  We report on a search in $e^+e^-$ annihilations for new $\pi^0$-like
particles produced in association with a $\tau$-lepton pair. These objects,
with a similar mass and similar decay modes to $\pi^0$ mesons, could provide an
explanation for the non-asymptotic behavior of the pion-photon transition form
factor observed by the Babar Collaboration. No significant signal is observed,
and limits on the production cross section at the level of 73 fb or 370 fb,
depending on the model parameters, are determined at 90% confidence level.
These upper limits lie below the cross section values needed to explain the
Babar form factor data.
