ELECTROWEAK THEORY OF NEUTRINO SCATTERING FROM LAMBDA-HYPERON: CASE OF NEUTRAL CURRENT PROCESS

Abstract

The main purpose of this study is to formulate the electroweak description of neutrino-induced weak transition of Lambda-hyperon. The norm-squared of invariant amplitude has been manipulated into contraction between leptonic and hadronic tensors. In the Laboratory (Lab) frame where the target Lambda-hyperon is at rest the kinematics and dynamics of the process of interest have been evaluated, separately. The electroweak (GWS) theory is used to calculate the leptonic tensor exactly. The hadronic current, however, has been expanded in terms of three unknown form factors in order to parameterize the hadronic vertex, which in turn have been estimated in the frameworks of the Cabibbo V-A theory and SU(3) symmetry. The model dependent calculation indicates that there is no contribution coming through the axial form factor. The Feynman rules, Casmir’s trick and trace theorems have been employed in the constructing the relativistic expression of spin-average invariant-amplitude. The numerical results for the differential cross section have been generated using Matlab R2016b programming language. The angular distribution indicates that in the intermediate energy region, the peak occurs not at, but near the forward angle. However, this is not the case for low energy region, as the peak gets broader and occurs far away from the forward scattering angle. On the other hand, the energy distribution of the differential cross section reveals that, at fixed small scattering angle, the low incident energy region has a vanishing contribution, while the dominant contribution comes from the intermediate energy regime. More so, as the scattering angle increases the peak of energy distribution gets sharper and drastically shifts towards the low incident energy region