Determination of the CKM-matrix element |Vub| from the electron energy spectrum measured in inclusive B -> X u e[Ypsilon] decay with the BABAR detector

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Determination of the CKM -matrix element | V

_ub

| from the electron energy spectrum measured in inclusive

B → X

_u

eν decay with the BABAR detector

D I S S E R T A T I O N

zur Erlangung des akademischen Grades Dr. rer. nat.

im Fach Physik eingereicht an der

Mathematisch-Naturwissenschaftliche Fakultät I Humboldt-Universität zu Berlin

von

Dipl. - Phys. Thomas Lück

Präsident der Humboldt-Universität zu Berlin:

Prof. Jan-Hendrik Olbertz, Ph.D.

Dekan der Mathematisch-Naturwissenschaftliche Fakultät I:

Prof. Stefan Hecht, Ph.D.

Gutachter:

1. Prof. Dr. Heiko Lacker 2. Prof. Dr. Alexander Kappes 3. Prof. Dr. Jochen Dingfelder eingereicht am: 27.09.2012

Tag der mündlichen Prüfung: 30.01.2013

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This document presents a measurement of theCKMmatrix-element|Vub|in inclusive semileptonicB →Xueν events on a dataset of 471 millionBB events recorded by theBABARdetector. InclusiveB→Xueνdecays are selected by reconstructing a high energetic electron (positron). Background suppression is achieved by selecting events with electron (positron) energies near the kinematical allowed endpoint ofB→Xueν decays. AB→D^∗eν veto is applied to further suppress background.

This veto usesD^∗ mesons which have been reconstructed with a partial reconstruction technique.

A partial branching fraction of B → Xueν decays with electron energies Ee >

2.2GeV of

∆B(B→Xueν)Ee>2.2GeV = (2.721±0.095±0.172)×10⁻⁴ (0.1) has been measured, where the first uncertainty is statistical and the second is systematic. This has been used to extract the CKM matrix-element |Vub| with two different theory calculations:

• BLNP [64]: |Vub|= (48.6±1.8^+5.6₋5.5)×10⁻⁴,

• DGE [14]: |Vub|= (41.6±1.5^+2.3₋2.7)×10⁻⁴,

where the first uncertainty is due to the measurement of the partial branching fraction and the second is theoretical.

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Contents Zusammenfassung

Dieses Dokument präsentiert eine Messung des CKM Matrixelementes |Vub| in inklusiven semileptonischen B → Xueν Ereignissen, auf einem Datensatz von 471 Millionen BB Ereignissen, aufgezeichnet vom BABAR Detektor. Inklusive B → Xueν Zerfälle wurden selektiert indem hochenergetische Elektronen (Positronen) rekonstruiert wurden. Untergrundunterdrückung wurde erreicht indem Ereignisse selektiert wurden mit Elektron- (Positron-) Energien in der Nähe des kinematischen Endpunktes vonB →Xueν Zerfällen. Ein Veto für B →D^∗eν wurde angewendet um den Untergrund weiter zu reduzieren. Dieses Veto benutzt D^∗ Mesonen die mit einer Partiellen Rekonstruktionstechnik rekonstruiert wurden.

Ein partielles Verzweigungsverhältnis von B →Xueν Zerfällen mit Elektronen- energienEe>2.2GeV von

∆B(B→Xueν)Ee>2.2GeV = (2.721±0.095±0.172)×10⁻⁴ (0.2) wurde gemessen, hierbei ist der erste Fehler statistisch und der zweite systematisch.

Dieser Wert wurde benutzt um dasCKM Matrixelement|Vub|mit zwei verschieden Theorievorhersagen zu berechnen:

• BLNP [64]: |Vub|= (48.6±1.8^+5.6₋5.5)×10⁻⁴,

• DGE [14]: |Vub|= (41.6±1.5^+2.3₋2.7)×10⁻⁴,

hierbei resultiert der erste Fehler aus der Messung des partiellen Verzweigungsver- hältnisses und der Zweite aus der Unsicherheit auf die Theorievorhersage.

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1 Introduction

The elements of the Cabibbo-Kobayashi-Maskawa-matrix (CKM-matrix) [62] are fundamental parameters of the standard model of particle physics, where fundamental means that they cannot be derived from first principle and need to be measured.

A special challenge is the measurement of the CKM-matrix element |Vub| which describes the transition of ab-quark into au-quark under emission of aW-boson: b→uW. Challenging is the measurement of|V_ub| ≈0.004 as it is the smallest of theCKM-matrix elements. It is around ten times smaller than the CKM-matrix element |Vcb| ≈ 0.04 which describes the transition of b-quark into ac-quark: b→ cW. Since the branching fraction of b → qlν is proportional to the CKM-matrix element squared the semileptonic transition ofb-quarks intoc-quarks is around 50 times larger than the semileptonic transition of b- intou-quarks (if phase-space differences are taken into account).

|V_ub| can be directly measured using leptonic and semileptonic B meson decays. In principle one could also measure |V_ub|in hadronic B decays. However hadronic decays of theB meson involve two vertices where aCKM-matrix element enters. An even more serious complication is the fact that the final states can exchange soft gluons with each other which makes theoretical predictions very difficult. Hence, there is no competitive determination of|V_ub|utilizing hadronicB decays.

