Dimension-8 SMEFT Analysis of Minimal Scalar Field Extensions of the Standard Model

We analyze the constraints obtainable from present data using the Standard Model Effective Field Theory (SMEFT) on extensions of the Standard Model with additional electroweak singlet or triplet scalar fields. We compare results obtained using only contributions that are linear in dimension-6 operator coefficients with those obtained including terms quadratic in these coefficients as well as contributions that are linear in dimension-8 operator coefficients. We also implement theoretical constraints arising from the stability of the electroweak vacuum and perturbative unitarity. Analyzing the models at the dimension-8 level constrains scalar couplings that are not bounded at the dimension-6 level. The strongest experimental constraints on the singlet model are provided by Higgs coupling measurements, whereas electroweak precision observables provide the strongest constraints on the triplet model. In the singlet model the present di-Higgs constraints already play a significant role. We find that the current constraints on model parameters are already competitive with those anticipated from future di- and tri-Higgs measurements. We compare our results with calculations in the full model, exhibiting the improvements when higher-order SMEFT terms are included. We also identify regions in parameter space where the SMEFT approximation appears to break down. We find that the combination of current constraints with the theoretical bounds still admits regions where the SMEFT approach is not valid, particularly for lower scalar boson masses.