Current conservation in the covariant quark-diquark model of the nucleon

Abstract

Abstract. The description of baryons as fully relativistic bound states of quark and glue reduces to an effective Bethe-Salpeter equation with quark-exchange interaction when irreducible 3-quark interactions are neglected and separable 2-quark (diquark) correlations are assumed. This covariant quark-diquark model of baryons is studied with the inclusion of the quark substructure of the diquark correlations. In order to maintain electromagnetic current conservation it is then necessary to go beyond the impulse approximation. A conserved current is obtained by including the coupling of the photon to the exchanged quark and direct "seagull" couplings to the diquark structure. Adopting a simple dynamical model of constituent quarks and exploring various parametrisations of scalar diquark correlations, the nucleon Bethe-Salpeter equation is solved and the proton and neutron electromagnetic form factors are calculated numerically. The resulting magnetic moments are still about 50% too small, the improvements necessary to remedy this are discussed. The results obtained in this framework provide an excellent description of the electric form factors (and charge radii) of the proton, up to a photon momentum transfer of 3.5GeV 2 , and the neutron.

Baryons as relativistic three-quark bound states

“…However, instead of determining the various ingredients from their own equations, for instance in a rainbow-ladder truncation, one may equally employ model parametrizations for the quark and diquark propagators, amplitudes and photon vertices. Extending early quark-diquark form factor calculations [350,493,494,[498][499][500][501], this is the avenue taken in the QCD-based model developed in Refs. [502] where the parameters were adjusted to reproduce the nucleon and ∆ masses (potentially leaving room for pion cloud effects) and to some extent also their electromagnetic form factors.…”

“…The electromagnetic current in the quark-diquark model was constructed and then applied in Refs. [493,494] and is depicted in the right panel of Fig. 4.8: it is the sum of impulse-approximation diagrams, where the photon couples to the quarks and diquarks, and the 'gauged' kernel where it couples to the exchanged quark and the scalar and axialvector diquark Bethe-Salpeter amplitudes.…”

Relativistic three-quark bound states in separable two-quark approximation

“…In this scheme, the covariant diquark-quark model, see refs. [9][10][11][12][13][14][15][16], we obtain a tractable set of equations for the components of the covariant nucleon wave function which can be solved without non-relativistic reductions.…”

“…We have introduced a momentum partitioning parameter η ∈ [0, 1] which distributes the total momentum P between quark and diquark. An analogous parameter could also be introduced in a more general definiton of the relative momentum q within the diquarks as discussed in [14]. The Faddeev equations (8) with the ansatz (18) now reduce to a system of effective 2-particle Bethe-Salpeter equations for a quark-diquark state bound by repeated quark-exchanges.…”

Goldberger–Treiman relation and from the three quark BS/Faddeev approach in the NJL model

“…(121), with the value η = 1/2. 13 The numerical procedure to obtain the mass and the associated Faddeev amplitudes is explained in detail in [6,7,8].…”