Nucleon Polarisabilities from Deuteron Compton Scattering, and Its Lessons for Chiral Counting

Chiral Effective Field Theory with explicit $\Delta(1232)$ degree of freedom is for photon energies up to $300$ MeV the tool to accurately determine the proton and neutron polarisabilities from Compton scattering in a model-independent and systematic way. It proves in particular indispensable to understand deuteron Compton scattering at $95$ MeV as measured at SAL. Simple consistency arguments derived from nuclear phenomenology lead for the deuteron to the correct Thomson limit, demonstrating gauge-invariance and shedding new light on Weinberg264s proposed power-counting of nuclear forces. In our global analysis of all elastic proton and deuteron Compton scattering up to $150\;\mathrm{MeV}$, we find for the static scalar dipole polarisabilities $\bar{\alpha}^p=(11.0\pm1.4_{\mathrm{stat}}\pm0.4_{\mathrm{sys}})\times10^{-4} \;\mathrm{fm}^3$, $\bar{\beta}^p=(2.8\mp1.4_{\mathrm{stat}}\pm0.4_{\mathrm{syst}})\times 10^{-4}\;\mathrm{fm}^3$ for the proton and $\bar{\alpha}^n=(11.6\pm1.5_{\mathrm{stat}}\pm0.6_{\mathrm{syst}})\times 10^{-4}\;\mathrm{fm}^3$ $\bar{\beta}^n=(3.6\mp1.5_{\mathrm{stat}}\pm0.6_{\mathrm{syst}})\times 10^{-4}\;\mathrm{fm}^3$ for the neutron. Thus, proton and neutron polarisabilities are identical within the accuracy of available data. New experiments e.g.~at MAXlab (Lund) will improve the statistical error-bar. [1] R.~P.~Hildebrandt, H.~W.~Grie{\ss}hammer and T.~R.~Hemmert, submitted to Phys.~Rev.~C~[nucl-th/0512063]. [2] H.~W.~Grie{\ss}hammer: \emph{Power-Counting in Chiral EFT from a Minimum of Phenomenology}, in preparation.