Covariant tetraquark equations in quantum field theory

Abstract

We derive general covariant coupled equations of QCD describing the tetraquark in terms of a mix of four-quark states $2q2\bar{q}$, and two-quark states $q\bar{q}$. The coupling of $2q2\bar{q}$ to $q\bar{q}$ states is achieved by a simple contraction of a four-quark $q\bar{q}$-irreducible Green function down to a two-quark $q\bar{q}$ Bethe-Salpeter kernel. The resulting tetraquark equations are expressed in an exact field theoretic form, and are in agreement with those obtained previously by consideration of disconnected interactions; however, despite being more general, they have been derived here in a much simpler and more transparent way.

Comments: 12 pages, 5 figures