Triangle singularities in $B^{-}\to K^{-}\ddot{I}{€}^{-}{D}_{s0}^{+}$ and $B^{-}\to K^{-}\ddot{I}{€}^{-}{D}_{s1}^{+}$

Abstract

We study the appearance of structures in the decay of the $B^{-}$ into $K^{-}\ddot{I}{€}^{-}{D}_{s0}^{+}(2317)$ and $K^{-}\ddot{I}{€}^{-}{D}_{s1}^{+}(2460)$ final states by forming invariant mass distributions of $\ddot{I}{€}^{-}{D}_{s0}^{+}$ and $\ddot{I}{€}^{-}{D}_{s1}^{+}$ pairs, respectively. The structure in the distribution is associated to the kinematical triangle singularity that appears when the $B^{-}\to K^{-}{K}^{\ast 0}{D}^0$ ($B^{-}\to K^{-}{K}^{\ast 0}{D}^{\ast 0}$) decay process is followed by the decay of the $K^{\ast 0}$ into $\ddot{I}{€}^{-}{K}^{+}$ 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 2850 MeV in the invariant mass of $\ddot{I}{€}^{-}{D}_{s0}$ pairs from $B^{-}\to K^{-}\ddot{I}{€}^{-}{D}_{s0}^{+}(2317)$ decays and around 3000 MeV in the invariant mass of $\ddot{I}{€}^{-}{D}_{s1}^{+}$ pairs from $B^{-}\to K^{-}\ddot{I}{€}^{-}{D}_{s1}^{+}(2460)$ decays. By employing the measured branching ratios of the $B^{-}\to K^{-}{K}^{\ast 0}{D}^0$ and $B^{-}\to K^{-}{K}^{\ast 0}{D}^{\ast 0}$ decays, we predict the branching ratios for the processes $B^{-}$ into $K^{-}\ddot{I}{€}^{-}{D}_{s0}^{+}(2317)$ and $K^{-}\ddot{I}{€}^{-}{D}_{s1}^{+}(2460)$, in the vicinity of the triangle singularity peak, to be about $8\times 10^{-6}$ 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 $D_{s1}^{+}(2460)$.

18 pages, 15 figures, accepted version for publication in Eur. Phys. J. A