How the recent BABAR data for $P\to\gamma\gamma^*$ affect the Standard Model predictions for the rare decays $P\to l^+l^-$

Measuring the lepton anomalous magnetic moments $(g-2)$ and the rare decays of light pseudoscalar mesons into lepton pairs $P\rightarrow l^+l^-$, 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.