Medium modifications of $1P$-wave charmonia ${\chi }_{cJ}(1P)$ in cold nuclear matter

In this work, we employ the quark-meson coupling model to investigate the mass shifts of $1P$-wave charmonia ${\chi }_{cJ}(1P)$ ($J=0,1,2$) in cold symmetric nuclear matter by incorporating in-medium loop contributions to the ${\chi }_{cJ}(1P)$ self-energy within the unquenched picture. At normal nuclear matter density, we obtain significant mass reductions of about 60 MeV for the ${\chi }_{cJ}(1P)$ states, with the ${\chi }_{c2}(1P)$ mass shift primarily arising from the vector-vector loop. Our results also indicate the absence of level crossing between the in-medium ${\chi }_{cJ}(1P)$ mass and the $D\bar{D}$ mass threshold up to ${\rho }_B<3{\rho }_0$-a feature that could be probed in the Compressed Baryonic Matter experiment at FAIR and the Beam Energy Scan program at RHIC.