General gauge-Yukawa-quartic β-functions at 4-3-2-loop order

Davies, Joshua; Herren, Florian; Thomsen, Anders Eller

doi:10.1007/jhep01(2022)051

Cited by 21 publications

(18 citation statements)

References 51 publications

(109 reference statements)

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“…It also has the advantage that group indices can be kept arbitrary. It is our ambition to implement the full set of β-functions up to order 4-3-2 in RGBeta pending ongoing work with J. Davies and F. Herren [16].…”

Section: Discussionmentioning

confidence: 99%

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Introducing RGBeta: a Mathematica package for the evaluation of renormalization group $$ \beta $$-functions

Thomsen

2021

Eur. Phys. J. C

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In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $$ \beta $$ β -functions are known to the 3–2–2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply these results to realistic models without the use of dedicated computer tools. We describe a procedure for extracting $$ \beta $$ β -functions using the general results and introduce , a dedicated Mathematica package for extracting the $$ \overline{\text {MS}} $$ MS ¯ $$ \beta $$ β -functions in broad classes of models. The package and example notebooks are available from the GitHub repository.

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Section: Discussionmentioning

confidence: 99%

“…RGBeta was originally developed to test the general β-function basis used and developed in Ref. [12] and is used in ongoing work on higher-order β-functions [16]. It is an implementation of the generally applicable MS β-function formulas for gauge-Yukawa theories presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Introducing RGBeta: a Mathematica package for the evaluation of renormalization group $$ \beta $$-functions

Thomsen

2021

Eur. Phys. J. C

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“…[27]. The finite part of υ in the SM uniquely fixes two of the pure-Yukawa fermion coefficients: The Weyl consistency conditions derived from Osborn's Equation [27] with input from a (currently) partial reconstruction of the generic 4-3-2 β-functions [41], provides the independent constraint…”

Section: Flavor-improved Rg Functions In the Smmentioning

confidence: 99%

On Ambiguities and Divergences in Perturbative Renormalization Group Functions

Herren,

Thomsen

2021

Preprint

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There is an ambiguity in choosing field-strength renormalization factors in the 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.

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“…While two-loop β-functions for the most general four-dimensional QFT have been known for almost four decades [6][7][8][9], higher orders only became available recently. The gauge coupling β-function for the most general QFT has been computed at three loops [10,11] and this year even the four-loop gauge coupling and threeloop Yukawa β-functions have become available [12,13].…”

Section: Introductionmentioning

confidence: 99%