Using Effective Field Theory to analyse low-energy Compton scattering data from protons and light nuclei

Compton scattering from protons and neutrons provides important insight into the structure of the nucleon. For photon energies up to about 300 MeV, the process can be parameterised by six dynamical dipole polarisabilities which characterise the response of the nucleon to a monochromatic photon of fixed frequency and multipolarity. Their zero-energy limit yields the well-known static electric and magnetic dipole polarisabilities α E 1 and β M 1 , and the four dipole spin polarisabilities. The emergence of full lattice QCD results and new experiments at MAMI (Mainz), HI γ S  at TUNL, and MAX-Lab (Lund) makes this an opportune time to review nucleon Compton scattering. Chiral Effective Field Theory ( χ EFT ) provides an ideal analysis tool, since it encodes the well-established low-energy dynamics of QCD while maintaining an appropriately flexible form for the Compton amplitudes of the nucleon. The same χ EFT  also describes deuteron and 3 He  Compton scattering, using consistent nuclear currents, rescattering and wave functions, and respects the low-energy theorems for photon–nucleus scattering. It can thus also be used to extract useful information on the neutron amplitude from Compton scattering on light nuclei. We summarise past work in χ EFT  on all of these reactions and compare with other theoretical approaches. We also discuss all proton experiments up to about 400 MeV, as well as the three modern elastic deuteron data sets, paying particular attention to the precision and accuracy of each set. Constraining the Δ ( 1232 ) parameters from the resonance region, we then perform new fits to the proton data up to ω lab = 170 MeV , and a new fit to the deuteron data. After checking in each case that a two-parameter fit is compatible with the respective Baldin sum rules, we obtain, using the sum-rule constraints in a one-parameter fit, α E 1 ( p ) = 10.7 ± 0.3 ( stat ) ± 0.2 ( Baldin ) ± 0.8 ( theory ) , β M 1 ( p ) = 3.1 ∓ 0.3 ( stat ) ± 0.2 ( Baldin ) ± 0.8 ( theory ) , for the proton polarisabilities, and α E 1 ( s ) = 10.9 ± 0.9 ( stat ) ± 0.2 ( Baldin ) ± 0.8 ( theory ) , β M 1 ( s ) = 3.6 ∓ 0.9 ( stat ) ± 0.2 ( Baldin ) ± 0.8 ( theory ) , for the isoscalar polarisabilities, each in units of 1 0 − 4 fm 3 . Finally, we discuss plans for polarised Compton scattering on the proton, deuteron, 3 He  and heavier targets, their promise as tools to access spin polarisabilities, and other future avenues for theoretical and experimental investigation.