  Recent measurement of the $\gamma\gamma^\ast$ form factor of the neutral pion
in the high $Q^2$ region disagrees with {\em a priori} predictions of QCD-based
calculations. We comment on existing explanations, and analyze a possibility
that this discrepancy is not due to poorly understood QCD effects, but is a
result of some new physics beyond the standard model (SM). We show that such
physics would necessarily involve a new neutral light state with mass close to
the mass of $\pi^0$, and with stronger than $\pi^0$ couplings to heavier SM
flavors such as $c$, $\tau$, and $b$. It is found that only the coupling to the
$\tau$ lepton can survive the existing constraints and lead to the observed
rise of the pion form factor relative to $Q^{-2}$ at high $Q^2$. We perform
numerical fits to data and determine the allowed range of masses and couplings
for such new particles. This range of masses and couplings could also reduce or
eliminate the tension between the $e^+e^-$ and $\tau$ decay determinations of
the hadronic vacuum polarization. Dedicated experimental analysis of $\tau$
pair production in association with such new states should provide a conclusive
test of the new physics hypothesis as an explanation to the pion form factor
rise. We also comment on the calculations of the pion form factor in the chiral
quark model, and point out a possible dynamical origin of the quark mass scale
inferred from the form factor measurement.
