Matching UV models to the Higgs effective field theory

Abstract In this review, we discuss how ultraviolet (UV) models describing physics beyond the Standard Model (BSM) can be matched to the most general effective field theory for the electroweak sector known as the Electroweak Chiral Lagrangian (EChL) or the Higgs Effective Field Theory (HEFT). We analyze both decoupling and non-decoupling scenarios, emphasizing the requirements of the matching procedure and the interpretation of the resulting anomalous HEFT couplings. As a case study, we perform the matching of the Two-Higgs-Doublet Model (2HDM) to HEFT, illustrating how different parameter hierarchies lead to distinct low-energy descriptions. Particular attention is devoted to the advantages of performing the matching to HEFT for decoupling scenarios, as compared to the usual matching to the Standard Model Effective Field Theory (SMEFT). Finally, we provide a survey of UV models that have been matched to HEFT, highlighting the patterns of their low-energy coefficients and their compatibility with a SMEFT description.