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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 Mπ < ∆≡M∆−MN < Λχ , through a counting Mπ/∆ ∼ ∆/Λχ ∼ δ . 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. This is designed to extend the region of χPT applicability to momenta p∼ ∆. We have computed the nucleon Compton amplitude in the delta expansion up to N3LO— O(e2δ 4)—for photon energies ω ∼ Mπ . 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 ∼ Λχ . 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 αp and βp.

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