Measurement of Cabibbo-suppressed {_t63 tau] lepton decays and the determination of [V_1tnu_1tns| [Elektronische Ressource] / presented by Stefan Schenk

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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 byDipl.-Phys. Stefan Schenkborn in Wurselen, Germany¨thOral examination: July 07 , 2008Measurement ofCabibbo-suppressed τ lepton decaysand the determination of|V |usReferees: Prof. Dr. Ulrich UwerProf. Dr. Johanna StachelAbstractThis work presents simultaneous branching fraction measurements of the decay− − 0 − − 0modes τ →K nπ ν with n = 0,1,2,3 and τ →π nπ ν with n = 3,4. Theτ τ6 + −analysis is based on a data sample of 427×10 τ τ pairs recorded with the−1BABAR detector, which corresponds to an integrated luminosity of 464.4fb .− − −3 −The measured values areB(τ →K ν ) = (6.57±0.03±0.11)×10 ,B(τ →τ− 0 −3 − − 0 0K π ν ) = (4.61±0.03±0.11)×10 , B(τ → K π π ν ) = (5.05±0.17±τ τ−4 − − 0 0 0 −4 −0.44)×10 , B(τ → K π π π ν ) = (1.31±0.43±0.40)×10 , B(τ →τ− 0 0 0 −2 − − 0 0 0 0π π π π ν ) = (1.263±0.008±0.078)×10 and B(τ → π π π π π ν ) =τ τ−4(9.6±0.5±1.2)×10 , where the uncertainties are statistical and systematic,respectively. All measurements are compatible with the current world averageswhereas the uncertainties are significantly smaller by a factor of up to five.− − 0 0 0 0The determination of B(τ → π π π π π ν ) is the first measurement of thisτbranching fraction. The measured branching fractions are combined with thecurrentworldaverages.

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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
Dipl.-Phys. Stefan Schenk
born in Wurselen, Germany¨
thOral examination: July 07 , 2008Measurement of
Cabibbo-suppressed τ lepton decays
and the determination of|V |us
Referees: Prof. Dr. Ulrich Uwer
Prof. Dr. Johanna StachelAbstract
This work presents simultaneous branching fraction measurements of the decay
− − 0 − − 0modes τ →K nπ ν with n = 0,1,2,3 and τ →π nπ ν with n = 3,4. Theτ τ
6 + −analysis is based on a data sample of 427×10 τ τ pairs recorded with the
−1BABAR detector, which corresponds to an integrated luminosity of 464.4fb .
− − −3 −The measured values areB(τ →K ν ) = (6.57±0.03±0.11)×10 ,B(τ →τ
− 0 −3 − − 0 0K π ν ) = (4.61±0.03±0.11)×10 , B(τ → K π π ν ) = (5.05±0.17±τ τ
−4 − − 0 0 0 −4 −0.44)×10 , B(τ → K π π π ν ) = (1.31±0.43±0.40)×10 , B(τ →τ
− 0 0 0 −2 − − 0 0 0 0π π π π ν ) = (1.263±0.008±0.078)×10 and B(τ → π π π π π ν ) =τ τ
−4(9.6±0.5±1.2)×10 , where the uncertainties are statistical and systematic,
respectively. All measurements are compatible with the current world averages
whereas the uncertainties are significantly smaller by a factor of up to five.
− − 0 0 0 0The determination of B(τ → π π π π π ν ) is the first measurement of thisτ
branching fraction. The measured branching fractions are combined with the
currentworldaverages. Usingthenewaverages, anupdateddeterminationof|V |us
from hadronic τ decays yields|V | = 0.2146±0.0025, which improves previousus
measurements by 19%. Its uncertainty is comparable to the one of the current
world average from semileptonic kaon decays.
