Exact Unified Tetraquark Equations

Recently we formulated covariant equations describing the tetraquark in terms of an admixture of two-body states \(D{\bar{D}}\) $D\overline{D}$ (diquark-antidiquark), MM (meson-meson), and three-body-like states where two of the quarks are spectators while the other two are interacting (Phys Rev D 107:094014, 2023). A feature of these equations is that they unify descriptions of seemingly unrelated models of the tetraquark, like, for example, the \(D{\bar{D}}\) $D\overline{D}$ model of the Moscow group (Faustov et al. in Universe 7:94, 2021) and the coupled channel \(D {\bar{D}}-MM\) $D\overline{D}-MM$ model of the Giessen group (Heupel et al. in Phys Lett B718:545, 2012). Here we extend these equations to the exact case where \(q\bar{q}\) $q\overline{q}$ annihilation is incorporated explicitly, and all previously neglected terms (three-body forces, non-pole contributions to two-quark t matrices, etc.) are taken into account through the inclusion of a single \(q\bar{q}\) $q\overline{q}$ potential \(\Delta \) $\mathrm{\Delta }$ .