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

TL;DR

This work investigates how the masses of the $χ_{cJ}(1P)$ ($J=0,1,2$) charmonia shift in cold symmetric nuclear matter using the quark-meson coupling framework combined with unquenched hadron-loop dynamics. The authors model in-medium effects by incorporating density-dependent $D^{(*)}$ masses from the QMC approach and compute the self-energies of $χ_{cJ}(1P)$ via loops involving $D\bar{D}$, $D^{*}\bar{D}$, $D\bar{D}^{*}$, and $D^{*}\bar{D}^{*}$ with dipole form factors and a cutoff $\\Lambda = m_E + \alpha \\Lambda_{QCD}$. They find sizable negative mass shifts at $ρ_0$, with the vector-vector channel playing a crucial role, especially for $χ_{c2}(1P)$, where the total shift can reach nearly $-100$ MeV; notably, no level crossing with the $D\bar{D}$ threshold occurs up to $ρ_B = 3ρ_0$. These results refine our understanding of cold nuclear matter effects on charmonia and provide input for CNM phenomenology and future experimental probes at facilities like FAIR-CBM and RHIC.

Abstract

In this work, we employ the quark-meson coupling model to investigate the mass shifts of $1P$-wave charmonia $χ_{cJ}(1P)$ ($J=0,1,2$) in cold symmetric nuclear matter by incorporating in-medium loop contributions to the $χ_{cJ}(1P)$ self-energy within the unquenched picture. At normal nuclear matter density, we obtain significant mass reductions of about 60 MeV for the $χ_{cJ}(1P)$ states, with the $χ_{c2}(1P)$ mass shift primarily arising from the vector-vector loop. Our results also indicate the absence of level crossing between the in-medium $χ_{cJ}(1P)$ mass and the $D\bar{D}$ mass threshold up to $ρ_B < 3ρ_0$-a feature that could be probed in the Compressed Baryonic Matter experiment at FAIR and the Beam Energy Scan program at RHIC.

Figures (7)

• Figure 1: Schematic diagram of the charmed-meson loop contributions to the $\chi_{c0}(1P)$ self-energy, where (1) and (2) represent the $D\bar{D}$ and $D^{*}\bar{D}^{*}$ loop contributions, respectively.
• Figure 2: Schematic diagram of the charmed-meson loop contributions to the $\chi_{c1}(1P)$ self-energy, where (1) and (2) represent the $D^{*}\bar{D}$ and $D\bar{D}^{*}$ loop contributions, respectively.
• Figure 3: Schematic diagram showing the charmed-meson loop contributions to the $\chi_{c2}(1P)$ self-energy: (1) $D\bar{D}$, (2) $D\bar{D}^{*}$, (3) $D^{*}\bar{D}$, and (4) $D^{*}\bar{D}^{*}$.
• Figure 4: Mass shift of the $\chi_{c0}(1P)$ meson as a function of baryon density $\rho_{B}$ (in units of the normal nuclear matter density, $\rho_{0} = 0.15\,\mathrm{fm}^{-3}$) arising from the $D\bar{D}$ loop (a), the $D^{*}\bar{D}^{*}$ loop (b), and their combined effect (c); the solid, dotted, and dashed lines represent cutoff values $\alpha = 2$, $3$, and $4$, respectively.
• Figure 5: Mass shift of the $\chi_{c1}(1P)$ meson as a function of baryon density $\rho_{B}$ (in units of $\rho_{0}$) arising from the $D\bar{D}^{*}$ or the $D^{*}\bar{D}$ loop (a), and their combined effect (b); the solid, dotted, and dashed lines represent cutoff values $\alpha = 2$, $3$, and $4$, respectively.