Kurzfassung
In der vorliegenden Arbeit werden die Verzweigungsverhaltniss¨ e der Zerf¨alle
− − 0 − − 0τ → K nπ ν mit n = 0,1,2,3 und τ → π nπ ν mit n = 3,4τ τ
6 + −gemessen. Der verwendete Datensatz von 427×10 τ τ -Paaren wurde mit
dem BABAR-Detektor aufgezeichnet und entspricht einer integrierten Luminositat¨
−1 − −von 464.4fb . Die gemessenen Verzweigungsverh¨altnisse sindB(τ →K ν ) =τ
−3 − − 0 −3(6.57±0.03±0.11)×10 , B(τ → K π ν ) = (4.61±0.03±0.11)×10 ,τ
− − 0 0 −4 − − 0 0 0B(τ → K π π ν ) = (5.05±0.17±0.44)×10 , B(τ → K π π π ν ) =τ τ
−4 − − 0 0 0 −2(1.31±0.43±0.40)×10 ,B(τ →π π π π ν ) = (1.263±0.008±0.078)×10τ
− − 0 0 0 0 −4undB(τ →π π π π π ν ) = (9.6±0.5±1.2)×10 , wobei die ersten Unsicher-τ
heiten statistischer und die zweiten systematischer Natur sind. Alle Messungen
sind mit den aktuellen Weltmittelwerten kompatibel, wobei die Unsicherheiten um
− − 0 0 0 0biszueinenFaktorfun¨ fkleinersind. DieBestimmungvonB(τ →π π π π π ν )τ
ist die erste Messung dieses Verzweigungsverhaltnisses. Die gemessenen Verzwei-¨
gungsverhaltnisse¨ werden mit den aktuellen Weltmittelwerten kombiniert. Eine
aktualisierte Bestimmung von|V | aus hadronischen τ-Zerfallen¨ unter Verwen-us
dung der neuen Mittelwerte ergibt |V | = 0.2146± 0.0025. Dies stellt eineus
Verbesserung bisheriger Messungen um 19% dar. Die Unsicherheit ist mit der
des aktuellen Weltmittelwertes aus semileptonischen Kaonzerfallen vergleichbar.¨Contents
Introduction 2
1 Theoretical background and experimental status 3
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 The electroweak interaction . . . . . . . . . . . . . . . . . . . . 5
1.1.2 Properties of the quark mixing matrix . . . . . . . . . . . . . . 7
1.1.3 The strong interaction . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Experimental status of hadronic τ decays . . . . . . . . . . . . . . . . . 9
1.2.1 Branching fractions of leptonic τ decays . . . . . . . . . . . . . 10
1.2.2 Branching fractions of hadronic τ decays . . . . . . . . . . . . . 11
1.2.3 Hadronic decay rate of the τ lepton . . . . . . . . . . . . . . . . 13
1.2.4 Spectral functions of hadronic τ decays . . . . . . . . . . . . . . 13
1.3 Hadronic τ decays and QCD . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 Hadronic decay rate of the τ lepton . . . . . . . . . . . . . . . . 15
1.3.2 Spectral moments of hadronic τ decays . . . . . . . . . . . . . . 18
1.4 Determination of|V | . . . . . . . . . . . . . . . . . . . . . . . . . . . 19us
1.4.1 Semileptonic kaon decays . . . . . . . . . . . . . . . . . . . . . . 19
1.4.2 Hadronic τ decays . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4.3 Summary of current|V | results. . . . . . . . . . . . . . . . . . 24us
2 The BABAR experiment 27
2.1 The PEP-II collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 The BABAR detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1 The silicon vertex tracker . . . . . . . . . . . . . . . . . . . . . 28
2.2.2 The drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.3 The Cherenkov detector . . . . . . . . . . . . . . . . . . . . . . 31
2.2.4 The electromagnetic calorimeter . . . . . . . . . . . . . . . . . . 32
2.2.5 The instrumented flux return . . . . . . . . . . . . . . . . . . . 33
2.3 Data and Monte Carlo simulated event samples . . . . . . . . . . . . . 34
2.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.2 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . 35
3 Particle reconstruction and identification 39
3.1 Charged particle reconstruction . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Neutral particle reconstruction . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Charged particle identification . . . . . . . . . . . . . . . . . . . . . . . 41
iii CONTENTS
3.3.1 Measured quantities . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Particle identification criteria . . . . . . . . . . . . . . . . . . . 43
