Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theory

Based on Compton scattering and meson photoproduction data the polarizabilities of the nucleon are precisely studied and well understood due to recent experimental and theoretical work based on nonsubtracted dispersion relations. The {\it recommended} experimental values are $\alpha_p=12.0\pm 0.6$, $(12.0)$, $\beta_p=1.9\mp 0.6$, $(1.9)$, $\alpha_n=12.5\pm 1.7$, $(12.7\pm 0.9)$, $\beta_n=2.7\mp 1.8$, $(2.5\mp 0.9)$ in units of $10^{-4}$fm$^3$ and $\gamma^{(p)}_\pi=-36.4\pm 1.5$, $(-36.6)$, $\gamma^{(n)}_\pi=+58.6\pm 4.0$, $(58.3)$, $(\gamma^{(p)}_0=-0.58\pm 0.20)$, $\gamma^{(n)}_0=0.38\pm 0.22)$ in units of $10^{-4}$fm$^4$ [1]. The numbers given in parentheses are predicted values. It is shown that all versions of chiral effective field theories applied in analyses of nucleon polarizabilities and Compton scattering ignore essential effects of $\omega$, $\rho$ and $\sigma$ exchanges and of pseudoscalar $\pi$N coupling.