Unified tetraquark equations

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