Triangle singularity as the origin of $X_0(2900)$ and $X_1(2900)$ observed in $B^{+}\to D^{+}{D}^{-}{K}^{+}$

Abstract

The LHCb collaboration reported the observation of a narrow peak in the $D^{-}{K}^{+}$ invariant mass distributions from the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay. The peak is parameterized in terms of two resonances $X_0(2900)$ and $X_1(2900)$ with the quark contents $\bar{c}\bar{s}ud$, and their spin-parity quantum numbers are $0^{+}$ and $1^{-}$, respectively. We investigate the rescattering processes which may contribute to the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decays. It is shown that the $D^{\ast -}{K}^{\ast +}$ rescattering via the ${\chi }_{c1}{K}^{\ast +}{D}^{\ast -}$ loop or the ${\bar{D}}_1^0{K}^0$ rescattering via the $D_{sJ}^{+}{\bar{D}}_1^0{K}^0$ loop simulate the $X_0(2900)$ and $X_1(2900)$ structures. Such phenomena are due to the analytical property of the scattering amplitudes with the triangle singularities located to the vicinity of the physical boundary.

Comments: 6 pages, 3 figures