BPC active area Data
-4 -2.4 -0.8 0.8 2.4 4
6 8 10 0
10 20 30 40 50
BPC fiducial Data
X BPC (cm) Y BPC (cm)
0 4 8 12 16 20
4 6 8 10
X BPC (cm)
BPT Hits
Data MC
BPC fiducial
0 4 8 12 16 20
-4 -2 0 2 4
Y BPC (cm)
BPT hits
Data MC
BPC fiducial
Figure 6.16: Determinationof the BPC ducial area. Shown are the reconstructed
impact p osition on the BPC front face for data (upp er left), the mean numb er of
BPT hits p er event(upp er right) for data, and the mean numb erof BPT hits as a
function of the reconstructedX- and Y-p osition for data andMC.
planesasafunctionofthereconstructedp osition(X
BPC
;Y
BPC
)intheBPCfordata. The mean
numb er of hits increases towards the edges of the active area, i.e. the b oundaries of the exit
window projected on to the BPC. The lower plots in gure 6.16 show the projection of the
meannumb erof BPThits onto the X-and Y-axisfordata andMC.In b othcases the numb er
of hits is at in the inner part of the plot. The mean numb er of hits is increasing towards
highervalues of X
BPC
and towards lowerand higher values of Y
BPC
. The smallshifts b etween
the distributionsindataand MCare aresultof theslightly dierentp ositions ofthe BPCand
reconstruction and inthe reconstruction of the kinematicvariableslike x, y, Q , and W. The
ducial area was chosen to b e the region inX and Y, where the mean numb erof BPT hits is
at for b oth data and MC as indicated ingure 6.16.
MC generation
7.1 Signal events
Figure7.1: Non-diractive(left)and diractive(right)eventpicturesfromthe data
sample used in the analysis. Both events pass all analysis cuts as describ ed in
chapter9.
Thehadronicnalstateininclusivemeasurementssuchas theonepresentedhereisamixtureof
twoclassesofevents. Ingure7.1b othtyp esofeventsareshown. Non-diractiveeventslikethe
one to the lefttypicallyhave ahigh particle multiplicityand the invariantmass reconstructed
from allmeasuredparticles in the maindetector excluding the scattered p ositron ishigh. For
this eventthep ositron was measuredinthe BPC,indicatedby the energydep osit on the right
hand outside the maincalorimeter. Usually,several tracks are reconstructed and a signicant
amount of energy is dep ositedin the forward part of the calorimeter(left sidein the plot). A
diractiveeventisshownintherightplotingure7.1. Fortheseeventstheparticlemultiplicity
andthe invariantmassreconstructedfromthe measuredhadronic nalstate islower. Feweror
no tracks are reconstructed in the CTD and no signicant energy is dep osited in the forward
direction. Two variables are generally used to separate the two dierent typ es of events: the
invariantmassofthehadronicnalstateM
X
asdenedinequation7.1,andthepseudorapidity
max
denedby equation7.2.
M
X
= q
E 2
h P
2
h
(7.1)
max
= ln(tan (
min
2
)) (7.2)
h h
nal state p ositron.
max
corresp onds to the reconstructedcalorimeterobject, which is closest
to the forward direction. This corresp onds to the smallest value of as denedin chapter 4.
The aim of this analysis is to measure the inclusive
p cross section, which is a sum of the
cross sections of diractive and non-diractive
p scattering. Therefore, the requirementson
thegeneratedMCeventsare lessrestrictivethantheywouldb eforexampleinan analysissuch
as [Ma98] whichmeasuresonlythe diractivecross section. In b oth casesa precisedescription
of the hadronic nal state isnecessary. In the later case the contributions fromnon-diractive
and diractive events haveto b e separated in order to determinethe diractivecross section.
Thisis notthe casefor inclusivemeasurements. A preciseknowledgeof thecontributions from
non-diractive and diractive events is not required provided that the hadronic nal state is
welldescrib edbytheweighted sumofb oth MCsamples. SeparateMCsamplesweregenerated
for non-diractive and diractive events. Both samples were mixed in order to describ e the
data. The determinationof the mixingfraction is discussedin section7.3.
the two MC generators used to generate the neutral current MC events were DJANGOH
1.1 [Sp99 ] and RAPGAP 2.06/51 [Ju99a]. In b oth cases the lepton vertex is generated by
HERACLES [Sp99], which includes radiative corrections. Single photon emission from the
p ositron or quarks, self energy corrections, and the complete setof one-lo op weak corrections
are taken into account. The hadronization is simulated by ARIADNE ([Lo92 ], [Bu92]) and
JETSET([Sj86 ],[Sj87 ],[Sj92 ]). Thedierenceb etweenDJANGOH1.1and RAPGAP2.06/51
is the interaction b etweenthe virtual photon and the constituentsof the proton. DJANGOH
1.1 is used to generate non-diractive events and RAPGAP 2.06/51 to generate diractive
events. Vector mesonpro ductionis includedinRAPGAP.BothMCsamplesare mixedtogive
theb estdescriptionofthehadronic nalstate. Thefollowingparameterswereusedtogenerate
the events:
Q 2
e
>0:03 GeV 2
W>3 GeV
F
2
=F
2;MRSA
F
L
=0
Energy of the nal state p ositron E 0
e
2GeV
!y0:93
The MRSA parametrization of F
2
was chosen b ecause it is implemented in PDFLIB [Pl97]
whichis required by all generators and programs used for this analysis. This parametrization
is valid at Q 2
ab ove 0.625 GeV 2
and x ab ove 10 6
. Below these values it is constant in the
implementationof PDFLIB7.09. Morerealisticparametrizationsforthe lowQ 2
regionsuchas
ALLM97 [Ab97], which gives a go o d description of the previous measurements inthe low Q 2
region,couldnot easilyb e interfaced to theMC generators. Therefore, MRSAwas chosenand
b othMCsamplesarereweightedto theALLM97 parametrization. TheMRSAparametrization
is constant in the generated Q 2
range. Therefore, relatively more eventsare generated in the
lower Q 2
region compared to the ALLM97 parametrization and the statistical error from MC
eventsisatoverthewholekinematicrangecoveredinthisanalysis. Mo dicationstoRAPGAP
to make it use the same underlying structure function (F
2;MRSA
) as used in DJANGOH are
discussed in section 7.2. The Z-vertex is taken from an unbiased estimate of the true vertex