Semileptonic Decay of $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ Via Neutral Meson Mixing

Abstract

Based on the mechanism of neutral meson mixing, we predict the branching fraction of the semileptonic decay of $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ ($\ell =e$, $\mu$) using recently measured branching fraction of $D_s^{+}\to \eta e^{+}{\nu }_e$ by BESIII experiment . We also give a formula that can describe the neutral meson mixing of ${\pi }^0$, $\eta$, ${\eta }^{\prime }$ and a pseudoscalar gluonium $G$ in a unified way. The predicted branching fraction of $D_s^{+}\to {\pi }^0{e}^{+}{\nu }_e$ decay is $\mathcal{B}(D_s^{+}\to {\pi }^0{e}^{+}{\nu }_e)=(2.65\pm 0.38)\times 10^{-5}$. It is important to search for the decay $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ in experiment, in order to understand the mechanism of ${\pi }^0$ production in $D_s^{+}\to {\pi }^0$ transition in semileptonic decay. We also estimate the branching fraction of $D_s^{+}\to {\pi }^0{\tau }^{+}{\nu }_{\tau }$, which is the only kinematically allowed semi-tauonic decay mode of the charmed meson, since the mass value of $D_s^{+}$ meson is just slightly above the threshold of ${\pi }^0{\tau }^{+}$ generation in the semi-tauonic decay.

Comments: 6 pages, 1 figure