Photon-induced production of the exotic charged charmonium-like state $Z_c(3900)$ off nuclear targets and its internal structure

Abstract

In this paper, we investigate the possibility to study the famous charged charmonium-like state $Z_c(3900)$ production off nuclear targets and its properties in inclusive photon-induced reactions near the kinematic threshold within the collision model based on the nuclear spectral function. The model accounts for its charged components $Z_c(3900)^{\pm}$ production in direct photon-nucleon interactions as well as three different popular scenarios for their internal structures: compact tetraquarks, molecules of the two open-charm mesons and mixtures of both of them. We calculate the absolute and relative excitation functions for production of $Z_c(3900)^{\pm}$ mesons on $^{12}$C and $^{184}$W target nuclei at initial photon energies of 9.0-17.5 GeV, the absolute momentum differential cross sections and their ratios for the $Z_c(3900)^{\pm}$ production off these target nuclei at laboratory polar angles of 0$^{\circ}$-10$^{\circ}$ and at photon energy of 14 GeV as well as the A-dependences of the ratios of the total cross sections for $Z_c(3900)^{\pm}$ production at photon energy of 14 GeV within the adopted scenarios for the $Z_c(3900)^{\pm}$ internal structures. We demonstrate that the absolute and relative observables considered show a certain sensitivity to the $Z_c(3900)^{\pm}$ internal structures which are by far the best known. Hence, they might be useful for the determination of these structures -- the issue which has attracted much attention in the hadron physics community -- from the comparison of them with the experimental data from the future high-precision experiments at the CEBAF facility.

Figures (10)

• Figure 1: (Color online.) Excitation functions for the production of $Z_c(3900)^+$ and $Z_c(3900)^-$ mesons off $^{12}$C , respectively, from the direct processes (1)--(4) and (5)--(8) proceeding on an off-shell target nucleons and on a free ones being at rest. The curves are calculations in the scenarios, in which the $Z_c(3900)^{\pm}$ are treated as a purely compact four quark (4$q$) states, as a purely molecular states, or as a hybrid states: mixtures of the non-molecular (compact) and molecular (non-compact) components, in which there are 50% of the 4$q$ components and 50% molecular components. The arrow indicates the threshold energy for the $Z_c(3900)^+$ and $Z_c(3900)^-$ photoproduction on a free nucleons in reactions (1) and (5), correspondingly.
• Figure 2: (Color online.) Excitation functions for the production of $Z_c(3900)^+$ (left panel) and $Z_c(3900)^-$ (right panel) mesons off $^{184}$W , respectively, from the direct processes (1)--(4) and (5)--(8) proceeding on an off-shell target nucleons and on a free ones being at rest. The curves are calculations in the scenarios, in which the $Z_c(3900)^{\pm}$ are treated as a purely compact four quark (4$q$) states, as a purely molecular states, or as a hybrid states: mixtures of the non-molecular (compact) and molecular (non-compact) components, in which there are 50% of the 4$q$ components and 50% molecular components. The arrows indicate the threshold energy for the $Z_c(3900)^+$ and $Z_c(3900)^-$ photoproduction on a free nucleons in reactions (1) and (5), correspondingly.
• Figure 3: (Color online.) Ratios between the $Z_c(3900)^{+}$ and between the $Z_c(3900)^-$ production cross sections on $^{12}$C, shown in Fig. 1 and calculated in the compact tetraquark and hybrid scenarios, in the hybrid and molecular scenarios of the $Z_c(3900)^{\pm}$ for an off-shell target nucleons, as functions of photon energy. The arrow indicates the threshold energy for the $Z_c(3900)^+$ and $Z_c(3900)^-$ photoproduction on a free nucleons in reactions (1) and (5), respectively.
• Figure 4: (Color online.) Ratios between the $Z_c(3900)^{+}$ (left panel) and between the $Z_c(3900)^-$ (right panel) production cross sections on $^{184}$W, shown in Fig. 2 and calculated in the compact tetraquark and hybrid scenarios, in the hybrid and molecular scenarios of the $Z_c(3900)^{\pm}$ for an off-shell target nucleons, as functions of photon energy. The arrows indicate the threshold energy for the $Z_c(3900)^+$ and $Z_c(3900)^-$ photoproduction on a free nucleons in reactions (1) and (5), respectively.
• Figure 5: (Color online.) Momentum differential cross sections for the production of $Z_c(3900)^+$ and $Z_c(3900)^-$ mesons, respectively, from the direct reactions (1)--(4) and (5)--(8) proceeding on an off-shell target nucleons in the laboratory polar angular range of 0$^{\circ}$--10$^{\circ}$ in the interaction of photons with energy of $E_{\gamma}=$ 14 GeV with $^{12}$C target nucleus in the considered theoretical pictures describing their intrinsic structures.