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

Abstract

The resonant contributions in the decays $\bar{B}^0_{(s)} \rightarrow D^0 \pi ^{+}\pi ^{-}$, $\bar{B}^0_{(s)} \rightarrow D^0 K^{+}K^{-}$, and $\bar{B}^{0} \rightarrow D^{0} \pi ^{0}\eta$ are investigated by considering the final state interactions within the chiral unitary approach, where the scalar resonances $f_{0}(500)$, $f_{0}(980)$, and $a_{0}(980)$ are dynamically generated from the final state interactions. In addition, the vector mesons $\rho$, $\phi$ and $D^*_0(2300)$ directly produced in p wave are also taken into account. From the invariant mass distributions of $B^{0}$ decays, it is found that the contributions of $f_{0}(500)$ and $a_{0}(980)$ are remarkably larger than those of $f_{0}(980)$. However, for the case of $B^{0}_{s}$ decays only a clear structure close to the $K^{+} K^{-}$ threshold appears, which corresponds to the $f_{0}(980)$ state and has no signal for the $f_{0}(500)$ resonance. For the decay $\bar{B}^0_s \rightarrow D^0 K^{+}K^{-}$, the $K^{+} K^{-}$ invariant mass distributions are consistent with the experimental data up to 1.1 GeV, and the dominant contributions come from the vector meson $\phi$. Moreover, the branching fractions and the ratios of branching fractions are also studied, some of which are compatible with the experimental measurements. The branching fraction $\text {Br}(\bar{B}^{0} \rightarrow D^{0} a_{0}(980) [a_{0}(980) \rightarrow \pi ^{0}\eta ])=(6.08 \pm 0.72)\times 10^{-5}$ 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.