3.4 Neutral pion identification . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.1 Photon selection . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.2 Neutral pion selection . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Efficiency corrections for simulated events . . . . . . . . . . . . . . . . 50
3.5.1 Tracking efficiency correction . . . . . . . . . . . . . . . . . . . 51
3.5.2 Charged particle identification efficiency correction . . . . . . . 51
4 Event selection 53
+ − + −4.1 Selection of e e →τ τ reactions . . . . . . . . . . . . . . . . . . . . 55
− − − 04.2 Selection of τ →π /K nπ ν decays . . . . . . . . . . . . . . . . . . 58τ
4.2.1 Identification of charged pions and kaons . . . . . . . . . . . . . 59
− − − 04.2.2 Separation into the decay modes τ →π /K nπ ν . . . . . . 60τ
4.3 Graphical display of simulated distributions . . . . . . . . . . . . . . . 60
4.4 Cross feed rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Rejection of remaining QED backgrounds . . . . . . . . . . . . . . . . . 64
4.6 of qq background . . . . . . . . . . . . . . . . . . . 67
4.7 Rejection of remaining ττ background . . . . . . . . . . . . . . . . . . 68
4.8 Summary of the selection criteria . . . . . . . . . . . . . . . . . . . . . 72
05 Systematics of the π selection 79
05.1 Determination of the π efficiency correction . . . . . . . . . . . . . . . 80
5.1.1 Description of the data by the Monte Carlo simulation . . . . . 83
05.1.2 The π efficiency correction . . . . . . . . . . . . . . . . . . . . 84
05.2 Application of the π efficiency correction. . . . . . . . . . . . . . . . . 85
5.2.1 Combinatorial photon pairs . . . . . . . . . . . . . . . . . . . . 86
5.3 Systematic studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
05.3.1 Precision of the π efficiency correction . . . . . . . . . . . . . . 88
5.3.2 Split-offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
05.3.3 Merged π mesons . . . . . . . . . . . . . . . . . . . . . . . . . 96
05.4 Systematic uncertainty of the π efficiency correction . . . . . . . . . . 98
− − 0 05.5 Kinematics of τ →π π π ν decays . . . . . . . . . . . . . . . . . . . 100τ
5.6 Critical discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6 Extraction of the branching fractions 103
6.1 Calculation of branching fractions . . . . . . . . . . . . . . . . . . . . . 104
6.2 Determination of the event migration . . . . . . . . . . . . . . . . . . . 106
6.3 Measurement of the branching fractions . . . . . . . . . . . . . . . . . . 108
6.4 Statistical uncertainties and their correlations . . . . . . . . . . . . . . 111
6.5 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 114
+ − + −6.5.1 ττ production cross section σ(e e →τ τ ) . . . . . . . . . . . 115
6.5.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.5.3 Background normalization . . . . . . . . . . . . . . . . . . . . . 116
6.5.4 Tracking efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.5.5 Charged particle identification efficiency . . . . . . . . . . . . . 118CONTENTS iii
6.5.6 Signal selection efficiencies . . . . . . . . . . . . . . . . . . . . . 119
6.5.7 Background misidentification probabilities . . . . . . . . . . . . 121
06.5.8 π efficiency correction . . . . . . . . . . . . . . . . . . . . . . . 122
6.5.9 Split-offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
06.5.10 Background with additional π mesons . . . . . . . . . . . . . . 123
6.5.11 Variation of the selection criteria . . . . . . . . . . . . . . . . . 126
6.5.12 Dependencies on the flavor of the tag lepton . . . . . . . . . . . 128
6.5.13 Depe on the run period . . . . . . . . . . . . . . . . . . 128
6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7 Extraction of|V | 135us
7.1 Branching fractions of strange τ decays . . . . . . . . . . . . . . . . . . 136
7.2 Calculation of|V | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139us
8 Summary and conclusion 141
A Distributions of selection variables 147
B Distributions of kinematic variables 159
C Correlation matrices 162
D Dependencies on the tag lepton and the run period 166
List of Figures 169
List of Tables 171
Bibliography 173
Acknowledgments 180