Extracting Neutron Polarizabilities from Compton Scattering on Quasi-Free Neutrons in $\gamma d \rightarrow \gamma n p$

Compton scattering processes are ideal to study electric and magnetic dipole polarizability coefficients of nucleons. These fundamental quantities parametrize the response to a monochromatic photon probe. In this work, the inelastic channel $\gamma d\rightarrow \gamma np$ is treated in $\chi$EFT, with a focus on the NQFP - neutron quasi-free peak - kinematic region. In this region, the momentum of the outgoing proton is small enough that it is considered to remain at rest. This provides access to the Compton scattering process $\gamma n \rightarrow \gamma n$ from which the neutron scalar polarizabilites $\alpha$ and $\beta$ are extracted. Using $\chi$EFT, differential cross-sections, $d^3\sigma/dE_nd\Omega_{\gamma'} \Omega_n$, in the photon energy range of 200-400 MeV are computed. The biggest contribution comes from the impulse approximation, with small corrections stemming from final state interaction, meson exchange currents and rescattering. A new extraction of neutron polarizabilities from a two-parameter fit to the Kossert et al. data taken at MAMI in 2002 is presented.