Resonances and loops: scale interplay in the Higgs effective field theory

Abstract

As there seems to be a large mass gap between the SM and new physics particles, the EFT framework emerges as the natural approach for the analysis and interpretation of collider data. However, this large gap and the fact that (so far) all the measured interactions look pretty much SM-like does not imply that the linear Higgs representation as a complex doublet $ϕ$ in the SMEFT is always appropriate. Although there is a wide class of SM extensions that accept this linear description, this realization does not always provide a good perturbative expansion. The HEFT and its organization according to a chiral expansion cures these issues. Path integral functional methods allow one to compute the corrections to the NLO effective action: at tree level, the heavy resonances only contribute to the $O(p^4)$ low-energy couplings (or higher) according to a pattern that depends on their quantum numbers and is suppressed by their masses; at the one-loop level, all the new-physics corrections go to the $O(p^4)$ effective action (or higher) and are suppressed by an intrinsic scale of the LO HEFT Lagrangian, which has been related in recent times with the curvature of the manifold of scalar fields (being the SM its flat limit and having the HEFT effective action an expansion in the curvature). This two suppression scales (resonance masses and non-linearity/curvature) compete at NLO and may, in principle, be very different/similar depending on the particular BSM scenario and the observable at hand. Likewise, experiments do not tell us yet whether $O(p^4)$ loops are essentially negligible or not, as it is shown with a couple of examples. In summary, the HEFT extends the range of applicability of the SMEFT, which, although justified for a pretty wide class of BSM scenarios, introduces a bias in the data analyses and does not provide the most general EFT framework.