Explicit solutions for effective four- and five-loop QCD running coupling

Details Explicit solutions for effective four- and five-loop QCD running coupling Explicit solutions for effective four- and five-loop QCD running coupling

2011-10-12

arxiv.org/abs/1110.2545v2

JHEP 1112:019,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

21 pages, 13 figures; in v2, minor changes in the text, two figures added, ref.[3] (2nd entry) is new; version to appear in JH

Scientific paper

10.1007/JHEP12(2011)019

We start with the explicit solution, in terms of the Lambert W function, of the renormalization group equation (RGE) for the gauge coupling in the supersymmetric Yang-Mills theory described by the well-known beta function of Novikov et al.(NSVZ). We then construct a class of beta functions for which the RGE can be solved in terms of the Lambert W function. These beta functions are expressed in terms of a function which is a truncated Laurent series in the inverse of the gauge coupling. The parameters in the Laurent series can be adjusted so that the first coefficients of the Taylor expansion of the beta function in the gauge coupling reproduce the four-loop or five-loop QCD (or SQCD) beta function.

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