Abstract
There is an ambiguity in choosing field-strength renormalization factors in the overline{mathrm{MS}} scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved β-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa β-functions and provide the first calculation of the flavor-improved 3-loop SM β-functions in the gaugeless limit.
Highlights
It was in connection with the 3-loop calculation of the SM matrix Yukawa βfunctions [9, 13] that the ambiguity subject to our investigation made its first appearance
We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry
We show that said divergences are related to GF, the global flavor symmetry of the kinetic terms of the matter fields
Summary
We begin with a rather long-winded review of the LRG, the purpose of which is twofold: there is a lot of notation to be introduced, not all of which is standard(ized) even among those working with the LRG; and many readers may be unfamiliar with the framework. We take this opportunity to spell out the inclusion of field sources in the framework
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