Study of ${\pi }^0$ and $\eta$ decays containing dilepton

Abstract

We calculate the momentum dependent form factors of $P\to {\gamma }^{\ast }{\gamma }^{\ast }$($P={\pi }^0,\eta$) within the light-front quark model. Using the form factors, we examine the decays of $P\to l^{+}{l}^{-}$, $P\to l^{+}{l}^{-}\gamma$ and $P\to l^{+}{l}^{-}{l}^{+}{l}^{-}$($l=e$ or $\mu$) and compare our results with the experimental data and other theoretical predictions. In particular, for ${\pi }^0\to e^{+}{e}^{-}$, we find that the decay branching ratio is $6.68\times 10^{-8}$, which is consistent with the recent measurement of $(7.48\pm 0.29\pm 0.25)\times 10^{-8}$ by E799 of KTeV/Fermilab.

Comments: 13 pages, 1 figures. 2 tables; Charge factors added and numerical results corrected