Shedding light on the $X(3930)$ and $X(3960)$ states with the $B^{-}\to K^{-}J/\psi \omega$ reaction

Abstract

We have studied the contribution of the state $X(3930)$, coming from the interaction of the $D\overline{D}$ and $D_s^{+}{D}_s^{-}$ channels, to the $B^{-}\to K^{-}J/\psi \omega$ decay. The purpose of this work is to offer a complementary tool to see if the $X(3930)$ state observed in the $D^{+}{D}^{-}$ channel is the same or not as the $X(3960)$ resonance claimed by the LHCb collaboration from a peak in the $D_s^{+}{D}_s^{-}$ mass distribution around threshold. We present results for what we expect in the $J/\psi \omega$ mass distribution in the $B^{-}\to K^{-}J/\psi \omega$ decay and conclude that a clear signal should be seen around $3930\mathrm{MeV}$. At the same time, finding no extra resonance signal at $3960\mathrm{MeV}$ would be a clear indication that there is not a new state at $3960\mathrm{MeV}$, supporting the hypothesis that the near-threshold peaking structure peak in the $D_s^{+}{D}_s^{-}$ mass distribution is only a manifestation of a resonance below threshold.

Comments: 15 pages; 10 figures; new version with improved discussion related to available experimental results