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

TL;DR

This paper proposes that the observed $X_0(2900)$ and $X_1(2900)$ peaks in $B^+ o D^+ D^- K^+$ decays are caused by triangle singularities from rescattering processes, not genuine resonances.

Contribution

It demonstrates that the $X_0(2900)$ and $X_1(2900)$ structures can be explained by triangle singularities in rescattering amplitudes, offering an alternative to resonance interpretations.

Findings

Triangle singularities can produce peaks mimicking resonances.

Rescattering processes involving $D^{*-}K^{*+}$ and $ar{D}_{1}^{0}K^{0}$ simulate observed structures.

The phenomena are due to the analytical properties of scattering amplitudes near physical boundaries.

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 $D^{*-}K^{*+}$ rescattering via the $\chi_{c1}K^{*+}D^{*-}$ 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.