Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q4)

We study Compton scattering in systems with A=1 and 2 using chiral perturbation theory up to fourth order. For the proton we fit the two undetermined parameters in the O(Q4)γp amplitude of McGovern to experimental data in the region ω,|t|⩽180MeV, obtaining a χ2/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: αp=(12.1±1.1(stat.))−0.5+0.5(theory) and βp=(3.4±1.1(stat.))−0.1+0.1(theory), both in units of 10−4fm3. We also compute Compton scattering on deuterium to O(Q4). The γd amplitude is a sum of one- and two-nucleon mechanisms, and contains two undetermined parameters, which are related to the isoscalar nucleon polarizabilities. We fit data points from three recent γd scattering experiments with a χ2/d.o.f.=26.6/20, and find αN=(13.0±1.9(stat.))−1.5+3.9(theory) and a βN that is consistent with zero within sizable error bars.