Unified tetraquark equations

Abstract

We derive covariant equations describing the three-quark bound state in terms of quark and diquark degrees of freedom. The equations are exact in the approximation where three-body forces are neglected. A feature of these equations is that they unify two often-used but seemingly unrelated approaches that model baryons as quark-diquark systems; namely, (i) the approach using Poincaré covariant quark+diquark Faddeev equations driven by a one-quark-exchange kernel [pioneered by

Exact Unified Tetraquark Equations

“…We refer to Eq. (3) as the "unified tetraquark equations" [10]. That these equations unify the works of the Giessen and Moscow groups can be seen from the fact that the equations of Heupel et al correspond to keeping just the term V (0) term in the kernel of Eq.…”

“…In the present work, we extend the unified tetraquark equations of Ref. [10], namely Eq. ( 3), to include all contributions that have been neglected in the derivation of these equations.…”

“…where V gluon is the q q one-gluon-exchange potential and V conf is a local confining potential. 1 Recently we have shown how these two seemingly unrelated approaches to the tetraquark can be unified by providing a common theoretical basis for the two separate models [10]. The key idea is based on the observation that the first two terms of Eq.…”

“…Thus, in Ref. [10], we applied KK's equations to the 2q2 q system, similarly to Heupel et al [2], but we retained the first two terms on the rhs of Eq. (1).…”

“…This means that 0 contains within it information about V (1) and all the rest of the contributions not explicitly appearing in Eq. (10). Similarly, we can consider the model where V = V (0) + V (1) , and then adjust the amplitude to the amplitude 1 , with the resulting kernel W being denoted by W 1 , such that the tetraquark equation…”