Streszczenie:
The Standard Model (SM) of particle physics is very successful, yet it leaves many basic
questions unanswered. This thesis is focused on some of these open problems. The aim
of this study is to explore and exploit the origins of the matter-antimatter asymmetry in
the Universe and the origins of dark matter (DM). Baryogenesis, the creation of the baryon
asymmetry in the Universe, is a long-standing problem in cosmology. Sakharov formulated
his well-known conditions for baryogenesis: baryon number violation, C and CP violation,
and a departure from thermal equilibrium. Among the many particle physics scenarios
that have been proposed in the past decades, electroweak baryogenesis is interesting. It
has become apparent that the SM of electroweak interactions is unable to account for the
observed magnitude of the BAU for at least two reasons. Firstly, the electroweak phase
transition is not strongly first-order and therefore, any baryon asymmetry created during
the transition would subsequently be washed out by unsuppressed baryon violating processes
in the broken phase. Secondly, there is not enough CP violation from the CKM matrix to
generate the baryon asymmetry.
With the motivation of investigating these problems, we extend the SM by a neutral
complex scalar singlet, and a pair of heavy iso-doublet vector quarks (VQ). We consider the
potential with a softly broken global U(1) symmetry, which we call the Constrained SM+CS
model (cSMCS). Assuming nonzero vacuum expectation value for the complex singlet, we
analyze the physical conditions for spontaneous CP violation. The mixing of SM quarks with
heavy VQ pairs result in the appearance of additional CP violation. This model provides
the strong enough first order EW phase transition and leads to a proper description of
baryogenesis. The scalar spectrum of the cSMCS includes three neutral Higgs particles with
the lightest one considered to be the 125 GeV SM-like Higgs boson found in 2012 at the
LHC. In the considered model, the SM-like Higgs boson comes mostly from the SM-like
SU(2) doublet, with a small correction from the singlet.
We present a prediction of the production rates of the cSMCS model Higgs bosons at the
LHC, using a conventional effective LO QCD framework and the unintegrated parton distribution
functions (UPDF) of Kimber-Martin-Ryskin (KMR). We first compute the SM Higgs
production cross-section and compare the results to the existing calculations from different
frameworks as well as to the experimental data from the CMS and ATLAS collaborations.
It is shown that our framework is capable of producing sound predictions in this case. Therefore
we use it for calculation of the cSMCS predictions for the Higgs boson production
at the LHC. These predictions for yet undetected Higgs bosons of the cSMCS model may
provide some clues for the future discovery.
On the other hand, the gravitational effects of DM have been observed in galaxies, clusters
of galaxies, the large-scale structure of the Universe and the Cosmic Microwave Background
Radiation. Since none of the particles in the cSMCS model satisfies these conditions, we
introduce, in addition a SU(2) doublet with zero vacuum expectation value (The Inert Doublet).
This model, that we call cIDMS has an exact Z2 symmetry and provides correct relic
density of DM while fulfilling direct and indirect DM detection limits and simultaneously
agree with the LHC results.
The last part of this thesis is devoted to the applying Veltman condition in the Two Higgs
Double Model (2HDM) in order to find the masses of the heavy scalars. The 2HDM is one
of the simplest extensions of the SM, providing rich phenomenology. It contains an extended
scalar sector which instead of one complex SU(2) doublet presence in the SM contains two of
the doublets, with weak hypercharges equal to 1. We analyze the soft Z2 symmetry breaking
version of the 2HDM with non-zero vacuum expectation values for both Higgs doublets
(Mixed vacuum). We assume that CP is conserved in the scalar sector. In the particle
spectrum of this model, there are two neutral CP-even scalars h and H, h being lighter
than H. These scalars are two possible candidates for the SM-like Higgs boson, forming two
possible scenarios. In the model, there are also a CP-even scalar (pseudoscalar) A and the
charged Higgs bosons H±. The results are constrained by comparing the properties of the
light Higgs particle with the corresponding LHC data. We have found that the consistent
solution exists only for the SM-like h scenario, with properties in agreement with the recent
experimental data.