The $X(3960)$ seen in $D_s^{+}{D}_s^{-}$ as the $X(3930)$ state seen in $D^{+}{D}^{-}$

Abstract

We perform a calculation of the interaction of the $D\bar{D}$, $D_s{\bar{D}}_s$ coupled channels and find two bound states, one coupling to $D\bar{D}$ and another one at higher energies coupling mostly to $D_s^{+}{D}_s^{-}$. We identify this latter state with the $X_0(3930)$ seen in the $D^{+}{D}^{-}$ mass distribution in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ decay, and also show that it produces an enhancement of the $D_s^{+}{D}_s^{-}$ mass distribution close to threshold which is compatible with the LHCb recent observation in the $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ decay which has been identified as a new state, $X_0(3960)$.

Comments: 9 pages, 4 figures