Probing proton structure through single polarisation observables of Compton scattering and pion photoproduction within the Delta(1232) region

Abstract

Nucleon polarisabilities are fundamental structure observables, like the nucleon mass or charge, which are sensitive to the internal quark dynamics of the nucleon. Polarised Compton scattering off the proton can be used to study the polarisabilities of the proton, thus probing the internal structure of the proton. Spin dependent terms of the nucleon polarisabilties quantify the response of the proton's spin to an applied electromagnetic field. The leading order polarisabilities, denoted by gamma_{E1E1}, gamma_{M1M1}, gamma_{E1M2}, and gamma_{M1E2}, quantify the spin response to electric and magnetic dipole and quadrupole interactions.

Single polarization observables for Compton scattering, which are sensitive to these polarisabilities, were measured along with single polarization observables neutral pion photoproduction within the Delta(1232) resonance region. Sigma_{3} is a single polarisation observable which connects the polarised and unpolarised cross sections for linearly polarised photons incident upon unpolarised protons. Within this work, the execution and analysis of an experiment completed at the MAMI tagged photon facility in Mainz, Germany, is presented. Sigma_{3} was measured for neutral pion photoproduction for incident photon energies of 210 MeV up to 307 MeV (just below two-pion threshold). Sigma_{3} was measured for Compton scattering for incident photon energies of 267 MeV to 307 MeV.

A new extraction of the leading order spin polarisabilties of the proton is presented. This extraction used Sigma_{3} results for Compton scattering from this work, and Sigma_{2x} results from previous measurements at the MAMI tagged photon facility. Through this analysis, the spin polarisabilities of the proton were determined to be gamma_{E1E1} = -5.0 pm 1.5, gamma_{M1M1} = 3.13 pm 0.88, gamma_{E1M2} = 1.7 pm 1.7, and gamma_{M1E2} = 1.26 pm 0.43, in units of 10^{-4} fm^{4}. These experimentally determined spin polarisabilities are in good agreement with dispersion theory, K-matrix theory, and Heavy Baryon chiral perturbation theory calculations.