Unified tetraquark equations

Abstract

We derive covariant equations describing the tetraquark in terms of an admixture of two-body states $D\overline{D}$ (diquark-antidiquark), $MM$ (meson-meson), and three-body-like states $q\overline{q}({T}_{q\overline{q}})$, $qq({T}_{\overline{q}\overline{q}})$, and $\overline{q}\overline{q}({T}_{qq})$ where two of the quarks are spectators while the other two are interacting (their t matrices denoted correspondingly as ${T}_{q\overline{q}}$, ${T}_{\overline{q}\overline{q}}$, and ${T}_{qq}$). This has been achieved by describing the $qq\overline{q}\overline{q}$ 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 $D\overline{D}$ model of the Moscow group [Faustov et al., Universe 7, 94 (2021)] and the coupled channel $D\overline{D}\ensuremath{-}MM$ model of the Giessen group [Heupel et al., Phys. Lett. B 718, 545 (2012)].