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arXiv · 2205.03142

On the analytically-improved running coupling in QCD

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 $\bar\alpha_t(Q^2=0)= 4 \pi /\beta_0$.

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F. T. Brandt, J. Frenkel, D. G. C. McKeon, G. S. S. Sakoda. 2022-05-06. On the analytically-improved running coupling in QCD. https://doi.org/10.1142/s0217732322500924

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