Decay at the Belle II Experiment

Universität Hamburg Fachbereich Physik

Bachelorarbeit in der Belle II Gruppe des Deutschen Elektronen Synchrotron, DESY

A sensitivity study of the B0 → K∗(892)0 µ+ µ− decay at the Belle II experiment

Merle Schreiber

1. Gutachterin: Prof. Dr. Caren Hagner 2. Gutachter: Dr. habil. Alexander Glazov Betreuer: Dr. Simon Wehle

21. November 2017

Abstract

Although the Standard Model of particle physics is well established by many experiments some phenomena are observed that cannot be explained by the Standard Model alone. Further- more recent evaluations of experimental data yield results deviating from the Standard Model's predictions with a significance of up to 4σ −5σ. The B0 → K∗0 l+ l− decay is one of those where new physics might arise. The Belle detector is being upgraded in order to achieve more precise measurements of many variables and to cope with the higher luminosity of the superKEKB collider. In this thesis the sensitivity of the B0 → K∗0 µ+ µ− decay at the new experimental setup, with the upgraded Belle II detector and superKEKB collider, is analyzed using data from Monte Carlo simulations of the Belle II group. The studies show that, even for the integrated luminosity of the Belle dataset, a higher amount of signal events and better statistical significance can be expected of the new setup. Even more so for a final integrated luminosity, which is 50 times higher than that of the previous experiment.

Zusammenfassung

Obwohl das Standardmodell der Teilchen experimentell gut bestätigt ist, gibt es einige be- obachtete Phänomene, die nicht allein durch das Standardmodell erklärt werden können. Des Weiteren haben kürzlich durchgeführte Auswertungen experimenteller Daten Ergebnisse her- vorgebracht, die mit einer Signifikanz von bis zu 4σ − 5σ von den Vorhersagen des Standard- modells abweichen. Der Zerfall B0 → K∗0 l+ l− ist einer derjenigen, bei neue Physik gefunden werden könnte. Der Belle Detektor wird nun aufgerüstet, um genauere Messungen vieler Varia- blen erreichen und der erhöhten Luminosität des SuperKEKB Beschleunigers gerecht werden zu können. In dieser Arbeit wird die Empfindlichkeit des neuen Aufbaus des Experiments, für den B0 → K∗0 µ+ µ− Zerfall, mit dem verbesserten Belle II Detektor und dem superKEKB Be- schleuniger, unter Verwendung von Daten aus Monte Carlo Simulationen der Belle II Gruppe, analysiert. Die Arbeit zeigt, dass mit dem neuen Aufbau, selbst bei einer integrierten Luminosi- tät, die der des Belle Datensatzes entspricht, eine höhere Anzahl an Signalereignissen und eine bessere statistische Signifikanz zu erwarten ist. Um so mehr sollte dies für eine letztendliche, integrierte Luminosität der Fall sein, die 50 mal so hoch ist, wie die des vorherigen Experiments.

Contents

1. Introduction 9 1.1. Motivation ...... 9 1.2. Theory ...... 10

2. Analysis Setup 13 2.1. The Belle II Experiment ...... 13 2.1.1. Vertex Detector ...... 14 2.1.2. Central Drift Chamber ...... 15 2.1.3. Particle Identification ...... 16 2.1.4. Electromagnetic Calorimeter ...... 17 0 µ 2.1.5. KL and Detector ...... 17 2.2. Belle II Analysis Software Framework ...... 18 2.2.1. The Analysis Script ...... 19

3. Analysis 21 3.1. Generation, Simulation and Reconstruction ...... 21 3.2. Classifier and variable tests ...... 27 3.2.1. Testing variables ...... 27 3.2.2. Testing different classifiers ...... 37 3.3. Results ...... 39

4. Conclusion and Outlook 43

A. Appendix: additional plots 47

1. Introduction

1.1. Motivation

Over the last years the Belle and BaBar experiments, as well as LHCb experiment conducted measurements with special focus on CP violation in the quark sector, mostly in the b-flavor sector. The results of those measurements revealed some deviations to the Standard Model's predictions. One of the observables deviating is the ratio of the branching fraction of the two decays B → K∗ µ+ µ− and B → K∗ e+ e− [7], which is expected to be close to 1 in the Stan- dard Model. Measurements of this branching ratio by the LHCb combined with the previously measured branching fraction RK result in a deviation of 3.5σ from the Standard Model [7]. In the Standard Model lepton flavor is supposed to be universal, however the deviations observed might hint at a New Physics scenario where lepton flavor universality is violated, since most of the deviations from the Standard Model are observed in decays including µ or τ leptons while the same decays including electrons seem to behave Standard Model like. Although the deviations may be correlated and can potentially be explained by a single theory, there are many theories that might explain those anomalies and up to now the results do not hint to one specific New Physics scenario, but allow several different theories. Combining all the deviations from the Standard Model that were observed at LHCb, BaBar and Belle a significance of up to 4σ - 5σ is reached [6]. For measurements with high statistics it is to be expected, that a few data points deviate with a significance of 3σ or more, due to statistical fluctuation. Therefore in particle physics a significance of at least 5σ is needed to call a result a new discovery. Statistically 99.9998% of all data are to be found within 5σ of the “true value”. Therefore even in very large data samples it is very improbable to observe a data point outside the 5σ region just due to statistical fluctuation. To get a better idea of what these results mean more precise measurements and better statistics are needed [6, 7, 8].

With the upgrade of the accelerator from KEKB to SuperKEKB a higher luminosity will be achieved at the Belle II experiment resulting in a data set that is estimated to reach 50 times the data of the Belle data set, leading to much better statistics. While the Belle II detector was also upgraded in order to yield measurements of higher precision, the raised luminosity of Su- perKEKB compared to KEKB resulted in a raised background level, making the upgrade of the detector inevitable. In the course of upgrading the experiment the software framework was rebuilt completely. This sensitivity study employs the new software framework as well as mul- tivariate analysis in order to estimate the efficiency and expected number of B0 → K0∗ µ+ µ−

9 decays at the new experimental setup and compare the results to those of the Belle experiment.

1.2. Theory

According to the Standard Model of particle physics all matter is composed of quarks and leptons, where both types of particles are fermions and are divided into three so called generations, which can be seen in Figure 1.1 together with all the other particles of the Standard Model. In this theory each generation contains two types of particles. In the case of leptons for electrons, muons (µ) and taus (τ), there exist corresponding neutrinos with a flavor named after their part- ner. While electrons, muons and taus carry a charge1 of 1 (depending on whether the particle or the antiparticle is referred to), the neutrinos are electrically neutral. The quark pairs making up the three quark generations are called up and down, charm and strange as well as top and bot- 2 tom, where the first named quark of each pair carries an electric charge of + 3 , while the second − 1 carries a charge of 3 . For each of those particles there exists a corresponding antiparticle with opposite quantum numbers.

Figure 1.1.: Visualization of the particles included in the Standard Model of particle physics. the figure is taken from [14].

Furthermore the Standard Model states that there exist bosons of spin 1, which mediate interactions between particles. There is the photon (γ) for the electromagnetic force, the gluon (g) for the strong force and the three bosons mediating the weak force (W , Z0). However up to now there is no tested theory that is able to describe gravitation on the scale of elementary particles. Thus, there is only one more particle in the Standard Model called the Higgs boson

1In this thesis the charge of all particles are presented in units of the electron charge

10 (H0), a particle of spin zero, which is responsible for the particles' inertia. Of all the mediator particles of the Standard Model only the W boson carries an electric charge.

The decay of interest in this thesis is a very rare one as it requires a bottom quark to turn into a strange quark. However the only interaction in the Standard Model which allows for a change of flavor between the initial and final state is the weak interaction, more specifically an interaction mediated by the W boson. Since the charge has to be conserved either two W-bosons or a W-boson and a Z-boson or a photon are needed for a process with the desired initial and final states. The corresponding Feynman diagrams are illustrated in Figure 1.2. These processes are suppressed, however, since W and Z bosons have a high mass, which reduces the allowed phase space compared to other processes.

Figure 1.2.: Lowest order penguin (top) and box (bottom) Feynman diagrams allowed in the Standard Model for B0 → K∗0 l+ l− .

The probability for a transition from one quark to another is described by the Cabbibo-Kobayashi- Maskawa (CKM) matrix. If there were no transitions across generations this would be an identity matrix. In reality, however, the CKM matrix is a unitary but not an identity matrix. The magnitude of the entries on the main diagonal marking transitions within the generation are still the biggest, while those of the entries marking a transition to the next generation are smaller and those describing transitions across two generations are the smallest. This also leads to a reduced probability of a bottom quark going to a strange quark, as they do not belong to the same generation.

11         d′ V V V d 0.9738 0.2272 0.0040    ud us ub     ′ · | | s  = Vcd Vcs Vcb s , Vi j = 0.2271 0.9730 0.0422 (1.1) ′ b Vtd Vts Vtb b 0.0081 0.0416 0.9991

The relations in eq. (1.1) show what the transition probabilities between the generations look like, or rather how the CKM matrix turns the quark mass eigenstates to weak eigenstates.

