Using Polarized Compton Scattering to Extract Proton Spin Polarizabilities

The MAMI A2 collaboration has recently taken data on the Compton scattering beam-target asymmetry $\Sigma_{2z}$ using a circularly polarized photon beam with a longitudinally polarized target. These data accompany previous A2 data using a transversely polarized target to obtain $\Sigma_{2x}$ and a linearly polarized photon beam on an unpolarized target to obtain $\Sigma_{3}$. The goal of this Compton scattering program at A2 is the extraction of the proton spin polarizabilities, parameters which describe the response of the proton spin to a scattering photon. Third order terms in the energy expansion of the Compton scattering amplitude, the spin polarizabilities provide a valuable test of nucleon structure, dispersion and effective field theories, and lattice calculations. While values have been determined for two linear combinations of the spin polarizabilities, their independent extraction requires the use of such complimentary data sets on different Compton scattering observables. These data were taken with the MAMI A2 Bremsstrahlung beam, either a frozen-spin butanol or an unpolarized hydrogen target, and the Crystal Ball and TAPS detectors. We will report on the $\Sigma_{2x}$ measurements, supplemented by preliminary $\Sigma_{3}$ and $\Sigma_{2z}$ measurements.