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

In this paper, we investigate the possibility to study the famous charged charmonium-like state $Z_c\left(3900\right)$ 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 $Z_c{\left(3900\right)}^{\pm }$ 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 $Z_c{\left(3900\right)}^{\pm }$ mesons on ¹²C and ¹⁸⁴W target nuclei at initial photon energies of 9.0–17.5 GeV, the absolute momentum differential cross sections and their ratios for the $Z_c{\left(3900\right)}^{\pm }$ production off these target nuclei at laboratory polar angles of 0^∘–10^∘ and at photon energy of 14 GeV as well as the A-dependences of the ratios of the total cross sections for $Z_c{\left(3900\right)}^{\pm }$ production at photon energy of 14 GeV within the adopted scenarios for the $Z_c{\left(3900\right)}^{\pm }$ internal structures. Our results in particular indicate that the total cross sections for $Z_c{\left(3900\right)}^{+}$$\left(Z_c{\left(3900\right)}^{-}\right)$ production have at above threshold photon energies of ∼ 13–17 GeV a well measurable strengths ∼ 50–200 (50–200) and 200–1500 (300–2000) nb for carbon and tungsten target nuclei, respectively. Therefore, one might expect to measure these strengths at the upgraded up to 22 GeV CEBAF facility. We also demonstrate that the absolute and relative observables considered show a certain sensitivity to the $Z_c{\left(3900\right)}^{\pm }$ 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 above facility.