On the other hand there are theories beyond the Standard Model that would allow for other interactions to yield the same transition. Therefore New Physics processes contributing to decays like B0 → K∗0 µ+ µ− that feature the transition from bottom to strange quarks could interfere with the Standard Model changing the amount of b → s transitions and the distribution of lepton flavor in the final state, if such New Physics interactions can happen in our world. One possible additional mechanism is the existence of a flavor changing mediator boson called Z′ that would allow for a direct transition form a bottom to a strange quark. Such processes, where only the flavor of a quark but not its charge changes, are called flavor changing neutral currents (FCNC). In the Standard Model they are not allowed on a tree level, meaning there are no closed loops in the Feynman diagram describing the process, in the Standard Model. Another possibility is posed by a scenario where two additional charged Higgs bosons exist and yield another box diagram similar to the one with two W bosons. For the corresponding Feynman diagrams see Figure 1.3.

Figure 1.3.: Possible New Physics Feynman diagrams with flavor changing Z′ boson and charged Higgs.

12 2. Analysis Setup

This chapter only includes information of interest for this thesis. For more details see [1].

2.1. The Belle II Experiment

Like its predecessor the Belle II experiment offers a good opportunity to study B meson decays in a clean experimental environment. The Belle II experiment is located at the SuperKEKB accelerator in Tsukuba, Japan. This accelerator will collide electrons and positrons at a center- of-mass energy that corresponds to the ϒ resonances, mainly at 10.58 GeV/c2 corresponding to the ϒ(4S) resonance. Since the ϒ(4S) almost always decays into two B-mesons the SuperKEKB and its predecessor KEKB are called B factories. Thus, the setup allows for good statistics in the B sector, because relatively many decays of B mesons can be observed. It also accounts for very well known initial conditions, which makes analyses working with missing energy much easier. With an instantaneous luminosity of 2.11×1034 cm−2s−1 the KEKB accelerator is hold- ing the record of the highest up to now. However, the goal for the SuperKEKB accelerator is to reach a luminosity, that is 40 times higher. Therefore the magnets of the SuperKEKB have been upgraded in order to achieve a better beam focus and a smaller interaction region, leading to a higher amount of interactions per second and a lot more background [1, 2].

Various subdetectors are needed to measure the momenta and energies of the particles as well as to reconstruct their tracks in the detector. For reconstructing a specific decay, however, it is also very important to gather information that will help to distinguish all the different types of particles from each other as well as being able to separate two simultaneous events from each other. Therefore, like most other particle detectors, the Belle II detector is built in an onion like structure with many layers of different detectors. A detailed technical sketch of the detector can be found in Figure 2.1.

Unlike some other particle detectors Belle II is built asymmetrically. This is due to the fact that SuperKEKB is an asymmetric ring collider, meaning that the electron and positron beams in the two accelerator rings have two different energies. The electrons in the High Energy Ring (HER) reach a beam energy of 7 GeV, while the positrons in the Low Energy Ring (LER) only reach a beam energy of 4 GeV. Therefore from the lab-frame point of view the center-of-mass frame has a boost in the direction of the electrons. This direction is labeled as the forward direction. The electrons and positrons collide at an angle of 83 mrad, in order to separate the two beams

13 after collision. [1, 2, 3]

Figure 2.1.: Technical sketch of the Belle II Detector. the Figure is from [16].

2.1.1. Vertex Detector

The Belle II vertex detector is the detector closest to the beam line and the interaction point (IP). It consists of six layers, where the two innermost belong to the Pixel Detector (PXD), whereas the other layers belong to the so called Silicon Vertex Detector (SVD). Although the technolo- gies used in the two detectors are different they serve to the same purpose, that is to track the passing particles close to the IP with high precision in order to reconstruct the corresponding vertices. In the Belle detector the vertex detector only consisted of silicon strip sensors, as used for the SVD in Belle II. However with the new SuperKEKB accelerator the luminosity and with it the amount of particles hitting a sensor as well as the level of radiation are increased to a level that silicon strip sensors cannot cope with. Therefore another type of sensors is needed for the innermost layers, while the strip sensors can still be used beyond a radial distance of 40 mm from the interaction point.

When the development of the pixels is done they should be able to work for about five years in the Belle II setup, withstanding up to 10 MRad without significant radiation damage [1]. Both types of sensors are mounted on ladders that are arranged in a windmill like structure as displayed in Figure 2.2 (top). In order to achieve a higher angular coverage, while, keeping all the needed sensors reasonably low the outermost three layers include slanted sensors in the forward

14 region as can be seen in Figure 2.2 (bottom).[1]

Figure 2.2.: Arrangement of the vertex detector's layers from forward to backward direction (top) and from side to side (bottom) with all axes in mm. This figure is from [1].

This detector also gives data for all the vertex variables that might be interesting for later analysis.

2.1.2. Central Drift Chamber

Like the vertex detector the Central Drift Chamber (CDC) fulfills the task of tracking charged particles. It is therefore surrounding the vertex detector. However the CDC is also capable of measuring the momentum of those particles, which is extremely important for the reconstruction of decays. Furthermore the CDC contributes to the particle identification. Usually the particle identification components of the detector fulfill the main part of that task, but particles with momenta too low to reach that part of the detector can be identified by the CDC. This is possible, because the CDC is also capable of measuring the ionization energy or energy loss of the passing particle, which is characteristic for each type of particle given a specific momentum.

The CDC is composed of many gas filled cells arranged in cylindrical layers. In those cells wires are spanned along the long axis of the cell. There are three types of layers in the CDC, the axial type (A) and two types of so-called stereo layers (U or V). The wires in the axial layers are strung in such a way, that they are parallel to the Z-axis of the detector. For better spatial resolution the wires in the stereo layers are oriented with a slight angle to the Z-axis as shown in Figure 2.3. The Z-axis of the detector coincides with, or rather is defined by the

15 direction of the magnetic field produced by the superconducting coil surrounding the barrel part of the electromagnetic calorimeter (described two sections below). The coil of Belle II creates a magnetic field of about 1.5 T at its center. The magnetic field is needed for momentum and charge measurements in the CDC, as those variables are obtained from the direction and the radius of the particle track's curvature.

Figure 2.3.: Definition of wire orientation in U and V stereo layers. This figure is taken from [17].

Apart from its contribution to particle identification and kinematic data of the particles the CDC signals can also serve as efficient and reliable trigger for charged particles, which is very helpful for handling the amount of data produced [1].

2.1.3. Particle Identification

The Particle Identification (PID) system of the Belle II detector is divided in two parts, one being the barrel PID system and the other the end-cap PID system. This is again in order to increase the angular coverage, although the end-cap PID system is only placed in the forward end-cap, as similar space in the backward direction is occupied by CDC readout electronics [1]. In general both systems utilize the same physical phenomenon of Cherenkov radiation. By passing through a medium with a velocity higher than the speed of light in this medium charged particles emit a shock wave of light called Cherenkov radiation. The Cherenkov radiation photons are emitted in a specific angle with respect to the particle's direction of flight, depending on the particle's boost. Therefore the particle's mass can be deduced from the Cherenkov angle and the momentum (measured in the CDC) of the particle [5].

In the barrel section a Time-Of-Propagation (TOP) counter with quartz radiators and attached photon detectors is used to determine the initial 3-dimensional direction of the Cherenkov photons, by measuring the x and y position of the photons on the detector as well as the propagation time of the photons in the radiator[1, 15].

16 For the end-cap an Aerogel Ring-Imaging Cherenkov detector (ARICH) is used. As the name indicates aerogel is used as a radiator. In this system however there is an expansion volume between radiator and the photon detector array in order to allow the cone of Cherenkov radiation to expand. The cones opening angle, that is the Cherenkov angle, can be inferred from the resulting ring image on the photon detectors. Both sections of the PID system are chosen in order to increase the detectors ability to separate kaons and pions [1]. This is important for the analysis, since the K∗0 decays into a pion and a kaon.

2.1.4. Electromagnetic Calorimeter

The Belle Electromagnetic calorimeter (ECL) has been working well during the data taking period of Belle and tests show, that its performance would still be good in the Belle II setup. Therefore not much will be changed for the shower energy measuring detector of Belle II. The ECL consists of a barrel section and two end-cap sections, one for the forward and one for the backward end-cap. In general the ECL consists of thallium doped CsI scintillator crystals of a truncated pyramid shape with a photodiode attached to its rear surface. The material of the scintillator crystals is chosen in such a way, that electrons and hadrons deposit almost all their energy in the form of light in this part of the detector. This is why this part of the detector is the outermost layer with exception of the muon detector. Apart from all sorts of kinematic calculations and reconstructions the energy measured in the ECL is also used for electron/hadron separation using the ratio of shower energy and track momentum E/p. Being able to detect photons and measuring their energy the data of the ECL is also a fundamental resource for reconstructing π0 mesons.[1, 2]

0 µ 2.1.5. KL and Detector

Only a few particles, like muons and charged hadrons that either decay in flight or do not interact 0 µ hadronically, reach the KL and detector (KLM) beyond the superconducting coil acting as magnet for the detector. The KLM is constructed in alternating layers of sensors and iron plates. 0 Here the iron plates serve two purposes, first they provide 3.9 interaction lengths for KL to shower hadronically and second they serve as magnetic flux return for the superconducting coil. The Belle KLM used small resistive plate chambers with glass electrodes filled with a gas mixture. These sensors will be used for Belle II again while the end-cap sections will be upgraded. The glass electrodes have a high resistance, but charged particles like muons can ionize the gas enclosed in between the glass electrodes causing an electric current, if a high voltage is applied to the electrodes. The KLM is the only source for a direct measurement of muon energies. The only other option to obtain the muon energy was to use the momentum measured by the CDC assuming the particles invariant mass to be that of a muon. Furthermore 0 the KLM contributes to the detection and identification of muons and KL mesons [1].

