$QQ\bar Q\bar Q$ Quark System and Gauge/String Duality

TL;DR

This paper models a four-quark system using gauge/string duality, analyzing string configurations and potential energies to explore possible bound states like molecules or tetraquarks.

Contribution

It introduces a string-based framework for the $QQar Qar Q$ system, providing analytical and numerical insights into its configurations and energy spectra.

Findings

Ground state varies with geometry and quark arrangement

Derived asymptotic energy expressions for tetraquark configurations

Demonstrated universality of string tension in multiquark systems

Abstract

We propose a stringy description of a system composed of two heavy quarks and two heavy antiquarks, mimicking that in pure $SU(3)$ gauge theory. We present both analytical and numerical studies of the string configurations for rectangular geometries. As an application, we analyze the two lowest Born-Oppenheimer potentials. Our results suggest that, depending on the geometry and quark ordering, the ground state of the $QQ\bar Q\bar Q$ system may be a hadronic molecule, a tetraquark state, or a superposition of the two. For general geometries, we derive the asymptotic expression for the energy of the tetraquark configuration in the infrared limit and extend this result to multiquark configurations. Here we also demonstrate the universality of the string tension.