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

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.