Covariant tetraquark equations in quantum field theory

TL;DR

This paper derives covariant quantum field equations for tetraquarks, unifying four-quark and two-quark states in a comprehensive, exact, and simplified framework within QCD.

Contribution

It presents a new, more transparent derivation of covariant tetraquark equations in QCD, unifying different quark state interactions in an exact field theoretic form.

Findings

Derived covariant coupled equations for tetraquarks in QCD

Unified four-quark and two-quark state descriptions

Equations consistent with previous disconnected interaction models

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.