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

Understand

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.