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arXiv · hep-th/9604114

Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory

M. Bonini·G. Marchesini·M. Simionato
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Abstract

We discuss the relation between the Gell-Mann-Low beta function and the ``flowing couplings'' of the Wilsonian action $S_Ł[ϕ]$ of the exact renormalization group (RG) at the scale $Ł$. This relation involves the ultraviolet region of $Ł$ so that the condition of renormalizability is equivalent to the Callan-Symanzik equation. As an illustration, by using the exact RG formulation, we compute the beta function in Yang-Mills theory to one loop (and to two loops for the scalar case). We also study the infrared (IR) renormalons. This formulation is particularly suited for this study since: $i$) $Ł$ plays the rôle of a IR cutoff in Feynman diagrams and non-perturbative effects could be generated as soon as $Ł$ becomes small; $ii$) by a systematical resummation of higher order corrections the Wilsonian flowing couplings enter directly into the Feynman diagrams with a scale given by the internal loop momenta; $iii$) these couplings tend to the running coupling at high frequency, they differ at low frequency and remain finite all the way down to zero frequency.

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M. Bonini, G. Marchesini, M. Simionato. 1996-04-19. Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory. https://doi.org/10.1016/s0550-3213(96)00571-8

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