Leptonic B → lν decays have been used to measure |V_ub| in the case where the lepton is a τ-lepton. These analysis suffer from low statistics ( B(B⁻ → τ⁻ν_τ) = (1.65±0.34)×10⁻⁴ [74] ). The leptonicB decays where the lepton is either an electron or muon are helicity suppressed and have not been observed so far (B(B⁻ → l⁻ν_l) <

1.56×10⁻⁵ CL= 90% with ;l=e, µ [74]).

Indirectly |V_ub|can be estimated by using the unitarity of the CKM-matrix, for example the determination of the angle β from the time dependent CP asymmetry in B →J/ψK_S⁰ decays [17]. Here,β is one of the angles in the unitary triangle, where the length of the side of the unitary triangle opposite toβis proportional to|V_ub|. In the standard model of particle physics the CP asymmetry is mediated by loop-diagrams, which are very sensitive to contributions from physics beyond the standard model. Therefore, a direct measurement of |V_ub|can be used to test the standard model by comparing it with the β measurements.

The analysis of semileptonic B → Xulν decays, where the B-meson decays into a X_u meson containing an uquark and another light quark (u- or d-quark) and a lepton- neutrino-pair, can also be used for the determination of|V_ub|. One differentiates between inclusive and exclusive semileptonic B-decays. So far branching fractions for thee ex- clusive decays B → πlν, B → ρlν, B⁻ → ωl⁻ν_l and B → η⁽^′⁾lν have been measured.

The determination of |V_ub|from exclusive semileptonic B decays relies on form-factors which have to be provided by theory. These induce currently the largest systematic

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uncertainty on|V_ub|determined from exclusive semileptonic B decays, where the most precise determination of|V_ub|is obtained from B→πlν decays.

One of the most precise determinations of |V_ub| is done with inclusive B → X_ulν decays, where Xu is a sum of for all possible final state mesons containing only light quarks. That is, inclusiveB →X_ulν decays means that no specific final state is reconstructed which makes the background suppression ofB →X_clν decays challenging. To suppress background these analyses are restricted to regions in the phase space where the dominant B → X_clν background is suppressed. Many inclusive measurements are done in the lepton energy region near the kinematic endpoint ofB →X_clν decays.

A consistent problem in the determination of |V_ub| is the discrepancy between the values of|V_ub|determined from inclusive semileptonicB decays and the one determined from exclusive semileptonic B decays. For example reference [63] quotes averages for

|Vub|determined from inclusive and exclusive semileptonic B decays, respectively, as:

• |V_ub|= (4.27±0.38)×10⁻³ (inclusive) [63],

• |V_ub|= (3.38±0.36)×10⁻³ (exclusive) [63],

which is a difference of 1.7σ between the inclusive and exclusive result of |V_ub|. This difference is not significant but it is consistently present for different experimental and theoretical approaches, therefore a precise estimation of |V_ub| (inclusive or exclusive) might help to shed more light into this problem. Currently no strong opinion exists on what causes the difference between the determination of |V_ub| from inclusive and exclusive semileptonic B decays. Some people argue that the theoretical uncertainties on the determination of |V_ub|are underestimated, but on the other hand different theoretical approaches give comparable results. Other authors proposed physical reasons for this difference, for example a possible contribution of right-handed currents to the semileptonic decay rate of B → X_ulν decays [45], which could explain the observed differences.

For all the above mentioned methods one distinguishes tagged and untagged analysis.

In tagged analyses one of the B-mesons is (fully) reconstructed (tagged B) and the semileptonic B decay is studied on the recoil of the tagged B meson. In tagged events the kinematic of the semileptonicB decay is fully known. This provides a very effective background suppression. Tagged analyses, however, suffer from low statistics as the efficiency for fully reconstructing a B-meson (the so called tagging efficiency) is of the order of 0.4%.

This document presents a measurement of inclusive untagged semileptonicB →X_ulν decays.

This document is structured as follows. The following Chapter 2 will outline the analysis-idea and the analysis-strategy. Data recorded with the BABAR detector is used for this analysis. Chapter 3 describes the accelerator and the BABAR detector.

In Chapter 4 a brief overview of the standard model of particle physics is given. The main focus of this chapter will be the description of decay models for semileptonic B-decays relevant for this analysis. The data samples used for this analysis will be characterized in Chapter 5. Background contributions are estimated from the simulation

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1.1 Comments and nomenclature (MC). Therefore special attention has been payed for the background description which is explained in Chapter 6. This analysis uses signal-MC to estimate the efficiency for selecting signal events. Chapter 7 specifies the underlying signal-model which is used to generate the signal-MC. The reconstruction of charged tracks and of the rest of the event is explained in Chapter 8. This chapter also contains the definition of the B → D^∗lν-veto. The procedure for the signal extraction is defined in Chapter 9. Some of the components of the background MC are controversial. Chapter 10 is dedicated for the discussion of alternative background components. The systematic uncertainties evaluated for this analysis are discussed in Chapter 11. Results of the partial branching fraction measurement are summarized in Chapter 12. These results will be used to extract the CKM-matrix element |V_ub| which will be discussed in Chapter 14. The stability of the analysis has been tested by varying input parameters and by performing the analysis on sub-samples of the total dataset. These stability tests are outlined in Chapter 13. Finally the analysis will be summarized and concluded in Chapter 15.

