Four-quark structure of Zc(3900), Z(4430) and Xb(5568) states

Abstract

We examine the four-quark structure of the recently discovered charged \(Z_c(3900)\), \(Z(4430)\) and \(X_b(5568)\) states. We calculate the widths of the strong decays \(Z_c^+ \to J/\psi \pi^+\) (\(\eta_c\rho^+\), \(\bar D^0D^{\ast\,+}\), \(\bar D^{\ast\,0}D^+\)), \(Z(4430)^+ \to J/\psi \pi^+\) (\(\psi(2s) \pi^+\)), and \(X^+_b\to B_s\pi^+\) within a covariant quark model previously developed by us. We find that the tetraquark-type current widely used in the literature for the \(Z_c(3900)\) leads to a significant suppression of the \(\bar D D^\ast\) and \(\bar D^\ast D\) modes. Contrary to this a molecular-type current provides an enhancement by a factor of 6-7 for the \(\bar D D^\ast\) modes compared with the \(Z_c^+\to J/\psi\pi^+\), \(\eta_c\rho^+\) modes in agreement with recent experimental data from the BESIII Collaboration. In case of \(Z(4430)\) state we test a sensitivity of the ratio \(R_Z\) of the \(Z(4430)^+ \to \psi(2s) \pi^+\) and \(Z(4430)^+ \to J/\psi \pi^+\) decay rates to a choice of the size parameter \(\Lambda_{Z(4430)}\) of the \(Z(4430)\). Using upper constraint for the sum of these two modes deduced from the LHCb Collaboration data we find that \(R_Z\) varies from 4.64 to 4.08 when \(\Lambda_{Z(4430)}\) changes from 2.2 to 3.2 GeV. Also we make the prediction for the \(Z(4430)^+ \to D^{\ast\,+} \bar D^{\ast\,0}\) decay rate.