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Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence

Elizabeth E. Jenkins, Aneesh V. Manohar, Michael Trott

TL;DR

The paper addresses the renormalization-group evolution of Standard Model dimension-six operators in the SMEFT, focusing on the Yukawa-dependence of the one-loop anomalous dimension matrix. It computes the complete $y^2$ and $y^4$ contributions (in the gauge-decoupled limit) to the operator mixing, revealing non-trivial flavor structure across the eight operator classes. The results show how Yukawa-induced mixing can feed into Higgs-fermion couplings and dipole operators, with implications for flavor-violating processes such as $\mu \to e \gamma$ and for interpreting precision Higgs data within SMEFT. These RG effects refine the interpretation of current flavor-violation limits and inform potential symmetry-based explanations of flavor, while leaving gauge-term contributions for subsequent work. Overall, the work provides essential inputs for accurate SMEFT phenomenology and flavor physics analyses.

Abstract

We calculate the complete order y^2 and y^4 terms of the 59 x 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order lambda, lambda^2 and lambda y^2 depending on the Standard Model Higgs self-coupling lambda which were calculated in a previous work, yield the complete one-loop anomalous dimension matrix in the limit of vanishing gauge couplings. The Yukawa contributions result in non-trivial flavor mixing in the various operator sectors of the Standard Model effective theory.

Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence

TL;DR

The paper addresses the renormalization-group evolution of Standard Model dimension-six operators in the SMEFT, focusing on the Yukawa-dependence of the one-loop anomalous dimension matrix. It computes the complete and contributions (in the gauge-decoupled limit) to the operator mixing, revealing non-trivial flavor structure across the eight operator classes. The results show how Yukawa-induced mixing can feed into Higgs-fermion couplings and dipole operators, with implications for flavor-violating processes such as and for interpreting precision Higgs data within SMEFT. These RG effects refine the interpretation of current flavor-violation limits and inform potential symmetry-based explanations of flavor, while leaving gauge-term contributions for subsequent work. Overall, the work provides essential inputs for accurate SMEFT phenomenology and flavor physics analyses.

Abstract

We calculate the complete order y^2 and y^4 terms of the 59 x 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order lambda, lambda^2 and lambda y^2 depending on the Standard Model Higgs self-coupling lambda which were calculated in a previous work, yield the complete one-loop anomalous dimension matrix in the limit of vanishing gauge couplings. The Yukawa contributions result in non-trivial flavor mixing in the various operator sectors of the Standard Model effective theory.

Paper Structure

This paper contains 18 sections, 71 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Formalism
  3. Discussion
  4. Conclusion
  5. Results
  6. $X^3$
  7. $H^6$
  8. $H^4D^2$
  9. $X^2H^2$
  10. $\psi^2 H^3$
  11. $\psi^2 X H$
  12. $\psi^2 H^2 D$
  13. $\psi^4$
  14. $(\overline L L) (\overline L L)$
  15. $(\overline R R) (\overline R R)$
  16. ...and 3 more sections

Figures (1)

  • Figure 1: A selection of graphs contributing to the one-loop anomalous dimension matrix. The solid square is a $\mathcal{L}^{(6)}$ vertex, and the dots are SM vertices. Some graphs containing gauge fields contribute to the anomalous dimension matrix in the limit $g^2 \to 0$ in the rescaled operator basis used for power counting. The first graph leads to anomalous dimension contributions seven pages long when all flavor combinations are evaluated.