Study of the $D_s^+\to a_0(980) ρ$ and $a_0(980) ω$ decays

Abstract: We study $D_{s}^{+}\to\rho^{0(+)}a^{+(0)}_{0}$, $D_{s}^{+}\to\omega a^{+}_{0}$, and the resonant $D_{s}^{+}\to\rho a_0$,$a_{0}\to \eta\pi(KK)$ decays. In the final state interaction, where $D_s^+\to (\eta^{(\prime)}\pi^+,K^+\bar K^0)$ are followed by the $(\eta^{(\prime)}\pi^+,K^+\bar K^0)$ to $\rho^{0(+)}a^{+(0)}_{0}$ rescatterings, we predict ${\cal B}(D_{s}^{+}\to\rho^{0(+)}a^{+(0)}_{0})=(3.0\pm 0.3\pm 1.0)\times 10^{-3}$. Due to the cancellation of the rescattering effects and the suppressed short-distance $W$ annihilation contribution, we expect that ${\cal B}(D_{s}^{+}\to\omega a^{+}_{0}) \simeq {\cal B}(D_s^+\to\pi^+\pi^0)<3.4\times 10^{-4}$. In our calculation, ${\cal B}(D_{s}^{+}\to\rho^{0}(a^{+}_{0}\to)\eta\pi^{+}) =(1.6^{+0.2}_{-0.3}\pm 0.6)\times 10^{-3}$ agrees with the data, whereas ${\cal B}(D_{s}^{+}\to\rho^{+}(a^{0}_{0}\to)K^+K^-)$ is 10 times smaller than the observation, which requires a careful examination.