Properties of the ${\pi }^0$, $\eta$, ${\eta }^{\prime }$, $\sigma$, $f_0(980)$ 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 ${\gamma }_{\pi }^{(n)}=57.6\pm 1.8$ ($10^{-4}$ fm${}^4$). New empirical information on the flavor wave functions of the $f_0(980)$ and the $a_0(980)$ meson is obtained.