  Measuring the lepton anomalous magnetic moments $(g-2)$ and the rare decays
of light pseudoscalar mesons into lepton pairs $P\to l^{+}l^{-} $, serve as
important tests of the Standard Model. To reduce the theoretical uncertainty in
the standard model predictions, the data on the charge and transition form
factors of the light pseudoscalar mesons play a significant role. Recently, new
data on the behavior of the transition form factors $P\to\gamma\gamma* $ at
large momentum transfer were supplied by the BABAR collaboration. There are
several problems with the theoretical interpretation of these data: 1) An
unexpectedly slow decrease of the pion transition form factor at high momenta,
2) the qualitative difference in the behavior of the pion form factor and the
$\eta$ and $\eta^\prime$ form factors at high momenta, 3) the inconsistency of
the measured ratio of the $\eta$ and $\eta^\prime$ form factors with the
predicted one. We comment on the influence of the new BABAR data on the rare
decay branchings.
