In this review we have outlined a very brief history of the Higgs boson search and the development of the strategies for searching for the Higgs boson in its diphoton decay channel.We have reviewed the methodology and tools that led to the first observation of the Higgs boson decaying to a pair of photons. We have presented the latest results from the measured properties of the newly found boson.We concentrate for most part on the analysis developed by the CMS experiment, but also present the latest results of the ATLAS experiment along with CMS results.

The discovery of a 125 GeV particle, announced by the ATLAS and CMS Collaborations on July 04, 2012, is one of the most important events in the recent history of particle physics. This particle could be the last missing particle of the Standard Model of particle physics or it could be the beginning of the long list of particles predicted by the physics beyond the Standard Model. Before we jump to make the final conclusion about this particle, it is imperative to study all the properties of this newly discovered particle. Since the model-dependentanalyses always have this danger of being biased, we can perform a model-independent search for the Higgs boson and also check if the 125 GeV particle is indeed the Standard Model Higgs boson or a particle belonging to the physics beyond the Standard Model.

The Naturalness Principle as a requirement that the heavy mass scales decouple from the physics of light mass scales is reviewed. In quantum field theories containing {\em elementary} scalar fields, such as the StandardModel of electroweak interactions containing the Higgs particle, mass of the scalar field is not a natural parameter as it receives large radiative corrections. How supersymmetry solves this Naturalness Problem is outlined. Thereare also other contexts where the presence of elementary scalar fields generically spoils the high–low mass scales decoupling in the quantum theory. As an example of this, the non-decoupling of possible Planck scale violationof Lorentz invariance due to quantum gravity effects from the physics at low scales in theories with elementary scalar fields such as the Higgs field is described. Here again supersymmetry provides a mechanism for ensuringthat the decoupling of heavy–light mass scales is maintained.

Assuming that there is some symmetry which keeps the SM Higgs boson at the electroweak scale, we discuss the feasibility of some minimalistic expansions of the SM.

The effective field theory approach to LHC Higgs data is reviewed.

A vast literature on the theory and phenomenology of two-Higgs-doublet models (2HDM) exists since long. However, the present situation demands a revisit of some 2HDM properties. Now that a 125 GeV scalar resonance has been discovered at the LHC, with its couplings to other particles showing increasing affinity to the Standard Model Higgs-like behaviour, the 2HDM parameter space is more squeezed than ever. We briefly review the different parametrizations of the 2HDM potential and discuss the constraints on the parameter spacearising from the unitarity and stability of the potential together with constraints from the oblique electroweak $T$ -parameter. We also differentiate the consequences of imposing a global continuous $U(1)$ symmetry on thepotential from a discrete $Z_2$ symmetry.

Updating various theoretical and experimental constraints on the four different types of two-Higgsdoublet models (2HDMs), we find that only the ‘lepton-specific’ (or ‘type-X’) 2HDM can explain the present muon $g−2$ anomaly in the parameter region of large tan $\beta$, a light CP-odd boson, and heavier CP-even and charged bosons which are almost degenerate. Severe constraints on the models come mainly from the consideration of vacuum stability and perturbativity, the electroweak precision data, the b-quark observables like $B_{S}\rightarrow \mu\mu$, the precision measurements of the lepton universality as well as the 125 GeV boson property observed at the LHC.

We discuss the present status of the Higgs sector of the CP-violating minimal supersymmetric Standard Model (CPVMSSM). In the Standard Model (SM) of particle physics, the only source of CP violation is the complex phase in the Cabibbo–Kobayashi–Maskawa (CKM) matrix. By now we all know that this singlephase is not large enough to explain the observed baryon asymmetry of our Universe. Hence, one require additional sources of CP violation. The MSSM with several complex phases is one such scenario. The tree-level CP invariance of the MSSM Higgs potential is broken at one-loop level in the presence of complex phases in the MSSM Lagrangian. The presence of these additional phases modifies Higgs masses, mixings and couplings significantly. These additional phases have non-trivial impact on several low-energy observables; like the electric dipole moments (EDMs) of atoms and molecules, the CP asymmetry in rare b-decays etc. We first present a brief outline of the CPVMSSM Higgs sector, and then discuss the current limits/bounds obtained from the measurementsof several low-energy observables. We also comment on the current bounds coming from the high-energy collider experiments, specially the Large Electron Positron (LEP) Collider and the ongoing Large Hadron Collider (LHC) at the CERN.

In this article, we give a bird’s eye view of the research on electroweak phase transition and some related phenomena, viz., cosmological baryogenesis, electroweak bubble dynamics and generation of gravitationalwaves. Our presentation revolves around the observation that a strong first-order electroweak phase transition cannot be obtained in the Standard Model for experimentally favoured Higgs mass and hence the cosmologicalevents associated with this kind of phase transition cannot be explained in this model. However, this phase transition can be achieved in a number of beyond Standard Models. As a prototype case, we consider the littlest Higgs model with T parity and show the results of some calculations within this model.

The Higgs boson, recently discovered with a mass of 125.7 GeV is known to mediate the masses of elementary particles, but only $2\%$ of the mass of the nucleon. Extending a previous investigation (Schumacher, {\it Ann. Phys. (Berlin) } {\bf 526}, 215 (2014)) and including the strange-quark sector, hadron masses are derived from the quark condensate of the QCD vacuum and from the effects of the Higgs boson. These calculations include the $\pi$ meson, the nucleon and the scalar mesons $\sigma(600), \kappa(800), a_{0}(980), f_{0}(980)$ and $f_{0}(1370)$. The predicted second $\sigma$ meson, $\sigma^{\prime}(1344) = |s \hbar{s})$, is investigated and identified with the $f_{0}(1370)$ meson. An outlook is given on the hyperons $\Lambda, \Sigma^{0,\pm}$ and $\Sigma^{0,−}$.