Isospin analysis of $B\to D^*\bar{D}K$ and the absence of the $Z_c(3900)$ in $B$ decays

Abstract

We study the isospin amplitudes in the exclusive $B$ to $D^*\bar{D}K$ decay process and fit the available $D^{*0}\bar{D}^0$ invariant mass distributions near threshold. The analysis demonstrates that the production of the isospin triplet $D^*\bar{D}$ state is highly suppressed compared to the isospin singlet one. That explains why the $Z_c(3900)$ has not been found in $B$ decays. In addition, the production of the negative charge-parity state might be further suppressed in the heavy quark limit. These two reasons which are based on the molecular assumption offer the first explanation why the $Z_c(3900)$ is absent in $B$ decays. Further studies of the absence from both the experimental and the theoretical side is extremely important for understanding the nature of the $X(3872)$ and the $Z_c(3900)$.