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

Oleg Andreev

TL;DR

The paper develops a holographic AdS/QCD description of the fully heavy tetraquark system $QQ\bar{Q}\bar{Q}$, using a soft-wall five-dimensional model to construct string configurations for two geometric orderings (type-A and type-B). It formulates a Born-Oppenheimer framework via a correlation-matrix Hamiltonian whose diagonal entries are stationary-string energies and whose off-diagonal terms encode configuration mixing, then analyzes the two lowest BO potentials across multiple geometric regimes. Key results show that in type-A ordering the ground state is generally a mixed hadronic-molecule/tetraquark state, with transitions governed by string interactions and angle- and length-dependent transitions, while in type-B ordering the ground state tends toward a hadronic-molecule-like configuration; the IR limit reveals a universal linear scaling with a Steiner-tree length, $E_{NQ}=\sigma L_{min}+C_{NQ}+o(1)$, with universal string tension $\sigma$ and $C_{NQ}$ depending only on $N$. The work highlights universal aspects of string tension and provides a detailed map of configuration transitions (reconnections, junction annihilation, pinching) that shape the multiquark spectrum, offering insights relevant to fully heavy tetraquarks observed experimentally. The approach connects nonperturbative QCD phenomena to gauge/string dual descriptions, suggesting avenues for lattice and phenomenological comparisons through BO potentials and IR asymptotics.

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 the ground state of the $QQ\bar Q\bar Q$ system is a mixed state of a hadronic molecule and a tetraquark state. 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.

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

TL;DR

The paper develops a holographic AdS/QCD description of the fully heavy tetraquark system , using a soft-wall five-dimensional model to construct string configurations for two geometric orderings (type-A and type-B). It formulates a Born-Oppenheimer framework via a correlation-matrix Hamiltonian whose diagonal entries are stationary-string energies and whose off-diagonal terms encode configuration mixing, then analyzes the two lowest BO potentials across multiple geometric regimes. Key results show that in type-A ordering the ground state is generally a mixed hadronic-molecule/tetraquark state, with transitions governed by string interactions and angle- and length-dependent transitions, while in type-B ordering the ground state tends toward a hadronic-molecule-like configuration; the IR limit reveals a universal linear scaling with a Steiner-tree length, , with universal string tension and depending only on . The work highlights universal aspects of string tension and provides a detailed map of configuration transitions (reconnections, junction annihilation, pinching) that shape the multiquark spectrum, offering insights relevant to fully heavy tetraquarks observed experimentally. The approach connects nonperturbative QCD phenomena to gauge/string dual descriptions, suggesting avenues for lattice and phenomenological comparisons through BO potentials and IR asymptotics.

Abstract

We propose a stringy description of a system composed of two heavy quarks and two heavy antiquarks, mimicking that in pure 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 the ground state of the system is a mixed state of a hadronic molecule and a tetraquark state. 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.

Paper Structure

This paper contains 50 sections, 148 equations, 29 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. General procedure
  4. A short account of the five-dimensional model
  5. String configurations in five dimensions for type-A ordering
  6. The disconnected configurations
  7. Configuration (a)
  8. Configuration (b)
  9. The tetraquark configuration
  10. Strings joining at a baryon vertex
  11. Configuration (I)
  12. Configuration (II)
  13. The pinched tetraquark configuration
  14. String configurations in five dimensions for type-B ordering
  15. The disconnected configuration (b')
  16. ...and 35 more sections

Figures (29)

  • Figure 1: Four-dimensional string configurations with type-A ordering: (a)-(b) disconnected configurations, (c) a tetraquark configuration, and (d) a pinched tetraquark configuration.
  • Figure 2: Four-dimensional string configurations with type-B ordering: (a)-(b') disconnected configurations and (d) a pinched tetraquark configuration. Here, the tetraquark configuration (c') formally coincides with the pinched configuration (d'), but this no longer holds in five dimensions.
  • Figure 3: Some string interactions: (1) reconnection, (2) junction annihilation, and (3) pinching.
  • Figure 4: A rectangle of length $\ell$ and width $w$. The quarks (antiquarks) are placed at the vertices according to type-A ordering.
  • Figure 5: $E^{\text{(a)}}$ vs $\ell$. The dotted line represents the large-$\ell$ asymptotics \ref{['Ea-large']}.
  • ...and 24 more figures