1.1 Comments and nomenclature

The abbreviationcmsstands for the center-of-momentum frame (also called Υ(4S) rest- frame). If not stated otherwise all quantities are given in the Υ(4S) rest-frame. All plots and distributions shown are done for all runs added up if not stated otherwise.

Throughout this work charge conjugation is assumed. The term "electrons" will be used for the sum of electrons and positrons. If either of them is meant it will be explicitly stated in the text.

This analysis uses electrons for the measurement. At electron energies relevant for this analysis the absolute value of the electron three-momentum is equivalent to its energy.

Both expressions will be used synonymically.

For neutrinos the lepton index which specifies the neutrino species is omitted. At places where it is of importance it will be shown. Also we do not differentiate between neutrino and anti-neutrino.

This analysis often deals with charmed mesons. A brief review of the nomenclature and quantum numbers of the charmed mesons relevant for this analysis can be found in the Appendix Section 11.

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2 Analysis strategy

This analysis performs a measurement of the partial branching fraction ∆B of inclusive B →X_ueνdecays. The partial branching fraction is defined as the branching fraction of all B →X_ueν events with electron energies above a certain lower energy cut. Inclusive means that no specific final state is reconstructed rather it is summed over all possible final states with X_u-mesons containing the light quarks u and d only. The inclusive reconstruction technique has the advantage of having higher selection efficiency than reconstructing a specific final state. Also theoretical predictions for inclusive B→Xulν decays have lower systematic uncertainties compared to calculations for single decay modes.

A dataset of (471±3)×10⁶ BB events recorded by the BABAR-detector is used for this measurement. Events are selected by requiring at least one high energetic electron in the event. For events with more than one high energetic electron the electron with the highest energy in the event is used for the analysis. In principle this measurement could also be performed with muons. But as this analysis is not statistically limited and as the particle identification for muons within the BABAR-detector is afflicted with larger systematic uncertainties it was decided to only use electrons for this analysis.

Several sources of backgrounds contribute to the electron energy spectrum. The predominant contribution comes from B → X_clν decays where X_c denotes charmed mesons. The kinematically allowed lepton energy endpoint for B → X_clν decays is around 2.4GeV in the Υ(4S)-rest-frame while it is at 2.81GeV for B → Xulν decays.

Therefore, the analysis is performed near the the kinematically allowed endpoint of the electron energy of B → X_ueν decays to suppress background from B → X_clν decays.

Partial branching fractions are extracted for lower electron energies between 1.8GeV and 2.4GeV in steps of 0.1GeV. A common upper electron energy cut of 2.81GeV is applied which is the kinematically allowed endpoint forB →X_ulν decays in the Υ(4S)- rest-frame. TheB →D^∗eνdecay contributes to about 50% of the totalB →Xclνdecay rate. Therefore, a veto forB→D^∗eν decays is applied to further reduce the background from B →D^∗eν decays. This veto uses partially reconstructed D^∗ mesons. The partial reconstruction technique reconstructsD^∗-mesons by selecting slow pions from the decay D^∗ →Dπ (B(D^∗⁰ → D⁰π⁰) = (61.9±2.9)% and B(D^∗⁺ →Dπ) = (98.4±0.7)% [74]).

Electrons identified as coming from the decays ψ(2S)→e⁺e⁻ or J/ψ→e⁺e⁻ are also rejected from the analysis.

The partial branching fraction of B → X_ulν decays is estimated from the number of selected B → Xulν decays. Where the number of B → Xulν decays is defined as number of selected events for data recorded at the center-of-momentum energy of Υ(4S) resonance (the so calledOnPeak data) where all possible contributions of backgrounds are subtracted. The backgrounds from continuum events (e⁺e⁻ → f f with

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f = u, d, s, c, e, µ, τ) are estimated from a large data sample of so called OffPeak events. This data sample was recorded 40M eV below the Υ(4S) energy which is below the production threshold for BB events. Backgrounds from BB-events are estimated from the simulation. The selection efficiency for B → Xulν decays is estimated on signal-MC.

To not bias the determination of |V_ub| by a fit all yields in this analysis are obtained by counting the number of events. Also a fit would need to include a signal model which would introduce further systematic uncertainties due to the underlying theory model.

During the analysis it turned out that the background for electron energies below 2.2GeV is not well understood. Therefore, the main result of this analysis is given for a electron energy cut ofE_e >2.2GeV. The results for lower cuts on the electron energy are nevertheless given for completeness.

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3 Detector

3.1 PEP-II

The BABAR experiment was operated at the SLAC National Accelerator Laboratory formerly known as Stanford Linear Accelerator Center (SLAC) in Menlo Park (USA).

