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

TL;DR

This paper uses Chiral Effective Field Theory to analyze proton Compton scattering data up to 325 MeV, extracting precise values for proton electric and magnetic polarisabilities while accounting for resonance effects and theoretical uncertainties.

Contribution

It introduces a comprehensive EFT framework incorporating Delta resonance effects and provides new, precise proton polarisability values constrained by experimental data and sum rules.

Findings

Extracted proton electric polarisability alpha = (10.65 ± 0.35(stat) ± 0.2(Baldin) ± 0.3(theory))×10^{-4} fm^3.

Extracted proton magnetic polarisability beta = (3.15 ± 0.35(stat) ± 0.2(Baldin) ± 0.3(theory))×10^{-4} fm^3.

Achieved a fit consistent with the Baldin sum rule and detailed the theoretical uncertainties.

Abstract

We analyse the proton Compton-scattering differential cross section for photon energies up to 325 MeV using Chiral Effective Field Theory and extract new values for the electric and magnetic polarisabilities of the proton. Our EFT treatment builds in the key physics in two different regimes: photon energies around the pion mass ("low energy") and the higher energies where the Delta(1232) resonance plays a key role. The Compton amplitude is complete at N4L0, 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 and beta (which are fixed from data below 170 MeV). In order to obtain a reasonable fit we find it necessary to add the spin polarisability gammaM1 as a free parameter, even though it is, strictly speaking, predicted in chiral 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+beta. In this way we obtain alpha=[10.65+/-0.35(stat})+/-0.2(Baldin)+/-0.3(theory)]10^{-4} fm^3, and beta =[3.15-/+0.35(stat)-/+0.2(Baldin)-/+0.3(theory)]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.