$ω$-$ϕ$ mixing and weak annihilation in $D_s$ decays

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

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