17 2.2. Belle II Analysis Software Framework

The Belle II Analysis Software Framework (basf2) includes tools necessary for simulating data of the particle interactions (Monte Carlo simulations), detector simulations and reconstruction as well as for the analysis of the produced data. It is mainly written in C++ and includes external libraries like ROOT, GEANT4 and others. The software is composed of many small modules performing some particular tasks of data processing. This is in order to keep the software framework flexible and the fixing of problems relatively easy. The software can also be interfaced via Python, which allows for a rather simple and intuitive communication with the software. The Python scripts, executing tasks as defined by the user, are called steering files. The steering files can arrange modules within a so-called path in a strict linear order, illustrated in Figure 2.4. Each module exchanges information with a common data store, hence making information obtained by one module accessible for all the following modules in the path, too [10].

Figure 2.4.: Simple example for modules in a path passing on information by using a common data store. The Figure is taken from [10].

For the analysis in this thesis mainly steering files for reading out the reconstructed data were used to reconstruct the decay of interest from simulated data and then to obtain the variables for the multi variate analysis. Generation as well as simulation and reconstruction scripts, however, were also needed in order to obtain data for the signal decay in the first place. Since the Belle II experiment has to deal with a lot of data, not only due to experimental data, but also due to Monte Carlo (MC) simulations, a computing network based on the so called Grid is used. The Grid is a computing network including many computing sites of institutes all over the world, allowing to join the computing capacity of groups that are part of the same collaboration. In the Grid network, data is distributed to all the computation sites of the collaboration, thus providing computing power for the analysis and offering enough storage for the raw data. The latter is very important in order not to interfere with the experimental data taking. It also allows the processing of the raw data, making large datasets accessible for each group without the necessity to store it at every computing site [1].

18 2.2.1. The Analysis Script

One very important part for this analysis are the Python analysis scripts used to prepare the simulated data in such a way, that variables which might be interesting for the analysis can be handled and looked at without a lot of effort. The analysis scripts used for this thesis create ROOT files whose content can be loaded by Python (in this case jupyter notebooks) in form of arrays, assigning a set of chosen variables to a certain particle, called pandas data frame.

First the data containing all the signals given by the detector is loaded. In the case of simulated data the information about the true data is accessible, too. Then lists of particles can be created from the data by using the “fillParticleList” function, where its first argument is a string of the format “particlename:listname” and its second argument is a string containing the requirements for the particle to be accepted into the list. The “fillParticleList” function can be used for final state particles only. Other particles need to be reconstructed from the particle lists of their decay products, also called daughter particles. The “reconstructDecay” function does this and creates a particle list of the reconstructed particle type. Finally a list of variables picked from the list of so called “Ntuple_tools”, which are defined within the Belle II software, can be assigned to any particle list, including those created by the “fillParticleList” function and particle lists of reconstructed particles alike.

However, for some variables the necessary data needs to be set up. This is the case for the variable set concerning the rest of event and for the vertex variables. In order to calculate the vertex variables the software needs to perform a fit of the particle tracks to determine where their interaction vertex is positioned. This can be done by calling the “fitVertex” function spec- ifying which particles of the decay are to be used for the fit and to which particle list the vertex variables are supposed to be assigned to. Apart from that the fit method needs to be specified. For the rest of event variables the data of all those particles in the event that have not been used for the reconstruction need to be made accessible. The functions “buildRestOfEven”, “ap- pendROEMask” and “buildContinuumSuppression” make all the variables used in this analysis accessible.

3. Analysis

The aim of this thesis was to estimate the sensitivity of the B0 → K∗0l+l− decay at the Belle II experiment. Various tests were performed in order to find an efficient method to distinguish signal and background events for this specific decay. To measure the quality of the separation √ nsig the figure of merit (FOM) given by FOM = was used, where nsig and nbkg are the nsig+nbkg amount of signal and background events given a certain data set, respectively. The background data used for this analysis is taken from the Monte Carlo campaign 8 of the Belle II group, whereas the signal data was generated separately by using the software framework of Belle II (more information in the section below). The Monte Carlo data corresponds to 1 ab−1, while the generated signal data includes one million signal events. Hence, the amount of expected signal data calculated form the analyzed data had to be scaled in order to match the amount of the Monte Carlo data. The amount of observed signal within the Belle corresponding to 0.711 ab−1 was used as a basis for scaling the signal data used in the analysis.

3.1. Generation, Simulation and Reconstruction

As mentioned above the data for our signal had to be generated and simulated. The generation as well as the simulation and reconstruction of the Monte Carlo data can be done by running Python scripts. Python functions for generating decays and simulating its interactions with the detector are defined in a part of the software called “modularAnalysis” and reconstruction respectively. The function “generateY4S(n, decayfile.dec)” generates n events of ϒ(4S), which decays according to a specific decay file using the “EvtGen” package. Such a file contains all the information about the probabilities for the ϒ(4S) to decay. An example of a decay file is given below:

Alias MyB0 B0 Alias Myanti-B0 anti-B0

Decay Upsilon(4S) 0.2500 Myanti-B0 B0 VSS; 0.2500 MyB0 anti-B0 VSS; Enddecay

21 Decay MyB0 0.5000 K*0 mu+ mu- PHOTOS BTOSLLBALL; Enddecay

Decay Myanti-B0 0.5000 anti-K*0 mu+ mu- PHOTOS BTOSLLBALL; Enddecay

End

This decay file defines a specific decay channel for the ϒ(4S) and the B-mesons. According to this decay file the ϒ(4S) always decays into a B0 − B¯0 pair. One of the B-mesons decays according to B0 → K∗0 µ+ µ− while the other B-meson of the pair decays generically. Half the cases the B0 decays to K∗0 µ+ µ− , and the other half the B¯0 decays to K∗0 µ− µ+. The K∗0 then decays generically as well, since nothing is specified in the decay file. In this context the generated decay of a particle is called generic, if all decays possible in the Standard Model are considered with their corresponding probability.

A second Python script can then load the file with generated decays and simulate their way through the belle detector using the “add_simulation” and the “add_reconstruction” functions of the software framework and generate an output file containing the detector's signals. This output file can then eventually be read by an analysis script, that does the actual decay reconstruction and writes out the desired variables. The decay is reconstructed reversely, starting from the final state particles, which are µ, π and K, for the decay studied in this thesis. With the basf2 it is possible to create particle lists of some particle type. This is the point where first cuts can be introduced to reduce the amount of data. Typically at this point cuts are made on the particle identification (PID) variables, which, using all the data collected by the detector responses, assign a probability to a particle to be of a certain type. Apart from that it is usually required, that the particle comes from a point not too far away from the interaction point (IP) and that the χ probe of the track fit is a bit higher than zero. For this analysis only the decay K∗0 → K+ π− will be considered, which means that Apart from the muon particle list a pion an kaon particle list is needed. This choice was made due to the fact that kinematic variables of the K∗0 daughters (K+ and π−) will be needed for the analysis and more decay channels would again make obtaining data in a format, that can be handled easily, difficult. Furthermore, vertex variables are to be considered in the analysis and the vertex fit does not work well if so many particles of the decay chain are neutral and therefore do not leave tracks in the detector.

After filling the particle lists first the K∗0 and then the B0 can be reconstructed. Since a new particle list is created when particles are reconstructed more cuts can be introduced. Typically

22 cuts on the invariant mass of the reconstructed particle are introduced since all combinations of final state particles of the event that are allowed by the decay are used. Therefore a cut on the invariant mass excludes combinations that would not fulfill energy momentum conservation within given limits assuming they came from a decay of the reconstructed particle. For the B0, however, there are two other variables, that are much more suitable to eliminate wrong combinations of final state particles, exploiting the fact that the two B-mesons produced of an

ϒ(4S) decay at the B-factory are produced almost at rest. Those variables are ∆E and Mbc, that is the difference between the energy of the B-meson and half the beam energy as well as the beam constrained mass. To start the analysis those cuts were chosen by trying a few combinations. Afterwards another analysis without any cuts was run to plot the efficiencies as function a of the cuts on the chosen variables. On account of the enormous combinatorial background that was created in that analysis, not all events could be used to generate the plots. 10 of 1000 files each containing data of 1000 events were chosen for plotting. Since all the data in each file comes from the random decay generation as described above, there should be nothing special about any file and it should make no difference which 10 files are finally used. Figures 3.1 to 3.8 show the created plots.

Figure 3.1.: Histograms of PID variable for µ (top left), π (top right) and K (bottom), each with dashes lines, indicating the final cut.

23 Figure 3.2.: Efficiency as a function of the PID variable cuts, with final cut for muons (0.9), pions and Kaons (0.6) indicated by the dashed vertical lines.

Figure 3.3.: Distribution and efficiency of the chiProb variable for µ, with dashed lines, where the final cut was chosen.

The following excerpt from my analysis script is an example code for filling a final state particle list with specific cuts and creating a list of variables that are to be saved. In this case the muon list is filled, but it works the same for the other particles, when “mu+” is replaced by “pi+” or “K+” and “muid” by “piid” or “Kid”. fillParticleList('mu+:Test', 'muid > 0.9 and chiProb > 0.001 and -1. < dr < 1. and -5. < dz < 5.') toolsTrackMu = ['EventMetaData', 'mu+'] toolsTrackMu += ['Kinematics', '^mu+'] toolsTrackMu += ['Track', '^mu+'] toolsTrackMu += ['PID', '^mu+'] toolsTrackMu += ['CustomFloats[isSignal]', '^mu+']

24 Figure 3.4.: Distribution and efficiency of radial distance to the IP for µ, with dashed lines, where the final cut was chosen. Final cuts chosen at |dr| < 1.

