Covariant equations for the tetraquark and more

TL;DR

This paper develops covariant equations for tetraquarks that incorporate quark-antiquark annihilation effects, ensuring no overcounting and enabling applications to various 2-particle plus 2-antiparticle systems.

Contribution

It introduces a novel covariant framework for tetraquark equations that accounts for annihilation effects and avoids overcounting, applicable to general two-body interactions.

Findings

Derived covariant tetraquark equations with annihilation effects.

Formulated equations for separable interactions involving meson-meson and diquark-antidiquark structures.

Enabled applications to other 2q2q̄ systems and processes.

Abstract

We derive covariant equations for a system of two quarks and two antiquarks where the effect of quark-antiquark annihilation is taken into account. In our approach, only pair-wise interactions are retained, while all possibilities of overcounting are excluded by (i) keeping terms in the kernel that are consistent with a meson-meson and diquark-antidiquark substructure, and (ii) introducing 4-body equations with a novel structure that specifically avoids the generation of overcounted terms. The resulting tetraquark bound state equations are given for the case of general two-body interactions, and for the specific case of separable interactions that lead to a description of the tetraquark in terms of meson-meson and diquark-antidiquark degrees of freedom where the effects of quark-antiquark annihilation is included. The inclusion of $2q2\bar{q}$- and $q\bar{q}$-channel coupling in our approach enables a wide variety of applications of our equations to other processes within the $2q2\bar{q}$ system, and to other 2-particle plus 2-antiparticle systems.