10 - H1 - Desy

1.2 Basics of electron - proton scattering 13
xP(x)
xP(x)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
a )
xS /20
H1PDF 2009
Q 2 = 1.9 GeV 2
xu v
xd v
xg/20
xP(x)
10 -1
10 -2
H1PDF 2009
Q 2 = 1.9 GeV 2
10 -4 10 -3 10 -2 10 -1 x
x
0
c )
xS /20
H1PDF 2009
Q 2 = 10 GeV 2
xg /20
xu v
xd v
xP(x)
10
1
10 -1
10 -2
b )
xu v
xd v
xS
10 -4 10 -3 10 -2 10 -1
10 -4 10 -3 10 -2 10 -1 x
x
10
1
d )
xu v
xg
H1PDF 2009
Q 2 = 10 GeV 2
xg
xd v
xS
10 -4 10 -3 10 -2 10 -1
Figure 1.8: Parton distributions as determined by the H1PDF 2009 QCD fit at
Q 2 = 1.9 GeV 2 (a, b) and at Q 2 = 10 GeV 2 (c, d). In a) and c) (linear vertical scale), the
gluon and sea-quark densities are downscaled by a factor 0.05. The inner error bands show
the experimental uncertainty, the middle error bands include the theoretical model uncertainties
of the fit assumptions, and the outer error band represents the total uncertainty
including the parameterisation uncertainty. The figure is taken from [24].
where P is the proton and q the photon four-momentum. The proton and electron masses
are here and in the following neglected.
The cross section σ ep→eX can be factorised into two parts:
∫
σ ep→eX = dyf γ/e (y)σ ep→eX (y), (1.27)
where f γ/e is the photon flux. Using the Weizsäcker-Williams approximation [28,29], which
neglects terms involving longitudinal photon polarisation, the flux of photons with energy
fraction y and up to virtuality Q 2 max can be calculated via
f γ/e (y) = α [ ( ) ( 1 + (1 − y)
2 Q
2
ln max 1
− 2m 2
2π y Q 2 e y − 1 )]
. (1.28)
min Q 2 min Q 2 max