  New high-statistics Belle data on the reaction \gamma\gamma\to\pi^0\eta are
analyzed to clarify the two-photon production mechanisms and the nature of the
a_0(980) meson. The obtained solution for the amplitude
\gamma\gamma\to\pi^0\eta is consistent with the chiral theory expectation for
the \pi\eta scattering length, with the strong coupling of the a_0(980) to the
\pi\eta, K\bar K, and \pi\eta' channels, and with a key role of the
rescattering mechanisms a_0(980)\to(K\bar K+
\pi^0\eta+\pi^0\eta')\to\gamma\gamma in the a_0(980)\to\gamma\gamma decay. Such
a picture argues in favor of the q^2\bar q^2 nature of the a_0(980) meson and
is in agreement with the properties of its partners, the \sigma_0(600) and
f_0(980) mesons, in particular, with those that manifest themselves in
\gamma\gamma\to\pi\pi. An important role of the vector meson exchanges in the
formation of the nonresonant background in \gamma\gamma\to\pi^0\eta is also
revealed. The preliminary information on the reaction \pi^0\eta\to\pi^0\eta is
obtained.