Data was taken in the time period between October 1999 and March 2008.

Main parts of the accelerator complex are a linear accelerator of approximately 3km length and the PEP-II-storage-rings consisting of a high-energy ring (HER) storing electrons and a low energy ring (LER) storing positrons. A schematic view of the accelerator complex is shown in Figure 3.1. Electrons and positrons were pre-accelerated by the linear accelerator to energies of 9.0GeV and 3.1GeV, respectively, and injected into thePEP-II-storage-rings. The electron and positron beam were brought to collision within theBABAR detector located at the interaction region two (IR-2).

ThePEP-II storage rings are operated at a center of momentum energy of 10.58GeV which corresponds to the mass of Υ(4S)-resonance. Around 10 % of the data was taken about 40M eV below this energy.

The performance of the storage rings was constantly improved during the time of operation. A list of beam parameters together with their design and best achieved values is given in Table 3.1.

Figure 3.1: PEP II storage rings and linear collider. Picture taken from [5].

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parameter design value best value (April 2008) Energy HER/LER (GeV) 9.0 / 3.1 9.0/3.1

Current HER/LER (A) 0.75/2.15 2.07/3.21

Number of bunches 1658 1732

β^∗ (mm) 15−25 9−10

Bunch length (mm) 15 10−12

ξy 0.03 0.05−0.065

Luminosity (10³³cm⁻²s⁻¹) 3 12

Int. Luminosity (pb⁻¹/day) 135 911

Table 3.1: PEP-II beam parameters. β^∗ is the vertical beta function at the collision point. ξ_y refers to the vertical beam-beam parameter limit. Numbers were taken from [20, 87].

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3.2 The BABARdetector

3.2 The BABAR detector

The data analysed in this work was recorded with the BABAR detector. The BABAR detector is a multipurpose detector consisting of several sub-detectors. A schematic of the BABAR detector is shown in Figures 3.2 and 3.3. It consists, starting from the innermost to the outermost sub-detector, of:

• aSilicon Vertex Tracker (SVT) for the reconstruction of charged track trajectories and production and decay vertices,

• the Drift Chamber (DCH) used for the charged track reconstruction and particle identification of charged particles,

• a Detector of Internally Reflected Cherenkov light (DIRC) used for particle identification of charged particles,

• an Electromagnetic Calorimeter (EMC) used for the detection of electromagnetic showers induced by charged particles and photons,

• theInstrumented Flux Return (IFR) used for the particle identification of neutral hadrons and muons.

The sub-detectors SVT, DCH, DIRC and EMC are surrounded by superconducting solenoid cooled by liquid helium which produces a 1.5T magnetic field along the direction of the beam axis. In the following subsections each of these sub-detectors and the trigger system is briefly described. A more detailed description of theBABAR detector and its components can be found in Ref. [20].

The right-handed coordinate system used for this analysis has its origin in the interaction point (IP) of the BABAR detector, where the positive z-axis of the coordinate system points along the beam axis pointing into the direction of the electron beam. The y-axis points upwards. It is convenient to introduce polar coordinates, with azimuthal angle φ defined as the angle in the x-y-plane with respect to the x-axis and the polar angle θ defined with respect to the z-axis.

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Figure 3.2: Schematic view of the cross section of theBABAR-detector in the transverse view [20]. All distances are given inmm.

Figure 3.3: Schematic view of the cross section of theBABAR -detector in the longitudinal view [20]. All distances are given inmm.

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3.2 The BABARdetector 3.2.1 Trigger system

The event selection already starts with the trigger system. BABAR uses a two-level trigger system, where the first stage, the so calledL1-trigger, is a hardware-based trigger.

It uses input from theDCH,EMC and IFRto select events of interest. The L1-trigger is designed to provide a trigger rate of less than 2kHz.

The second trigger stage, the so calledL3 -trigger, is a software trigger. TheL3-trigger uses software algorithms to process the events selected by theL1-trigger system. These algorithms decide which events are interesting for physics analyses. Events selected by the L3-trigger are stored for further analysis. To prevent overload of the data storage and processing system theL3-trigger is limited to a trigger rate of 120Hz.

A detailed description of theBABAR trigger system can be found for example in [23].

3.2.2 Silicon Vertex Tracker (SVT)

The detector closest to the interaction point (IP) is the Silicon Vertex Tracker (SVT).

The task of the SVT is the detection of charged particles and reconstruction of their trajectories and momenta. It is the only detector which provides information for charged particles with transverse momentum of less than 120M eV /c.

TheSVT consists of five layers of double-sided silicon strip detectors which are symmetrically arranged around the beam pipe. The two inner layers have six sensor modules per layer while layer four and five have sixteen and eighteen sensor modules, respectively.

