Some Explorations of New Physics Beyond The Standard Model

Some new physics beyond the Standard Model of particle physics, like Supersymmetry, Extra-dimensions etc., and their effect on the nature of different standard model phenomena are explored in this thesis. We discuss the power law scaling of the gauge, Yuakawa and quartic scalar couplings in the Universal Extra-Dimensional scenario assuming compactification on an $S^1/Z_2$ orbifold. We get a low unification scale around 30 TeV for a radius $R \sim 1 TeV^{-1}$. We show that the effect of one (two) extra-dimension(s) will allow to relax the upper limit on the mass of the lightest CP-even neutral Higgs in the minimal supersymmetric standard model upto around 200 GeV (300 GeV). We obtain a low intermediate scale $(M_R)$, a desirable feature to accommodate leptogenesis, within minimal supersymmetric SO(10) Grand Unified Theory with the help of any one of three options -- threshold corrections, non-renormalizable operators or presence of additional light Higgs multiplets. In the triplet Higgs scalar model irrespective of these corrections, from the perturbitivity requirement, we find a lower bound $M_R > 10^9$ GeV. On the other hand remaining in the standard quark model we estimate the pentaquark mass after taking care of the colour-spin symmetry properties for the triquark $(qq\bar q)$ state