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

Abstract

The signs and values of the two-photon couplings $F_{M\gamma\gamma}$ 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 $\alpha_n=13.4\pm 1.0$, $\beta_n=1.8\mp 1.0$ ($10^{-4}$ fm$^3$), and $\gamma^{(n)}_\pi=57.6\pm 1.8$ ($10^{-4}$ fm$^4$). New empirical information on the flavor wave functions of the $f_0(980)$ and the $a_0(980)$ meson is obtained.