10 - H1 - Desy

1.2 Basics of electron - proton scattering 5
Neglecting particle masses, the quantities given above may be related by
Q 2 = x · y · s. (1.7)
Figure 1.2 shows the neutral and charged current cross sections measured by the H1
experiment as a function of Q 2 . Below Q 2 ≈ 3000 GeV the neutral current cross section
clearly dominates. Due to high masses of the Z 0 and W ± bosons, at lower Q 2 their
exchanges are kinematically suppressed. In the following only the pure photon exchange
is considered. The differential NC cross section for the process e ± p → e ± X is given by
d 2 σ ± NC
dxdQ 2 = 2πα2
xQ 4 Y +
(F 2 (x, Q 2 ) − y2
Y +
F L (x, Q 2 )
)
. (1.8)
Here, α denotes the fine structure constant, Y + = (1 + (1 − y) 2 ) is the helicity factor and
F 2 (x, Q 2 ) and F L (x, Q62) are called proton structure functions, which parametrise the
proton content as probed by the virtual photon. The F L contribution is kinematically
suppressed compared to F 2 and becomes significant only at very high event inelasticities
y.
1.2.1 Quark - parton model
In the infinite momentum frame (P 2 ≫ m 2 P ), the proton can be considered as a parallel
stream of independent partons, from which every one carry the fraction ξ p,i of the longitudinal
proton momentum. This picture is used in the quark parton model (QPM).
Deep inelastic scattering processes can then be interpreted as elastic electron scattering
on a single parton, as visualised in the figure 1.3. Other partons, not participating in the
hard interaction form the proton remnant and are referred to as spectator partons. The
individual partons within the proton are not directly visible and the proton content can
be described by universal probabilistic parton densities. Since the partons in the proton
have been identified as quarks and gluons, for each quark flavour and gluon parton density
functions (PDFs) exist, which give the probability of finding a parton i with a momentum
fraction ξ p in the proton.
In the QPM, F 2 depends only on x and can be written as
F 2 (x) = x ∑ [
e 2 q f
p
q (x) + f p¯q (x) ] , (1.9)
q
where the sum runs over all the quark flavours q, e q are the quark charges and the functions
f p q and fp¯q contain the quark and antiquark densities in the proton. In this picture the
longitudinal structure function F L disappears
F L (x) = 0. (1.10)
Early experimental results on F 2 were effectively in agreement with the so-called scaling
behaviour of F 2 (no Q 2 dependence of F 2 ). Later, from the observation of the scaling
violation at lower x values, it was concluded that also gluons and gluon splitting into
quark-antiquark pairs have to be considered for the successful description of the proton
content.