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On Ambiguities and Divergences in Perturbative Renormalization Group Functions
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abstract
There is an ambiguity in choosing field-strength renormalization factors in the $ \overline{\text{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 $ \beta $-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa $ \beta $-functions and provide the first calculation of the flavor-improved 3-loop SM $ \beta $-functions in the gaugeless limit.
Forward citations
Cited by 4 Pith papers
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On the Renormalization Group in EFTs: On-Shell Bases, Ambiguities, and Divergences
Two-loop RG divergences in on-shell EFT bases are spurious: they vanish when non-minimal source terms are included, leaving only unphysical flavor-rotation flow.
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Gradient RG Flow in Scalar-Fermion QFTs
RG flow in scalar-fermion theories is gradient through four loops only when the 'beta shift' is included, via over a thousand scheme-independent constraints that hold wherever current data allow a check.
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Renormalization of general Effective Field Theories: Formalism and renormalization of bosonic operators
The authors compute, for the first time, the one-loop renormalization group equations of the bosonic operators of a completely general EFT up to mass dimension 6.
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Gradient properties of $\varphi^3$ in $d=6-\varepsilon$
The d = 6 gradient (A-function) structure of the phi^3 RG flow extends to d = 6 − epsilon, requiring one new three-loop constraint, Eq. (22), that the MS coefficients satisfy.
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