Measuring the Spin-Polarizabilities of the Proton in Polarized Compton scattering at MAMI-Mainz

At $O(\omega^{3})$ four new structure constants are present in the nucleon Compton scattering amplitude; these are the spin-polarizabilities $\gamma _{E1E1} $, $\gamma_{M1M1} $, $\gamma_{E1M2} $, and $\gamma_{M1E2} $. The most model independent way to determine the spin-polarizabilities is by measuring a double-polarized Compton scattering asymmetry with polarized target and circularly polarized photons, and by measuring an in-plane/transverse-plane Compton scattering asymmetry with linearly polarized photons ($\Sigma_{3} )$. This talk will present new Compton scattering asymmetry data taken in the $\Delta $ region by the A2 Collaboration using the Crystal Ball at Mainz, with transverse polarized proton target and circularly polarized photons, the $\Sigma_{2x} $ asymmetry (1). A dispersion model and an EFT calculation of Compton scattering are used to fit the four spin-polarizabilities to the new experimental data on $\Sigma_{2x} $, earlier results (2) on $\Sigma_{3} $, and previous determinations of $\gamma_{0} $ and $\gamma_{\pi } $. The results of the fits are compared with theoretical calculations. \\[4pt] [1] P. Martel, Ph.D. thesis, University of Massachusetts, unpublished (2012).\\[0pt] [2] G. Blanpied, et al., Phys. Rev. C, 64, 025203 (2001)