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

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 $Z_c^+ \to J/ψπ^+$ ($η_cρ^+$, $\bar D^0D^{\ast\,+}$, $\bar D^{\ast\,0}D^+$), $Z(4430)^+ \to J/ψπ^+$ ($ψ(2s) π^+$), and $X^+_b\to B_sπ^+$ 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 $Z_c^+\to J/ψπ^+$, $η_cρ^+$ modes in agreement with recent experimental data from the BESIII Collaboration. In case of the $Z(4430)$ state we test a sensitivity of the ratio $R_Z$ of the $Z(4430)^+ \to ψ(2s) π^+$ and $Z(4430)^+ \to J/ψπ^+$ decay rates to a choice of the size parameter $Λ_{Z(4430)}$ 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 $Λ_{Z(4430)}$ 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.