Search for extra Higgs bosons (theory)

We provide an overview of the theory motivations for extra Higgs bosons, focussing on models that address the hierarchy problem (Twin Higgs, the MSSM and the NMSSM), and on the reasons why new Higgses could be the first particles seen in these models. We then discuss a phenomenological framework to describe the phenomenology of extra Higgs doublets and/or singlets, that easily maps on the above and other models, and that allows to set a strategy to perform experimental searches. We finally summarise the LHC8 status of these searches, as well as their prospects at the next runs of the LHC. In particular we describe the interplay of the following measurements: i) SM Higgs couplings to other SM particles, ii) SM Higgs self coupling, iii) direct searches for extra Higgses.