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

88 6.5. Nucleon electromagnetic form factors: results
Q 2 F 2p
/(κ p
F 1p
)
Q F 2p
/(κ p
F 1p
)
4.0
3.0
2.0
1.0
0.0
1.5
1
0.5
SLAC
JLab1
JLab2
0
0 2 4 6 8 10
Q 2 [GeV 2 ]
Figure 6.8: The same as figure 6.7 for set B only, cf. [H + 05]: the calculation is expanded
to higher momenta.
principle, and the numerical challenge are met by choosing something more powerful than
a single desktop computer.
One needs an estimate of a reasonable value for Λ. The nucleon’s mass, M N , is one natural
mass-scale in our calculation. Other relevant mass-scales are those which characterise
the electromagnetic size of the nucleon and its constituents. A dipole mass-scale for the
proton is approximately 0.85 GeV. The dressed-quark-photon-vertex is characterised by a
monopole mass-scale of 0.8 GeV [BKR03] and the diquark-photon vertices by monopole
mass-scales √ 3 m J P ≈ 1.0 - 1.5 GeV, equations(6.62) and (6.72).
As an adjunct one can consider the dressed-quark mass function, defined in equation(6.30)
and discussed thereabout. A nonzero mass function in the chiral limit is an
essentially nonperturbative phenomenon. Hence the ratio
R 0 u(Q 2 ) := M ˆm=0(Q 2 )
M ˆmu (Q 2 )
(6.101)
vanishes on the perturbative-Q 2 domain. For Q 2 = 0, on the other hand, calculations
typically yield [HKRW05] Ru(0) 0 = 0.96; i.e., the mass function’s behaviour is almost completely
nonperturbative. The Q 2 -evolution of Ru 0(Q2 ) can therefore guide in demarcating
the nonperturbative domain. Reference [BPRT03] provides a mass-function that agrees
pointwise with quenched-QCD lattice data and gives a unique chiral-limit mass function.