Figure 3.5.: Histogram and efficiency of distance in the z-direction to the IP for µ, with dashes lines, where the final cut was chosen. The Final cuts were chosen at -5 < dz < 5.

(b) Efficiency as a function of the invariant K∗0 (a) Distribution of invariant K∗0 mass. mass.

Figure 3.6.: Plots for the cuts on the invariant K∗0 mass, with the selected region between the dashed lines.

25 This excerpt of my analysis script below reconstructs the K∗0, implements the cuts on the invariant mass a shown in the Figure 3.6 and also creates a short list of variables to be saved. reconstructDecay('K*0:char -> K+:Test pi-:Test', '0.6 < M < 1.4') matchMCTruth('K*0:char') toolsKst02 = ['InvMass', '^K*0'] toolsKst02 += ['MCTruth', '^K*0 -> ^K+ ^pi-'] toolsKst02 += ['CustomFloats[isSignal]', '^K*0']

(b) Efficiency as a function of the beam constrained (a) Distribution of beam constrained mass. mass cuts.

Figure 3.7.: Plots for the cuts on the beam constrained mass Mbc, with everything right of the dashed line accepted.

(a) Distribution of |∆E|. (b) Efficiency as a function of |∆E| cuts.

Figure 3.8.: Plots for the cut on |∆E|, with everything left of the dashed line accepted.

The piece of code below also belongs to my analysis script. It implements the last cuts as shown in Figures 3.7 and 3.8 while reconstructing the B0 particle. It also initiates the vertex fit for the B-meson using the particles marked with a “ ^”. This is necessary in order to save the vertex variables later.

26 reconstructDecay("B0:mu -> K*0:char mu-:Test mu+:Test", "5.22 < Mbc and abs(deltaE)<1.0 ") matchMCTruth('B0:mu') fitVertex('B0:mu', 0, 'B0 -> [K*0 -> ^K+ ^pi-] ^mu- ^mu+', 'rave')

As the plots above show, the most efficiency is lost by using high PID cuts. However in order to avoid a high amount of combinatorial background high PID cuts are needed. This also helps to keep the necessary computation time low. The analysis proceeded with cuts as presented in those figures. Another set of low cuts was chosen for a very rough comparison. For the low cuts only the PID cuts were lowered, as they have the strongest effect on the efficiency. There was however not enough time to complete the whole analysis for the lower cuts as well. This would be necessary to decide which set of cuts is preferable.

3.2. Classifier and variable tests

Once the reconstruction and variable selection is done all the data is saved in a ROOT file containing one or more so called trees with the variables saved for a specific particle list. It is possible to access some variables of daughter particles, too. A Python script or jupyter note- book can load such a tree in the form of a pandas data frame. There are two aspects that need to be optimized. The best classifier to separate signal and background events has to be found as well as the best set of training variables. Finding the best classifier can be done by looking at a purity versus efficiency plot or ROC curve. The classifiers used for this analysis are taken from the “sklearn” library of Python. Regarding the variables correlations among them need to be considered. Since variables like the beam constrained mass, the invariant mass of the two lepton system and the angle variables cos(θK), cos(θl) and cos(ϕ), described in section 3.2.1, are essential for further analysis, not discussed in this thesis, variables which are correlated to those variables can not be used as classifier input. Using such variables during the classification process would influence the distribution of the variables still needed for later analyses and therefore bias results obtained by those analyses.

For the decay studied in this thesis there are two types of background events. One is the e+e− → qq¯ process, also called continuum background, and the other includes generic B-meson decays. The latter can be divided into charged background, for a B+ −B− pair, and mixed background, for B0 −B¯0 pair. A good separation method has to reduce both backgrounds efficiently.

3.2.1. Testing variables

For finding good variables two things need to be considered. First a good separation variable must not be correlated to either Mbc, the invariant mass of the two leptons squared or any of the angle variables cos(θK), cos(θl) or cos(ϕ), since those variables are used for further analysis.

27 Second a chosen variable should have a high separation power. This is the case if the variable has a distinctively different distribution for signal candidates compared to background candidates. However, even if a variable is distributed the same for signal and background the classifier might still be able to obtain a few separation information of it by combining the variable with another variable. Likewise using several variables correlated to one another is not particularly helpful since the classifier can only obtain the information from one of the variables.

The software framework allows to record a set of variables called continuum suppression variables, which were specifically designed to separate signal and so called continuum background. Events in which up, down, charm or strange quarks are produced are called continuum background. There are several groups of continuum suppression variables, but most of them take distributions of flight directions and angles between those or to the z-axis into account. There are four variables related to the thrust, which is a value defined by relation (3.1), where T is the so called thrust axis, a unit vector with a direction defined such that the sum of the particle th momenta's projection is maximal and pi is the momentum of the i particle [2].

∑N |T · p | T = i=1 i (3.1) ∑N | | i=1 pi

The thrust related variables are called “ThrustB”, “TrustO”, “CosTBTO” and “CosTBz”. Where ThrustB and ThrustO are the thrust of the B-meson candidate's decay particles and the thrust of the ROE particles in the event respectively. CosTBTO is the cosine of the angle between the thrust axes of the B-meson decay particles and the ROE particles, whereas CosTBz represents the cosine of the angle between the z-axis and the thrust axis of the B-meson decay particles. All the thrust variables shown in Figure 3.9 were used for the final analysis as they worked quite well for separating signal and background by using a classifier.

Apart form the thrust variables there are the Fox-Wolfram moments and the Cleo cone variables in the group of continuum suppression variables. The Cleo cones make use of the fact, that the two B-mesons are almost produced at rest, when colliding electrons and positrons at the ϒ(4S) resonance. Therefore the flight directions of the two B-mesons' decay products are uncorrelated, whereas a qq¯ event usually has a distinct two-jet structure. In order to distinguish the two shapes 9 cones extending in both directions of the tip are laid around the B-meson candidate's thrust axis in polar angle intervals of 10◦. The event is then “folded” such that the content of two cones of the same polar angle pointing in opposite directions are combined. For each of these Cleo cones a momentum flow is calculated by summing over the scalar of the charged track's momenta as well as the momenta of neutral showers pointing into the cone [9]. The plots in Figure 3.10 show the distributions of a few Cleo cone momentum flows for signal and background.

28 charged backgound 7 charged backgound 12 mixed backgound mixed backgound continuum backgound continuum backgound Signal 6 Signal 10

8 4

6 3

4 2

2 1

0 0 0.70 0.75 0.80 0.85 0.90 0.95 1.00 0.60 0.65 0.70 0.75 0.80 0.85 0.90 B0_ThrustB B0_ThrustO

1.6 charged backgound charged backgound 7 mixed backgound mixed backgound continuum backgound 1.4 continuum backgound Signal Signal 6 1.2

5 1.0

4 0.8

3 0.6

2 0.4

1 0.2

0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 B0_CosTBTO B0_CosTBz

Figure 3.9.: Distributions of thrust variables for signal as well as for charged, mixed and continuum backgrounds.

The Fox-Wolfram moments also deal with the phase-space distribution of momenta of an th event. The definition of the l Fox- Wolfram moment is given in (3.2), where Pk(cos(θi j)) is the lth order Legendre polynomial of the cosine of the angle between the ith and jth momentum.

N | | | | θ Hl = ∑ pi p j Pl(cos( i, j)) (3.2) i, j

Alternatively, the normalized Fox-Wolfram moment R = Hl can also be used. In this analysis l H0 only normalized Fox-Wolfram moments were used, R2 being one of them, while the others are defined by ∑ |⃗pi| |⃗p j| Pl(cosθi, j) k i, j hl = (3.3) ∑ |⃗pi| |⃗p j| i, j where k = so,oo, meaning if k = so the ith particle is from the B-candidate while the jth is from the ROE and if k = oo both particles are form the ROE [2]. Figure 3.11 shows some example distributions for this type of variables.

29 3.0 3.0 charged backgound charged backgound mixed backgound mixed backgound continuum backgound continuum backgound Signal 2.5 Signal 2.5

2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5

0.0 0.0 0 1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 B0_cc2 B0_cc3

1.6 charged backgound mixed backgound 1.4 continuum backgound Signal 1.2

1.0

0.8

0.6

0.4

0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 B0_cc7

Figure 3.10.: Distributions of Cleo cone variables for signal as well as for charged, mixed and continuum backgrounds.

30 3.5 charged backgound charged backgound mixed backgound mixed backgound continuum backgound 8 continuum backgound 3.0 Signal Signal

2.5 6

2.0

1.5 4

1.0 2

0.5

0.0 0 0.4 0.2 0.0 0.2 0.4 0.2 0.1 0.0 0.1 0.2 B0_hso02 B0_hso12

40 charged backgound charged backgound mixed backgound mixed backgound 6 continuum backgound continuum backgound 35 Signal Signal

5 30

25 4

20 3

15 2 10

1 5

0 0 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.1 0.2 0.3 0.4 0.5 B0_hoo2 B0_R2

Figure 3.11.: Distributions of normalized Fox-Wolfram moments for signal, charged, mixed and continuum backgrounds.

