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We consider the 2 Higgs Doublet Model (2HDM) and compare two effective fieldtheory (EFT) approaches to it, according to whether the heavy degrees offreedom are integrated out before (SMEFT) or after (HEFT) spontaneous symmetrybreaking. %We show that, in the HEFT, an inconsistent EFT is obtained if oneconsiders an expansion simply in inverse powers of the heavy masses. %Weconsider a HEFT expansion consistent with perturbativity %We show that, if theHEFT approach is required to comply with perturbativity, it ends up obeying thesame power counting as the SMEFT one. % By requiring decoupling andperturbativity in the 2HDM, we define a consistent EFT expansion in inversepowers of the heavy masses which is applied to both the SMEFT and the HEFTmatchings to the 2HDM. We organize this expansion with a dimensionlessparameter $\xi$, and investigate the tree-level scatterings $hh\rightarrow hh$and $WW\rightarrow hh$ up to $\mathcal{O}(\xi^2)$. We find no differencesbetween the HEFT and the SMEFT approaches at this order. We show scenarioswhere even including dimension-8 operators of the SMEFT is insufficient toobtain an accurate matching to the 2HDM.

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