Production rates of $D_s^{+}{D}_s^{-}$ and $D\bar{D}$ molecules in $B$ decays

Abstract

Motivated by the recent discovery of a charmonium $X(3960)$ in $B$ decays by the LHCb Collaboration, the likely existence of two bound/virtual states (denoted by $X_{s\bar{s}}$ and $X_{q\bar{q}}$) below the $D_s^{+}{D}_s^{-}$ and $\bar{D}D$ mass thresholds has been re-examined recently. In this work, we employ the effective Lagrangian approach to calculate their production rates in $B$ decays utilizing triangle diagrams. Our results show that the production yields of $B^{+}\to X_{s\bar{s}}{K}^{+}$ and $B^{+}\to X_{q\bar{q}}{K}^{+}$ are of the order of $10^{-4}$, in agreement with the relevant experimental data, which indicates that, if the $D_s^{+}{D}_s^{-}$ and $\bar{D}D$ bound states indeed exist, they can be detected in $B$ decays. Moreover, we calculate the production rate of $B^{+}\to X(3960)K^{+}$ assuming that $X(3960)$ is a resonant state of $D_s^{+}{D}_s^{-}$ and find that it is also of the order of $10^{-4}$ but a bit smaller than that as a $D_s^{+}{D}_s^{-}$ bound state.

accepted for publication in PRD