All the variables discussed up to now are very efficient in separating signal and continuum background, but as the figures above show there is not a lot of difference between the signal decay and generic B-meson decays regarding this variables. Therefore other variables are needed, in order to separate different B-meson decays as well. One of the variables with the highest separation power is ∆E. Fortunately the correlation between ∆E and Mbc is not strong enough to influence the shape of the background Mbc. Another good variable turned out to be the invariant mass of the K∗0, as it allows to suppress particle combinations, that probably don't come from a K∗0 decay. The distributions of those two variables can be seen in Figure 3.12. A few ROE variables turned out to have good separation power for both types of background as well. Figure 3.13 shows some example ROE variables chosen for the final classifier input.

Apart from that the vertex variables displayed in Figure 3.14 were helpful for separating signal and background events. Some other variables did not seem to contribute a lot to the separation from how their distributions looked but turned out to be used by the classifiers more than expected. All the variables used in the actual separation must not be correlated to either Mbc, the invariant B0 mass or the angle variables. A correlation plot for all the variables discussed so far was made in order to ensure that no unwanted correlations occur. Due to this restriction on correlations, none of the momentum variables can be used for classification as Figures 3.15 and 3.16 (top right) show.

31 30 charged backgound charged backgound 12 mixed backgound mixed backgound continuum backgound continuum backgound 25 Signal Signal 10

20 8

15 6

10 4

5 2

0 0 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.8 0.9 1.0 1.1 1.2 1.3 B0_deltae B0_KST0_M

Figure 3.12.: Distributions of |∆E| (left) and the invariant K∗0 mass (right) for signal as well as for charged, mixed and continuum backgrounds.

charged backgound charged backgound 0.35 mixed backgound 0.35 mixed backgound continuum backgound continuum backgound Signal Signal 0.30 0.30

0.25 0.25

0.20 0.20

0.15 0.15

0.10 0.10

0.05 0.05

0.00 0.00 1 2 3 4 5 6 7 8 2 3 4 5 6 7 8 9 B0_ROE_M__bosimple__bc B0_ROE_E__bosimple__bc

charged backgound charged backgound 0.5 mixed backgound mixed backgound continuum backgound continuum backgound Signal 0.4 Signal

0.4

0.3 0.3

0.2 0.2

0.1 0.1

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 2 4 6 8 10 12 14 B0_ROE_eextra__bosimple__bc B0_nROETracks__bosimple__bc

Figure 3.13.: Distributions of some ROE variables for signal as well as for charged, mixed and continuum backgrounds.

32 0.12 charged backgound charged backgound mixed backgound mixed backgound 40 continuum backgound continuum backgound Signal 0.10 Signal

30 0.08

0.06 20

0.04

10 0.02

0 0.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 10 20 30 40 50 60 B0_distance B0_significanceOfDistance

charged backgound charged backgound 2.5 2.5 mixed backgound mixed backgound continuum backgound continuum backgound Signal Signal

2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 B0_mu0_VtxPvalue B0_mu1_VtxPvalue

Figure 3.14.: Distributions of some vertex variables for signal, charged, mixed and continuum backgrounds.

The x-components of the momentum in the lab and the center-of-mass frame were not too strongly related to Mbc, but it turned out that those pose problems in combination with other variables, as they can be combined to something very closely related to Mbc. Therefore even when considering the correlations shown here checking the Mbc distribution after the classification is important in order to be sure, that it has not changed its shape on account of the classification. The top and bottom left subfigures of Figure 3.16 also show that some of the continuum suppression variables and some ROE variables are correlated among each other. Therefore only a few have been chosen in order to reduce the calculation time and the risk of over-fitting. The variables were picked by training a classifier on a set of variables and checking which variables were used most by the classifier using the feature importance method of the sklearn library.

Finally the classifier was trained on the big data set several times and by comparing the max- imum of the resulting figure of merit depending on the classifier output and crosschecking the feature importances as well as the Mbc distribution at the cut with the highest figure of merit 34 variables listed in table 3.1 were chosen as input for the classifier. The PID variables were added, because harder cuts on those variables might be helpful in combination with other information.

33 34 3.15. Figure B0_daughterInvariantMass__bo1__cm__sp2__bc B0_missM2__bosimple__cm__sp0__bc : B0_missM2OverMissE__bosimple__bc B0_missE__bosimple__cm__sp0__bc B0_missP__bosimple__cm__sp0__bc B0_missE__bosimple__cm__sp0__bc iulzto fcreain mn aibe neetn o eaainadvari- and analysis. separation for for needed interesting ables variables among correlations of Visualization B0_ROE_neextra__bosimple__bc B0_ROE_charge__bosimple__bc B0_nROETracks__bosimple__bc B0_ROE_eextra__bosimple__bc B0_ROE_deltae__bosimple__bc B0_ROE_mbc__bosimple__bc B0_ROE_Pz__bosimple__bc B0_ROE_Py__bosimple__bc B0_ROE_Px__bosimple__bc B0_ROE_M__bosimple__bc B0_ROE_P__bosimple__bc B0_ROE_E__bosimple__bc B0_significanceOfDistance B0_mu1_VtxPvalue B0_mu0_VtxPvalue B0_VtxPvalue B0_CosTBTO B0_P4cms_3 B0_P4cms_2 B0_P4cms_1 B0_P4cms_0 B0_KST0_M B0_M2recoil B0_distance B0_ThrustO cosTheta_K B0_CosTBz B0_ThrustB cosTheta_l B0_Erecoil B0_Precoil B0_hso24 B0_hso22 B0_hso20 B0_hso14 B0_hso12 B0_hso10 B0_hso04 B0_hso03 B0_hso02 B0_hso01 B0_hso00 B0_deltae B0_Pcms B0_q2Bh B0_P4_3 B0_P4_2 B0_P4_1 B0_P4_0 B0_hoo4 B0_hoo3 B0_hoo2 B0_hoo1 B0_hoo0 B0_mm2 B0_mbc B0_cc9 B0_cc8 B0_cc8 B0_cc6 B0_cc5 B0_cc4 B0_cc3 B0_cc2 B0_cc1 B0_R2 cosPhi sinPhi B0_et B0_M B0_P q2

B0_M B0_mbc B0_deltae B0_P B0_P4_0 B0_P4_1 B0_P4_2 B0_P4_3 B0_KST0_M B0_Pcms B0_P4cms_0 B0_P4cms_1 B0_P4cms_2 B0_P4cms_3 B0_Precoil B0_Erecoil B0_M2recoil B0_ThrustB B0_ThrustO B0_CosTBTO B0_CosTBz B0_R2 B0_cc1 B0_cc2 B0_cc3 B0_cc4 B0_cc5 B0_cc6 B0_cc8 B0_cc8 B0_cc9 B0_mm2 B0_et B0_hso00 B0_hso01 B0_hso02 B0_hso03 B0_hso04 B0_hso10 B0_hso12 B0_hso14 B0_hso20 B0_hso22 B0_hso24 B0_hoo0 B0_hoo1 B0_hoo2 B0_hoo3 B0_hoo4 B0_q2Bh B0_daughterInvariantMass__bo1__cm__sp2__bc B0_distance B0_significanceOfDistance B0_ROE_E__bosimple__bc B0_ROE_M__bosimple__bc B0_ROE_P__bosimple__bc B0_ROE_Px__bosimple__bc B0_ROE_Py__bosimple__bc B0_ROE_Pz__bosimple__bc B0_ROE_charge__bosimple__bc B0_ROE_deltae__bosimple__bc B0_ROE_eextra__bosimple__bc B0_ROE_neextra__bosimple__bc B0_ROE_mbc__bosimple__bc B0_nROETracks__bosimple__bc B0_missE__bosimple__cm__sp0__bc B0_missM2__bosimple__cm__sp0__bc B0_missM2OverMissE__bosimple__bc B0_missP__bosimple__cm__sp0__bc B0_missE__bosimple__cm__sp0__bc q2 cosTheta_l cosTheta_K cosPhi sinPhi B0_VtxPvalue B0_mu0_VtxPvalue B0_mu1_VtxPvalue 0.0 0.4 0.8 0.8 0.4 B0_CosTBTO B0_missM2__bosimple__cm__sp0__bc B0_missM2OverMissE__bosimple__bc B0_missE__bosimple__cm__sp0__bc B0_missP__bosimple__cm__sp0__bc B0_missE__bosimple__cm__sp0__bc B0_ThrustO cosTheta_K B0_CosTBz B0_ThrustB cosTheta_l B0_hso24 B0_hso22 B0_hso20 B0_hso14 B0_hso12 B0_hso10 B0_hso04 B0_hso03 B0_hso02 B0_hso01 B0_hso00 B0_deltae B0_hoo4 B0_hoo3 B0_hoo2 B0_hoo1 B0_hoo0 B0_mm2 B0_mbc B0_cc9 B0_cc8 B0_cc8 B0_cc6 B0_cc5 B0_cc4 B0_cc3 B0_cc2 B0_cc1 B0_ROE_neextra__bosimple__bc B0_R2 cosPhi B0_ROE_charge__bosimple__bc B0_nROETracks__bosimple__bc sinPhi B0_ROE_eextra__bosimple__bc B0_et B0_M B0_ROE_deltae__bosimple__bc B0_ROE_mbc__bosimple__bc iue3.16. Figure q2 B0_ROE_Pz__bosimple__bc B0_ROE_Py__bosimple__bc B0_ROE_Px__bosimple__bc B0_ROE_M__bosimple__bc B0_ROE_P__bosimple__bc B0_ROE_E__bosimple__bc

