The QCD Quark Propagator in Coulomb Gauge and - Institut für Physik

58 6.2. Two-quark correlations
constant in the diquark channel to the coupling constant in the pseudoscalar meson channel.
With scalar and axialvector diquarks introduced in [HK95] the spectrum of octet and
decuplet baryons was calculated from the Bethe-Salpeter equation. For the quark exchange
kernel a static approximation was used and therefore momentum dependence of
the exchanged quark was not taken into account. This approach violates covariance and
therefore the rich relativistic structure of models from the type which is used in the present
work is approximated by the leading non-relativistic component, which is the s wave. Calculations
of static nucleon observables with the scalar diquark sector revealed deficiencies
in the magnetic moments, which called for an inclusion of the axialvector diquark. This
was done in [IBY95, MBIY02] with better success, what seems to support the separable
approximation for the two-quark correlation matrix.
If one overcomes the ladder approximation by including higher order perturbation
graphs in the quark-quark scattering kernel, the diquark poles disappear both in the NJL
model [HAR97] and in the Munczek-Nemirowsky model [BRVS96]. The latter uses a
δ-function for the gluon propagator in momentum space and can be regarded as complementary
to the former. This suggests that with a more sophisticated gluon propagator
the diquark poles might disappear from the quark-quark scattering amplitude.
However, the phenomenological quality of using a diquark correlator to approximate
the two-quark correlation matrix does not rely on the existence of asymptotic diquark
states. The diquark correlator is allowed to have no singularities for timelike momenta,
which is a possible realization of diquark confinement. One can even employ models with
a general, separable diquark correlator which does not have to possess a simple analytic
structure, implying that no particle interpretation in terms of a diquark is possible. The
reason for this is that the attractive nature of the interaction mechanism in the diquarkquark
picture (the quark exchange) is independent of the details of the diquark correlations
of the model. This comes from the antisymmetry of the diquark and baryon vertices, which
is visible in the colour and flavour factors of the baryon Bethe-Salpeter equation.
Of course the applicability of the diquark-quark picture and the usage of specific diquark
correlations has in the end to be judged by comparison to experimental data. This
has to include more than the octet and decuplet spectrum as these masses are not very
sensitive to the level of sophistication in the treatment.