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Two near-threshold peaking structures with spin-parities $J^{PC}=0^{++}$ wererecently discovered by the LHCb Collaboration in the $D_s^+D_s^-$ invariantmass distribution of the decay process $B^+\to D_s^+D_s^-K^+$. In our study, weemployed a coupled-channel model to fit the experimental results published bythe LHCb collaboration, simultaneously fitting the model to the invariant massdistributions of $M_{D_s^+D_s^-}$, $M_{D_s^+K^+}$, and $M_{D_s^-K^+}$. Weutilized 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 italso 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 achange in the fitting quality, the effect was almost entirely due to the peakof $X(3960)$, so we suggest that $X(3960)$ may not be a kinematic effect.

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