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

We examine the four-quark structure of the recently discovered charged Zc(3900), Z(4430), and Xb(5568) states. We calculate the widths of the strong decays Z+c→J/ψπ+ (ηcρ+, D¯0D*+, D¯*0D+), Z(4430)+→J/ψπ+ (ψ(2s)π+), and X+b→Bsπ+ within a covariant quark model previously developed by us. We find that the tetraquark-type current widely used in the literature for the Zc(3900) leads to a significant suppression of the D¯D∗ and D¯∗D modes. Contrary to this a molecular-type current provides an enhancement by a factor of 6–7 for the D¯D∗ modes compared with the Z+c→J/ψπ+, ηcρ+ modes in agreement with recent experimental data from the BESIII Collaboration. In the case of the Z(4430) state we test a sensitivity of the ratio RZ of the Z(4430)+→ψ(2s)π+ and Z(4430)+→J/ψπ+ decay rates to a choice of the size parameter ΛZ(4430) of the Z(4430). Using the upper constraint for the sum of these two modes deduced from the LHCb Collaboration data we find that RZ varies from 4.64 to 4.08 when ΛZ(4430) changes from 2.2 to 3.2 GeV. Also we make the prediction for the Z(4430)+→D*+D¯*0 decay rate.