Measurement and QCD analysis of diffractive jet cross sections in deep inelastic scattering at HERA [Elektronische Ressource] / presented by Matthias Ulrich Mozer

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DISSERTATIONsubmitted to theCombined Faculties for the Natural Sciences and Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofdoctor rerum naturaliumpresented byMatthias Ulrich Mozer, M.S.born in Hannover, GermanythOral examination: July 24 2006Measurement and QCD Analysisof Diffractive Jet Cross Sectionsin Deep-Inelastic Scattering at HERAReferees: Prof. Dr. Franz EiseleProf. Dr. Otto NachtmannAbstractDifferential cross sections for the production of two jets in diffractive deep inelasticscattering (DIS) at HERA are presented. The process studied is of the typeep→eXY, where the central hadronic system X contains at least two jets and isseparated from the system Y by a gap in rapidity. The forward system Y consistsof an elastically scattered proton or a low mass dissociation system.The data were taken with the H1 detector during the years of 1999 and 2000 and−1correspond to an integrated luminosity of 51.5 pb .The measured cross sections are compared to fixed order NLO QCD predictions,that use diffractive parton densities which have previously been determined bya NLO QCD analysis of inclusive diffractive DIS at H1. The prediction and thedata show significant differences. However, the dijet cross section is dominatedby the diffractive gluon density, which can be extracted by the above mentionedanalysis only with considerable uncertainty.

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Publié le 01 janvier 2006
Nombre de lectures 13
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DISSERTATION
submitted to the
Combined Faculties for the Natural Sciences and Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
doctor rerum naturalium
presented by
Matthias Ulrich Mozer, M.S.
born in Hannover, Germany
thOral examination: July 24 2006Measurement and QCD Analysis
of Diffractive Jet Cross Sections
in Deep-Inelastic Scattering at HERA
Referees: Prof. Dr. Franz Eisele
Prof. Dr. Otto NachtmannAbstract
Differential cross sections for the production of two jets in diffractive deep inelastic
scattering (DIS) at HERA are presented. The process studied is of the type
ep→eXY, where the central hadronic system X contains at least two jets and is
separated from the system Y by a gap in rapidity. The forward system Y consists
of an elastically scattered proton or a low mass dissociation system.
The data were taken with the H1 detector during the years of 1999 and 2000 and
−1correspond to an integrated luminosity of 51.5 pb .
The measured cross sections are compared to fixed order NLO QCD predictions,
that use diffractive parton densities which have previously been determined by
a NLO QCD analysis of inclusive diffractive DIS at H1. The prediction and the
data show significant differences. However, the dijet cross section is dominated
by the diffractive gluon density, which can be extracted by the above mentioned
analysis only with considerable uncertainty. Hence a combined QCD analysis of
the previously published inclusive diffractive data and the dijet data is performed.
This combined fit analysis allows the determination of diffractive quark and
gluon densities with comparable precision. The common description of inclusive
diffractive data and the dijet data confirms QCD factorization.
Kurzfassung
Die Messung differentieller Wirkungsquerschnitte von Zwei-Jet Produktion in
diffraktiver tief inelastischer Streuung am HERA Beschleuniger wird pr¨asentiert.
Der untersuchte Prozeß ist vom Typ ep→eXY, wobei das zentrale hadronische
System X mindestens zwei Jets umfaßt und vom System Y durch eine Luc¨ ke in
der Rapidit¨at getrennt ist. Das vorw¨arts liegende System Y besteht aus einem
elastisch gestreuten Proton oder einem Dissotiationssystem niedriger Masse.
Die Daten wurden w¨ahrend der Jahre 1999 und 2000 mit dem H1 Detektor
−1aufgenommen und entsprechen einer integrierten Luminosit¨at von 51.5 pb .
Die gemessene Wirkungsquerschnitte werden mit NLO QCD Vorhersagen fester
Ordnung verglichen. Die Vorhersagen basieren dabei auf diffraktiven Par-
tondichten, diebereitsbeiH1durcheineNLOQCDAnalyseinklusiverdiffraktiver
tief inelastischerStreuung bestimmtwurden. DieVorhersageund dieDatenzeigen
signifikanteUnterschiede. AllerdingswirdderZwei-JetWirkungsquerschnittdurch
die diffraktive Gluondichte dominiert, die in der oben genannten Analyse nur
mit erheblichen Unsicherheiten extrahiert werden konnte. Deshalb wurde eine
kombinierte QCD Analyse der bereits publizierten inklusiven diffraktiven Daten
und der Zwei-Jet Daten durchgefuhrt¨ . Die kombinierte Analyse erlaubt die Be-
stimmungderdiffraktivenQuark-undGluondichtemitvergleichbarerGenauigkeit.
