Study of the $$D_s^+\rightarrow a_0(980) \rho $$ and $$a_0(980) \omega $$ decays

Abstract

AbstractWe study $$D_{s}^{+}\rightarrow \rho ^{0(+)}a^{+(0)}_{0}$$ D s + → ρ 0 ( + ) a 0 + ( 0 ) , $$D_{s}^{+}\rightarrow \omega a^{+}_{0}$$ D s + → ω a 0 + , and the resonant $$D_{s}^{+}\rightarrow \rho a_0$$ D s + → ρ a 0 , $$a_{0}\rightarrow \eta \pi (KK)$$ a 0 → η π ( K K ) decays. In the final state interaction, where $$D_s^+\rightarrow (\eta ^{(\prime )}\pi ^+,K^+{{\bar{K}}}^0)$$ D s + → ( η ( ′ ) π + , K + K ¯ 0 ) are followed by the $$(\eta ^{(\prime )}\pi ^+,K^+{{\bar{K}}}^0)$$ ( η ( ′ ) π + , K + K ¯ 0 ) to $$\rho ^{0(+)}a^{+(0)}_{0}$$ ρ 0 ( + ) a 0 + ( 0 ) rescatterings, we predict $$\mathcal{B}(D_{s}^{+}\rightarrow \rho ^{0(+)}a^{+(0)}_{0})=(3.0\pm 0.3\pm 1.0)\times 10^{-3}$$ B ( D s + → ρ 0 ( + ) a 0 + ( 0 ) ) = ( 3.0 ± 0.3 ± 1.0 ) × 10 - 3 . Due to the cancellation of the rescattering effects and the suppressed short-distance W annihilation contribution, we expect that $${{\mathcal {B}}}(D_{s}^{+}\rightarrow \omega a^{+}_{0}) \simeq \mathcal{B}(D_s^+\rightarrow \pi ^+\pi ^0)<3.4\times 10^{-4}$$ B ( D s + → ω a 0 + ) ≃ B ( D s + → π + π 0 ) < 3.4 × 10 - 4 . In our calculation, $${{\mathcal {B}}}(D_{s}^{+}\rightarrow \rho ^{0}(a^{+}_{0}\rightarrow )\eta \pi ^{+}) =(1.6^{+0.2}_{-0.3}\pm 0.6)\times 10^{-3}$$ B ( D s + → ρ 0 ( a 0 + → ) η π + ) = ( 1 . 6 - 0.3 + 0.2 ± 0.6 ) × 10 - 3 agrees with the data, whereas $${{\mathcal {B}}}(D_{s}^{+}\rightarrow \rho ^{+}(a^{0}_{0}\rightarrow )K^+K^-)$$ B ( D s + → ρ + ( a 0 0 → ) K + K - ) is 10 times smaller than the observation, which requires a careful examination.