Measurement of Compton Scattering at MAMI for the Extraction of the Electric and Magnetic Polarizabilities of the Proton

A precise measurement of the differential cross sections d sigma/d Omega and the linearly polarized photon beam asymmetry Sigma(3) for Compton scattering on the proton below pion threshold has been performed with a tagged photon beam and almost 4 pi detector at the Mainz Microtron. The incident photons were produced by the recently upgraded Glasgow-Mainz photon tagging facility and impinged on a cryogenic liquid hydrogen target, with the scattered photons detected in the Crystal Ball/TAPS setup. Using the highest statistics Compton scattering data ever measured on the proton along with two effective field theories (both covariant baryon and heavy-baryon) and one fixed-t dispersion relation model, constraining the fits with the Baldin sum rule, we have obtained the proton electric and magnetic polarizabilities with unprecedented precision: alpha(E1) = 10.99 +/- 0.16 +/- 0.47 +/- 0.17 +/- 0.34, beta(M1) = 3.14 +/- 0.21 +/- 0.24 +/- 0.20 +/- 0.35; in units of 10(-4) fm(3) where the errors are statistical, systematic, spin polarizability dependent, and model dependent.