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

Chapter 5. Meson Observables, Diquark Confinement and Radii 53
Exemplarily for a π + one gets [GMW83]
F π (−q 2 ) = N ∫ (
c d 4 k
N 2 E (2π) 4tr[S
S
k 0 + E )Γ
(k
2 ,k + q )
4 , E
(
k 0 − E 2 ,k − q 2
(
k 0 − E 2 ,k + q )
γ 0
2
S
)
Γ
(k − q )
4 , −E ] , (5.16)
where N is the Bethe-Salpeter normalisation factor, which can be computed from the
normalisation condition (5.14).
For both mesons and diquarks we get finite results for the charge radii in the limit
µ IR → 0. Plots of these pion and scalar diquark radii are shown in figure 5.5. The results for
vector-mesons and axial-vector-diquarks are analogous. Consequently though the diquarks
7
1/2
6
5
π
SD
4
10 -4 10 -3 10 -2
µ IR
Figure 5.5: Charge radii for π meson as well as scalar diquark (SD) as functions of the
infrared regulator µ IR . All quantities are given in appropriate units of √ σ c .
are removed from the physical spectrum, which reflects confinement of coloured quarkquark
correlations, their charge radii remain finite. Diquarks therefore possess a welldefined
size, which adds to the motivation of nucleon studies in a covariant quark-diquark
picture, what is the topic of the following chapter.