Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom

We analyse the proton Compton-scattering differential cross section for photon energies up to 325 MeV using Chiral Effective Field Theory (chi EFT) and extract new values for the electric and magnetic polarisabilities of the proton. Our approach builds in the key physics in two different regimes: photon energies omega less than or similar to m(pi) (low energy), and the higher energies where the Delta(1232) resonance plays a key role. The Compton amplitude is complete at (NLO)-L-4, O(e(2)delta(4)), in the low-energy region, and at NLO, O(e(2)delta(0)), in the resonance region. Throughout, the Delta-pole graphs are dressed with pi N loops and gamma N Delta vertex corrections. A statistically consistent database of proton Compton experiments is used to constrain the free parameters in our amplitude: the M1 gamma N Delta transition strength b(1) (which is fixed in the resonance region) and the polarisabilities alpha(E1) and beta(M1) (which are fixed from data below 170 MeV). In order to obtain a reasonable fit, we find it necessary to add the spin polarisability gamma(M1M1) as a free parameter, even though it is, strictly speaking, predicted in chi EFT at the order to which we work. We show that the fit is consistent with the Baldin sum rule, and then use that sum rule to constrain alpha(E1) + beta(M1). In this way we obtain alpha(E1) = [10.65 +/- 0.35(stat) +/- 0.2(Baldin) +/- 0.3(theory)] x 10(-4) fm(3) and beta(M1) = [3.15 -/+ 0.35(stat) +/- 0.2(Baldin) -/+ 0.3(theory)] x 10(-4) fm(3), with chi(2) = 113.2 for 135 degrees of freedom. A detailed rationale for the theoretical uncertainties assigned to this result is provided.