Unified tetraquark equations

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)].