Pion-Mass Dependence of the Nucleon Polarisabilities: A Reappraisal

The static electric and magnetic scalar dipole polarisabilities and the four spin polarisabilities parametrise the nucleon's two-photon response. At next-to-next-to-leading order in Chiral Effective Field Theory ($\chi$EFT) with dynamical $\Delta(1232)$s, they have recently been extracted from Compton scattering data; ongoing experiments at HI$\gamma$S, MAMI and MAXlab test proton-neutron differences and chiral symmetry breaking. Comparing lattice QCD simulations at pion masses $m_\pi > 220$MeV to data and $\chi$EFT predictions requires a reliable extrapolation to the physical point. Since $\chi$EFT provides a systematically improvable, model-independent parametrisation of the polarisabilities, it is well-suited for that task. The relative theoretical uncertainties increase with increasing $m_\pi$: the magnitudes of the polarisabilities decrease; the $\chi$EFT expansion parameter itself increases; and the $\Delta(1232)$ becomes more important, leading to a re-ordering of contributions. After a review of $\chi$EFT, this presentation offers a method to quantitatively assess error-bands for chiral lattice extrapolations which can also be applied to other cases. Published errors appear to be underestimated.