Search for the Rare Decay of a B Meson Into a Lambda Baryon, Proton and Neutrino-Antineutrino Pair at the BABAR and Belle II Experiments

Home , Lambda baryon

Search for the rare decay of a B meson into a Lambda baryon, proton and neutrino-antineutrino pair at the BABAR and Belle II experiments

Robert Seddon

Department of Physics McGill University Montreal, Canada

7th August 2019

A thesis submitted to McGill University in partial fulfilment of the requirements for the degree of Doctor of Philosophy ©Robert Seddon, 2019 Acknowledgements

With thanks to PEP-II and BABAR collaboration members, support staff and organisations for making the BABAR analysis possible; Belle II collaboration members, support staff and organisations for making the Belle II analysis possible; members of the McGill BABAR and Belle II groups for assistance and suggestions with various analysis issues; Auriane Canesse for translation.

Special thanks to my supervisor, Steve Robertson, for advice and guidance over many years in performing the analyses and writing this thesis.

Special thanks to my parents, Angela and Derek, for their unconditional and unwavering support throughout.

ii Abstract

We present two analyses of the rare B−→ Λpνν decay. Within the Standard Model, the process B−→ Λpνν is permitted but highly suppressed, with an expected branching fraction of (7.9 1.9) × 10−7. This rarity makes it a sensitive probe for the existence of new physics, which may be discoverable in the form of a higher than predicted branching fraction.

The first analysis is conducted on data collected atthe BABAR experiment, which ran from

− 1999-2008. BABAR collected 433 fb 1 of integrated luminosity at the Υ(4S) resonance; Υ(4S) decays almost exclusively into BB pairs, and this analysis uses hadronic tag reconstruction to fully reconstruct one of the B-mesons in this pair. The search for B−→ Λpνν is then conducted among the decay products of the second, unreconstructed B-meson. Using both real data and Monte Carlo simulations, we develop and implement a signal selection that selects candidates conforming to the expected characteristics of B−→ Λpνν decays. The result of the analysis is an upper limit on the branching fraction at the 90% confidence level of 3.02 × 10−5. This is the world’s first experimental result in the search for B−→ Λpνν decays.

The second analysis is conducted on Monte Carlo simulations of data that will be collected at Belle II, the world’s only next-generation B-meson facility. Over its lifetime Belle II will

− collect 50 ab 1 of data, approximately 100 times that of BABAR. This increase in data, along with more capable hardware and software, should allow Belle II to search for B−→ Λpνν decays with greater sensitivity than BABAR. Using a simulated dataset equivalent in size to that used in our BABAR study, we employ Full Event Interpretation to fully reconstruct the decay of one B-meson in each BB pair, and conduct our signal selection in the remainder of the data. The result of the analysis is a predicted upper limit on the branching fraction

iii − at the 90% confidence level of 1.2 × 10 4. A comparison of the Belle II and BABAR results highlights several areas where Belle II will need to improve in order to make best use of its projected dataset.

iv Résumé

Deux analyses de la désintégration rare B−→ Λpνν sont présentées dans cette thèse. Dans le cadre du Modèle Standard, ce processus est permis mais extrêmement faible et son rapport d’embranchement est de (7.9 1.9) × 10−7. Cette rareté en fait une sonde sensible à de nouveaux processus physiques dont l’existence serait signalée par la mesure d’une rapport d’embranchement plus élevé que prévu.

La première analyse est menée avec les données collectées par le détecteur BABAR qui était

− en fonction de 1999 à 2008. BABAR a collecté 433 fb 1 de luminosité intégrée de données à la résonance Υ(4S); Υ(4S) se désintègre presque exclusivement en une paire BB. Cette analyse utilise une méthode de reconstruction hadronique pour reconstruire complètement l’un des B-méson de la paire. La recherche de la désintégration B−→ Λpνν est alors menée avec les produits de désintégration du second B-méson non reconstruit. En utilisant de vraies données et des simulations Monté Carlo, nous avons développé et procéder à une sélection du signal pour isoler les évènements candidats qui sont conformes aux caractéristiques atten- dues d’évènements B−→ Λpνν . Le résultat de l’analyse est la détermination d’une limite supérieure sur la rapport d’embranchement de 3.02 × 10−5 au niveau de confiance de 90%. Il s’agit du premier résultat jamais obtenu pour la désintégration B−→ Λpνν .

