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We calculate one loop contributions to $\Gamma(h \rightarrow \gamma \,\gamma)$ from higher dimensional operators, in the Standard Model EffectiveField Theory (SMEFT). Some technical challenges related to determiningElectroweak one loop "finite terms" are discussed and overcome. Although werestrict our attention to $\Gamma(h \rightarrow \gamma \, \gamma)$, severaldevelopments we report have broad implications. Firstly, the running of thevacuum expectation value modifies the $\log(\mu)$ dependence of processes in amanner that is not captured in some past SMEFT Renormalization Group (RG)calculations. Secondly, higher dimensional operators can source ghostinteractions in $R_\xi$ gauges due to a modified gauge fixing procedure.Lastly, higher dimensional operators can contribute with pure finite terms atone loop in a manner that is not anticipated in a RG analysis. These resultscast recent speculation on the nature of one loop corrections in the SMEFT inan entirely new light.

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