Properties of the $pi^0$, $eta$, $eta$, $sigma$, $f_0(980)$ and $a_0(980)$ mesons and their relevance for the polarizabilities of the nucleon

The signs and values of the two-photon couplings $F_{Mgammagamma}$ of mesons $(M)$ and their couplings $g_{MNN}$ to the nucleon as entering into the $t$-channel parts of the difference of the electromagnetic polarizabilities $(alpha-beta)$ and the backward angle spin polarizabilities $gamma_pi$ are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are $alpha_n=13.4pm 1.0$, $beta_n=1.8mp 1.0$ ($10^{-4}$ fm$^3$), and $gamma^{(n)}_pi=57.6pm 1.8$ ($10^{-4}$ fm$^4$). New empirical information on the flavor wave functions of the $f_0(980)$ and the $a_0(980)$ meson is obtained.