Renormalization Group Scaling of Higgs Operators and Γ(h -> γγ)

TL;DR

The paper studies how dimension-six Higgs–gauge operators in a SM EFT renormalize and mix under RG flow, focusing on operators that modify $h\to\gamma\gamma$ and $h\to Z\gamma$ at tree level. It computes the one-loop anomalous-dimension matrix for a specific bosonic operator basis and shows that operator mixing, notably between $O_{WB}$ and the diphoton/higgs operators, can substantially alter NP contributions to Higgs decays, sometimes dominating direct matching effects. The work also revises the connection between the S parameter and Higgs observables by incorporating full RG evolution, deriving explicit relations that tie $S$ to $\mu_{\gamma\gamma}$ and $\mu_{\gamma Z}$ and demonstrating that RG effects can weaken or enhance EWPD constraints. The findings emphasize that a RG-consistent EFT treatment is essential for reliable Higgs phenomenology and global NP analyses, and they provide a framework to interpret potential deviations in $\Gamma(h\to\gamma\gamma)$ within a broader, scale-aware NP context, including pseudo-Nambu-Goldstone Higgs scenarios.

Abstract

We compute the renormalization of dimension six Higgs-gauge boson operators that can modify Γ(h -> γγ) at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consistent with renormalization group evolution. We study the implications of our results for Higgs phenomenology and for new physics models which attempt to explain a deviation in Γ(h -> γγ). We derive a new relation between the S parameter and the Γ(h -> γγ) and Γ(h ->Z γ) decay rates.

Figures (2)

• Figure 1: One-loop diagrams for the renormalization of the operators in Eq. (\ref{['ops']}). Graph (e) has a partner graph where the loop is on the other gauge boson line. Graphs (g,h,i,j) have partner graphs where the gauge bosons couple to the incoming scalar line. Wavefunction graphs have not been shown. Here, the complex scalar field is shown as a dashed line, while the gauge fields are shown as wavy lines; in each diagram, the gauge fields are the $B$ or $W^a$ fields depending on the operator considered.
• Figure 2: Plot of the top-Yukawa renormalization factor $r(\mu)$ vs $\mu$ in GeV.