Compton scattering from the proton: An analysis using the delta expansion up to N3LO

TL;DR

This paper presents a chiral effective field theory calculation of proton Compton scattering using the delta expansion up to N3LO, incorporating pions, nucleons, and the Delta resonance, to extract proton polarizabilities from experimental data.

Contribution

It introduces a novel application of the delta expansion up to N3LO for Compton scattering, including explicit Delta degrees of freedom and resummation techniques.

Findings

Calculated proton Compton amplitudes up to N3LO.

Fitted contact operator coefficients to experimental data.

Extracted new values for proton polarizabilities alpha and beta.

Abstract

We report on a chiral effective field theory calculation of Compton scattering from the proton. Our calculation includes pions, nucleons, and the Delta(1232) as explicit degrees of freedom. It uses the "delta expansion", and so implements the hierarchy of scales m_pi < M_Delta-M_N < Lambda_chi. In this expansion the power counting in the vicinity of the Delta peak changes, and resummation of the loop graphs associated with the Delta width is indicated. We have computed the nucleon Compton amplitude in the delta expansion up to N3LO for photon energies of the order of m_pi. This is the first order at which the proton Compton scattering amplitudes receive contributions from contact operators which encode contributions to the spin-independent polarisabilities from states with energies of the order of Lambda_chi. We fit the coefficients of these two operators to the experimental proton Compton data that has been taken in the relevant photon-energy domain, and are in a position to extract new results for the proton polarisabilities alpha and beta.