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

Chapter 6. Nucleon Form Factors in a Covariant Diquark-Quark model 87
Q 2 F 2p
/(κ p
F 1p
)
Q F 2p
/(κ p
F 1p
)
3.0
2.0
1.0
0.0
0.9
0.6
0.3
set A
set B
SLAC
JLab1
JLab2
0
0 1 2 3 4 5 6
Q 2 [GeV 2 ]
Figure 6.7: Proton Pauli/Dirac form factor ratios, cf. [AHK + 05]. The data are as described
in figure6.5, as are the bands except that here the upper border is obtained with µ 1 + = 1,
χ 1 + = 1 and κ T = 2, and the lower with µ 1 + = 3.
ultraviolet momenta [MR98]. These components are required by covariance [MRT98] and
signal the presence of quark orbital angular momentum in the pseudoscalar pion.
In figure 6.9 we plot another weighted ratio of Pauli and Dirac form factors. A perturbative
QCD analysis [BJY03] that considers effects arising from both the proton’s leadingand
subleading-twist light-cone wave functions, the latter of which represents quarks with
one unit of orbital angular momentum, suggests
Q 2
[ln Q 2 /Λ 2 ] 2 F 2 (Q 2 )
F 1 (Q 2 ) = constant, Q2 ≫ Λ 2 , (6.100)
where Λ is a mass-scale that corresponds to an upper-bound on the domain of nonperturbative
(soft) momenta. This scaling hypothesis is not predictive unless the value of Λ is
known a priori. However, Λ cannot be computed in perturbation theory.
A scale of this type is not an elemental input to our calculation. It is instead a
derivative quantity that expresses the net integrated effect of many basic features, among
which are the mass-scale characterising quark-dressing and that implicit in the support
of the Faddeev amplitude. Extending our calculation to larger Q 2 is not a problem in