Neighbouring detector modules overlap at the edges to guarantee full coverage in the azimuthal angle. Each sensor module is made from 300µm thick double sided silicon strip detectors. To fit the geometrical constraints sensor modules were produced in six different shapes. The strips measuring φ- and z-direction are oriented orthogonal to each other. Strips measuring the φ -direction of charged tracks are oriented along the beam pipe. Perpendicular to those are the strips measuring the z-direction. The SVT has around 150000 readout channels. To reduce the material inside the detector the readout electronics was placed outside the active detector volume. To reduce noise and to remove the heat produced by the electronics the SVT is cooled down to 8^◦C by a water cooling. Figures 3.4 and 3.5 depict the layout of the SVT.

Figure 3.4: Schematic view of the SVT: transverse section [20]. Shown are the five different layers of silicon strip detectors positioned around the beam pipe.

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Figure 3.5: Schematic view of the SVT: longitudinal cross section [20]. The roman nu- merals label the six different sensor shapes.

The SVT was designed to have a spatial single-hit resolution of 10−15µm for the three inner layers and 40µm for the two outer layers for tracks perpendicular to the sensor modules. In the lab frame a polar angle between 20^◦ ≤ θ_lab ≤ 150^◦ is covered by theSVT. This corresponds to an acceptance of 90 % of the solid angle in the Υ(4S) rest-frame.

The alignment of theSVT with respect to the drift chamber is done with the help of e⁺e⁻ →µ⁺µ⁻ events and with cosmic events.

3.2.3 Drift Chamber (DCH)

The second component of theBABAR tracking system it theDrift Chamber (DCH). It is used for the reconstruction of trajectories of charged tracks and measurement of the track momenta. Also the DCH provides input for the trigger system. A further task of theDCH is the measurement of the energy loss per path length of charged particles which is used for particle identification.

The DCH is structured into 7104 drift cells which are arranged in 40 layers. Each drift cell has hexagonal shape with a 11.9mmdiameter in radial direction and 19.0mm in azimuthal direction. A drift cell consists of one sense wire which is surrounded by six field wires. The field wires have ground potential while a high voltage of +1960V is applied to the sense wires. The layout of DCH cells is shown in Figure 3.6 for the first 16 layers. A longitudinal view of the drift chamber is shown in Figure 3.7. Due to the boosted center-of-momentum system of the colliding electron positron beam the

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3.2 The BABARdetector DCH is not positioned symmetrically with respect to the interaction point. Tracks with a lab polar angle of 17.2^◦ hit at least five drift chamber layers. Tracks with polar angle of 152.6^◦ hit twenty layers. The DCH is filled with a gas mixture of helium and isobutan with proportions 80%:20%. At normal incident the DCH contributes 1.08% of a radiation length of material.

For tracks with transverse momentum larger than 180M eV /c theDCH provides up to 40 measurements of energy loss and position. The energy loss per path lengthdE/dx is estimated from the total charge deposited in a drift chamber cell. The achieved resolution for dE/dxis 6.9%.

TheBABAR drift chamber is not only able to measure the position of charged tracks in the x-y-plane it is also able to measure the position of charged tracks in the z-direction.

This is achieved by tilting the wires in 24 of the layers by a small angle with respect to the z-axis. A spatial resolution of around 1mmin the z-direction is achieved.

Figure 3.6: Schematic of the layout of the first sixteen drift chamber layers [20]. The field wires are connected by lines to illustrate the geometry of the drift cells.

The numbers on the right give the tilt angle the sense wire has with respect to the z-axis inmrad.

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Figure 3.7: Longitudinal view of the drift chamber [20]. Distances are given inmmand angles are given in degree.

3.2.4 Detector of Internally Reflected Cherenkov light (DIRC)

The Detector of Internally Reflected Cherenkov light (DIRC) is used for particle identification at BABAR. It is designed to achieve a π/K separation of at least 4σ in the momentum range between 700M eV /cand 4GeV /c. TheDIRC measures the Cherenkov angle of the photons emitted by charged tracks when traversing the DIRC, which pro- vides information about the particle’s velocity.

The DIRC consists of 144 bars of synthetic fused silica. Each bar is 17mm thick 35mmwide and 4.9mlong. Twelve bars are grouped together and arranged in a twelve- sided polygonal around the drift chamber. Charged particles traversing the bars with a velocity faster than the speed emit Cherenkov light. The opening angle of the emitted light cone with respect to the particles trajectory is given by the so called Cherenkov angleθ_C with:

cosθ_C = 1

βn; β = v

c, (3.1)

where c is the speed of light in vacuum, v the velocity of the charged particle and n= 1.473 the index of refraction of silica. The bars serve as radiator material and as light pipes for the produced Cherenkov photons. The photons propagate through the bars by total internal reflection to the backward end of the bars where the so called standoff box is placed. Photons traveling in the other direction are reflected by a mirror placed at the forward end of the silica bar. The standoff box is filled with 6000 liter of purified water. Its walls are packed with 10752 photomultiplier tubes. The pattern of the emitted Cherenkov light detected by the photomultiplier tubes in the standoff box is a section of a light cone. The opening angle of the light cone corresponds to the Cherenkov angle θ_C. The Cherenkov angle together with the momentum information measured in theSVT and theDCH allows to determine the mass of charged particles.

