, one-dimensional numerical integration involving A₁(Q²)${\mathcal{A}}_1\left(Q^2\right)$ is sufficient to evaluate any A_ν(Q²)${\mathcal{A}}_{\nu }\left(Q^2\right)$ coupling.

Restrictions:   For unphysical choices of the input parameters the results are meaningless. When Q²$Q^2$ is close to the cut region of the couplings (Q²$Q^2$ real negative), the calculations can take more time and can have less precision.

Running time:   For evaluation of a set of about 10 related couplings, the times vary in the range t∼10¹–10²$t\sim {10}^1\text{–}{10}^2$ s. MPT requires less time, t∼1–10¹$t\sim 1\text{–}{10}^1$ s.

References:

[1]

C. Ayala and G. Cvetic, anQCD: a Mathematica package for calculations in general analytic QCD models, Comput. Phys. Commun. 190 (2015) 182. arXiv:1408.6868 [hep-ph].