| The discovery of a new particle with mass of about 125 GeV was a real triumph of run-1 of the Large Hadron Collider (LHC). To date, the analysis of the full data collected clearly shows that its properties match very well those expected for the Higgs boson in the Standard Model (SM). However, the SM itself leaves many serious questions unsolved and cannot completely describe all the observed phenomena. Hence, it must be only a component of a more complete theory. Theories that go beyond the SM typically require an extended Higgs sector. Although stringently constrained by the LHC run-1 data, a non-minimal Higgs sector is theoretically very attractive and, if confirmed, would shine light on the mechanism of electroweak symmetry breaking (EWSB).;Followed by a historical review of the birth of the Higgs boson, this volume supplies a brief introduction to SM Higgs boson physics and topical issues on Higgs searches at the LHC. An updated overview of the property analysis for the newly-discovered 125 GeV Higgs and other beyond-the-SM (BSM) Higgs bosons will be presented. We will also discuss its implications for various BSM Higgs models without and within the framework of supersymmetry (SUSY).;The two-Higgs-doublet model (2HDM) is a very simple and appealing framework for such considerations. Either of the two CP-even Higgs bosons in the Type I and II 2HDM is able to provide a consistent description of the LHC Higgs signal. I will illustrate its status after LHC run-1 analysis and present the prediction for higher precision at the run-2. Given the very SM-like nature of this discovered particle, one often considers the decoupling limit in which the lightest one is the SM-like Higgs boson discovered at the LHC while others are very heavy. However, such a SM-like scalar Higgs boson can also be obtained in the alignment limit without the masses of other Higgs being large. In particular, I will address the seemingly extreme case in which there is a (pseudoscalar) Higgs light enough so that the SM-like state would have a rare decay mode. Finally, the results achieved in the case of alignment will be compared to those present in the decoupling limit and the prospects for searching for non-SM Higgs bosons at future experiments will be discussed in detail.;In the framework of supersymmetry, the next-to-minimal supersymmetric SM (NMSSM) that has been widely studied is a most promising possibility because it allows for less fine-tuning. Following an analysis of the theoretical structure of this model, we first assessed the extent to which various semi-constrained NMSSM (scNMSSM) scenarios with one of the CP-even Higgs bosons, h1 (the lightest) or h2 (the second lightest), are able to describe the LHC signal as a SM-like Higgs. Meanwhile, if the h1 and h 2 are approximately degenerate in mass then an enhancement of the di-photon signal is very possible, although a SM-like level is also easily achieved. To experimentally probe the possibility of degeneracy, we developed diagnostic tools that could discriminate whether or not there are two (or more) Higgs bosons versus just one contributing to the LHC signals at 125 GeV. In addition, we considered the case where the h1 provides a consistent description of the small LEP excess at 98 GeV whereas the h2 possesses the primary features of the LHC Higgs-like signals at 125 GeV.;Beyond the SM, the Higgs sector and dark matter (DM) sector may be intimately connected. With protection by an extra discrete symmetry, a certain non-SM scalar boson (Higgs partner) could be a possible DM candidate. As typical examples, we consider the lightest neutralino supersymmetric DM and the Higgs-portal scalar DM in the singlet extension of the 2HDM (2HDMS) together with presenting a decent description of the models. In both cases, implications for DM physics are discussed in various scenarios. Intriguingly, violating the isospin symmetry in the DM interaction with nucleons could result in a large suppression of the DM-nucleon cross section, approaching a level that is hardly reachable by many ambitious projects for DM direct detection. Given this dramatic change in the analysis of DM direct detection, I include an in-depth examination of this possibility in the generic Higgs-portal DM model. |
