Solving RG equations with the Lambert W function

Abstract

It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed point to construct RG invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for the O(N) linear sigma model in four dimensions.

14 pages, 4 figures; errors corrected, relevant references added, 3 figures added

References in corpus (3)

• Can the QCD running coupling have a causal analyticity structure?
• Analytic Invariant Charge in QCD
• Renormalization Group Functional Equations

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