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

90 6.5. Nucleon electromagnetic form factors: results
From these results one finds that R 0 u(Q 2 > 4M 2 N ) < 0.5 R0 u(0). Therefore perturbative
effects are dominant in the u-quark mass function on Q 2 ∈ (4MN 2 , ∞). On the other hand,
0.8 < Ru(Q 0 2 < MN 2 ) and hence the u-quark mass function is principally nonperturbative
on Q 2 ∈ [0, MN 2 ].
Together these observations suggest that, in our model and in QCD, a judicious estimate
of the least-upper-bound on the domain of soft momenta is Λ = M N , and this
is the value employed in figure6.9: the figure does not provide compelling evidence for
equation(6.100) on the domain up to 6 GeV 2 . One can attempt to fit equation(6.100) to
the calculated results or data, and [BJY03] Λ = Λ fit ≈ 0.3 GeV, provides fair agreement.
However, this value is significantly smaller than the natural scales we have identified in the
model and R 0 u (Λ2 fit ) = 0.98 R0 u (0). In figure 6.10 we extended the calculations for set B to
higher momenta. The results hint that the relation (6.100) may be valid for Q 2 6 GeV 2 .