Structure of two-loop SMEFT anomalous dimensions via on-shell methods
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Springer
Received: June 22, Revised: September 9, Accepted: September 11, Published: October 30,
2020 2020 2020 2020
Zvi Bern, Julio Parra-Martinez and Eric Sawyer Mani L. Bhaumik Institute for Theoretical Physics, UCLA Department of Physics and Astronomy, Los Angeles, CA 90095, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of this analysis we verify a variety of one-loop SMEFT anomalous dimensions computed by Alonso, Jenkins, Manohar and Trott. Keywords: Beyond Standard Model, Effective Field Theories, Renormalization Group, Scattering Amplitudes ArXiv ePrint: 2005.12917v1
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)211
JHEP10(2020)211
Structure of two-loop SMEFT anomalous dimensions via on-shell methods
Contents 1 Introduction
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3 One-loop amplitudes and anomalous dimensions 3.1 One-loop amplitudes from generalized unitarity 3.2 One-loop UV anomalous dimensions 3.3 Structure of one-loop amplitudes and rational terms
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4 Two-loop zeros in the anomalous dimension matrix 4.1 Zeros from length selection rules 4.2 Zeros from vanishing one-loop rational terms 4.2.1 Oψ4 ← OD2 ϕ4 4.2.2 OD2 ϕ4 ← O(ψ4 )1 4.2.3 General comments about scheme redefinition 4.3 Zeros from color selection rules 4.3.1 Oϕ2 F 2 ← Oψ4 4.4 Outlook on additional zeros
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5 Implications for the SMEFT 5.1 Mapping our theory to the SMEFT 5.2 Verification of one-loop anomalous dimensions 5.3 Two-loop implications
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6 Conclusions
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A Integral reduction via gauge-invariant tensors
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B Tree-level and one-loop amplitudes B.1 Four-vector amplitudes B.2 Four-fermion amplitudes B.3 Four-scalar amplitudes B.4 Two-fermion, two-vector amplitudes B.5 Two-scalar, two-vector amplitudes B.6 Two-fermion, two-scalar amplitudes
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JHEP10(2020)211
2 Setup and formalism 2.1 Conventions and basic setup 2.2 Anomalous dimensions from UV divergences 2.3 Anomalous dimensions directly from unitarity cuts 2.3.1 Simplifying strategies 2.4 Comments on evanescent operators 2.5 Anomalous dimensions and non-interference
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Introduction
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JHEP10(2020)211
Effective Field Theory (EFT) approaches have risen to prominence in recent years as a systematic means for quantifying new physics beyond the Standard Model. The Standard Model Effective Field Theory (SMEFT) incorporates the effects of
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