Strong $Z_c^{+}(3900)\to J/\psi {\pi }^{+}$; ${\eta }_c{\rho }^{+}$ decays in QCD

The widths of the strong decays $Z_c^{+}(3900)\to J/\psi {\pi }^{+}$ and $Z_c^{+}(3900)\to {\eta }_c{\rho }^{+}$ are calculated. To this end, the mass and decay constant of the exotic $Z_c^{+}(3900)$ state are computed by means of a two-point sum rule. The obtained results are then used to calculate the strong couplings $g_{Z_{c}J/\psi \pi }$ and $g_{Z_c{\eta }_c\rho }$ employing QCD sum rules on the light cone supplied by a technique of the soft-meson approximation. We compare our predictions on the mass and decay widths with available experimental data and other theoretical results.

Figure 1

Sample diagram for the decay $Z_c\to J/\psi \pi$.

Figure 2

The mass $m_{Z_c}$ as a function of the Borel parameter $M^2$ for different values of $s_0$.

Figure 3

The decay constant $f_{Z_c}$ vs Borel parameter $M^2$. The values of the parameter $s_0$ are shown in the figure.