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 $Z_c{M}_h{M}_l$ and $Z{M}_h{M}_l$, with $M_h$ and $M_l$ being the heavy and light mesons, and evaluate the strong couplings $g_{Z_c{M}_h{M}_l}$ and $g_{Z{M}_h{M}_l}$ using QCD sum rule on the light cone. The extracted couplings allow us to find the partial width of the decays $Z_c(3900)\to J/\ddot{I}ˆ\ddot{I}€;\ddot{I}{ˆ}^{\prime }\ddot{I}€;\hat{I}{\cdot }_c\ddot{I}$ and $Z(4430)\to \ddot{I}{ˆ}^{\prime }\ddot{I}€;J/\ddot{I}ˆ\ddot{I}€;\hat{I}{\cdot }_c^{\prime }\ddot{I};\hat{I}{\cdot }_c\ddot{I}$, 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