La seconde analyse est menée avec des simulations Monté Carlo de données qui seront ré- coltées par l’expérience Belle II, une expérience unique au monde appartenant à la prochaine génération de détecteurs de B-méson. Au cours de sa période d’exploitation, Belle II col-

− lectera plus de 50 ab 1 de données, soit 100 fois plus que BABAR. Cette augmentation de la quantité de données ainsi que l’amélioration des logiciels et du hardware devrait permettre à Belle II d’étudier les désintégrations B−→ Λpνν avec une plus grande sensibilité que

v celle de BABAR. En utilisant un ensemble de données équivalent en taille à celui utilisé pour notre étude BABAR, nous employons une méthode d’interprétation complète de l’évènement afin d’entièrement reconstruire la désintégration d’un des B-méson dans chaque paire BB et de sélectionner notre signal dans le reste des données. Le résultat de cette analyse est la prédiction d’une limite supérieure sur la rapport d’embranchement de 1.2 × 10−4 au niveau de confiance de 90%. La comparaison des résultats de Belle IIetde BABAR permet de déter- miner certains domaines où Belle II devra améliorer sa performance afin d’utiliser au mieux l’ensemble de données attendu.

vi Preface

The analyses described in Chapters 5 and 6, and the conclusions drawn from them given in Chapter 7, are the work of the author. The analyses use tools and data produced by the

BABAR and Belle II collaborations, of both of which the author is a member. The analysis in Chapter 5 builds on an earlier work by the author, as explained at the beginning of the chapter. Chapters 1 - 4 provide background information, presented by the author to provide context for the later chapters, and are based on the references given therein. There are no co-authors of this thesis.

vii Contents

1 Introduction 1

2 Background 3 2.1 The Standard Model of particle physics ...... 4 2.1.1 Fermions ...... 5 2.1.2 Hadrons ...... 9 2.1.3 Bosons ...... 11 2.1.4 The weak force and flavour changes ...... 13 2.2 Motivation for B−→ Λpνν search ...... 17 2.2.1 New physics possibilities ...... 19 2.2.2 Related studies ...... 22

3 The BABAR experiment 24 3.1 The PEP-II accelerator ...... 24

3.2 The BABAR detector ...... 27 3.2.1 Silicon vertex tracker (SVT) ...... 27 3.2.2 Drift chamber (DCH) ...... 30 3.2.3 Detector of internally-reflected Cherenkov light (DIRC) . . . . . 34 3.2.4 Electromagnetic calorimeter (EMC) ...... 35 3.2.5 Instrumented flux return (IFR) ...... 40

viii 4 The Belle II experiment 43 4.1 The SuperKEKB accelerator ...... 43 4.2 The Belle II detector ...... 47 4.2.1 Pixel detector (PXD) ...... 47 4.2.2 Silicon vertex detector (SVD) ...... 50 4.2.3 Central drift chamber (CDC) ...... 53 4.2.4 Time-of-propagation counter (TOP) ...... 54 4.2.5 Aerogel ring-imaging Cherenkov detector (ARICH) ...... 57 4.2.6 Electromagnetic calorimeter (ECL) ...... 59 4.2.7 K-long and muon detector (KLM) ...... 61

5 Analysis at BABAR 65 5.1 Analysis tools ...... 66

5.1.1 Hadronic Btag reconstruction ...... 66

5.1.2 BABAR dataset ...... 71 5.1.3 Background Monte Carlo ...... 71 5.1.4 Signal Monte Carlo ...... 75 5.1.5 Blinding ...... 75 5.2 Signal selection ...... 76 5.2.1 Skim ...... 76 5.2.2 Explanation of histograms ...... 77

5.2.3 Btag mES cut ...... 78 5.2.4 B-mode purity cut ...... 80 5.2.5 Continuum suppression ...... 83 5.2.6 Extra energy ...... 86 5.2.7 Particle identification ...... 89 5.2.8 Distance of closest approach ...... 90

ix 5.2.9 Λ reconstruction ...... 93 5.2.10 MC correction ...... 95 5.2.11 Summary of signal selection ...... 103 5.3 Results ...... 105 5.3.1 Systematic uncertainties ...... 105 5.3.2 Calculation of branching fraction limit ...... 114 5.3.3 Final results ...... 118 5.3.4 New physics implications ...... 119

