A log story short: running contributions to radiative Higgs decays in the SMEFT

TL;DR

This paper explores the renormalization of Higgs radiative decays within the SMEFT framework at dimension eight, highlighting potential observable effects at future high-energy experiments that could reveal new physics insights.

Contribution

It provides the first detailed analysis of dimension-eight operators' effects on Higgs radiative decays, especially on the $h\to \gamma Z$ process, including tree-level matching conditions.

Findings

Dimension-eight operators can induce $h\to \gamma Z$ decay at tree level.

Logarithmic enhancements could make these effects experimentally detectable.

Certain UV models with heavy vectors influence the renormalization and observable signatures.

Abstract

We investigate the renormalization of the radiative decays of the Higgs to two gauge bosons in the Standard Model Effective Field Theory at mass dimension eight. Given that these are loop-level processes, their one-loop renormalization can be phenomenologically important when triggered by operators generated through the tree-level exchange of heavy particles (assuming a weakly coupled UV model). By computing the tree-level matching conditions of all relevant extensions of the Standard Model, we demonstrate that this effect is indeed present in the $h\to \gamma Z$ decay at dimension eight, even though it is absent at dimension six. In contrast, the $h\to gg$ and $h\to \gamma\gamma$ decays can only be renormalized by operators generated by one-loop processes. For UV models with heavy vectors, this conclusion hinges on the specific form of their interaction with massless gauge bosons which is required for perturbative unitarity. We study the quantitative impact of the possible logarithmic enhancement of $h\to \gamma Z$, and we propose an observable to boost the sensitivity to this effect. Given the expected increased precision of next-generation high-energy experiments, this dimension-eight contribution could be large enough to be probed and could therefore give valuable clues about new physics by revealing some of its structural features manifesting first at dimension eight.