$Q\bar Qqqq$ Quark System, Compact Pentaquark, and Gauge/String Duality (Part II)

This is the second of two companion papers in which we continue to develop the construction of the doubly heavy pentaquark systems using the gauge/string duality. In this paper, we propose a stringy description of the $Q\bar Qqqq$ system in the case of two light flavors. Our goal is to explore the lower-lying Born-Oppenheimer potentials as a function of the separation distance between the heavy quark-antiquark pair. The analysis shows that the ground state Born-Oppenheimer potential is described in terms of both hadro-quarkonia and hadronic molecules. Meanwhile a standard pentaquark configuration, which describes a genuine five-quark interaction, makes the dominant contribution to a higher lying potential. This configuration has an antiquark-diquark-diquark structure $\bar Q[qq][Qq]$ for separations larger than $0.1\,\text{fm}$. The latter enables us to establish a relation among the masses of hadrons in the heavy quark limit. To describe the structure of the potentials more clear, we define some critical separations that are related to the processes of string reconnection, breaking and junction annihilation. Additionally, we consider the generalized baryon vertices, where more than three strings can meet, and explore their implications for the pentaquark systems.