Extracting the Proton Backward Spin Polarizability using Compton Scattering

The proton spin-polarizabilities (SPs) are properties that quantify the response of the proton spin to electromagnetic waves. The SPs can be expressed in a linear combination called the backward spin polarizability ($\gamma \pi )$ which arises in the cross-section of a Compton scattering event in which the incident photon is scattered at 180 degrees. As the cross-section at this angle cannot be experimentally determined, measurements of $\gamma \pi $ are fitted using data with scattering angles close to 180 degrees. However, as the scattering angle is reduced the cross-section rapidly becomes determined by the values of the individual SPs, not $\gamma \pi $. This project investigated the viability of using cross-section data from different energy and angle bins to extract the $\gamma \pi $ in order to optimize future experiments for $\gamma \pi $ extraction. A Dispersion Relation was used to generate theory points based on randomly specified values of $\gamma \pi $ and SPs for data sets of different energy and scattering angle. This was repeated 2000 times and the $\chi $2 of each iteration was measured to determine if fits to a data set were dependent on the individual SPs values or $\gamma \pi $.