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

Chapter 5
Meson Observables, Diquark
Confinement and Radii
In the preceding section we have seen, that at the moment the solution of the gap equation
in Coulomb gauge is not sufficient in order to calculate observables in a quantitative
satisfactory manner. In this section we therefore aim for qualitative results and employ
the solution of the gap equation without transverse gluons and retardation using in the
time-time component of the gluon propagator the colour Coulomb potential
V C (k) = 3/2 σ c
k 4 . (5.1)
The presented results were published in [AKKW06] and are obtained in the chiral limit.
Obviously, also in this case V C (k) is infrared singular. It is regulated by a parameter
µ IR such that the momentum dependence is modified to
V C (k) = 3/2 σ c
(k 2 ) → 3/2 σ c
. (5.2)
2 (k 2 + µ 2 IR
)2
In this fashion all quantities and observables become µ IR dependent and one obtains the
final result for some f(µ IR ) by taking the limit f = lim µIR →0 f(µ IR ). The result for the
mass function is displayed in figure 5.1 in appropriate units of the Coulomb string tension
σ c . The parametrisation of the quark propagator is again
S −1 (p) = −i · (γ 0 p 0 − γ · p C(|p|) − B(|p|) + iǫ) (5.3)
We employ the Bethe-Salpeter equation in the ladder approximation for mesons and
48