B0_M B0_mbc B0_deltae B0_ThrustB B0_ThrustO cosTheta_K

cosTheta_l B0_CosTBTO B0_deltae

B0_mbc B0_CosTBz cosPhi sinPhi B0_M B0_R2 B0_cc1 q2 B0_cc2 B0_cc3 B0_M B0_cc4 B0_mbc B0_cc5 : B0_deltae B0_cc6

at ftebgcreainmpwt ee aibe o oedetails. more for variables fewer with map correlation big the of Parts B0_ROE_E__bosimple__bc B0_cc8 B0_cc8 B0_ROE_M__bosimple__bc B0_cc9 B0_ROE_P__bosimple__bc B0_mm2 B0_ROE_Px__bosimple__bc B0_et B0_ROE_Py__bosimple__bc B0_hso00 B0_ROE_Pz__bosimple__bc B0_hso01 B0_hso02 B0_ROE_charge__bosimple__bc B0_hso03 B0_ROE_deltae__bosimple__bc B0_hso04 B0_ROE_eextra__bosimple__bc B0_hso10 B0_ROE_neextra__bosimple__bc B0_hso12 B0_hso14 B0_ROE_mbc__bosimple__bc B0_hso20 B0_nROETracks__bosimple__bc B0_hso22 B0_missE__bosimple__cm__sp0__bc B0_hso24 B0_missM2__bosimple__cm__sp0__bc B0_hoo0 B0_missM2OverMissE__bosimple__bc B0_hoo1 B0_hoo2 B0_missP__bosimple__cm__sp0__bc B0_hoo3 B0_missE__bosimple__cm__sp0__bc B0_hoo4 q2 q2 cosTheta_l cosTheta_l cosTheta_K cosTheta_K cosPhi cosPhi sinPhi sinPhi 0.0 0.4 0.8 0.0 0.4 0.8 0.8 0.4 0.8 0.4 B0_P4cms_3 B0_P4cms_2 B0_P4cms_1 B0_P4cms_0 B0_significanceOfDistance B0_KST0_M B0_M2recoil cosTheta_K cosTheta_l B0_Erecoil B0_Precoil B0_deltae B0_Pcms B0_P4_2 B0_P4_1 B0_P4_0 B0_P4_3 B0_mbc cosPhi B0_mu1_VtxPvalue B0_mu0_VtxPvalue sinPhi B0_M B0_P q2 B0_VtxPvalue B0_distance cosTheta_K cosTheta_l B0_deltae B0_M B0_mbc

cosPhi B0_mbc sinPhi B0_M B0_deltae q2 B0_P B0_P4_0 B0_M B0_P4_1 B0_mbc B0_P4_2 B0_P4_3 B0_deltae B0_KST0_M B0_distance B0_Pcms B0_significanceOfDistance B0_P4cms_0 B0_P4cms_1 B0_VtxPvalue B0_P4cms_2 B0_mu0_VtxPvalue B0_P4cms_3 B0_Precoil B0_mu1_VtxPvalue B0_Erecoil q2 B0_M2recoil cosTheta_l q2 cosTheta_l cosTheta_K cosTheta_K cosPhi cosPhi sinPhi sinPhi 0.0 0.4 0.8 0.0 0.4 0.8 0.8 0.4 0.8 0.4 35 Table 3.1.: Variables used for the separation of signal and background within this analysis with explanations

Ntuple name function

B0_deltae ∆E = E − 1/2 Ebeam B0_KST0_M invariant mass of K∗0 B0_KST0_SigM significance of invariant mass peak B0_Z z coordinate of B0 vertex B0_mu0_VtxPvalue Vertex Quality for µ1 B0_mu1_VtxPvalue Vertex Quality for µ2 B0_ThrustB thrust of B-candidate B0_ThrustO rest of event trust B0_CosTBTO cos of angle between thrust axes of B- and ROE-particles B0_CosTBz cos of angle between B-candidate thrust axis and z-axis B0_R2 normalized 2nd order Fox-Wolfram moment B0_mm2 missing mass squared B0_et transverse energy B0_cc2 2nd Cleo cone momentum flow B0_cc3 3rd Cleo cone momentum flow B0_cc7 7th Cleo cone momentum flow B0_hso02 modified Fox-Wolfram moment with ROE and B-candidates B0_hso12 modified Fox-Wolfram moment with ROE and B-candidates B0_hoo2 2nd order normalized Fox-Wolfram moment of ROE B0_distance distance of B0 vertex to IP B0_significanceOfDistance significance of vertex distance to IP B0_ROE_eextra__bosimple__bc extra energy in the calorimeter not associated to the B-candidate B0_ROE_M__bosimple__bc invariant mass of all ROE particles combined B0_ROE_E__bosimple__bc energy in ROE B0_nROETracks__bosimple__bc number of tracks in ROE B0_mu0_PIDk probability for µ1 to be K B0_mu0_PIDpi probability for µ1 to be π B0_mu0_PIDe probability for µ1 to be e B0_mu0_PIDmu probability for µ1 to be µ B0_mu0_PIDp probability for µ1 to be proton B0_mu1_PIDk probability for µ2 to be K B0_mu1_PIDpi probability for µ2 to be π B0_mu1_PIDe probability for µ2 to be e B0_mu1_PIDmu probability for µ2 to be µ

36 3.2.2. Testing different classifiers

For testing a set of classifiers of the “sklearn” library a large set of variables was chosen which all classifiers were given as input. For a first test many classifiers were trained on a data sample combined of the generated signal data and the MC background data split in a training and a test half in order to avoid that a classifier was chosen due to over fitting, that is due to memorizing data points. All the continuum suppression variables, the PID variables, the invariant K∗0 mass, the distance of the B0 and the IP as well as the significance of the last two were chosen as input variables for the classifiers. This selection resulted in the test scores listed in table 3.2 and the purity versus efficiency plot shown in figure 3.17.

Table 3.2.: Test scores of different sklearn classifiers on signal data with MC background. Test score Classifier 0.937917 BoostedDecisionTree 0.936163 xgboost 0.931724 Adaboost 0.926882 RandomForest 0.906181 MLPClassifier 0.874388 ExtraTree 0.255280 NaiveBayes

1.2

1.0

0.8

0.6 purity

0.4 BoostedDecisionTree MLPClassifier Adaboost 0.2 RandomForest NaiveBayes xgb ExtraTree 0.0 0.0 0.2 0.4 0.6 0.8 1.0 efficiency

Figure 3.17.: Purity versus efficiency plot for sklearn classifiers on signal data and MC background with continuum suppression, PID and vertex variables as well as the invariant K∗0 mass.

From the result shown in table 3.2 and Figure 3.17 it was decided to make a second test since the difference between best results was not significant enough to make a choice. The Gradient Boosting Classifier (called Boosted Decision Tree), the xg boost classifier as well as the Ada

37 boost classifier, the Random Forest classifier and the MLP classifier (neural network) were picked for this second test. For the second test the same data set was used for classification. All classifiers were given the same input again and both signal background data was separated into a training and a test set of data, but this time a smaller set of variables was used. Only the continuum suppression variables were chosen, because these variables were found to suppress continuum background well, and are certainly not correlated to Mbc or ∆E.

Table 3.3.: Test scores of selected classifiers on test data of signal and background with only continuum suppression variables as input. Test score Classifier 0.770775 BoostedDecisionTree 0.770034 xgboost 0.763720 AdaBoostClassifier 0.761312 MLPClassifier 0.757729 RandomForest

1.2 RandomForest Adaboost BoostedDecisionTree 1.0 MLPClassifier xgb

0.8

0.6 purity

0.4

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 efficiency

Figure 3.18.: Purity versus efficiency plot for selected classifiers on test data sample with signal and MC background and only continuum suppression variables as input.

The result is displayed in table 3.3 and Figure 3.18. From the results of the two tests it was decided to use the Boosted Decision Tree for the final separation of signal and background data. Although the efficiency versus purity plots don't show a real difference between the two, the test score of the Boosted Decision is minimally higher than that of the xg classifier. The difference, however, is so small, that it should make no actual difference which classifier is finally used, even more, since they are based on the same method.

38 3.3. Results

A boosted decision tree was eventually given the set of variables determined in section 3.2.1. However two more steps were taken to achieve a data set with as little background as possible. The decay of the J/ψ

∗ B0 → J/ψ K 0 (3.4) ,→ l+ l− looks barely different from the studied signal decay and therefore it is not possible to distinguish between the two decays properly. The same is true for the B0 → ψ(2S)K∗0 decay.

It is therefore necessary to omit those candidates that might come from this decay instead. This is what the q2 variable, the invariant mass of the two lepton system, is used for in this analysis. The background data distribution shows two distinctive peaks at the squared invariant mass of the J/ψ and ψ(2S) resonances. Hence all data with a q2 value of 9 < q2 < 10 or 13 < q2 < 14 is omitted. Second there can only be one true B-candidate in each event. Since the run, experiment and event number for each candidate is recorded, it is preferable to only keep the best candidate for each event. This choice can be made by looking at either the output of the classifier and choosing the candidate with the highest probability according to the classifier, or by looking at ∆E and choosing the candidate with the lowest absolute value. For the evaluation only the signal Region Mbc was used.