6 Analysis at Belle II 121 6.1 Motivation ...... 121 6.2 Analysis tools ...... 124 6.2.1 Full event interpretation ...... 124 6.2.2 Background Monte Carlo ...... 127 6.2.3 Signal Monte Carlo ...... 128 6.2.4 Belle II Analysis Software Framework ...... 129 6.3 Signal selection ...... 130 6.3.1 Skim ...... 130 6.3.2 Particle identification ...... 132 6.3.3 Λ reconstruction ...... 134 6.3.4 Event reconstruction ...... 136 6.3.5 Distance of closest approach ...... 138 6.3.6 Best Λ selection ...... 141 6.3.7 Continuum suppression ...... 142 6.3.8 Extra energy ...... 146

6.3.9 Btag Mbc cut ...... 149

6.3.10 mΛ cut ...... 150

x 6.3.11 Summary of signal selection ...... 150 6.4 Results ...... 153 6.4.1 Systematic uncertainties ...... 153 6.4.2 Final results ...... 154 6.4.3 Implications for Belle II ...... 155

7 Conclusion 164

A Signal MC reweighting 173

B Eextra adjustment 177

xi List of Figures

2.1.1 Beta decay...... 14 2.1.2 b → s flavour-changing-neutral-current process...... 15 2.2.1 Feynman diagrams for B−→ Λpνν decays in the Standard Model...... 17 2.2.2 An anomalous tcZ0 coupling...... 21

3.1.1 PEP-II integrated luminosity ...... 25

3.1.2 PEP-III and BABAR ...... 26

3.2.1 Cross sections of the BABAR detector...... 28

3.2.2 Cross sections of the BABAR SVT...... 29

3.2.3 Energy loss rates of charged particles in the BABAR drift chamber...... 31 3.2.4 Cross section of drift chamber cells...... 33

3.2.5 BABAR’s detector of internally-reflected Cherenkov light (DIRC) . . . 36

3.2.6 Longitudinal cross-section of the BABAR electromagnetic calorimeter (EMC). 38 3.2.7 Diagram of a single calorimeter crystal...... 39

3.2.8 Barrel and endcap sections of the Instrumented Flux Return at BABAR after upgrade...... 41

4.1.1 Luminosity projections for SuperKEKB...... 44 4.1.2 SuperKEKB and Belle II...... 45 4.2.1 Cross-section of the Belle II detector...... 48

xii 4.2.2 Belle II pixel detector (PXD)...... 50 4.2.3 Belle II vertex detector...... 51 4.2.4 Belle II SVD strip sensors...... 52 4.2.5 Belle II CDC sense wires...... 53 4.2.6 Belle II TOP...... 55 4.2.7 Principle of operation of a Belle II TOP module...... 56 4.2.8 Particle identification at Belle II TOP...... 56 4.2.9 Focussing effect of the ARICH aerogel layers...... 58 4.2.10 Cherenkov ring image in the ARICH...... 59 4.2.11 Belle II electromagnetic calorimeter...... 60 4.2.12 Belle II K-long and muon detector...... 62 4.2.13 Layout of scintillating strips in the Belle II KLM...... 63 4.2.14 Belle II KLM scintillator...... 64

5.1.1 Hadronic Btag reconstruction...... 69

5.2.1 Btag mES after hadronic Btag reconstruction and skim cuts...... 79 5.2.2 B-mode purity...... 81 5.2.3 Expected branching fraction limit as a function of B-mode purity...... 82 5.2.4 Cartoon of BB and continuum event shapes...... 83

5.2.5 Event-shape variables used in continuum suppression, after hadronic Btag

reconstruction, skim and Btag mES cuts...... 85 5.2.6 BB likelihood...... 86 5.2.7 Expected branching fraction upper limit as a function of BB lieklihood cut. 87

