Unified triquark equations

Sasha Kvinikhidze, Boris Blankleider

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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 Cahill et al., Aust. J. Phys. 42, 129 (1989) and Reinhardt, Phys. Lett. B 244, 316 (1990)], and (ii) the approach using the quasipotential quark-diquark bound-state equation where the kernel consists of the lowest-order contribution from an underlying quark-quark potential [pioneered by Ebert et al., Z. Phys. C 76, 111 (1997)]. In particular, we show that each of these approaches corresponds to the unified equations with its kernel taken in different, nonoverlapping, approximations.
Original languageEnglish
Article number054016
Number of pages6
JournalPhysical Review D
Issue number5
Publication statusPublished - 1 Sept 2023


  • Bethe-Salpeter equation
  • Bound states
  • Feynman diagrams
  • Quantum field theory
  • Quark model


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