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

Chapter 6. Nucleon Form Factors in a Covariant Diquark-Quark model 55
• Bag models imagine hadrons as colour singlett bag out of perturbative vacuum with
relativistic quarks and gluons.
• Soliton models picture baryons as a localised lump of energy density, which consists of
mesons. One ansatz is the topological soliton, where the baryon number is identified
with a topological winding number, which is connected to the boundary conditions
for the meson field configurations. An interesting variation are chiral solitons, which
are non-linear interacting systems of quarks and pions.
Most of these models describe static and a few dynamic observables quite well on the
usual twenty-percent scale of accuracy. However, none of these can be formulated in
a covariant manner. A model with this feature could also succeed in the intermediate
energy regime. Outstanding observables with an interesting behaviour on such energy
scales are the electromagnetic form factors of the nucleon.
In order to understand the structure of the nucleon large experimental and theoretical
effort is undertaken [TW]. An important branch is the exploration of the electromagnetic
structure [ARZ06, PPV06]. Modern, high-luminosity experimental facilities that
employ large momentum transfer reactions are providing remarkable and intriguing new
information in this field [Gao03, BL04]. For an example one need only look so far as
the discrepancy between the ratio of electromagnetic proton form factors extracted via
Rosenbluth separation and that inferred from polarisation transfer. This discrepancy is
marked for Q 2 ∼ > 2 GeV2 and grows with increasing Q 2 . At such values of momentum
transfer, Q 2 > M 2 , where M is the nucleon’s mass, a real understanding of these and
other contemporary data require a Poincaré covariant description of the nucleon. This is
apparent in applications of relativistic quantum mechanics, e.g. [B + 02].
In this chapter we introduce shortly such a model, which we gain by reducing the
relativistic three-quark problem, and use it in order to calculate nucleon form factors.
The formal setting for such a model was already clarified more than two decades ago
[AT77, Glo83]. In the quantum field theory framework the few-body problem is somewhat
ill-posed, since a rigorous treatment should take infinitely many degrees of freedom into
account. However, the observed spectrum of mesons and baryons advises us that a good
physical description is probably possible using the constituent quarks as degrees of freedom.
Therefore we consider matrix elements of three quarks between the non-perturbative
vacuum and a bound state with certain observable quantum numbers, which we call wave
functions, in order to calculate observables (since the QCD vacuum is a non-trivial condensate
it contains sea quarks and gluonic fractions). With this conditions the quantum
mechanical formulation of the three-body problem can be adopted in the Green’s functions
formulation.