Renormalization Group Evolution from On-shell SMEFT

Abstract

We describe the on-shell method to deriving the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 $H^4{D}^4$ operators to the running of $V^{+}{V}^{-}{H}^2$ operators, as well as the running of $B^{+}{B}^{-}{H}^2{D}^{2n}$ from $H^4{D}^{2n+4}$ for general $n$.

arXiv comment19 page, 2 figures

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Cited by in corpus (26)

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• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Building blocks of the flavourful SMEFT RG
• On-shell effective theory for higher-spin dark matter
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• RG of GR from On-shell Amplitudes
• EFT matching from analyticity and unitarity
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• Gearing up for the next generation of LFV experiments, via on-shell methods
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• Amplitudes and partial wave unitarity bounds
• Renormalising the Field-Space Geometry
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• Constructing the general partial waves and renormalization in EFT