Covariant tetraquark equations in quantum field theory

Abstract

We derive covariant equations describing the tetraquark in terms of an admixture of two-body states D D (diquark-antidiquark), M M (meson-meson), and three-body-like states q q(T q q), qq(T q q), and q q(T qq ) where two of the quarks are spectators while the other two are interacting (their t matrices denoted correspondingly as T q q, T q q, and T qq ). This has been achieved by describing the qq q 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 D model of the Moscow group [Faustov et al., Universe 7, 94 (2021)] and the coupled channel D D − M M model of the Giessen group [Heupel et al., Phys. Lett. B718, 545 (2012)].

Exact Unified Tetraquark Equations

“…That this is possible has been demonstrated by us in Ref. [11] on the example where the first two terms of Eq. ( 1) have been neglected.…”

“…[10], by exploiting the same procedure as we previously used in Ref. [11] to incorporate q q absorption into the tetraquark model of the Giessen group. This procedure is described in Sect.…”

“…As previously introduced in Ref. [11], our key idea for describing a tetraquark in the presence on q q annihilation, is to: (i) express G (4) ir in terms of some model for the 2q2 q system in absence of q q annihilation, and (ii) to then express the q q kernel K (2) , defined through the Dyson equation…”

“…( 1) have been neglected. By following the same approach as [11], but retaining the first two terms of Eq.…”

“…The amplitude 1 then contains within it information about V (2) and all the rest of the contributions not explicitly appearing in Eq. (11). Equation ( 11) is then the exact tetraquark equation that includes q q annihilation into the unified description of the Giessen and Moscow models of the tetraquark as described by Eq.…”