Abstract:
In this thesis, we have carried out the theoretical formalism of the neutrino-induced neutral current(NC) neutral Sigma-hyperon elastic scattering process. The Feynman rules, Casimir’s Trick, Trace theorems and the form factor of weak neutral hadronic current have been constructed in terms of the relativistic expression of spin-average invariant amplitude. Moreover, by integrating over the Dirac-delta function has revealed the dependence of differential cross section on the incident energy and scattering angle. The kinematics of the process is set such that the incident and scattered particles are constrained on the zx-plane. The kinematics system in which neutrino-neutral sigma elastic scattering has been derived based on energy and momentum conservation laws. MatLab R2016a has been employed to generate the numerical results and plots of the unpolarized differential cross section for neutrino induced neutral-Sigma elastic scattering process in Lab frame at low and intermediate incident energy regions. For fixed values of incident energy, the peak of angular distribution increases with incident energy while at the same time getting sharper and shifting towards the forward scattering angle. Moreover, for fixed values of scattering angles, it is found out that the peak of energy distribution of the differential cross section is higher for lower scattering angles and occurs in the intermediate energy region. But at larger scattering angles, the peak drastically decreases and shifts toward the low energy region. Therefore, the elastic scattering under study within the framework of the SU(3) symmetry and Cabibbo vector-axial theory has been shown to be an intermediate energy process.
