Unified tetraquark equations

Abstract

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 $q\bar{q}(T_{q\bar{q}})$, $qq(T_{\bar{q}\bar{q}})$, 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)].

Comments: 23 pages, 6 figures