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arXiv 1204.2679hep-phhep-thmath-phmath.MP
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FAPT：用于QCD分数阶解析摄动理论计算的Mathematica软件包

FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

Alexander P. Bakulev, Vyacheslav L. Khandramai

备注：
23 pages, 6 figures. Citations added. Now it matches version approved for publication in Comp. Phys. Commun
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摘要：

我们在这里提供了计算闵可夫斯基强耦合常幂的解析图像所需的\texttt{Mathematica}中的所有步骤（${\bar{\mathfrak A}_ν(s;n_f)}$和${\mathfrak A_ν^\text{glob}(s)}$）和欧几里得（${\bar{\mathcal A}_ν(Q^2;n_f)}$和${\mathcal A_ν^\text{glob}(Q^2)}$）域在任意能量尺度（${s}$和${Q^2}$，相应地）对于两个方案-具有固定数量的活动味${n_f=3, 4, 5, 6}$和考虑所有重夸克阈值的全局味。这些无奇性耦合是QCD中分析微扰理论（APT）及其推广--分数APT的必然元素，需要将APT命令应用于重整化群改进的强子观测量。

英文摘要：

We provide here all the procedures in \texttt{Mathematica} which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (${\bar{\mathfrak A}_ν(s;n_f)}$ and ${\mathfrak A_ν^\text{glob}(s)}$) and Euclidean (${\bar{\mathcal A}_ν(Q^2;n_f)}$ and ${\mathcal A_ν^\text{glob}(Q^2)}$) domains at arbitrary energy scales (${s}$ and ${Q^2}$, correspondingly) for both schemes --- with fixed number of active flavours ${n_f=3, 4, 5, 6}$ and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD and its generalization --- Fractional APT, needed to apply the APT imperative for renormalization-group improved hadronic observables.

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