Comprehensive Study of Observables in Compton Scattering on the Nucleon

We present an analysis of $13$ observables in Compton scattering on the proton. Cross sections, asymmetries with polarised beam and/or targets, and polarisation-transfer observables are investigated for energies up to the $\Delta(1232)$ resonance to determine their sensitivity to the proton's dipole scalar and spin polarisabilities. The Chiral Effective Field Theory Compton amplitude we use is complete at N$^4$LO, $\mathcal{O(}e^2\delta^4)$, for photon energies $\omega\sim m_\pi$, and so has an accuracy of a few per cent there. At photon energies in the resonance region it is complete at NLO, $\mathcal{O}(e^2\delta^0)$, and so its accuracy there is about $20$\%. We find that for energies from pion-production threshold to about $250\;\mathrm{MeV}$, multiple asymmetries have significant sensitivity to presently ill-determined combinations of proton spin polarisabilities. We also argue that the broad outcomes of this analysis will be replicated in complementary theoretical approaches, e.g., dispersion relations. Finally, we show that below the pion-production threshold, $6$ observables suffice to reconstruct the Compton amplitude, and above it $11$ are required. Although not necessary for polarisability extractions, this opens the possibility to perform "complete" Compton-scattering experiments. An interactive Mathematica notebook, including results for the neutron, is available from judith.mcgovern@manchester.ac.uk .