Exact Unified Tetraquark Equations

Abstract

Recently we formulated covariant equations describing the tetraquark in terms of an admixture of two-body states $$D{\bar{D}}$$ D 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 D ¯ model of the Moscow group (Faustov et al. in Universe 7:94, 2021) and the coupled channel $$D {\bar{D}}-MM$$ D D ¯ - M M 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 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 q ¯ potential $$\Delta $$ Δ .