Die gleichzeitige Beschreibung inklusiver Diffraktion und der Zwei-Jet Daten
best¨atigt die QCD-Faktorisierung.Contents
List of Figures iii
List of Tables v
1 Introduction 1
2 Theory 3
2.1 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 The Quark Parton Model . . . . . . . . . . . . . . . . . . . . . 3
2.2 Quantum Chromo Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Renormalization. . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Factorization and Evolution of Parton Distributions . . . . . . . 7
2.2.3 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Diffractive Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Regge Phenomenology . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 Diffraction in DIS . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.3 Factorization in Diffractive DIS . . . . . . . . . . . . . . . . . . 11
3 HERA and the H1 Detector 15
3.1 HERA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Liquid Argon (LAr) Calorimeter . . . . . . . . . . . . . . . . . . 17
3.2.2 Backward Lead and Scintillator Calorimeter . . . . . . . . . . . 18
3.3 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Forward Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.1 Forward Muon Detector . . . . . . . . . . . . . . . . . . . . . . 20
3.4.2 Proton Remnant Tagger and Forward Tagging System . . . . . 20
3.5 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.6 Luminosity System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Monte Carlo Models and Fixed Order QCD Predictions 23
4.1 Monte Carlo Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.1.1 Signal Monte Carlo Models . . . . . . . . . . . . . . . . . . . . 23
4.1.2 Non-Diffractive Background . . . . . . . . . . . . . . . . . . . . 28
4.1.3 Proton Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Next to Leading Order Predictions . . . . . . . . . . . . . . . . . . . . 29
4.2.1 nlojet++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
iii CONTENTS
4.2.2 Adaption to Diffractive Processes . . . . . . . . . . . . . . . . . 29
4.2.3 Hadronization Corrections . . . . . . . . . . . . . . . . . . . . . 30
5 Data Selection 35
5.1 Event Rate and Integrated Luminosity . . . . . . . . . . . . . . . . . . 36
5.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.2.1 SPACAL Calibration . . . . . . . . . . . . . . . . . . . . . . . . 36
5.2.2 Calibration of the LAr Calorimeter for Hadron Response . . . . 40
5.3 Reconstruction of Kinematic Variables . . . . . . . . . . . . . . . . . . 42
5.4 DIS- and Jet Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.4.1 Positron Identification . . . . . . . . . . . . . . . . . . . . . . . 44
5.4.2 Jet Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.5 Diffractive Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.6 Correction of Detector Effects . . . . . . . . . . . . . . . . . . . . . . . 51
5.6.1 Correction for Proton Dissociation . . . . . . . . . . . . . . . . 51
5.6.2 Rapidity Gap Selection Inefficiency . . . . . . . . . . . . . . . . 52
5.6.3 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.6.4 Treatment of Detector Noise . . . . . . . . . . . . . . . . . . . . 54
5.6.5 Radiative Corrections . . . . . . . . . . . . . . . . . . . . . . . . 55
5.7 Description of Diffractive Dijet Events at Detector Level by the Monte
Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.7.1 Kinematic Distributions . . . . . . . . . . . . . . . . . . . . . . 56
5.7.2 Energy Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.8 Correction to Hadron Level . . . . . . . . . . . . . . . . . . . . . . . . 59
6 Cross Sections 65
6.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 Dijet Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7 Determination of Diffractive Parton Densities 73
7.1 NLO QCD Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.1.1 Generation of Candidate Parton Densities . . . . . . . . . . . . 74
7.1.2 Parameterization of Dijet Cross Sections . . . . . . . . . . . . . 75
7.1.3 Prediction of the Inclusive Cross Section . . . . . . . . . . . . . 76
7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.3 Diffractive Parton Densities . . . . . . . . . . . . . . . . . . . . . . . . 78
8 Conclusion 93
Bibliography 95
Acknowledgements 99List of Figures
2.1 Feynman diagram of deep inelastic scattering in the quark parton model. 4
2.2 Feynman diagrams of deep inelastic scattering in the quark parton model
including QCD corrections up to order α . . . . . . . . . . . . . . . . . 6s
2.3 Ladder diagram of the QCD parton evolution. . . . . . . . . . . . . . . 8
2.4 Diagram of diffractive scattering in DIS. . . . . . . . . . . . . . . . . . 10
2.5 Diagram of diffractive sca in DIS in the resolved pomeron model. 12
