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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, andto $\mathcal{O}(\bar{v}_T^4/\Lambda^4)$ using the geometric formulation of theSMEFT. We combine and modify recent results in the literature into a completeset of consistent results, uniforming conventions, and simultaneously completethe one loop results for these processes in the BFM. We emphasise calculationalscheme dependence present across these processes, and how the operator and loopexpansions are not independent beyond leading order. We illustrate severalcross checks of consistency in the results.

the journal of high energy physics/the journal of high energy physics

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