Abstract:
In this thesis, the main purpose was provided the electroweak description of elastic neutral current (NC) neutrino-nucleon scattering in the low energy region. The relativistic formalism has allowed us allows treating the kinematical and dynamical parts separately. The kinematics part was developed in the Lab frame in which the initial nucleon is at rest and under coplanar geometric setting was considered. The norm squared invariant matrix element has been derived as the contraction between the leptonic tensor and the hadronic tensor. Weak hadronic transitions lack well tested gauge theories to calculate the hadronic tensor, and hence the scattering vertex was approximated in two different ways: first by treating the nucleon as Dirac particle allowing the hadronic vertex to be considered as a pure weak interaction and second by treating the nucleon as having internal structure in which case the hadronic vertex is represented in terms of three form factors, which in turn are estimated in the framework of SU(3) symmetry and conserved vector current (CVC) hypothesis. The evaluation of the norm squared invariant matrix element was performed by using Casimir’s trick and trace technique allowing it to be expressed in terms of the inner product of fourmomentum observables. Eventually, the final expression of the differential cross section was converted into a MATLAB R2016a code and the numerical results are plotted against scattering angle. The results show that the differential cross section of neutrino scattering from composite nucleon dominates that of neutrino scattering from point-like nucleon. For incident energies above 100 MeV, both results are forward-peaked, whereas below 100 MeV, they exhibit different characteristics.