2.6 Diagram showing diffractive dijet production in the resolved pomeron
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1 The HERA ep collider facility and its injection and pre-acceleration
systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 The H1 detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Cross section view of the LAr calorimeter along the beam direction. . . 17
3.4 The H1 tracking system. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1 Correlation and resolution between detector and hadron quantities. . . 25
4.2 Correlation and reso betweenr and hadron quantities. . . 26
4.3 Correlation and resolution between detector and hadron quantities. . . 27
4.4 Correlation and reso between parton and hadron quantities. . . . 31
4.5 Correlation and resolution between parton and hadron quantities. . . . 32
4.6 Hadronization correction factors. . . . . . . . . . . . . . . . . . . . . . 33
5.1 A diffractive dijet event in the H1 detector. . . . . . . . . . . . . . . . . 35
5.2 Number of diffractive dijet events per luminosity as a function of inte-
grated luminosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.3 Impact positions of candidates for scattered positrons in the SPACAL
relative to the beam axis.. . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.4 Positron calibration with the double angle method. . . . . . . . . . . . 39
5.5 Energy dependence of the positron calibration. . . . . . . . . . . . . . . 39
5.6 distribution of positrons detected in the SPACAL. . . . . . . . 40
5.7 Energy calibration of the LAr calorimeter. . . . . . . . . . . . . . . . . 41
5.8 The distributions of the positron identification criteria. . . . . . . . . . 45
5.9 Control plots for the inclusive dijet sample. . . . . . . . . . . . . . . . . 47
5.10 Effects of QED radiation on the y distribution. . . . . . . . . . . . . . . 48
5.11 Control plots for diffractive quantities. . . . . . . . . . . . . . . . . . . 50
5.12 The M and |t| migration correction as determined from the RAPGAPY
Monte Carlo model including proton dissociation. . . . . . . . . . . . . 52
iiiiv LIST OF FIGURES
5.13 Trigger efficiency as determined from data and simulation. . . . . . . . 54
5.14 Average noise in the forward muon detector. . . . . . . . . . . . . . . . 55
QED5.15 Radiative correction factors (C ) for key kinematic quantities. . . . 56
5.16 Reweighting of thehηi distribution. . . . . . . . . . . . . . . . . . . . . 57
5.17 Reweighting of the yion. . . . . . . . . . . . . . . . . . . . . . 57
5.18 Detector level control plots. . . . . . . . . . . . . . . . . . . . . . . . . 58
5.19 level control plots. . . . . . . . . . . . . . . . . . . . . . . . . 59
5.20 The transverse energy flow for diffractive dijet events as a function of
pseudorapidity in the laboratory frame. . . . . . . . . . . . . . . . . . . 60
5.21 Jet profiles for the diffractive di- and trijet events. . . . . . . . . . . . . 61
5.22 Purity and Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.23 Purity and Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
detector5.24 Correction factors to hadron level (C ). . . . . . . . . . . . . . . . 64
6.1 Comparison of the data to the QCD predictions based on the H1 2006
DPDF fit A and the H1 2006 DPDF fit B. . . . . . . . . . . . . . . . . 70
6.2 Comparison of the data to the QCD predictions based on the H1 2006
DPDF fit A and the H1 2006 DPDF fit B. . . . . . . . . . . . . . . . . 71
2 ?26.3 Diffractive dijet cross section double differentially in z and Q +p . . 72IP ⊥
D(3)27.1 The β and Q dependence of the diffractive reduced cross section σr
multiplied by x at x =0.001. . . . . . . . . . . . . . . . . . . . . . . 81IP IP
D(3)27.2 The β and Q dependence of the diffractive reduced cross section σr
multiplied by x at x =0.003. . . . . . . . . . . . . . . . . . . . . . . 82IP IP
D(3)27.3 The β and Q dependence of the diffractive reduced cross section σr
multiplied by x at x =0.01. . . . . . . . . . . . . . . . . . . . . . . . 83IP IP
D(3)27.4 The β and Q dependence of the diffractive reduced cross section σr
multiplied by x at x =0.03. . . . . . . . . . . . . . . . . . . . . . . . 84IP IP
7.5 Cross section of diffractive dijets double differential in z and the scaleIP
2 2 ?2μ =Q +p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85⊥
7.6 Comparison of the data to the QCD predictions based on the combined fit. 86
7.7 Comparison of the data to the QCD predictions based on the combined fit. 87
7.8 Diffractive parton densities from the combined fit. . . . . . . . . . . . . 88
7.9ctive parton de from the combined fit. . . . . . . . . . . . . 89
7.10 Parton densities for different initial parameterizations. . . . . . . . . . 90
7.11 Parton densities for different initial parameterizations. . . . . . . . . . 91