On the $QQ\bar q\bar q$-Quark Potential in String Models

TL;DR

This paper models the potential of a tetraquark system using string theory, revealing universality of string tension, factorization at small separations, and comparing with lattice QCD results and other quark systems.

Contribution

It introduces a string theory framework for the $QQar qar q$ system, highlighting potential behaviors, universality, and mechanisms of string breaking and junction annihilation.

Findings

Potential shows universality of string tension.

Factorization occurs at small quark separations.

Screening length aligns with lattice QCD estimates.

Abstract

We propose a string theory construction for the system of two heavy quarks and two light antiquarks. The potential of the system is a function of separation between the quarks. We define a critical separation distance below which the system can be thought of mainly as a compact tetraquark. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. Our estimate of the screening length is in the range of lattice QCD. We also make a comparison with the potential of the $QQq$ system. The potentials look very similar at small quark separations but at larger separations they differ. The reason for this is that the flattening of the potentials happens at two well-separated scales as follows from the two different mechanisms: string breaking by light quarks for $QQq$ and string junction annihilation for $QQ\bar q\bar q$. Moreover, a similar construction can also be applied to the $\bar Q\bar Q qq$ system.