Measurements of Double-Polarized Compton Scattering Asymmetries and Extraction of the Proton Spin Polarizabilities

The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to measure the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the $\Delta(1232)$ region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a dispersion model calculation yields $\gamma_{E1E1} = -3.5 \pm 1.2$, $\gamma_{M1M1}= 3.16 \pm 0.85$, $\gamma_{E1M2} = -0.7 \pm 1.2$, and $\gamma_{M1E2} = 1.99 \pm 0.29$, in units of $10^{-4}$ fm$^4$.