Table 3.4.: Expected amount of signal and background and figure of merit with ∆E ranking for some luminosities. Efficiency ≈ 15.73% −1 Luminosity [ab ] nsig nbkg Figure of merit 0.711 127.63 31.284 10.12 1 179.76 44 12.02 5 897.56 220 26.85 20 3590.23 880 53.70 50 8975.58 2200 84.90

The resulting amount of signal and background candidates as well as the Figure of merit can be seen in tables 3.7 and 3.4 if assuming a naive, linear scaling of the signal and data candidates. √ In that case the figure of merit keeps it's shape, but is multiplied by a factor c if the luminosity is scaled by a factor c. The two tables also show that there is no big difference between using the ∆E and the classifier ranking. Both rankings result in an efficiency a little below 16%. However, since the classifier ranking is less dependent on a single variable and its assumed distribution in the Monte Carlo simulation, it is reasonable to rather use the classifier ranking.

39 figure of merit 12 figure of merit 12

10 10

8 8

6 6

figure of merit 4 figure of merit 4

2 2

0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 cut (probability) cut (probability) (a) Figure of Merit for classifier ranking (b) Figure of Merit for ∆E ranking

Figure 3.19.: Figure of merit plots for the ∆E ranking compared to the classifier ranking at 1 ab−1 luminosity.

Afterwards the whole data set was split in half to obtain one dataset for training and one for testing. This was done in order to crosscheck that no over-fitting happened. The results of this test, displayed in table 3.5, show that there is no over-fitting in this analysis, since the results of the test and the training sample are very similar. The little deviation is probably due to the fact, that an absolutely accurate partitioning of the data in two sets of exactly the same size is not entirely possible. If there was some actual over fitting and the classifier had memorized data points the results of on the training data should be significantly better than those on the test data.

Table 3.5.: Results for analysis with split data sample scaled to 1 ab−1. Comparison training and test data set

nsig nbkg figure of merit efficiency in % training data 190.75 34 12.72 16.72 test data 179.26 26 12.51 15.72

Finally, as table 3.6 shows, the eventually selected method combined with the Belle II setup yields better results than the Belle selection. The efficiency and the amount of expected signal events is slightly raised, while the amount of expected background events is strongly reduced compared to the Belle selection. This shows that the efforts made upgrading the Belle II detector in order to better distinguish signal from background candidates combined with the presented method using the new software framework and the best candidate selection, have been success- ful so far. There might be some background that was not considered in this analysis, because it was not simulated within the Monte Carlo campaign. However, based on the currently available information, a very good sensitivity for the studied decay can be expected of the Belle II experiment as can be seen in tables 3.6 and 3.7.

40 Table 3.6.: Comparison of Belle and Belle II final dataset for 0.711 ab−1. Belle results taken from [4].

experiment nsig nbkg figure of merit efficiency in % Belle 116 199 7.05 14.28 Belle II 129.71 18.5 10.66 15.99

Table 3.7.: Expected amount of signal and background and figure of merit with classifier ranking for some luminosities. Efficiency ≈ 15.99% −1 Luminosity [ab ] nsig nbkg Figure of merit 0.711 129.71 18.486 10.66 1 182.70 26 12.65 5 912.22 130 28.26 20 3648.86 520 56.51 50 9122.15 1300 89.35

4. Conclusion and Outlook

In this thesis the efficiency and quality of signal and background of the new Belle II setup was studied for the B0 → K∗0 µ+ µ− decay. First the efficiency losses for the preselection cuts in the analysis scripts were considered and thus hard cuts, which don't drop the efficiency too much were chosen. For the machine learning selection step a variety classifiers were tested on the data set with different sets of variables. From this the Gradient Boosting Classifier (Boosted Decision Tree) was chosen for background signal separation. Many variables were tested for their separation power and how much they were used by the classifier, as well as their correla- 2 tion among each other and to the analysis variables Mbc, q , cos(θK), cos(θl) and cos(ϕ). The classifier selection was combined with the best candidate selection choosing only the candidate best suited for a B-meson of each event. In order to do that all candidates in one event were on the one hand ranked according to the classifier output and on the other hand according to the magnitude of the ∆E variable. As the Classifier ranking yielded better results it was chosen for the final selection. The optimization of these selection steps resulted in a signal selection with 15.99% efficiency and a purity of 87%.

As table 3.6 shows, the new Belle II setup combined with the method used in this thesis reduces the background to 9.3% of the background events in the corresponding Belle data set, while even raising the efficiency and therefore the number of expected signal events in the final data set.

The analysis in this thesis was done on simulated data from the Monte Carlo campaign 8. Therefore a few deviations to the results calculated in this thesis might occur when actual data is taken depending on how well the simulations represent reality. This, however, can not be judged before the actual data taking begins.

These results indicate that with the new Belle II setup and the method used in this thesis the sensitivity for the rare B0 → K∗(892)0 µ+ µ− decay can even be increased. Assuming the same ′ ∗ central values for measurements like P5 or RK [12, 11] the Belle II experiment might even be able to discover New Physics at a 5σ level at only 5 ab−1 of data. However, it is planned to collect as much as 50 ab−1 of data at the Belle II experiment. If there is New Physics to be found in the studied decay, it should therefore definitely be found when this big data set is complete.

Bibliography

[1] T. Abe et al. Belle II Technical Design Report. 2010. arXiv:1011.0352 [physics.ins-det].

[2] Ed. A.J. Bevan, B. Golob, Th. Mannel, S. Prell, and B.D. Yabsley, Eur. Phys. J. C74 (2014) 3026, SLAC-PUB-15968, KEK Preprint 2014-3. Also available online on arXiv at arXiv:1406.6311 [hep-ex]

[3] Emi Kou, Phillip Urquijo, The Belle II collaboration, and The B2TiP theory community. The Belle II Physics Book. Unpublished report of Belle II Theory Interface Platform. Draft of 21.08.2017

[4] S. Wehle. Angular Analysis of B → K∗ ll and search for B+ → K+ ττ at the Belle Experi- ment Doctoral Thesis at Universität Hamburg. 2016.

[5] C. Lippmann. Particle identification. 12.07.2011. arXiv:1101.3276 [hep-ex]

[6] A. Crivellin. B-anomalies related to leptons and lepton flavour universality violation. 22.06.2016. arXiv:1606.06861 [hep-ph]

[7] G. Hiller, I. Nisandizic. RK and RK∗ beyond the Standard Model. 18.04.2017. arXiv:1704.05444 [hep-ph]

[8] T. Gershon. Experimental summery of the 52nd Rencontres de Moriond session on Elec- troweak Interactions and Unified Theories. 18.07.2017. arXiv:1707.05290

[9] CLEO Collaboration, D.M. Anser et al. Search for Exclusive Charmless Hadronic B Decays. 03.08.1995. arXiv:hep-ex/9508004

[10] A. Moll. The Software Framework of the Belle II Experiment. Max-Planck-Institute for Physics, Munich 2011. J. Phys.: Conf. Ser. 331 032024 https://iopscience.iop.org/ article/10.1088/1742-6596/331/3/032024/meta

[11] The LHCb collaboration Test of lepton universality with B0 → K∗0l+l− decays. 16.08.2017. Journal of High Energy Physics https://doi.org/10.1007/JHEP08(2017) 055

[12] S. Wehle et al. (Belle Collaboration) Lepton-Flavor-Dependant Anglar Analysis of B → K∗l+l−. 13.03.2017. Phys. Rev. Lett. 118, 111801 https://doi.org/10.1103/ PhysRevLett.118.111801

45 [13] D. Griffith. Introduction to Elementary Particles. Second, Revised Edition. 2010. Wiley- VCH Verlag GmbH & Co. KGaA, Weinheim

[14] Standard Model. https://en.wikipedia.org/wiki/Standard_Model. Accessed on 11.10.2017

[15] KEKB (accelerator). https://en.wikipedia.org/wiki/KEKB_(accelerator). Ac- cessed on 21.11.2017

[16] Belle II Detector “BELLE II and QSC design”. at https://confluence.desy.de/ display/BIAD/Detector. Accessed on 25.09.2017

[17] CDC Web Home: CDC Hardware. https://confluence.desy.de/display/BI/CDC+ Hardware#CDCHardware-CDCconstruction. Accessed on 25.09.2017

[18] Belle II Detector Picture Gallery. https://confluence.desy.de/display/BIAD/ Belle+II+Detector+Picture+Gallery. Accessed on 22.09.2017.

46 A. Appendix: additional plots

2.00 charged backgound charged backgound mixed backgound mixed backgound 1.75 continuum backgound 2.0 continuum backgound Signal Signal

1.50

1.5 1.25

1.00 1.0 0.75

0.50 0.5

0.25

0.00 0.0 0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 B0_cc1 B0_cc4

1.75 charged backgound charged backgound mixed backgound mixed backgound 1.4 continuum backgound continuum backgound 1.50 Signal Signal 1.2

1.25 1.0

1.00 0.8

0.75 0.6

0.50 0.4

0.25 0.2

0.00 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 B0_cc5 B0_cc6

1.75 charged backgound 2.00 charged backgound mixed backgound mixed backgound continuum backgound continuum backgound 1.75 1.50 Signal Signal

1.50 1.25

1.25 1.00

1.00 0.75 0.75

0.50 0.50

0.25 0.25

0.00 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 B0_cc8 B0_cc9

Figure A.1.: Additional distributions of Cleo cone variables for signal as well as, charged, mixed and continuum backgrounds.

