Exact Unified Tetraquark Equations

Recently we formulated covariant equations describing the tetraquark in terms of an admixture of two-body states DD̅ (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 DD̅ model of the Moscow group (Faustov et al. in Universe 7:94, 2021) and the coupled channel D D̅-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 qq̅ 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 qq̅ potential Δ .