The Interaction of Moving $\mathbf{Q\bar{Q}}$ and QQq in the Thermal Plasma

TL;DR

This paper develops a unified holographic (gauge/gravity) model to study heavy quark interactions in a quark-gluon plasma at finite temperature $T$ and rapidity $\eta$, applying an effective string picture to both $Q\overline{Q}$ and $QQq$ systems. It fits lattice potentials with an AdS-like background and analyzes long-range interactions via effective string tension and short-range interactions via an effective running coupling, yielding $T$-$\eta$ phase diagrams and screening distances. The results show $Q\overline{Q}$ interactions are consistently stronger than those in $QQq$, with higher critical temperatures and longer screening lengths; $QQq$ exhibits a smaller maximum coupling and a shorter screening distance, and is more sensitive to $T$ and $\eta$, especially due to the light-quark dynamics. These findings illuminate the relative stability of mesonic versus baryonic heavy-quark bound states in the QGP and have implications for heavy-ion phenomenology, including production rates like $\Xi_{cc}^{++}$ and energy-loss mechanisms for light quarks.

Abstract

The strength of the interaction between heavy quarks is studied for heavy quarkonium ($\mathrm{Q\bar{Q}}$) and doubly heavy baryons ($\mathrm{QQq}$) at finite temperature and rapidity using the gauge/gravity duality in this paper. We show that this theoretical framework is capable of simultaneously and accurately describing both $\mathrm{Q\bar{Q}}$ and $\mathrm{QQq}$ by fitting lattice potentials. In this framework, we study their interaction at long distances or low temperature and rapidity through effective string tension, while the interaction at short distances or high temperature and rapidity is studied through effective running coupling. Additionally, we plot their state diagram in the $T-η$ plane and systematically calculate their respective screening distances.

Figures (19)

• Figure 1: The black curve represents the $\mathrm{Q\Bar{Q}}$ potential at $T=0, \eta =0$. The black solid dot represents the lattice data from quenched QCD Kaczmarek:2004gv.
• Figure 2: The effective running coupling of $\mathrm{Q\Bar{Q}}$ at $T=0, \eta =0$. The black solid dot represents the lattice data from quenched QCD Kaczmarek:2004gv.
• Figure 3: String structure of the double heavy baryon (distance $L$ increases from left to right). The heavy quark pair is located in the $x_1$ direction, while the baryon vertex $\mathrm{v}$ and the light quark $\mathrm{q}$ are on the $r$-axis. The rapidity $\eta$ is along the $x_3$-axis direction. The heavy quark, light quark, and baryon vertex are connected by blue strings. The black arrows represent forces. $r_{h}$ is the position of the black hole horizon. $r_{w}$ is the position of an imaginary wall when the $\mathrm{QQq}$ is confined.
• Figure 4: The top-left plot shows the string angle $\alpha$ at the baryon vertex as a function of $r_v$ for the small-$L$ configuration; the top-right plot shows $\alpha(r_v)$ for the intermediate-$L$ configuration; the bottom-left plot shows $\alpha(r_v)$ for the large-$L$ configuration; and the bottom-right plot shows $r_0$ as a function of $r_v$ for the large-$L$ configuration.
• Figure 5: The potential of $\mathrm{QQq}$ and $\mathrm{Q\Bar{Q}}$ at $T=0, \eta =0$. The solid black lines represent the $\mathrm{Q\Bar{Q}}$ potential. The curves composed of dotted lines in three colors represent the $\mathrm{QQq}$ potential, with red indicating small $L$, blue for intermediate $L$, and green representing large $L$. The black solid dot represents the lattice data from quenched QCDKaczmarek:2004gvYamamoto:2008jzNajjar:2009da.