47 charged backgound charged backgound 7 mixed backgound 2.5 mixed backgound continuum backgound continuum backgound Signal Signal 6

2.0 5

4 1.5

3 1.0

0.5 1

0 0.0 5.4 5.5 5.6 5.7 5.8 5.9 26 27 28 29 30 31 32 B0_Erecoil B0_M2recoil

charged backgound 4.0 charged backgound mixed backgound mixed backgound continuum backgound continuum backgound 2.0 Signal 3.5 Signal

3.0

1.5 2.5

2.0 1.0 1.5

1.0 0.5

0.5

0.0 0.0 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 B0_Precoil B0_daughterInvariantMass__bo1__cm__sp2__bc

1.2 0.16 charged backgound charged backgound mixed backgound mixed backgound continuum backgound 0.14 continuum backgound 1.0 Signal Signal

0.12

0.8 0.10

0.6 0.08

0.06 0.4

0.04

0.2 0.02

0.0 0.00 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 q2 B0_q2Bh

Figure A.2.: Additional distributions of kinematic recoil variables and variables concerning the invariant mass of the two muon system for signal as well as charged, mixed and continuum backgrounds.

48 charged backgound charged backgound mixed backgound mixed backgound 0.35 0.175 continuum backgound continuum backgound Signal Signal 0.30 0.150

0.25 0.125

0.20 0.100

0.15 0.075

0.10 0.050

0.05 0.025

0.00 0.000 5 6 7 8 9 10 11 80 60 40 20 0 B0_et B0_mm2

charged backgound charged backgound mixed backgound mixed backgound 10 continuum backgound continuum backgound Signal 80 Signal

40 4

20 2

0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.03 0.02 0.01 0.00 0.01 0.02 0.03 B0_hoo0 B0_hoo1

140 charged backgound 60 charged backgound mixed backgound mixed backgound continuum backgound continuum backgound 120 Signal Signal 50

100 40

30 60

20 40

10 20

0 0 0.02 0.01 0.00 0.01 0.02 0.02 0.00 0.02 0.04 0.06 0.08 0.10 B0_hoo3 B0_hoo4

Figure A.3.: Additional distributions of continuum suppression variables for signal, charged, mixed and continuum backgrounds.

49 charged backgound charged backgound mixed backgound mixed backgound 1.2 continuum backgound 4 continuum backgound Signal Signal

1.0

3 0.8

0.6 2

0.4

0.2

0.0 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 0.4 0.2 0.0 0.2 0.4 B0_hso00 B0_hso01

6 6 charged backgound charged backgound mixed backgound mixed backgound continuum backgound continuum backgound Signal 5 Signal 5

4 4

3 3

2 2

1 1

0 0 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.2 0.1 0.0 0.1 0.2 0.3 B0_hso03 B0_hso04

2.00 charged backgound charged backgound mixed backgound 14 mixed backgound 1.75 continuum backgound continuum backgound Signal Signal 12 1.50

10 1.25

1.00 8

0.75 6

0.50 4

0.25 2

0.00 0 0.0 0.2 0.4 0.6 0.8 1.0 0.15 0.10 0.05 0.00 0.05 0.10 0.15 B0_hso10 B0_hso14

Figure A.4.: Additional distributions of Fox-Wolfram moments for signal, charged, mixed and continuum backgrounds.

50 3.0 charged backgound charged backgound mixed backgound mixed backgound 6 continuum backgound continuum backgound 2.5 Signal Signal

2.0

1.5 3

1.0 2

0.5 1

0.0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 B0_hso20 B0_hso22

25 charged backgound charged backgound mixed backgound mixed backgound 10 continuum backgound continuum backgound Signal Signal 20

15 6

10 4

5 2

0 0 0.2 0.1 0.0 0.1 0.2 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 B0_hso24 B0_M

charged backgound charged backgound 140 mixed backgound mixed backgound continuum backgound continuum backgound Signal 8 Signal 120

100 6

4 60

40 2

0 0 5.250 5.255 5.260 5.265 5.270 5.275 5.280 5.285 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 B0_mbc B0_Pcms

51 1.75 charged backgound 1.75 charged backgound mixed backgound mixed backgound continuum backgound continuum backgound 1.50 Signal 1.50 Signal

1.25 1.25

1.00 1.00

0.75 0.75

0.50 0.50

0.25 0.25

0.00 0.00 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 B0_P4_0 B0_P4_1

charged backgound 1.75 charged backgound mixed backgound mixed backgound continuum backgound continuum backgound 2.0 Signal 1.50 Signal

1.25 1.5

1.00

1.0 0.75

0.50 0.5

0.25

0.0 0.00 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 B0_P4_2 B0_P4cms_0

1.75 charged backgound charged backgound mixed backgound mixed backgound continuum backgound continuum backgound 1.50 Signal 2.0 Signal

1.25

1.5 1.00

0.75 1.0

0.50

0.5

0.25

0.00 0.0 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 B0_P4cms_1 B0_P4cms_2

Figure A.6.: Additional distributions of kinematic variables for signal, charged, mixed and continuum backgrounds.

30 charged backgound charged backgound 7 mixed backgound mixed backgound continuum backgound continuum backgound 25 Signal Signal 6

5 20

4 15

3 10

5 1

0 0 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 4.8 4.9 5.0 5.1 5.2 5.3 5.4 B0_P4_3 B0_P4cms_3

Figure A.7.: Additional distributions of kinematic variables for signal, charged, mixed and continuum backgrounds.

52 0.6 charged backgound charged backgound 0.35 mixed backgound mixed backgound continuum backgound continuum backgound Signal 0.5 Signal 0.30

0.4 0.25

0.20 0.3

0.15 0.2

0.10

0.1 0.05

0.00 0.0 6 4 2 0 2 10 5 0 5 10 B0_missE__bosimple__cm__sp0__bc B0_missM2__bosimple__cm__sp0__bc

0.5 charged backgound charged backgound 0.8 mixed backgound mixed backgound continuum backgound continuum backgound Signal 0.7 Signal 0.4

0.6

0.3 0.5

0.4

0.2 0.3

0.2 0.1

0.1

0.0 0.0 20 15 10 5 0 5 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 B0_missM2OverMissE__bosimple__bc B0_missP__bosimple__cm__sp0__bc

Figure A.8.: Additional distributions of missing energy or momentum for signal, charged, mixed and continuum backgrounds.

0.8 charged backgound charged backgound 0.7 mixed backgound mixed backgound continuum backgound 0.7 continuum backgound Signal Signal 0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2

0.1 0.1

0.0 0.0 1 2 3 4 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 B0_ROE_P__bosimple__bc B0_ROE_Px__bosimple__bc

0.8 charged backgound charged backgound mixed backgound mixed backgound 0.6 0.7 continuum backgound continuum backgound Signal Signal

0.6 0.5

0.5 0.4

0.4 0.3

0.3

0.2 0.2

0.1 0.1

0.0 0.0 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 1 0 1 2 3 B0_ROE_Py__bosimple__bc B0_ROE_Pz__bosimple__bc

Figure A.9.: Additional distributions of ROE kinematic variables for signal, charged, mixed and continuum backgrounds.

53 charged backgound 0.5 charged backgound mixed backgound mixed backgound 0.35 continuum backgound continuum backgound Signal Signal 0.30 0.4

0.25 0.3

0.20

0.15 0.2

0.10 0.1 0.05

0.00 0.0 3 2 1 0 1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 B0_ROE_deltae__bosimple__bc B0_ROE_neextra__bosimple__bc

Figure A.10.: Additional distributions of ROE variables for signal, charged, mixed and continuum backgrounds.

charged backgound charged backgound mixed backgound 2.00 mixed backgound continuum backgound continuum backgound 2.0 Signal 1.75 Signal

1.50 1.5 1.25

1.00 1.0

0.75

0.50 0.5

0.25

0.0 0.00 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 cosPhi sinPhi

charged backgound charged backgound 1.6 mixed backgound mixed backgound continuum backgound 2.0 continuum backgound 1.4 Signal Signal

1.2 1.5

1.0

0.8 1.0

0.6

0.4 0.5

0.2

0.0 0.0 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 cosTheta_K cosTheta_l

Figure A.11.: Additional distributions of angle variables for signal, charged, mixed and continuum backgrounds.

1.75 charged backgound charged backgound mixed backgound 25000 mixed backgound continuum backgound continuum backgound 1.50 Signal Signal

20000 1.25

1.00 15000

0.75 10000

0.50

5000 0.25

0.00 0 4 3 2 1 0 1 2 3 4 0.9986 0.9988 0.9990 0.9992 0.9994 0.9996 0.9998 1.0000 B0_ROE_charge__bosimple__bc phisum

54 Hiermit bestätige ich, dass die vorliegende Arbeit von mir selbständig verfasst wurde und ich keine anderen als die angegebenen Hilfsmittel – insbesondere keine im Quellenverzeichnis nicht benannten Internet-Quellen – benutzt habe und die Arbeit von mir vorher nicht einem anderen Prüfungsverfahren eingereicht wurde. Die eingereichte schriftliche Fassung entspricht der auf dem elektronischen Speichermedium. Ich bin damit einverstanden, dass die Bachelorarbeit veröffentlicht wird.

Hamburg, 21. November 2017 Merle Schreiber