Higgs Decays to $ZZ$ and $Z\gamma$ in the SMEFT: an NLO analysis

We calculate the complete one-loop electroweak corrections to the inclusive $H\rightarrow ZZ$ and $H\rightarrow Z\gamma$ decays in the dimension-$6$ extension of the Standard Model Effective Field Theory (SMEFT). The corrections to $H\rightarrow ZZ$ are computed for on-shell $Z$ bosons and are a precursor to the physical $H\rightarrow Z f {\overline{f}}$ calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coefficients are larger than the finite NLO contributions to the decay widths. As a by-product of our calculation, we obtain the first complete result for the finite corrections to $G_\mu$ in the SMEFT.
Comment: Published Version. The results for $\Delta r$ in the SMEFT are now given in $R_\xi$ gauge; V3: corrected a typo in eq 38 and 39, updated eq. 41; V4: corrected a typo in eq 39 (global minus sign)