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

Abstract

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 ≲ m _π (“low energy”), and the higher energies where the Δ(1232) resonance plays a key role. The Compton amplitude is complete at N⁴LO, $\mathcal{O}\left( {e^2 \delta ^4 } \right)$, in the low-energy region, and at NLO, $\mathcal{O}\left( {e^2 \delta ^0 } \right)$, in the resonance region. Throughout, the Delta-pole graphs are dressed with π N loops and γNΔ vertex corrections. A statistically consistent database of proton Compton experiments is used to constrain the free parameters in our amplitude: the M1 γNΔ transition strength b ₁ (which is fixed in the resonance region) and the polarisabilities α _E1 and β _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 γ _M1M1 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 α _E1 + β _M1. In this way we obtain α _E1 = [10.65 ± 0.35(stat) ± 0.2(Baldin) ± 0.3(theory)] × 10⁻⁴ fm³ and β _M1 = [3.15 ∓ 0.35(state) ± 0.2(Baldin) ∓ 0.3()theory] × 10⁻⁴ fm³, with χ² = 113.2 for 135 degrees of freedom. A detailed rationale for the theoretical uncertainties assigned to this result is provided.