Various aspects of BSM

Abstract

We study various aspects of the physics Beyond the Standard Model (BSM). In particular, this dissertation mainly deals with two different topics. The first part is about the particle production and its application to the relaxation mechanism. We propose a universal group theoretic description of the fermion production through any type of interaction to scalar or pseudo-scalar. Our approach relies on the reparametrization group, which corresponds to the freedom in choosing representations of the Dirac gamma matrices in Clifford algebra. In this group theoretic approach, the equation of motion takes a universal form for any system, and the expression of the fermion number density becomes greatly simplified compared to the traditional way using the Bogoliubov transformation. It provides us with a simple geometric interpretation of the fermion production dynamics. As phenomenological application of the particle production, we show that the relaxation mechanism with the fermion production could be the dynamical solution to the electroweak hierarchy problem. In our model, the fermions are produced from the relaxion source through the derivative coupling, which can be a dominant frictional force compared to the Hubble expansion. We also show that our scenarios safely avoid downsides appearing in the original relaxation model such as super-Planckian field excursions, a large number of e-folds and scanning over thermal Higgs mass squared. In the second part, we study the effective field theory sensitivity of an LHC analysis for the $\tau \nu$ final state with an associated $b$-jet. To illustrate the improvement due to the $b$-tagging, we recast the recent CMS analysis in the $\tau\nu$ channel, using an integrated luminosity of 35.9 fb$^{-1}$ at $\sqrt{s}=13$ TeV, and provide limits on all the dimension-six effective operators which contribute to the process. The expected limits from the $b$-tagged analysis are then derived and compared. We find an improvement of approximately $\sim 30\%$ in the bounds for operators with a $b$ quark. We also study the impact of these limits on some simplified scenarios aimed at addressing the observed deviations from the Standard Model in lepton flavor universality ratios of semileptonic $B$-meson decays.