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3.2 The BABARdetector Figure 3.8 shows the size and the position of the DIRC with respect to the drift chamber. The operation principle of the DIRC is illustrated in Figure 3.9.

Figure 3.8: Schematic view of the DIRC mounted outside the drift chamber [20]. The standoff box with the photomultiplier tubes is shown to the left.

Figure 3.9: Shown is the principle of operation of theDIRC [20].

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3.2.5 Electromagnetic calorimeter (EMC)

The task of theElectomagnetic calorimeter (EMC) is to measure electromagnetic showers with high efficiency. The EMC is also part of the trigger system of the BABAR experiment. The particle identification also uses quantities measured in theEMC. These play an important role in the identification of electrons and photons.

TheEMC is structured into two main parts. One part is the cylindrical barrel consisting of 5760 crystals arranged in 48 rings with 120 identical crystals each. The other part is the conical shaped endcap consisting of 820 crystals arranged in 8 rings. The EMC covers a polar angle of 15.8^◦ ≤θ_lab≤141.8^◦ in the lab frame. This corresponds to 90%

of the total solid angle in the Υ(4S) rest-frame. Figure 3.10 illustrates the arrangement of the crystals within the detector.

Figure 3.10: Shown is the arrangement of crystals in the EMC [20]. The EMC is sym- metrical with respect to the beam axis. It is only the top half of the EMC shown. All distances are given inmm.

Each of the EMC crystals is made from a thallium-doped cesium iodide (CsI(Tl)) mono-crystal. The fraction of thallium is 0.1 %. The crystal’s front is typically of the size of 4.7×4.7cm² while its back has a size of 6.1×6.0cm². The length of the crystals varies from 29.6cm for the backward part of the detector to 32.4cm for the forward region. Each of the crystals is wrapped in two layers of reflector material to prevent the leakage of light. In addition it is wrapped in a layer of thin aluminium foil to provide a Faraday shield and a layer of mylar for electrical insulation. The crystals are read out with two 2×1cm² PIN diodes which are glued onto the back face of the crystal. A schematic view of a singleEMC crystal is shown in Figure 3.11.

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Figure 3.11: Schematic of one of the EMC crystals [20].

The crystals are hold in place by an external support structure made from aluminium.

Energy calibration of a single crystal for low energies is performed with a radioactive source producing 6.13M eV photons. For high energies (3 −9GeV) calibration is done with a pure sample of Bhabha events (e⁺e⁻ →e⁺e⁻) where the energy dependence on the polar angle is known. For clusters (electromagnetic showers extending over several adjacent crystals) the calibration for low energies (E < 0.8GeV) is done with photons from the π⁰ → γγ decay, where the invariant mass of the two photons is constraint to have the nominal π⁰ - mass. At high energies (0.8GeV < E < 9GeV) calibration is done with single photon MC and with a pure sample of radiative Bhabha-events (e⁺e⁻→ e⁺e⁻γ). For the latter case the energy of the photon is kinematically defined by the measured momenta of the electron and the positron and thus can be used for calibration. A light pulser system is used to monitor the light response for each crystal.

An electromagnetic shower can extend over severalEMC crystals (a so-called cluster).

Dedicated algorithms have been developed to identify single clusters and to differentiate merged clusters from single clusters. Single bumps (local maxima within a merged cluster) are identified within the merged clusters.

The trajectories of charged particles are extrapolated to the innerEMC surface. If the extrapolated trajectory matches the position of a bump, the bump is associated with the charged track. Bumps which have not been associated with charged tracks are assumed to originate from neutral particles.

The energy resolution of theEMC for reconstructed bumps has been measured with a radioactive source and withBhabhaevents over a wide range of energies with a empirical

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formula:

σ_E

E = (2.32±0.30)%

p4

E(GeV) ⊕(1.85±0.12)%, (3.2) where ⊕ denotes the sum in quadrature. The angular resolution for single bumps is measured with π⁰ and η -decays. The obtained value for the angular resolution is described by an empirical formula:

σ_φ=σ_θ = (3.87±0.07)

pE(GeV) + (0.00±0.04)

!

mrad. (3.3)

3.2.6 Instrumented Flux Return (IFR)

TheInstrumented Flux Return(IFR) is used for particle identification of neutral hadrons (neutrons andK_L⁰ mesons) and muons and is also part of theBABAR trigger system.

The iron flux return of the solenoid is used as muon filter and absorber material for hadrons. The steel is finely segmented into 18 plates of increasing thickness. The inner nine plates have a thickness of 2cm and the outer plates have a thickness of 10cm.

Between the plates are gaps 3.2cm−3.5cmwide which are instrumented withResistive Plate Chambers(RPC). The barrel part contains 19 layers ofRPC the end doors contain 18 layers of RPC. Figure 3.12 depicts the segmentation and the geometry of the IFR.

Neutral hadrons interact with the steel flux return. The so produced shower of charged particles can be detected by theRPC.

Due to unexpected fast aging in connection with the loss of efficiency the RPC were replaced by Limited Streamer Tubes (LST) [24]. The replacement was performed between August and September 2004 for the barrel’s upper and lower sextant. Between August 2006 and January 2007 the rest of theRPC were replaced by LST.

