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 (χEFT) 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 ω ∼ mπ (“low energy”), and the higher energies where the ∆(1232) resonance plays a key role. The Compton amplitude is complete at N4LO, O(e2δ4), in the low-energy region, and at NLO, O(e2δ0), in the resonance region. Throughout, the Delta-pole graphs are dressed with πN loops and γN∆ vertex corrections. A statistically consistent database of proton Compton experiments is used to constrain the free parameters in our amplitude: the M1 γN∆ transition strength b1 (which is fixed in the resonance region) and the polarisabilities αE1 and βM1 (which are fixed from data below 170 MeV). In order to obtain a reasonable fit, we find it necessary to add the spin polarisability γM1M1 as a free parameter, even though it is, strictly speaking, predicted in χEFT 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 αE1+βM1. In this way we obtain αE1 = [10.65±0.35(stat)±0.2(Baldin)±0.3(theory)]×10−4 fm and βM1 = [3.15∓ 0.35(stat)± 0.2(Baldin)∓ 0.3(theory)]× 10−4 fm, with χ2 = 113.2 for 135 degrees of freedom. A detailed rationale for the theoretical uncertainties assigned to this result is provided. ‡ Permanent address ¶ Permanent address Electronic address: [email protected] Electronic address: [email protected] Electronic address: [email protected]