Spin-dependent Compton scattering within the spin-helicity framework

This is the authors' abstract. We don't add key points for this paper.

This work presents a detailed computation of Compton scattering cross sections using the spin-helicity formalism. The analysis begins with the unpolarised case in the laboratory frame, where we recover the well-known Klein-Nishina formula along with its classical limit, the Thomson formula. We then examine polarised Compton scattering in the centre-of-mass frame, introducing the concepts of spin-flip and spin non-flip differential cross sections. A key consistency check confirms that the sum of these two spin-resolved contributions reproduces the unpolarised differential cross section. The results are discussed and interpreted within the context of spin-dependent scattering processes. All trace calculations have been performed using the symbolic computation software REDUCE due to their complexity. This study aims to provide a deeper understanding of spin effects in quantum electrodynamics processes and to support future investigations involving polarised particles in scattering experiments.