  In quantum systems with large $n$ (radial quantum number) or large angular
momentum the semiclassical (WKB) approximation is valid. A physical content of
the semiclassical approximation is that the quantum fluctuations effects are
suppressed and vanish asymptotically. The chiral as well as $U(1)_A$ breakings
in QCD result from quantum fluctuations. Hence these breakings must be
suppressed high in the spectrum and the spectrum of high-lying hadrons must
exhibit $U(2)_L \times U(2)_R$ symmetry of the classical QCD Lagrangian. This
argument can be made stronger for mesons in the large $N_c$ limit. In this
limit all mesons are stable against strong decays and the spectrum is infinite.
Hence, one can excite mesons of arbitrary large size with arbitrary large
action, in which case the semiclassical limit is manifest. Actually we do not
need the exact $N_c=\infty$ limit. For any large action there always exist such
$N_c$ that the isolated mesons with such an action do exist and can be
described semiclassically. From the empirical fact that we observe multiplets
of chiral and $U(1)_A$ groups high in the hadron spectrum it follows that
$N_c=3$ is large enough for this purpose.
