Semidileptonic decays of the light vector mesons in the light-front quark model

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 $\varphi$, $P={\pi }^0$, $\eta$, 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 $\varphi \to {\pi }^0{e}^{+}{e}^{-}$ from the NA60 Collaboration and $\varphi \to \eta e^{+}{e}^{-}$ with the Spherical Neutral Detector. We also predict that the branching ratios of $\varphi \to {\pi }^0{\mu }^{+}{\mu }^{-}$, $\omega \to \eta e^{+}{e}^{-}$, $\omega \to \eta {\mu }^{+}{\mu }^{-}$, $\varphi \to \eta {\mu }^{+}{\mu }^{-}$, and $\varphi \to {\eta }^{\prime }{e}^{+}{e}^{-}$ to be around $3.48\times {10}^{-6}$, $3.22\times {10}^{-6}$, $1.81\times {10}^{-9}$, $6.86\times {10}^{-6}$, and $2.97\times {10}^{-7}$, respectively.

Figure 1

$F_{\omega }\left(q^2\right)\equiv f_{\omega \to {\pi }^0}\left(q^2\right)/f_{\omega \to {\pi }^0}\left(0\right)$ in the LFQM.

Figure 2

Differential decay width of $\omega \to {\pi }^0{\mu }^{+}{\mu }^{-}$ as a function of $q$ in the LFQM, where the small band is due to the uncertainty of the data in Eq. (26).

Figure 3

Same as Fig. 2, but for the $e$ mode.

Figure 4

Differential decay width of $\varphi \to {\pi }^0{\mu }^{+}{\mu }^{-}$ as a function of $q$ in the LFQM.

Figure 5

Same as Fig. 4, but for the $e$ mode.

Figure 6

$F_{\varphi }\left(q^2\right)\equiv f_{\varphi \to \eta }\left(q^2\right)/f_{\varphi \to \eta }\left(0\right)$ in the LFQM.