  The structure of the $\sigma$ meson and the diamagnetism of the nucleon are
shown to be topics which are closely related to each other. Arguments are found
that the $\sigma$ 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,
(\alpha-\beta)^t$, containing the diamagnetism of the nucleon. The prediction
is $(\alpha-\beta)^t_{p,n}=(5\alpha_e g_{\pi MM})/(6\pi^2 m^2_\sigma
f_\pi)=15.3$ in units of $10^{-4}{\rm fm}^3$ to be compared with the
experimental value $(\alpha-\beta)^t_p=15.1\pm 1.3$ for the proton and
$(\alpha-\beta)^t_n=14.8\pm 2.7$ for the neutron. The equivalent approach to
exploit the $\pi\pi$ structure component of the $\sigma$ meson via the BEFT sum
rule leads to $(\alpha-\beta)^t_{p,n}=14\pm 2$, what also is in agreement with
the experimental results.
