Compton Scattering and Nucleon Polarizabilities at HI$\gamma$S

The electromagnetic polarizabilities of the nucleon are fundamental quantities related to nucleon structure. In the past decade, effective field theories have successfully established a bridge between QCD and low-energy description of the nucleon and made predictions for the polarizabilities. Lattice QCD calculations are also eminent on electromagnetic polarizabilities. High precision data are now needed to benchmark these calculations. To this end, the Compton scattering program at the High Intensity $\gamma$-ray Source (HI$\gamma$S) has provided the Compton scattering cross sections on the deuteron at 65 and 85 MeV to extract the neutron polarizabilities. Recently, data have also been collected at HI$\gamma$S to measure the beam asymmetry of linearly polarized Compton scattering on the proton at 84 MeV to extract the proton polarizabilities independently from the Baldin sum rule. In addition, the Compton scattering cross sections on $^4$He were also measured using a circularly polarized photon beam at 84 MeV. In this talk, I will present the details of the experimental method, the analysis and the results of the 84 MeV Compton scattering data on $^4$He.