On one-loop corrections in the standard model effective field theory; the $\Gamma(h \rightarrow \gamma \, \gamma)$ case

TL;DR

This paper calculates one-loop corrections to Higgs decay into two photons within the SMEFT framework, revealing new effects from higher dimensional operators on RG running, gauge fixing, and finite terms.

Contribution

It introduces methods to accurately compute finite one-loop terms in SMEFT, highlighting effects overlooked in previous RG analyses.

Findings

Vacuum expectation value running affects log(mu) dependence.

Higher dimensional operators induce ghost interactions in R_xi gauges.

Finite one-loop contributions from operators are significant and previously unaccounted.

Abstract

We calculate one loop contributions to $\Gamma(h \rightarrow \gamma \, \gamma)$ from higher dimensional operators, in the Standard Model Effective Field Theory (SMEFT). Some technical challenges related to determining Electroweak one loop "finite terms" are discussed and overcome. Although we restrict our attention to $\Gamma(h \rightarrow \gamma \, \gamma)$, several developments we report have broad implications. Firstly, the running of the vacuum expectation value modifies the $\log(\mu)$ dependence of processes in a manner that is not captured in some past SMEFT Renormalization Group (RG) calculations. Secondly, higher dimensional operators can source ghost interactions in $R_\xi$ gauges due to a modified gauge fixing procedure. Lastly, higher dimensional operators can contribute with pure finite terms at one loop in a manner that is not anticipated in a RG analysis. These results cast recent speculation on the nature of one loop corrections in the SMEFT in an entirely new light.