Study of $\bar{B}^0_{(s)}$ decaying into $D^0$ and $π^{+}π^{-}$, $K^{+}K^{-}$, or $π^{0}η$ with final state interactions

Abstract: We investigate the resonant contributions in the decays $\bar{B}^0_{(s)} \to D^0 \pi^{+}\pi^{-}$, $\bar{B}^0_{(s)} \to D^0 K^{+}K^{-}$, and $\bar{B}^{0} \rightarrow D^{0} \pi^{0}\eta$ by considering the final state interactions within the chiral unitary approach. The scalar resonances produced dynamically from the final state interactions of these decays are the ones of $f_{0}(500)$, $f_{0}(980)$, and $a_{0}(980)$. In addition, the vector mesons $\rho$ and $\phi$ produced in the $p$-wave are also taken into account. From the invariant mass distributions of $B^{0}$ decays, one can see that the contributions of the states $f_{0}(500)$ and $a_{0}(980)$ are remarkably larger than the one of $f_{0}(980)$. However, for the case of $B^{0}_{s}$ decays only a clear structure closed to the $K^{+} K^{-}$ threshold appears, which corresponds to the $f_{0}(980)$ state and has no signal for the $f_{0}(500)$ resonance. The dominant contributions are from the vector meson $\phi$ for the decay $\bar{B}^0_s \to D^0 K^{+}K^{-}$, where the results of the $K^{+} K^{-}$ invariant mass distributions are in agreement with the experimental data up to $1.1$ GeV. Moreover, the branching fractions and the ratios of branching fractions are also investigated, where some of them are consistent with the experimental measurements, and the branching fraction $\text{Br}(\bar{B}^{0} \rightarrow D^{0} a_{0}(980) [a_{0}(980) \to \pi^{0}\eta])=(6.08 \pm 0.72)\times 10^{-5}$ and the ratio of branching fractions $\text{Br}(\bar{B}^{0}\rightarrow D^0 f_{0}(980))/\text{Br}(\bar{B}^{0}\rightarrow D^0 a_{0}(980))=0.13 \pm 0.03$ are predicted.