Signatures of chiral dynamics in low-energy Compton scattering off the nucleon

We present a projection formalism which allows us to define dynamical polarizabilities of the nucleon from a multipole expansion of the nucleon Compton amplitudes. We give predictions for the energy dependence of these dynamical polarizabilities both from Dispersion Theory and from leading-one-loop Chiral Effective Field Theory. Based on the good agreement between the two theoretical frameworks, we conclude that the energy dependence of the dynamical polarizabilities is dominated by chiral dynamics, except in those multipole channels where the first nucleon resonance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta$\end{document}(1232) can be excited. Both the Dispersion Theory framework and a Chiral Effective Field Theory with explicit \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta$\end{document}(1232) degrees of freedom lead to a very good description of the available low-energy proton Compton data. We discuss the sensitivity of the proton Compton cross-section to dynamical polarizabilities of different multipole content and present a fit of the static electric and magnetic dipole polarizabilities from low-energy Compton data up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega \sim 170\;\mathrm{MeV}$\end{document}, finding \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bar{\alpha}_{E} = (11.04\pm1.36)\cdot 10^{-4}\;\mathrm{fm}^3,\; \bar{\beta}_{M} = (2.76\mp1.36)\cdot 10^{-4}\;\mathrm{fm}^3$\end{document}.