Triangle singularities in $B^{-} \rightarrow K^{-}\pi^{-}D^{+}_{s0}$ and $B^{-} \rightarrow K^{-}\pi^{-}D^{+}_{s1}$

Abstract.

We study the appearance of structures in the decay of the $B^{-}$ into $K^{-} \pi^{-} D_{s0}^{+}(2317)$ and $K^- \pi^- D_{s1}^+(2460)$ final states by forming invariant mass distributions of $\pi^- D_{s0}^+$ and $\pi^- D_{s1}^+$ pairs, respectively. The structure in the distribution is associated to the kinematical triangle singularity that appears when the $B^- \rightarrow K^- K^{\ast 0} D^0$ ($B^- \rightarrow K^- K^{\ast 0} D^{\ast 0}$) decay process is followed by the decay of the $K^{\ast 0}$ into $\pi^- K^+$ and the subsequent rescattering of the $K^+ D^0$ ($K^+ D^{\ast 0}$) pair forming the $D_{s0}^+(2317)$ ( $D_{s1}^+(2460)$ resonance. We find this type of non-resonant peaks at 2850MeV in the invariant mass of $\pi^- D_{s0}$ pairs from $B^- \rightarrow K^- \pi^- D_{s0}^+(2317)$ decays and around 3000MeV in the invariant mass of $\pi^- D_{s1}^+$ pairs from $B^- \rightarrow K^- \pi^- D_{s1}^+(2460)$ decays. By employing the measured branching ratios of the $B^- \rightarrow K^- K^{\ast 0} D^0$ and $B^- \rightarrow K^- K^{\ast 0} D^{\ast 0}$ decays, we predict the branching ratios for the processes $B^-$ into $K^- \pi^- D_{s0}^+(2317)$ and $K^- \pi^- D_{s1}^+(2460)$ , in the vicinity of the triangle singularity peak, to be about $8\times10^{-6}$ and $1\times 10^{-6}$ , respectively. The observation of this reaction would also give extra support to the molecular picture of the $D_{s0}^+(2317)$ and $D_{s1}^+(2460)$ .