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

TL;DR

This paper investigates meson properties and their couplings to nucleons, enabling precise predictions of neutron polarizabilities and providing new insights into the flavor structure of specific scalar mesons.

Contribution

It determines meson-photon and meson-nucleon couplings, improving predictions of neutron polarizabilities and revealing new empirical data on scalar meson flavor wave functions.

Findings

Predicted neutron electric polarizability: 13.4±1.0

Predicted neutron magnetic polarizability: 1.8∓1.0

New empirical data on $f_0(980)$ and $a_0(980)$ meson structures

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.