Consistent higher order $\sigma(\mathcal{G} \,\mathcal{G}\rightarrow h)$, $\Gamma(h \rightarrow \mathcal{G} \,\mathcal{G})$ and $\Gamma(h \rightarrow \gamma \gamma)$ in geoSMEFT

TL;DR

This paper provides a consistent set of one-loop calculations for Higgs decay and production processes in the SMEFT framework, using different gauge fixing and geometric approaches, highlighting scheme dependence and ensuring theoretical consistency.

Contribution

It combines and refines recent SMEFT results into a unified, scheme-consistent set of one-loop calculations for Higgs processes, incorporating geometric formulation and background field method approaches.

Findings

Unified one-loop results for Higgs decay and production in SMEFT.

Analysis of scheme dependence in SMEFT calculations.

Cross checks confirming the consistency of the results.

Abstract

We report consistent results for $\Gamma(h \rightarrow \gamma \gamma)$, $\sigma(\mathcal{G} \,\mathcal{G}\rightarrow h)$ and $\Gamma(h \rightarrow \mathcal{G} \,\mathcal{G})$ in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $\mathcal{O}(\bar{v}_T^2/16 \pi^2 \Lambda^2)$ in the Background Field Method (BFM) approach to gauge fixing, and to $\mathcal{O}(\bar{v}_T^4/\Lambda^4)$ using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasise calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.