LOWP Y ISR
0 0.08 0.16 0.24 0.32 0.4
10 -6 10 -5 10 -4 10 -3
x
f
η max
E-p Z +p T
Figure 7.4: Parametrization of the diractive fraction. The upp er plot shows the
(x Q 2
)-plane overlaid by the binning used for the extraction of F
2
. The two
parametrizations ofthe mixingfraction f(x;Q 2
)as afunctionof xare shown inthe
lowerplot [Am99]. The mean of the twoparametrizations is also shown.
from F Data
2
b efore the iterative unfolding of F
2
(see chapter 10.3.4) is nished. n
norm;bin was
foundtob ecompatiblewith1aftertheunfolding. Inthenextstepthettedvaluesoff(x;Q 2
)
i
from all bins i were tted by a continuous function f(x;Q 2
). f(x;Q 2
) is a function of the
generated MC quantities x and Q 2
. In order to determine f(x;Q 2
), the distributions which
are available for b oth data and MC had to b e used. In the case of MC these distributions
dier from the true distributions in MC for example due to the reconstruction and detector
simulation. To minimizethe impact of these errors on the determined function f(x;Q 2
), the
iterations the pro cedureconverges.
Two dierent approaches were used to determine the mixing fraction f(x;Q 2
). In the rst
approach the
max
-distribution was used, b ecause
max
is usually used to describ e the fraction
of non-diractive and diractive events. In the secondapproach, the hadronic quantitiesused
inthe dataselectionand reconstruction ofthe kinematicquantitieswereusedin thet. These
are the dierence of the energy and the longitudinal momentumÆ
h
= P
h (E
h p
Z;h
) and the
transversemomentump
T;h
ofthehadronicnalstateasdenedinsection3.4. Itwasfoundthat
forb othapproachesf(x;Q 2
)couldb eparametrizedasafunctionofonekinematicvariableand
thata parametrizationas afunction ofx resultedinthesmallest 2
. f(x)forb oth approaches
is shown in gure 7.4. In the medium y region f(x) as determined from the
max
and the
Æ
h
- and p
T;h
-distributions are in go o d agreement. The results of the two approaches interms
of f(x) dier signicantly at low and high y. It was chosen to use the average of the two
parametrizations and to take into account their dierence in the evaluation of the systematic
uncertainties(seechapter10.3.4).
7.4 Background MC events
The dominant source of background are events at values of Q 2
lower than the range covered
inthe analysis,which are reconstructedat higher values of Q 2
and pass allanalysis cuts. The
scattered p ositron leaves the detector through the rear b eam pip e, and one or more photons
originating from the hadronic nal state fake a p ositron signal in the BPC. In most cases the
photons are pro ducedin 0
decays. These eventsare referred to as photopro duction events.
Photopro ductioneventsweregeneratedusingthePHYTHIA5.724generator. 109Kdirectand
115 K resolved events were generated, which corresp onds to a luminosity of 300 nb 1
and 30
nb 1
resp ectively. The following parameters wereused to generate the events:
Q 2
e
0:0 GeV 2
F
2
=F
2;ALLM97
F
L
=0
Energy of the nal state p ositron E 0
e
17:64GeV
!y0:36
Thedistributionofthephotopro ductionMCeventsinthe(x Q 2
)-planeoverlapswiththesignal
MC for Q 2
e
0:03 GeV 2
and 0:36 y 0:93. To avoid double counting of MC events,these
photopro duction MC eventswere excluded fromthe sample. The eventsweregenerated using
the ALLM97 parametrization of F
2
, which gives a go o d description of 1995 BPC data [Br97]
and the direct measurementsof the photon-proton cross sectionat Q 2
=0 GeV 2
fromH1 and
ZEUS(see chapter11). Therefore, the photopro duction MC eventswerenot reweighted.
Other sourcesof backgroundeventswerefound to b e negligible(seesection9.7) and therefore
not simulated.
EÆciency and data quality studies
8.1 Introduction
An accurate reconstruction of the kinematic variables in the case of p ositrons scattered at
angles close to requires a precise knowledge of the p osition of the interaction p oint and the
p ositron b eamtilt. In this analysis, p ositrons at scattering angles#= of(15 40) mrad
are detectedusing the BPC and BPT. Evena p ositron b eam tiltof the orderof 0.1 mrad has
a signicant impact on the reconstructed kinematic variables (see section 3.4). The same is
true for the reconstructedvertex. A change in the reconstructed X-vertex of the order of the
resolution of the CTD in X (1 mm)changes # by 0.3 mrad. Therefore, it is necessary to take
into accountthe p ositron b eamtiltand the resolution of the reconstructed eventvertex. This
isdiscussed insection 8.2.
Foraprecisemeasurementitisrequiredto estimatetheeÆciencyofthetriggers,detectors,and
cutsapplied. The selectednumb erofeventsmustalso b ecorrectedfortheeÆciency. BPCand
BPT are used to select the signal eventsand to reducethe amountof background. Therefore,
the eÆciency of the BPC trigger and the BPT track nding has a signicant impact on the
selectednumb erofeventsandhas to b etakeninto account. Section8.4and 8.5 concentrateon
the BPT and BPC eÆciencies,resp ectively. The BPC timing, which is also used in the event
selection,is discussedin section8.3.
8.2 Vertex and beam tilt
The resolution of the X- and Y-vertex measured by the CTD amounts to 1 mm, which is
considerably worse than the spread of the HERA b eams of ab out 300 m inX and 70 min
Y. Instead of using the measured event-by-eventX- and Y-vertexin the reconstruction of the
kinematicquantities, the mean values for each run are calculated. They were determined by
applyingalltriggerandanalysis cutsusedintheselectionofthe datasamplefor theextraction
of F
2
. Figure 8.1 shows the mean X- and Y-vertex as a function of the run numb er. The
variations oftheZ-vertexare considerablylargerthan theresolutionsof b oththe CTD(4 mm)
and the BPT (3 cm). Therefore, no averaging was done and the Z-vertex as determined on
an event-by-event basis was used. The p ositron b eam is tilted w.r.t. the ZEUS co ordinate
system. Forlargep ositronscattering angles,the eectof theb eamtilton thereconstruction of
the kinematicvariablesx, y, and Q 2
is negligible. Atsmall scattering angles w.r.t. the initial
p ositronb eam((15 40) mradinthis analysis)theb eamtiltmustb etakeninto account. The
p ositronb eamtiltwithresp ecttothe ZEUSco ordinate systemisdeterminedbymeasuringthe
impactp osition ofbremsstrahlung photons inthe LUMIG detector. The b eamtiltinXand Y