Matching the 2HDM to the HEFT and the SMEFT: Decoupling and perturbativity

Abstract

We consider the 2 Higgs doublet model (2HDM) and compare two effective field theory (EFT) approaches to it, according to whether the heavy degrees of freedom are integrated out before [standard model EFT (SMEFT)] or after [Higgs EFT (HEFT)] spontaneous symmetry breaking. By requiring decoupling and perturbativity in the 2HDM, we define a consistent EFT expansion in inverse powers of the heavy masses which is applied to both the SMEFT and the HEFT tree-level matchings to the 2HDM. We organize this expansion with a dimensionless parameter ζ, and investigate the tree-level scatterings hh→hh and WW→hh up to O(ζ2). We find no differences between the HEFT and the SMEFT approaches at this order. We show scenarios where even including dimension-8 operators of the SMEFT is insufficient to obtain an accurate matching to the 2HDM.