Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)

Abstract

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(Q^4) $\gamma$p amplitude of McGovern to experimental data in the region $\omega,\sqrt{|t|} \leq 180$ MeV, obtaining a chi^2/d.o.f. of 133/113. This yields a model-independent extraction of proton polarizabilities based solely on low-energy data: alpha_p=12.1 +/- 1.1 (stat.) +/- 0.5 (theory) and beta_p=3.4 +/- 1.1 (stat.) +/- 0.1 (theory), both in units of 10^{-4} fm^3. We also compute Compton scattering on deuterium to O(Q^4). The $\gamma$d 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 $\gamma$d scattering experiments with a chi^2/d.o.f.=26.6/20, and find alpha_N=13.0 +/- 1.9 (stat.) +3.9/-1.5 (theory) and a beta_N that is consistent with zero within sizeable error bars.Comment: 57 pages, 16 figures. Substantial changes. Correction of errors in deuteron calculation results in different values for isoscalar polarizabilities. Results for the proton are unaffected. Text modified to reflect this change, and also to clarify various point