Properties of $Z_c\mathbf{(}3900\mathbf{)}$ tetraquark in a cold nuclear matter

The study of medium effects on properties of particles embedded in nuclear matter is of great importance for understanding the nature and internal quark-gluon organization as well as exact determination of the quantum numbers, especially of the exotic states. In this context, we study the physical properties of one of the famous charmoniumlike states, $Z_c(3900)$, in a cold dense matter. We investigate the possible shifts in the mass and current-meson coupling of the $Z_c(3900)$ state due to the dense medium at saturation density ${\rho }^{\text{sat}}$ by means of the in-medium sum rules. We also estimate the vector self-energy of this state at saturation nuclear matter density. We discuss the behavior of the spectroscopic parameters of this state with respect to the density up to a high density corresponding to the core of neutron stars, $\rho \approx 5{\rho }^{\text{sat}}$. Both the mass and current coupling of this state show nonlinear behavior and decrease with respect to the density of the medium: the mass reaches roughly 30% of its vacuum value at $\rho =5{\rho }^{\text{sat}}$, while the current coupling approaches zero at $\rho \approx 2.1{\rho }^{\text{sat}}$, when the central values of the auxiliary and other input parameters are used.

Figure 1

The pole contribution in the $Z_c$ channel as a function of $M^2$ at saturation nuclear matter density and different fixed values of the in-medium continuum threshold.

Figure 2

The ratios $m_{Z_c}^{*}/m_{Z_c}$ and $f_{Z_c}^{*}/f_{Z_c}$ as functions of $M^2$ at the saturated nuclear matter density ${\rho }^{sat}=0.11^3{\mathrm{GeV}}^3$ and at fixed values of the continuum threshold.

Figure 3

The ratios $m_{Z_c}^{*}/m_{Z_c}$ and ${\mathrm{\Sigma }}_{\nu }/m_{Z_c}$ as functions of $M^2$ at average values of the continuum threshold and at saturation nuclear matter density.

Figure 4

The ratios $m_{Z_c}^{*}/m_{Z_c}$ and $f_{Z_c}^{*}/f_{Z_c}$ as functions of $\rho /{\rho }^{\text{sat}}$ at mean values of the continuum threshold and Borel parameter.

Figure 5

Comparison between exponential and $p$-pole fit functions for $m_{Z_c}^{*}/m_{Z_c}$ changes with respect to $\rho /{\rho }^{\text{sat}}$.

Figure 6

Comparison between polynomial and exponential fit functions for $f_{Z_c}^{*}/f_{Z_c}$ changes with respect to $\rho /{\rho }^{\text{sat}}$.

Figure 7

The ratios $m_{Z_c}^{*}/m_{Z_c}$ and $f_{Z_c}^{*}/f_{Z_c}$ as functions of $\rho /{\rho }^{\text{sat}}$ when the uncertainties of the auxiliary and other input parameters are considered.