10 - H1 - Desy

12 Theoretical framework
for the emitted gluons. The maximum allowed angle is defined by the hard scattering,
where the quark pair is produced. This is combined with unintegrated gluon densities and
off-shell partons, like in the BFKL approach. This method seems very promising, as it
can (approximately) reproduce the DGLAP and BFKL equations within the appropriate
limits. However, it is still incomplete. Currently, it does not include quark evolution
contribution.
1.2.5 Proton structure
The parton density functions of the proton are not physical observables and need to be
determined from fits to the measured F 2 (x, Q 2 ) data. The quark densities are very well
known in the kinematical range accessible by the present experiments, while the gluon
density has still uncertainties of the order of 10% to 40%. In figure 1.8 the parton density
of the proton as a function of x for a fixed Q 2 = 1.9 GeV 2 and Q 2 = 10 GeV 2 is shown,
as extracted with the help of recent H1 data [24]. It can be seen that the valence quarks
u and d dominate at high x, whereas the gluons come into play at lower x exceeding
the quark contribution by far at low enough x. This behaviour is correlated with the
large scaling violations of F 2 (x, Q 2 ) observed at low x. In the linear scale plots the gluon
contribution is scaled down by factor 20.
Figure 1.9 shows the proton structure F 2 as a function of Q 2 for various x values as
obtained by the H1 collaboration [25]. Clear scaling violation can be observed. The radiation
of a gluon reduces the original momentum fraction of the scattering quark and in
addition gluons can split into quark-antiquark pairs with relatively small momentum fractions
of the proton. At higher momentum transfers more such processes can be resolved
and hence the quark densities are expected to rise with Q 2 at low x and to decrease with
Q 2 at high x.
A lot of PDF sets from different groups are available which are based on global fits to
the data, primary inclusive DIS data. In this analysis the results of two different proton
PDF groups are used, the parton distribution functions fitted by CTEQ [26] group and
by MRST [27] group.
1.2.6 Photoproduction
In the region of small Q 2 electron-proton scattering can be simplified by factorising radiation
of a photon from the electron and the subsequent interaction of the photon with the
proton. This particular domain of electron-proton scattering is called photoproduction.
Since the photon propagator gives rise to a factor 1/Q 2 in the inclusive NC DIS cross
section, photoproduction dominates the ep scattering cross section. In photoproduction
processes, the electron radiates a quasi-real (Q 2 < 1 GeV 2 ) photons with energy fractions
y according to the Weizsäcker-Williams approximation. The variable y is directly related
to the centre of mass energy W γp of the photon proton system:
W 2 γp = (q + P)2 = y · s − Q 2 ≈ y · s, (1.26)