Heavy Quarkonium-nuclear bound states within a generalized linear sigma model

We estimate the binding energies of charmonium ($J/\psi$, $\psi(2S)$, $\psi(1D)$, $\chi_{c0}$, $\chi_{c1}$, $\chi_{c2}$) and bottomonium ($\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon_2(1D)$, $\chi_{b0}$, $\chi_{b1}$, $\chi_{b2}$) states bound in various nuclei (${\rm{^{4}He}}$, ${\rm{^{12}C}}$, ${\rm{^{16}O}}$, ${\rm{^{40}Ca}}$, ${\rm{^{90}Zr}}$, and ${\rm{^{208}Pb}}$) using the quarkonia-nuclei potentials obtained from their mass shifts in nuclear matter within the generalized linear sigma model. In the absence of light partons in heavy quarkonia, at the tree level, the medium modifications are driven by the gluon condensate, which is simulated within this model through a scalar dilaton field, $\chi$, by introducing broken scale invariance of QCD. Our study shows that charmonium states bind more deeply with the atomic nuclei as compared to bottomonium states, providing a better probe for nuclear medium effects. Such bound states' investigations are particularly interesting for the upcoming J-PARC-E29, $\rm{\bar{P}ANDA}$@FAIR, and CEBAF@JLab experiments. The mass shifts of the heavy quarkonium states in hot isospin asymmetric nuclear matter are investigated and are observed to receive an appreciable medium modification. These medium effects are anticipated at FAIR@GSI, where such neutron-rich hot nuclear matter is expected to be produced.