Covariant tetraquark equations in quantum field theory

A. N. Kvinikhidze, B. Blankleider

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We derive exact yet practical covariant equations of quantum field theory describing a tetraquark in terms of a mix of four-quark states 2q2q¯, and two-quark states qq¯. A feature of our approach is that it avoids the overcounting problems that usually plague quantum field theory formulations of few-body covariant equations (the only exception being the two-body Bethe-Salpeter equation). This is achieved by describing the coupling of 2q2q¯ to qq¯ states through the use of model operators that contract a four-quark qq¯-irreducible Green function down to a two-quark qq¯ Bethe-Salpeter kernel. Although the model chosen in the current work describes the four-quark dynamics in terms of meson-meson and diquark-antidiquark states, the derived equations have a form that is exact, as all corrections due to the use of a particular model are taken into account through the use of a well-defined special four-point amplitude Δ entering the equations. The equations 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.

Original languageEnglish
Article number054024
Number of pages10
JournalPhysical Review D
Issue number5
Publication statusPublished - 22 Sept 2022


  • Bethe-Salpeter equation
  • Bound states
  • Quantum chromodynamics
  • Quantum field theory
  • Scattering amplitudes
  • Strong interaction


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