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

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.

6 pages, 7 figures