Pros and cons of EFTs for new physics

Physics beyond the Standard Model (BSM) can be described in a consistent and general way through an Effective Field Theory (EFT). Ultimately, the goal is to associate eventual deviations of the SM with a particular BSM model. In this talk, I discuss the quality of that association, taking the 2 Higgs Doublet Model (2HDM) as BSM model. More specifically, I consider two EFT approaches to it: the Standard Model EFT (SMEFT) and the Higgs EFT (HEFT). In the former, I compare not only different truncations in the SMEFT expansion, but I also ascertain the importance of loop matching. As for the HEFT, I question the assumption according to which the matching is unique. I present three HEFT matchings to the 2HDM, and show that different  ones should be used according to the process and the region of parameter space.