Hadronic molecules in B decays

There are eighteen possibly existing $D^{(\ast )}{\bar{D}}^{(\ast )}$, $D^{()} \bar K^{()}$,and$D^{()} D_s^{()-}$ hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in $B$ and $B^{\ast }$ decays through the current algebra, and calculate their relative branching ratios through the Fierz rearrangement, as summarized in Table III. Our results support the interpretations of the $X(3872)$, $Z_c(3900)$, $Z_c(4020)$, and $X_0(2900)$ as the molecular states $D \bar D^$of$J^{PC} = 1^{++}$,$D \bar D^$of$J^{PC} = 1^{±}$,$D^* \bar D^$of$J^{PC} = 1^{±}$,and$D^ \bar K^*$of$J^P = 0^{+}$, respectively. Our results also suggest that the $Z_{cs}(3985)$, $Z_{cs}(4000)$, and $Z_{cs}(4220)$ are strange partners of the $X(3872)$, $Z_c(3900)$, and $Z_c(4020)$, respectively. In the calculations we estimate the lifetime of a weakly-coupled composite particle $A=\mathrm{\mid }BC⟩$ to be $1/t_A \approx 1/t_B + 1/t_C + \Gamma_{A \to BC} + \cdots$,with$\cdots$ partial widths of other possible decay channels.