NEUTRINO INDUCED MUON PAIR PRODUCTION IN UNIFORM BACKGROUND MAGNETIC FIELD: CASE OF NEUTRAL CURRENT PROCESS

Abstract

Neutrino is core in understanding the weak interaction and it is the only fundamental particle whose interactions are dominated by the weak interaction. The main goal of this study is to apply Glashow-Weinberg-Salam theory to study of neutrino-induced muon-antimuon pair production in the presence of uniform background magnetic field. Within the framework of the standard model, the determination of scattering amplitude in terms of the lowest order Feynman diagram and production rate for neutral current reaction are the main goal of this work. In the presence of magnetic field, the modified Dirac equation is derived for both positive and negative energy solutions. The Fenman rules, Casmir’s trick and trace theorems have been employed in constructing the relative description of modulus square of spin averaged invariant amplitude. In doing so, the modulus square of spin averaged invariant amplitude has been described as the contraction between lepton tensors enabling straight forward calculation of production rate. The kinematics of the process is set so that the incident, scattered and produced particles were confined on the 𝑧𝑥­plane. By taking into account different values of Landau levels, the production rate as a function of incident energy has been plotted by using Matlab programming language; and for numerical integration we have used the Gaussian quadrature with 10 integration points. Besides, we have presented the numerical results for the rate of pair production for NC process near to the critical field. Different Landau levels considered for a fixed incident energy production rate has been found to increase as field strength increases. Even though production rate increases for different Landau levels considered, it increases to a great extent when the Landau levels of muon and antimuon are equal