$\omega$-$\varphi$ mixing and weak annihilation in $D_s$ decays

Abstract

The mixing between nonstrange and strange quark wavefunctions in the $\omega$ and $\varphi$ mesons leads to a small predicted branching ratio $\text{b}(D_s^{+}\to \omega e^{+}{\nu }_e)=\mathcal{O}(10^{-4})(\delta /3.34^{\circ }{)}^2$, where $\delta$ is the mixing angle. The value $\delta =-3.34^{\circ }$ is obtained in a mass-independent analysis, while a mass-dependent analysis gives $\delta =-0.45^{\circ }$ at $m(\omega )$ and $-4.64^{\circ }$ at $m(\varphi )$. Measurement of this branching ratio thus can tell whether the decay is dominated by $\varphi$--$\omega$ mixing, or additional nonperturbative processes commonly known as "weak annihilation" (WA) contribute. The role of WA in the decay $D_s^{+}\to \omega {\pi }^{+}$ and its possible use in estimating WA effects in $D_s^{+}\to \omega e^{+}{\nu }_e$ are also discussed. Assuming that the dynamics of WA in $D_s^{+}\to \omega {\pi }^{+}$ is similar in $D_s^{+}\to \omega e^{+}{\nu }_e$ we estimate $\text{b}(D_s^{+}\to \omega e^{+}{\nu }_e)=(1.3\pm 0.5)\times 10^{-3}$.

Comments: 15 pages, 6 figures, to be submitted to Physical Review D. Reference added