Doctor of Philosophy / Department of Physics / Andrew G. Ivanov / A search is performed for heavy vector-like top quark partner (T) with electric charge +2/3 by using proton-proton collision events from Large Hadron Collider (LHC) at a centre- of-mass energy of 13 TeV. The data corresponds to an integrated luminosity of 35.9fb−1 collected by the Compact Muon Solenoid (CMS) experiment during 2016. The production of this new hypothetical particle is assumed to be in pairs and strong interaction is responsible for such production mechanism. T quarks can decay to various combinations of third generation quarks and standard model bosons: T → bW, tZ, or tH, and hence the final states consist of pair of opposite-sign leptons consistent with coming from a Z boson and jets. No significant excess has been observed and hence 95% CL upper limits are obtained on TT production cross section by assuming different branching ratios. T quark mass values below 1280 GeV are excluded in case of 100% branching fraction for T → tZ.

Composite Higgs Models (CHMs) are formulated in terms of strongly coupled theories. They often predict fermionic top partners with a mass around the TeV scale. Going beyond minimality enriches the spectrum of the theory with additional hypothetical scalars that significantly change the phenomenology. In this thesis, we explore an SO(6)/SO(5) CHM with an additional pseudo-scalar custodial singlet. The latter has anomalous couplings to the Standard Model vector bosons. We study the phenomenology of the singlet, including bounds from the available ATLAS and CMS searches in the relevant channels with di-boson and fermionic final states. We used HiggsBounds tool to test the model theoretical predictions against the current exclusion limits. The study is performed at the 8 and 13 TeV experiments at the LHC. We present a model parameter space from which the bounds on the (most sensitive) signal cross sections of the hypothetical singlet can be easily extracted.