Structure of the $σ$-meson and diamagnetism of the nucleon

Abstract

The structure of the $σ$ meson and the diamagnetism of the nucleon are shown to be topics which are closely related to each other. Arguments are found that the $σ$ meson couples to two photons via its non-strange $q\bar{q}$ structure component. This ansatz leads to a quantitative explanation of the $t$-channel component of the difference of electromagnetic polarizabilities, (α-β)^t$, containing the diamagnetism of the nucleon. The prediction is $(α-β)^t_{p,n}=(5α_e g_{πMM})/(6π^2 m^2_σf_π)=15.3$ in units of $10^{-4}{\rm fm}^3$ to be compared with the experimental value $(α-β)^t_p=15.1\pm 1.3$ for the proton and $(α-β)^t_n=14.8\pm 2.7$ for the neutron. The equivalent approach to exploit the $ππ$ structure component of the $σ$ meson via the BEFT sum rule leads to $(α-β)^t_{p,n}=14\pm 2$, what also is in agreement with the experimental results.