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

Abstract

We investigate the resonant contributions in the decays ${\bar{B}}_{(s)}^0\to D^0{\pi }^{+}{\pi }^{-}$, ${\bar{B}}_{(s)}^0\to D^0{K}^{+}{K}^{-}$, and ${\bar{B}}^0\to D^0{\pi }^0\eta$ 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 $\varphi$ 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 $B_s^0$ 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 $\varphi$ for the decay ${\bar{B}}_s^0\to D^0{K}^{+}{K}^{-}$, 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 $\text{Br}({\bar{B}}^0\to D^0{a}_0(980)[a_0(980)\to {\pi }^0\eta ])=(6.08\pm 0.72)\times 10^{-5}$ and the ratio of branching fractions $\text{Br}({\bar{B}}^0\to D^0{f}_0(980))/\text{Br}({\bar{B}}^0\to D^0{a}_0(980))=0.13\pm 0.03$ are predicted.

Comments: More comments have been done with more references. Welcome for comments