Was the Higgs boson discovered?

The standard model has postulated the existence of a scalar boson, named the Higgs boson. This boson plays a central role in a symmetry breaking scheme called the Brout-Englert-Higgs mechanism (or the Brout-Englert-Higgs-Guralnik-Hagen-Kibble mechanism, for completeness) making the standard model realistic. However, until recently at least, the 50-year-long-sought Higgs boson had remained the only particle in the standard model not yet discovered experimentally. It is the last but very important missing ingredient of the standard model. Therefore, searching for the Higgs boson is a crucial task and an important mission of particle physics. For this purpose, many theoretical works have been done and different experiments have been organized. It may be said in particular that to search for the Higgs boson has been one of the ultimate goals of building and running the LHC, the world's largest and most powerful particle accelerator, at CERN, which is a great combination of science and technology. Recently, in the summer of 2012, ATLAS and CMS, the two biggest and general-purpose LHC collaborations, announced the discovery of a new boson with a mass around 125 GeV. Since then, for over two years, ATLAS, CMS and other collaborations have carried out intensive investigations on the newly discovered boson to confirm that this new boson is really the Higgs boson (of the standard model). It is a triumph of science and technology and international cooperation. Here, we will review the main results of these investigations following a brief introduction to the Higgs boson within the theoretical framework of the standard model and Brout-Englert-Higgs mechanism as well as a theoretical and experimental background of its search. This paper may attract interest of not only particle physicists but also a broader audience.Comment: LateX, 23 pages, 01 table, 9 figures. To appear in Commun. Phys. Version 2: Minor changes, two references adde

Perturbative approach to f(R)f(R)-gravitation in FLRW cosmology

The $f(R)$ theory of gravitation developed perturbatively around the general theory of relativity with cosmological constant (the \text{$\Lambda$}CDM model) in a flat FLWR geometry is considered. As a result, a general explicit cosmological solution that can be used for any model with an arbitrary, but well-defined, $f(R)$ function (just satisfying given perturbation conditions) is derived. This perturbative solution shows how the Hubble parameter $H (t)$ depends on time (along with the cosmological constant and the matter density) to adapt to the evolution of the Universe. To illustrate, this approach is applied to some specific test models. One of these models appears to be more realistic as it could describe three phases of the Universe's evolution. Despite the fact that the perturbation is applied for a flat FLWR geometry (according to the current cosmological observation) indicates that the obtained solution can mainly describe the evolution of the late Universe, it may also work for an early Universe. As a next step, the present method can be applied to the case with a more general FLRW geometry to increase the precision of the description of different stages in the evolution of the Universe. Finally, it is shown that in a desription of the Universe's evolution the perturbative $f(R)$-theory can be considered as an effective GR with the cosmological constant $\Lambda$ replaced by an effective parameter $\Lambda_{eff}[\rho(t)]$. This trick leads to a simpler way of solving an $f(R)$-theory regardless its specific form

Scalar sextet in the 331 model with right-handed neutrinos

A Higgs sextet is introduced in order to generate Dirac and Majorana neutrino masses in the 331 model with right-handed neutrinos. As will be seen, the present sextet introduction leads to a rich neutrino mass structure. The smallness of neutrino masses can be achieved via, for example, a seesaw limit. The fact that the masses of the charged leptons are not effected by their new Yukawa couplings to the sextet is convenient for generating small neutrino masses.Comment: RevTeX4, 5 pages, no figure. To appear in Phys. Rev. D. Misprints removed (v.2

Model of neutrino effective masses

It is shown that an effective (nonrenormalizable) coupling of lepton multiplets to scalar triplets in the 331 model with sterile/exotic neutrinos, can be a good way for generating neutrino masses of different types. The method is simple and avoids radiative/loop calculations which, sometimes, are long and complicated. Basing on some astrophysical arguments it is also stated that the scale of SU(3)L symmetry breaking is at TeV scale, in agreement with earlier investigations. Or equivalently, starting from this symmetry breaking scale we could have sterile/exotic neutrinos with mass of a few keV's which could be used to explain several astrophysical and cosmological puzzles, such as the dark matter, the fast motion of the observed pulsars, the re-ionization of the Universe, etc

Testing the f(R)f(R)-theory of Gravity

A procedure of testing the $f(R)$-theory of gravity is discussed. The latter is an extension of the general theory of relativity (GR). In order this extended theory (in some variant) to be really confirmed as a more precise theory it must be tested. To do that we first have to solve an equation generalizing Einstein's equation in the GR. However, solving this generalized Einstein's equation is often very hard, even it is impossible in general to find an exact solution. It is why the perturbation method for solving this equation is used. In a recent work \cite{Ky:2018fer} a perturbation method was applied to the $f(R)$-theory of gravity in a central gravitational field which is a good approximation in many circumstances. There, perturbative solutions were found for a general form and some special forms of $f(R)$. These solutions may allow us to test an $f(R)$-theory of gravity by calculating some quantities which can be verified later by the experiment (observation). In \cite{Ky:2018fer} an illustration was made on the case $f(R)=R+\lambda R^2$. For this case, in the present article, the orbital precession of S2 orbiting around Sgr A* is calculated in a higher-order of approximation. The $f(R)$-theory of gravity should be also tested for other variants of $f(R)$ not considered yet in \cite{Ky:2018fer}. Here, several representative variants are considered and in each case the orbital precession is calculated for the Sun--Mercury- and the Sgr A*--S2 gravitational systems so that it can be compared with the value observed by a (future) experiment. Following the same method of \cite{Ky:2018fer} a light bending angle for an $f(R)$ model in a central gravitational field can be also calculated and it could be a useful exercise