Semileptonic Decay of $D_s^+\to π^0 \ell^+ ν_\ell$ Via Neutral Meson Mixing

Abstract

Based on the mechanism of neutral meson mixing, we predict the branching fraction of the semileptonic decay of $D_s^+\to π^0 \ell^+ ν_\ell$ ($\ell=e$, $μ$) using recently measured branching fraction of $D_s^+\to ηe^+ν_e$ by BESIII experiment . We also give a formula that can describe the neutral meson mixing of $π^0$, $η$, $η'$ and a pseudoscalar gluonium $G$ in a unified way. The predicted branching fraction of $D_s^+\toπ^0 e^+ν_e$ decay is $\mathcal{B}(D_s^+\toπ^0 e^+ν_e)=(2.65\pm 0.38)\times 10^{-5}$. It is important to search for the decay $D_s^+\to π^0 \ell^+ ν_\ell$ in experiment, in order to understand the mechanism of $π^0$ production in $D_s^+\toπ^0$ transition in semileptonic decay. We also estimate the branching fraction of $D_s^+\to π^0τ^+ν_τ$, 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 $π^0τ^+$ generation in the semi-tauonic decay.