Semi-dileptonic decays of the light vector mesons in Light Front Quark Model

Abstract

We study the transition form factors of the light vector to pseudoscalar mesons as functions of the momentum transfer $q^2$ within the light-front quark model. With these form factors, we calculate the decay branching ratios of all possible modes for $V\to P\ell^+\ell^-$ ($V=\omega$ and $\phi$, $P=\pi^0$, $\eta$ and $\eta^{\prime}$ and $\ell=e$ and $\mu$). We find that our numerical results fit with the data, such as those of $\omega \to \pi^0 \ell^+\ell^-$ and $\phi\to \pi^0 e^+e^-$ by NA60 and $\phi \to\eta e^+e^-$ by SND. We also predict that the branching ratios of $\phi \to \pi^0 \mu^+\mu^-$, $\omega\to \eta e^+e^-$, $\omega\to \eta \mu^+\mu^-$, $\phi\to \eta \mu^+\mu^-$ and $\phi\to \eta^{\prime} e^+e^-$ to be aroud $3.48\times 10^{-6}$, $3.22\times 10^{-6}$, $1.81\times 10^{-9}$, $6.86\times 10^{-6}$ $2.97\times 10^{-7}$, respectively.