Pole determination of $X(3960)$ and $X_0(4140)$ in decay $B^+\to K^+D_s^+D_s^-$

TL;DR

This study employs a coupled-channel model to analyze LHCb data, identifying poles associated with $X(3960)$ and $X_0(4140)$ in $B^+ o D_s^+D_s^-K^+$ decays, and suggests $X(3960)$ is likely a genuine state.

Contribution

The paper introduces a coupled-channel analysis to determine the poles of $X(3960)$ and $X_0(4140)$, providing new insights into their nature and challenging the kinematic effect hypothesis for $X(3960)$.

Findings

Identified poles for $X(3960)$ and $X_0(4140)$ in experimental data.

Suggested $X(3960)$ is not a kinematic effect based on fit quality.

Provided a foundation for future studies on these states.

Abstract

Two near-threshold peaking structures with spin-parities $J^{PC}=0^{++}$ were recently discovered by the LHCb Collaboration in the $D_s^+D_s^-$ invariant mass distribution of the decay process $B^+\to D_s^+D_s^-K^+$. In our study, we employed a coupled-channel model to fit the experimental results published by the LHCb collaboration, simultaneously fitting the model to the invariant mass distributions of $M_{D_s^+D_s^-}$, $M_{D_s^+K^+}$, and $M_{D_s^-K^+}$. We utilized a coupled-channel model to search for the poles of $X(3960)$ and $X_0(4140)$. The determination of the poles is meaningful in itself, and it also lays an foundation for the future research on $X(3960)$ and $X_0(4140)$. Upon turning off the coupled-channel and performing another fit, we observed a change in the fitting quality, the effect was almost entirely due to the peak of $X(3960)$, so we suggest that $X(3960)$ may not be a kinematic effect.