Some aspects of the phenomenology of supersymmetric theories and the Large Hadron Collider

In spite of its enormous success, the Standard Model (SM) of particle physics suffers from a few drawbacks. For example, the SM cannot account for the observations of neutrino mass and mixing and the existence of dark matter (DM). Supersymmetry (SUSY) is capable of addressing these issues in an elegant manner. Nevertheless, the non-observations of the superpartners to date has put stringent constraints on their masses. In the light of this, in this thesis, we consider a U(1)R symmetric model where the R-charges are identified with lepton numbers in such a way that one of the leftchiral sneutrinos can acquire a large vacuum expectation value (vev) and can play the role of a down type Higgs field. Models with U(1)R symmetry and Dirac gauginos are well motivated since they can address the issues relating to the Higgs boson mass, DM and neutrino mass generation. Most importantly, the presence of Dirac gluinos can relax the bound on superpartner masses. We augment the model with a right handed neutrino superfield to have a small Dirac neutrino mass at the tree level with an order one neutrino Yukawa coupling f. We observe, that the Higgs boson mass receives an additional contribution at the tree level, proportional to f, which can ameliorate the Higgs naturalness problem when f ∼ O(1). In the context of a locally supersymmetric theory, R-symmetry is mildly broken by a non-zero gravitino mass. In such a scenario, neutrino Majorana masses can be generated at the tree level as well as at the one loop level. In addition, for an order one f, we also obtain a very light bino-like neutralino with mass around a few hundred MeV. Such a light neutralino has important implications at the LHC as well as in the cosmological sector. On the other hand, the small f(∼ 10−4) case is also interesting as we obtain a sterile neutrino with mass around a few keV which can be an excellent warm dark matter candidate. The model also fares very well when studied in conjunction with the latest LHC results pertaining to different decay modes of the Higgs boson. Finally, an added advantage of this model is that it can conceive light top squarks. We also study some interesting and distinct signatures of these top squarks at the LHC.The research was conducted under the supervision of Prof. Sourov Ray of Theoretical Physics division under the SPS [School of Physical Sciences]The research was carried out under CSIR fellowshi