5.2.8 Eextra...... 88

5.2.9 Expected branching fraction upper limit as a function of Eextra cut. . . . . 89 5.2.10 Cartoon of expected DOCA order in a B−→ Λpνν event...... 91

xiii 5.2.11 Distance of closest approach (DOCA) for ID-tagged charged tracks in signal MC...... 92 5.2.12 Reconstructed Λ mass...... 94

5.2.13 MC correction variables RMC and Cpeak as a function of sequential signal selection cut...... 101

5.2.14 Btag mES as a function of signal selection cut...... 102

5.3.1 PID performance of BABAR’s TightKMProton selector...... 110

5.3.2 Momentum distributions for tracks ID’ed as protons after hadronic Btag reconstruction, skim and PID+DOCA cuts...... 111 5.3.3 Mass of Λ candidates reconstructed using PID information only in a control

sample comprising the mES sideband region after hadronic Btag reconstruction and skim cuts...... 112 5.3.4 Mass of Λ candidates selected using PID, DOCA and Λ reconstruction in

a control sample comprising the mES sideband region after hadronic Btag reconstruction and skim cuts...... 112 5.3.5 Signal efficiency versus q2 ...... 119

6.2.1 B-meson reconstruction by FEI...... 124 6.3.1 Reconstructed Λ candidates after Λ reconstruction cuts...... 135 6.3.2 Reconstructed Λ candidates after KFit...... 136 6.3.3 Reconstructed Λ candidates after event reconstruction...... 138 6.3.4 Distance of closest approach...... 140 6.3.5 Reconstructed Λ candidates after DOCA cut...... 140 6.3.6 Reconstructed Λ candidates after best Λ selection...... 141 6.3.7 Event-shape variables used to calculate BB likelihood, after FEI, skim, and

Mbc cuts. Charge consistency is also imposed (i.e. the charge of the Btag must be equal-and-opposite to that of all remaining tracks in the event). . 144

xiv 6.3.8 BB likelihood...... 145 6.3.9 Expected branching fraction upper limit as a function of BB lieklihood cut. 145

6.3.10 Eextra...... 148

6.3.11 Expected branching fraction upper limit as a function of Eextra cut. . . . . 148

6.3.12 Mbc ...... 149 6.3.13 Final Λ mass...... 150

6.4.1 Comparison of reconstructed Λ masses at BABAR and Belle II...... 156

A.0.1 Definitions of angles used in Figure A.0.1 ...... 174 A.0.2 Predicted distributions of invariant masses and angles for B−→ Λpνν ... 174

A.0.3 mΛp before and after signal MC reweighting ...... 175 A.0.4 Sum of proton momenta before and after signal MC reweighting ...... 176

B.0.1 Unadjusted and adjusted Eextra ...... 178

B.0.2 Unadjusted Eextra after mES sideband substitution and corresponding Btag

mES distribution...... 179

B.0.3 Unadjusted Eextra, after local-skim, Btag mES, B-mode purity and BB like-

lihood cuts, before and after mES sideband substitution; and corresponding

Btag mES distribution...... 180

B.0.4 Eextra adjusted by −5 MeV and −10 MeV, and mES sideband-substituted versions...... 181

xv List of Tables

2.1 Fermions of the Standard Model ...... 9 2.2 Hadrons relevant to the analyses presented in this thesis...... 11 2.3 Standard Model gauge bosons...... 11

4.1 Comparison of SuperKEKB and PEP-II...... 46

5.1 Integrated luminosity and B-count values for the BABAR dataset at the Υ(4S) resonance...... 71

5.2 Background Monte Carlo used in BABAR analysis...... 74

5.3 Values of Ri and Fi...... 103 5.4 Summary of sequential background yield and signal efficiency as a function of signal selection cut...... 104 5.5 Summary of marginal background yield and signal efficiency as a function of signal selection cut...... 104 5.6 Signal efficiency for different MC reweightings ...... 106 5.7 Final background and signal efficiency estimates at the end of the signal selection using an MC correction procedure with different background composition assumptions...... 109 5.8 Signal efficiency at the end of the signal selection with different definitions

of Eextra...... 114

xvi 5.9 Data/MC ratio with different definitions of Eextra...... 114 5.10 Summary of systematic uncertainties...... 115 5.11 Numbers of events required to calculate final background yield using the MC correction procedure...... 116 5.12 Final background estimates after the full signal selection...... 116 5.13 Branching fraction central values and upper limits at the 90% confidence level...... 118

