  We investigate the physical consequences of the survival of the effects of
the U(1)_A anomaly in the chiral symmetric phase of QCD, and show that the free
energy density is a singular function of the quark mass m, in the chiral limit,
and that the $\sigma$ and $\bar\pi$ susceptibilities diverge in this limit at
any $T\ge T_c$. We also show that the difference between the $\bar\pi$ and
$\bar\delta$ susceptibilities diverges in the chiral limit at any $T\ge T_c$, a
result which seems to be excluded by recent results of Tomiya et al. from
numerical simulations of two-flavor QCD. We also discuss on the generalization
of these results to the $N_f\ge 3$ model.
