Treating $Z_c(3900)$ and $Z(4430)$ as the ground-state and first radially excited tetraquarks

Abstract

Exploration of the resonances $Z_c(3900)$ and $Z(4430)$ are performed by assuming that they are ground-state and first radial excitation of the same tetraquark with $J^{P}=1^{+}$. The mass and current coupling of the $ Z_c(3900)$ and $Z(4430)$ states are calculated using QCD two-point sum rule method by taking into account vacuum condensates up to eight dimensions. We investigate the vertices $Z_cM_hM_l$ and $ZM_hM_l$, with $M_h$ and $M_l $ being the heavy and light mesons, and evaluate the strong couplings $ g_{Z_cM_hM_l}$ and $g_{ZM_hM_l}$ using QCD sum rule on the light cone. The extracted couplings allow us to find the partial width of the decays $ Z_c(3900) \to J/ψπ; \,ψ^{\prime} π;\, η_c ρ$ and $Z(4430) \to ψ^{\prime} π;\, J/ψπ;\, η_c^{\prime}ρ;\, η_cρ$, which may help in comprehensive investigation of these resonances. We compare width of the decays of $Z_c(3900)$ and $Z(4430)$ resonances with available experimental data as well as existing theoretical predictions.

12 Pages, 3 Figures and 5 Tables