On the analytically-improved running coupling in QCD

F. T. Brandt; J. Frenkel; D. G. C. McKeon; G. S. S. Sakoda

doi:10.1142/S0217732322500924

On the analytically-improved running coupling in QCD

High Energy Physics - Theory 2022-07-27 v1 High Energy Physics - Phenomenology

Authors: F. T. Brandt , J. Frenkel , D. G. C. McKeon , G. S. S. Sakoda

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Abstract

We examine, in the `t Hooft renormalization scheme, the analytic running coupling $\bar\alpha_t(Q^2)$ in QCD, using the two-loop $\beta$ -function with positive expansion parameters $\beta_0$ and $\beta_1$ . An exact integral representation is derived for this causal coupling, which is fully expressed in terms of the imaginary part of the Lambert function $W$ . This integral form manifestly accounts for the universal value of the infrared limit $\bar\alpha_t(Q^2=0)= 4 \pi /\beta_0$ .

Keywords

qcd coupling constant

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@article{arxiv.2205.03142,
  title  = {On the analytically-improved running coupling in QCD},
  author = {F. T. Brandt and J. Frenkel and D. G. C. McKeon and G. S. S. Sakoda},
  journal= {arXiv preprint arXiv:2205.03142},
  year   = {2022}
}

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9 pages, one figure; accepted for publication in Modern Physics Letters A

On the analytically-improved running coupling in QCD

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