NLO SMEFT Electroweak Corrections to Higgs Decays to 4 Leptons in the Narrow Width Approximation

Some of the most precise measurements of Higgs boson couplings are from the Higgs decays to 4 leptons, where deviations from the Standard Model predictions can be quantified in the framework of the Standard Model Effective Field Theory (SMEFT). In this work, we present a complete next-to-leading order (NLO) SMEFT electroweak calculation of the rate for $H\rightarrow \ell^+\ell^- Z$ which we combine with the NLO SMEFT result for $Z\rightarrow\ell^+\ell^-$ to obtain the NLO rate for the $H\rightarrow$ 4 lepton process in the narrow width approximation. The NLO calculation provides sensitivity to a wide range of SMEFT operators that do not contribute to the rate at lowest order and demonstrates the importance of including correlations between the effects of different operators when extracting limits on SMEFT parameters. We show that the extraction of the Higgs tri-linear coupling from the decay $H\rightarrow \ell^+ \ell^- Z, \ Z\rightarrow \ell^+\ell^-$ in the narrow width approximation strongly depends on the contributions of other operators that first occur at NLO.