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

The strength of the interaction between heavy quarks is studied for heavy quarkonium ($\mathrm{Q}\bar{\mathrm{Q}}$) and doubly heavy baryons ($\mathrm{Q}\mathrm{Q}\mathrm{q}$) 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 $\mathrm{Q}\bar{\mathrm{Q}}$ and $\mathrm{Q}\mathrm{Q}\mathrm{q}$ 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 $T-\eta$ plane and systematically calculate their respective screening distances.