6.1 Background Monte Carlo used in the Belle II sensitivity study...... 128

6.2 ECL cuts for Eextra calculation...... 147 6.3 Summary of marginal background yield and signal efficiency as a function of signal selection cut...... 151

6.4 Comparison of PID and DOCA cuts at BABAR and Belle II...... 157

6.5 Comparison of Eextra cuts at BABAR and Belle II...... 159

6.6 Comparison of continuum suppression cuts at BABAR and Belle II...... 159

xvii Chapter 1

Introduction

Particle physics is the study of the particles and forces that govern our universe at the smallest and most fundamental level. An understanding of what our universe is made of and how its constituents interact forms the foundation upon which much of our scientific and technological achievement rests.

Our current understanding of particle physics is expressed in the Standard Model [1], the theoretical framework that describes the matter we are made of and interact with and how that matter interacts with itself. The Standard Model has passed numerous, stringent tests and is a remarkable achievement. However, it only describes approximately 5% of the universe.

We know from our observations that there must be more to the universe than the matter which is described by the Standard Model. Approximately 95% of the universe is made from so-called dark matter [2] and dark energy [3, 4], neither of which have been directly observed and neither of which are included in the Standard Model. The Standard Model also fails to incorporate gravity among the fundamental forces and it does not fully explains why matter, rather than antimatter, came to dominate the universe as it does today. As

1 particle physicists, we are therefore motivated to carry out investigations to search for so- called “new physics”, physics that lies beyond the current Standard Model, and to test the Standard Model ever further to see if any cracks appear.

In this thesis we present two analyses of the B−→ Λpνν particle decay. This decay is predicted [5] by the Standard Model to be extremely rare, and therefore an observation of this decay at a rate higher than predicted would be an indication of the existence of new physics. Even if we are unable to observe the decay and measure it’s branching fraction, a measurement of an upper limit on the branching fraction can be used to inform new physics models.

The first analysis we present is conducted using data from the BABAR [6, 7] experiment. It is the world’s first experimental search for B−→ Λpνν decays, and we aim to measure the branching fraction of, or the branching fraction upper limit of, B−→ Λpνν decays.

The second analysis we present is conducted using a simulation of data that will be collected at the Belle II [8] experiment, the world’s only next-generation facility that will be capable of making a future competitive measurement of B−→ Λpνν decays. The objective of the analysis is to estimate the branching fraction upper limit that Belle II will be able to measure, and thus to test the capabilities and competitiveness of Belle II. It is the world’s first sensitivity study for B−→ Λpνν decays at such a next-generation facility.

Chapter 2 provides the necessary background information that informs the analyses, namely an overview of particle physics theory and the motivations behind our analyses. Chapters

3 and 4 provide a description of the BABAR and Belle II detectors respectively. Chapters 5

− and 6 describe the analyses of B → Λpνν conducted at BABAR and Belle II respectively. A conclusion and comment on future prospects is given in Chapter 7.

2 Chapter 2

Background

Particle physics is the study of nature at the smallest scales, it is the study of elementary particles and compound particles comprising these elementary particles, and the ways in which they interact with each other via the strong, electromagnetic and weak fundamental forces.

Particle physicists seek to understand the elementary building blocks of nature at the most fundamental level, and thus to answer some of the most fundamental questions that humans ask ourselves, including the origin of matter which we comprise and thus the explanation of our very existence.

Our understanding of particle physics, and thus of the universe in which we live, is, however, only partially complete. Particle physicists are thus motivated to study nature at greater energies and with more and better data in an attempt to answer outstanding questions and deepen our understanding of the fundamental building blocks and forces of nature.

3 2.1 The Standard Model of particle physics

The Standard Model (SM) of particle physics describes the particles that make up the visible matter of the universe in which we live, as well the interactions between them via the strong, electromagnetic and weak forces.

