Bound-state spectra of ${\chi }_{cJ}$ in finite nuclei and the universal pattern of mass levels

Abstract

In this work, we investigate possible ${\chi }_{cJ}$--nuclear bound states with $J=0,1,2$ using in-medium mass shifts generated by virtual $D^{(\ast )}{\bar{D}}^{(\ast )}$ loops within an unquenched framework. The resulting ${\chi }_{cJ}$--nucleus potentials are constructed in the local density approximation, and the bound state spectra are calculated for ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, ${}^{197}\mathrm{Au}$, and ${}^{208}\mathrm{Pb}$. Bound states are obtained for all systems considered. The ${\chi }_{c0}(1P)$ and ${\chi }_{c1}(1P)$ spectra are nearly degenerate, whereas the larger in-medium mass shift of ${\chi }_{c2}(1P)$ leads to deeper binding. Although the absolute bound state energies depend appreciably on the cutoff parameter, the energy differences relative to the $1s$ level are considerably less sensitive to it and exhibit a regular pattern that decreases approximately as $A^{-2/3}$ with increasing nuclear mass number. A cosh-type potential with a common nuclear geometry provides a compact description of these spectra. The predicted bound-state structures and level-spacing systematics could be investigated in future high-statistics near-threshold photoproduction experiments at the upgraded JLab facility.

Comments: 14 pages, 5 figures and 5 tables