Unified triquark 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 Poincar\'{e} covariant quark+diquark Faddeev equations driven by a one-quark-exchange kernel [pioneered by Cahill {\it et al.}, Austral.\ J.\ Phys.\ {\bf 42}, 129 (1989) and Reinhardt, Phys.\ Lett.\ B {\bf 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 {\it et al.}, Z.\ Phys.\ C {\bf 76} 111 (1997)]. In particular, we show that each of these approaches corresponds to the unified equations with its kernel taken in different, non-overlapping, approximations.