| Since the establishment of the Standard Model (SM), almost all of the high-energy physics experimental results have been perfectly consistent with the SM predictions. The new～125GeV boson discovered at the LHC recently is very likely to be the SM Higgs boson. Nevertheless, there are still flaws in the SM, such as the hierarchy problem, neutrino oscillation experiments and so on. People realized the limitations of the SM and began to look for new physics beyond the SM. Various new physics models, such as the Little Higgs models(LH), the Extra Dimension Model(ED) and the Minimal Supersymmetry Standard Model(MSSM), were gradually raised and built up. Among these new models, the MSSM is regarded as one of the most hopeful candidates for the physics beyond the SM because of its elegant mathematical formation and physical meaning. So searching for SUSY will be one of the central focus of the future particle physics experiments. The present running Large Hadron Collider(LHC) and the proposed Large Hadron election Collider(LHeC) at the CERN will provide a good experimental platform for exploring new physics beyond the SM.In the MSSM, the R-parity conservation is a phenomenological assumption and the R-parity conservation or not does not affect the self-consistency of the theory. The R-parity violating MSSM and the R-parity conservative MSSM have the same theoretical status. The most general MSSM should contain the R-parity violating part. Top quark is the heaviest elementary fermion in the SM, whose mass is most close to the scale of electroweak spontaneous breeking (EWSB). And the top quark could participate in the interactions of new physics because of it’s heavy mass. So the top quark physics is one of the important windows leading to the new physics. The polarization of the top quark can be measured, which also provides a convenient measurement of the interactions involving top quark. What’s more, the typical signal feature of the single top quark production processes makes it easier to suppress experimental backgrounds. So the single top quark production in association with a SUSY particle production process is a powerful way to study the R-parity violating MSSM. In this thesis we study the single top quark production associated with a SUSY particle processes through the R-parity violating couplings at the LHC and the LHeC, and provide a theoret-ical guidance to the experiments to find the SUSY signal or to limit the R-parity violating coupling coefficients. In chapter2and chapter3, we provide an accurate calculation of the single top quark production associated with a SUSY particle process at the LHC and LHeC, respectively. In these works, we adopt complex mass scheme(CMS), two cutoff phase space slicing method(TCPSS), dipole sub-straction method(DPS) and narrow-width approximation(NWA) method to deal with the problems we encountered in the calculations.In chapter2, we calculate the single top quark production associated with a slepton process at the LHC in NLO QCD. We investigate the dependence of the LO and NLO QCD corrected integrated cross sections on the factoriza-tion/renormalization energy scale, slepton, stop quark and gluino masses. We analyse the impact of the tj-dk-li coupling up to the QCD NLO. We show the numerical results with different jet event selection schemes in the NLO QCD and point out that the exclusive jet event selection scheme can keep the convergence of the perturbative series. The results show that in the exclusive jet selection scheme the NLO QCD correction can be larger than LO results as large as28%in some parameter space.In chapter3, we calculate the single top quark production in association with a lightest neutralino process at the LHeC at the LO and the QCD NLO in the pMSSM-19model within the latest experimental constraints on the SUSY parameters. Because of the possible stop quark resonance, the s-channel Feynman diagram is the major contribution to the total cross section in most cases, but we find that the contributions of t-,u-channel Feynman diagrams are not ignorable in some SUSY parameter space (where the slepton is relatively light and the stop quark is relatively heavy) in the allowed SUSY parameter space under the experimental constraints. Therefore, all the Feynman diagrams should be included in the NLO QCD correction calculation. In order to show the contribution of non-resonant part more clearly, we compare the integrated cross sections obtained by using three approaches in the LO calculations:(1) including all the contributions of the tree-level diagrams,(2) including only the contributions of the s-channel diagrams,(3) narrow-width approximation. We find out that the contribution of non-resonant part can reach50%of the cross section obtained by using the approach (1) or more. We investigate the effects of the relevant SUSY parameters on the cross section, and present the transverse momentum distributions of final top quark at both the LO and the QCD NLO. It shows that the NLO QCD corrections increase the LO cross sections in most chosen parameter space, but in some cases the NLO QCD correction is hardly resolvable in high precision measurement.The innovative points of this thesis are listed as below:●We firstly studied the NLO QCD correction of the single slepton associated with a top quark production process at the LHC systematically. We analyse the impacts of the SUSY parameters on the integrated cross section and study the top quark polarization effects at the LO and QCD NLO. We consider the subsequential decay of the slepton and show the transverse momentum distributions of final particles. Our study provides a precise theoretical predictions for the experiments.●We provided firstly the full and deep investigations on the single top quark associate with the lightest neutralino production process at the LHeC within the latest experimental limitations on the SUSY parameters. We find that the contribution of the non-resonant diagrams can not be neglected in some SUSY parameter space. Our predictions are more accurate than that in the previous work where only the resonance contribution was considered. The results show that the NLO QCD correction is resolvable, especially in the transverse momentum distributions of the final top quark in the favorable SUSY parameter phase space. |
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