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

## TL;DR

This paper investigates how triangle singularities can produce observable peaks in certain B meson decays, supporting the molecular nature of specific charmed-strange resonances.

## Contribution

It identifies non-resonant triangle singularity peaks in B decay invariant mass distributions and predicts their branching ratios, providing evidence for the molecular structure of D_{s0}^+(2317) and D_{s1}^+(2460).

## Key findings

- Peaks at 2850 MeV and 3000 MeV in invariant mass distributions.
- Predicted branching ratios around 8×10^{-6} and 1×10^{-6}.
- Support for the molecular interpretation of the resonances.

## 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 $B^- \to K^- K^{*\,0} D^0$ ($B^- \to K^- K^{*\,0} D^{*\,0}$) decay process is followed by the decay of the $K^{*\,0}$ into $\pi^- K^+$ and the subsequent rescattering of the $K^+ D^0$ ($K^+ D^{*\,0}$) 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 $\pi^- D_{s0}$ pairs from $B^- \to K^- \pi^- D_{s0}^+(2317)$ decays and around 3000 MeV in the invariant mass of $\pi^- D_{s1}^+$ pairs from $B^- \to K^- \pi^- D_{s1}^+(2460)$ decays. By employing the measured branching ratios of the $B^- \to K^- K^{*\,0} D^0$ and $B^- \to K^- K^{*\,0} D^{*\,0}$ 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 $D_{s1}^+(2460)$.