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Figure 3.12: Dimensions (in mm) and the structure of the Instrumented Flux Return [20].

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4 Theory

4.1 The standard model of particle physics

This section represents a very condensed summary of the standard model of particle physics (SM). A more detailed introduction into the standard model can be found e.g.

in [58].

The standard model of particle physics describes our current knowledge about the fundamental particles and their interactions. The SM consists of three generations of quarks:

u d

!

, c

s

!

, t

b

!

, (4.1)

and three generations of leptons:

ν_e e⁻

!

, ν_µ µ⁻

!

, ν_τ τ⁻

!

. (4.2)

For each of these particles the corresponding anti particle exists. There are three interactions in the standard model which are mediated by the exchange of 12 gauge bosons.

These interactions are the weak interaction which is mediated by the three massive vector bosons:

W^±, Z⁰. (4.3)

As the weak interaction is the most relevant for this analysis it will be reviewed in more detail in one of the following sections. In particular the connection between weak interaction and semileptonic B-meson decays will be discussed.

The strong interaction is mediated by 8 gluons:

g_i (i= 1, ...,8), (4.4)

where each gluon carries a colour charge. The underlying theory describing the strong interaction is the Quantum-Chromodynamic (QCD). The coupling constant for the strong interaction is α_s. It has an energy dependence, calculated at one-loop level (see e.g.

[58]), of:

α_s= 12π

(33−2n_flog (q²/Λ²_QCD)), (4.5) where q² is the momentum transfer squared, n_f the number of active flavours at that energy scale and Λ_QCD the typical energy scale at which the strong interaction becomes non-perturbative. In the region where q² < Λ²_QCD the coupling constant can become

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larger than one. In this region QCD predictions cannot be described anymore in a perturbation series. Which means that other means of calculation have to be used e.g.

effective theories orlattice QCD.

And the photon as force carrier for the electromagnetic interaction:

γ. (4.6)

The electromagnetic interaction describes the interaction between particle carrying an electric charge. The theory describing the electromagnetic interaction is the Quantum- Electrodynamic (QED).

4.2 The CKM matrix

In the theory of electro-weak-interaction the mass eigenstates of quarks do not coincide with the quark eigenstates which participate in the weak interaction (see e.g. [58]). The two eigenstates are related by the so calledCabibbo-Kobayashi-Maskawa-matrix (short CKM-matrix):





 d^′ s^′ b^′





=







V_ud V_us V_ub Vcd Vcs Vcb

V_td V_ts V_tb











 d s b





, (4.7)

where theq^′ (q=d, s, b) are the quark eigenstates of the weak interaction, theqare the mass eigenstates of the quarks and the V_ij are the elements of the CKM-matrix. The CKM -matrix goes back to Cabibbo [40] who proposed that weak decays of quarks from the first and second family can be described by a mixing of the down type quarks from the first and second quark-family. In 1973 Kobayashi and Maskawa extended this idea resulting in a 3×3 matrix describing the mixing of down-type quark for 3 families of quarks [62].

Not all elementsV_ij of theCKM-matrix are independent from each other. TheCKM- matrix is a 3×3 -complex matrix which has in general eighteen free real parameters.

By construction theCKM -matrix is unitary (V_CKM^† V_CKM =V_CKMV_CKM^† =1) which reduces the number of free real parameters to nine. One phase can be absorbed by each of the quark fields (mass- and weak-eigenstates) except for a global phase. This leaves in the case of three quark families four independent real parameters. Where three of these free parameters are rotation anglesθ1 (i= 1,2,3) and one is a complex phase factor δ [72, 62]:

V_CKM =







c₁ s₁c₃ s₁s₃

−s₁c₂ c₁c₂c₃−s₂s₃e^iδ c₁c₂s₃+s₂c₃e^iδ

−s₁s₂ c₁s₂c₃+c₂s₃e^iδ c₁s₂s₃−c₂c₃e^iδ





, (4.8)

wheres_i= sinθ_i andc_i= cosθ_i with i= 1,2,3 and the real parameter δ.

Another parametrization which emphasises the magnitude of the single matrix elements is the Wolfenstein parametrization of the CKM-matrix [94]. Wolfenstein per-

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4.2 The CKMmatrix formed a series expansion of the CKM-matrix in the small expansion parameterλ:

V_CKM =







1−λ²/2 λ Aλ³(ρ−iη)

−λ 1−λ²/2 Aλ² Aλ³(1−ρ−iη) −Aλ² 1





+O(λ⁴), (4.9) where λ ≈ |Vus| ≈ 0.22 (the other parameter are of the order of one as will be seen below).

The unitarity condition for the first and third column of the CKM-matrix can be written as:

V_udV_ub^∗

V_cdV_cb^∗ +V_cdV_cb^∗

V_cdV_cb^∗ + V_tdV_tb^∗

V_cdV_cb^∗ = 0 . (4.10)

where it was divided by V_cdV_cb^∗ to follow the conventions theCKMfitter [42] group uses.

