Renormalization of dimension-six operators relevant for the Higgs decays $h\rightarrow \gamma\gamma,\gamma Z$

TL;DR

This paper calculates the one-loop renormalization of dimension-six operators affecting Higgs decays to photons and Z bosons, showing no log-enhanced mixing from current-current operators and highlighting the role of fermion dipole operators.

Contribution

It provides a simplified calculation of operator mixing for Higgs decay processes and clarifies the absence of certain log-enhanced effects in the renormalization group evolution.

Findings

No mixing from current-current operators leading to log-enhanced effects.

RG mixing from operators with Wilson coefficients of one-loop size.

Fermion dipole-moment operators can influence Higgs decay amplitudes.

Abstract

The discovery of the Higgs boson has opened a new window to test the SM through the measurements of its couplings. Of particular interest is the measured Higgs coupling to photons which arises in the SM at the one-loop level, and can then be significantly affected by new physics. We calculate the one-loop renormalization of the dimension-six operators relevant for $h\rightarrow \gamma\gamma, \gamma Z$, which can be potentially important since it could, in principle, give log-enhanced contributions from operator mixing. We find however that there is no mixing from any current-current operator that could lead to this log-enhanced effect. We show how the right choice of operator basis can make this calculation simple. We then conclude that $h\rightarrow \gamma\gamma, \gamma Z$ can only be affected by RG mixing from operators whose Wilson coefficients are expected to be of one-loop size, among them fermion dipole-moment operators which we have also included.