Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence

TL;DR

This paper computes the one-loop anomalous dimension matrix for dimension-six operators in the Standard Model, including lambda and y couplings, revealing operator mixing effects and their impact on parameter evolution.

Contribution

It provides the first complete calculation of the one-loop anomalous dimensions of all dimension-six operators in the Standard Model, including lambda and y dependence.

Findings

Calculated the 59 x 59 anomalous dimension matrix at one-loop order.

Identified operator mixing effects due to equations of motion.

Analyzed the impact of dimension-six operators on Standard Model parameter running.

Abstract

We calculate the order \lambda, \lambda^2 and \lambda y^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where \lambda and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.