Unified tetraquark equations

TL;DR

This paper develops covariant four-body equations for tetraquarks, unifying various models by including all two-body interactions and describing the system with a Faddeev-like approach.

Contribution

It introduces a comprehensive covariant framework for tetraquarks that incorporates multiple two-body configurations and unifies existing models.

Findings

Derived covariant tetraquark equations with all two-body interactions.

Unified different tetraquark models within a single formalism.

Provided a basis for future numerical and phenomenological studies.

Abstract

We derive covariant equations describing the tetraquark in terms of an admixture of two-body states $D\bar D$ (diquark-antidiquark), $MM$ (meson-meson), and three-body-like states $q\bar q (T_{q\bar q})$, $q q (T_{\bar q\bar q})$, and $\bar q\bar q (T_{qq})$ where two of the quarks are spectators while the other two are interacting (their t matrices denoted correspondingly as $T_{q\bar q}$, $T_{\bar q\bar q}$, and $T_{qq}$). This has been achieved by describing the $qq\bar q\bar q$ system using the Faddeev-like four-body equations of Khvedelidze and Kvinikhidze [Theor. Math. Phys. 90, 62 (1992)] while retaining all two-body interactions (in contrast to previous works where terms involving isolated two-quark scattering were neglected). As such, our formulation, is able to unify seemingly unrelated models of the tetraquark, like, for example, the $D\bar D$ model of the Moscow group [Faustov et al., Universe 7, 94 (2021)] and the coupled channel $D \bar D-MM$ model of the Giessen group [Heupel et al., Phys. Lett. B718, 545 (2012)].