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

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before we employ Landau gauge for these examinations.
We solved the covariant Faddeev equations numerically to obtain masses and amplitudes
for the nucleon and ∆. Scalar and axial-vector diquark masses were fixed by fitting
stipulated masses of the baryons. We interpreted the masses and Faddeev amplitudes thus
obtained as representing properties of the baryons’ “quark core”.
We explained subsequently the formulation of a nucleon-photon vertex, which ensures
the vector Ward-Takahashi identity is fulfilled. The vertex ansatz involves three parameters.
Two of these specify electromagnetic properties of axial-vector diquarks and a third
measures the strength of electromagnetically induced axial-vector- ↔ scalar-diquark transitions.
These quantities are also properties of the nucleons’ quark core.
We explored a reasonable range of these parameter values and found that an accurate
description of the nucleons’ static properties was not possible. This mismatch with experiment
was greatly reduced by the inclusion of chiral corrections. The calculated behaviour
of the proton’s form factors G p E (Q2 )/G p M (Q2 ) for Q 2 2 GeV 2 agrees with that inferred
from contemporary polarisation transfer data. Moreover, with the same insensitivity to
parameters, the ratio was seen to give √ Q 2 F 2 (Q 2 )/F 1 (Q 2 ) ≈ constant on Q 2 ∈ [2, 6] GeV 2 .
Since the parameters in the nucleon-photon vertex do not influence these outcomes, we
judge they are manifestations of features intrinsic to the nucleon’s Faddeev amplitude. In
the nucleon’s rest frame, this amplitude corresponds to a relativistic wave function with
s-, p- and even d-wave quark orbital angular momentum components.
In our view baryons can realistically be seen as a dominant Poincaré covariant quark
core, augmented by pseudoscalar meson cloud contributions that, e.g., make a noticeable
contribution to form factors for Q 2 2 GeV 2 . Meson compositeness ensures that such contributions
diminish with increasing Q 2 . Hence future experiments at larger Q 2 will serve
as an instructive probe of correlations in baryon wave functions, i.e. their Faddeev amplitudes.
Combined with further knowledge about QCD’s quark propagator, the structure
of the 2-quark correlations and a more sophisticated treatment of chiral corrections this is
likely to make clear if quarks and diquarks are suitable degrees of freedom for describing
the nucleon.