COMPARATIVE STUDY OF SCATTERING AND ANNIHILATION CHANNELS OF THE BHABHA PROCCESES

Abstract

This thesis provides a relativistic description of electron-positron scattering and pair annihilation in quantum electrodynamics. By evaluating the modulus square of the invariant matrix elements, the differential cross-section for unpolarized electron-positron elastic scattering is calculated using leading-order Feynman diagrams. The study considers spin-half electrons and positrons, ensuring a consistent quantum electrodynamical framework. The relativistic expression of the spin-average invariant amplitude is constructed using Feynman rules, Completeness relation, and trace theorems. Integration over the Dirac-delta function reveals the dependence of the differential cross-section on the energy and scattering angle. Theoretical predictions are verified through computer simulations, confirming the behavior of the model. The study highlights the dominance of the t-channel contribution in the angular distribution plots and emphasizes the importance of the scattering term in Bhabha processes. Recommendations include exploring quantum corrections, external fields, radiative and polarization effects, electroweak corrections, and investigating practical implications in particle physics, astrophysics, and medical imaging