Higgs couplings parameterisations

The discovery of a Higgs boson at the Large Hadron Collider (LHC) has provided a proof of the structure for the spontaneous breaking of the electroweak interactions, described as a gauge theory, in its simplest and most concise form. However this simple description in terms of a single complex scalar doublet giving rise to the masses of the weak gauge bosons and to a physical scalar Brout-Englert-Higgs boson demands closer scrutiny, both for the detailed properties of the boson couplings with respect to the values expected from the Standard Model (SM) and with respect to the existence of other scalar states. Indeed extensions of the SM built to answer more detailed questions about the weak interactions and beyond, typically require either an extended scalar sector or a composite nature for the Higgs boson, or both. These detailed analyses can be performed at different levels, going from simple coupling-based descriptions inspired from the experimental measurements of the Higgs boson properties, to effective Lagrangian descriptions, to studies performed in specific models. In any case no description is completely general as a set of assumptions are required as starting points for its validity. Instead of selecting specific models I will mainly discuss in the following a coupling-based description, both for a single physical neutral scalar field and for two neutral scalar fields, as this is relevant in various extensions of the SM.