This relation spans a triangle in the complex plain, the so called unitary triangle. In particular this is the unitary triangle for the B-meson system. Its apex is given in the complex plain by:

ρ+iη=−V_udV_ub^∗

V_cdV_cb^∗ . (4.11)

The relation between ρ and η and the Wolfenstein parameters ρand η is given by:

ρ+iη=

√1−A²λ⁴(ρ+iη)

√1−λ²(1−A²λ⁴(ρ+iη)). (4.12) The unitary triangle is over constrained by complementary observables which allows to perform a fit for the best parameters for the CKM-matrix. There are currently two different groups using alternative statistical approaches to fit for the parameters of the CKM-matrix using input from measurements in the flavour sector (the CKMfitter collaboration uses a frequentist approach [42] while a bayesian approach is used by the UTfit collaboration for performing the fit [3]). Figure 4.1 shows a recent fit for CKM parameters performed by theCKMfitter collaboration. It shows the unitary triangle for theB-meson sector and the constraints used for the fit.

The current CKM parameters obtained by the CKMFitter-group [42] which corre- spond to the fit presented in Figure 4.1 are given by (Preliminary results as of Moriond 2012):

A= 0.812^+0.015₋_0.022, λ= 0.22543^+0.00059₋_0.00095, ρ= 0.145^+0.027₋_0.027, η= 0.343^+0.015₋_0.015.

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γ

γ α

α

md

∆ εK

εK

ms

& ∆ md

∆

Vub

β sin 2

(excl. at CL > 0.95) < 0 β sol. w/ cos 2 exclu

ded a t CL > 0.95

α

β γ

ρ

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

η

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

excluded area has CL > 0.95

Winter 12

CKM

f i t t e r

Figure 4.1: The unitary triangle in theρ-η- plane. The plot is taken from theCKMFit- ter group [42] which was presented as preliminary results as of winter 2012 (Moriond conference).

4.3 Semileptonic B -meson decays

For this analysis the theory of semileptonicB-meson decays is of special interest. The following section therefore briefly introduces the theoretical concepts used for the description of semileptonic B-decays. For explanations which go more into the details the reader is referred to [85] and the reference therein or to [78]. The explanations in this section follow the publication of Richman and Burchat [85] who wrote a review on semileptonic and leptonic decays of charm and bottom hadrons.

The underlying theory of semileptonic B-meson decays is the theory of the electro- weak-interaction. For semileptonic B-decays only the charged current exchange is of importance which is mediated by the exchange of a massiveW^±-boson. This is depicted in form of a Feynman graph in Figure 4.2. It shows the semileptonic decay of aB-meson into a final-state meson X⁰. The b-quark within theB-meson decays by emission of a W^±-boson into an up-type quarkq (whereq can be anu- or ac-quark). TheW^±-boson itself decays into a lepton-neutrino-pair. This process is theoretical described by the transition matrix element for the quark transitionb→qlν [58]:

M(b→qlν) =

V_qbg_W

√2q1

2γ^µ(1−γ⁵)b

g_µν−^q_m^µ²^q^ν

W

q²−m²_W g_W

√2u_l1

2γ^µ(1−γ⁵)v_ν

, (4.13) with theCKM-matrix elementVqb,gW the weak interaction constant,mW theW-boson

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4.3 Semileptonic B -meson decays

V

_qb

W

⁻

ℓ

⁻

ν ¯

_ℓ

b

u ¯ q

u ¯

Figure 4.2: Feynman graph depicting the semileptonic B-meson decay B⁻ → X⁰l⁻ν decay into a final-state meson X⁰.

mass, g_µν the Lorentz metric, the Dirac matrices γⁱ, q the transfered four-momentum and the Dirac spinors of the quarks q and b, the lepton Spinor u_l and the neutrino Spinorvν, respectively. InB-decays the momentum transferqis limited by theB-meson mass. As the B-meson mass m_B is much smaller than the mass of the W^±-bosonm_W (m_B= (5279.1±0.4)M eV /c² andm_W = (80.399±0.023)GeV /c² [74]) the momentum dependence of the W-propagator can be integrated out. Which leads to the effective matrix element:

M(b→qlν) = G_FV_qb

√2

hqγ^µ(1−γ⁵)b^{i h}u_lγ_µ(1−γ⁵)v_νⁱ, (4.14) where G_F, the so called Fermi constant, is defined as

G_F =

√2g_W²

8m²_W = (1.16637±0.00001)×10⁻⁵GeV⁻² [74]. (4.15) So far the decays were discussed on quark level only. But as the quarks are bound in mesons the quark spinors in Equation (4.14) have to be "sandwiched" between the physical meson states. For a semileptonic decayB →X_qlν the transition matrix element can be written as:

M(B →X_ql⁻ν) =¯ −iG_F

√2V_qbL^µH_µ, (4.16) where the hadronic current,H_µ, can be written in terms of the hadronic vector current, V^µ=qγ^µb, and the hadronic axial current, A^µ=qγ^µγ⁵b:

Hµ=hX|Vµ−Aµ|Bi, (4.17)