The Standard Model is a gauge theory based on the symmetry groups SU(3)×SU(2)×U(1). These gauge groups represent the fundamental forces of the SM: SU(3) the strong force, SU(2)×U(1) the electroweak force [9]. The particle interpretations of the fields these gauge groups represent are the gauge bosons, the force carriers of the standard model: gluons in the case of the strong force, the W and Z0 bosons for the weak force, and the photon for the electromagnetic force. Fermions, the massive particles that constitute the matter of our universe, interact via exchange of the relevant gauge bosons [10].

The Standard Model includes twelve fermions, divided into six leptons and six quarks, which are the building blocks of all visible matter. Additionally, each fermion particle has an associated antiparticle with opposite quantum numbers (i.e. there are six antileptons and six antiquarks). Interactions between the (anti)fermions are mediated by gauge bosons which act as force carriers for three of the fundamental forces. The last element of the Standard Model is the Higgs boson, a product of the Higgs mechanism responsible for the masses of the gauge bosons and fermions.

With the detection of the Higgs boson in 2012 [11, 12], the Standard Model is “complete” in the sense that all predicted particles have now been observed. However, the SM is clearly incomplete in terms of its ability to describe our universe - the SM does not incorporate gravity, it assumes neutrinos are massless when they are in fact not, it provides no explanation for the dark energy and dark matter that together make up approximately 95% of our universe, and it does not sufficiently account for the fact that our present-day universe is dominated by matter rather than antimatter [10].

4 These outstanding questions motivate us to conduct experiments to find evidence for physics outside the scope of the SM, so-called “new physics”, also known as non-SM or beyond-SM physics. The fact that new physics must exist is beyond question, the problem is that we have so far failed at direct detection of any new-physics particles and we are thus ignorant of what kind of particles and forces comprise new physics.

In the following sections we describe the particles and forces of the Standard Model in more detail, as well as discuss possibilities for beyond-SM physics. We also introduce the main

− topic of this thesis, the search for particle decays of the form B → Λpνν at the BABAR and Belle II experiments, and explain how our search is motivated by our understanding of the Standard Model and our desire to investigate physics beyond the SM.

2.1.1 Fermions

Fermions are elementary particles, that is, as far as we know they are not composed of smaller constituent particles [10]; i.e. within the SM they are assumed to be fundamental and point-like. Fermions make up the visible matter of the universe in which we live and with which we interact in our everyday lives. The protons, neutrons and electrons that make up ourselves, the food we eat and the air we breathe are either composed of fermions (in the case of protons and neutrons) or are fermions themselves (the electron). Fermions also constitute more exotic types of matter which, while not immediately evident in our everyday existence, provide interesting avenues via which we can explore particle physics, such as B mesons which we will discuss later.

The fermions of the SM are divided into two types: leptons and quarks. All fermions are spin-1/2 particles that interact via the exchange of spin-1 gauge bosons (see Section 2.1.3), but are otherwise quite different in character.

5 Leptons

There are six types of leptons in the Standard Model [10]: the electron (e−), the muon (µ−)

− and the tau (τ ), and their three associated neutrinos the electron neutrino (νe), the muon neutrino (νµ) and the tau neutrino (ντ ). The leptons are arranged in three generations of weak isospin doublets which associate each neutral neutrino with its corresponding charged lepton. All leptons are capable of existing in isolation, although in the case of the two most- massive charged leptons (the µ− and τ −) they in practice have a limited lifetime as they will decay into lighter particles [9].

The e−, µ− and τ − have an electrical charge of −1 and masses ranging from approximately 0.5 MeV/c2 in the case of the e− up to 1.8 GeV/c2 in the case of the τ −. Apart from effects brought about by their different masses, these different types (or “flavours”) of leptons are believed to experience identical couplings via the fundamental forces, a concept known as lepton universality. This means that, with the exception of effects brought about by their different masses, their interactions with the forces of the SM should be identical [10].The charged leptons interact via the electromagnetic and weak forces; however, at low energies the weak force appears much weaker than the electromagnetic interaction due to the mass of the W and Z0 bosons, so electromagnetic interactions will dominate where permitted.

The other class of leptons, the neutrinos, are electrically neutral. In the Standard Model neutrinos are assumed to be massless; however, we know from the phenomenon of neutrino oscillation that this cannot be the case [10]. The absolute mass of each neutrino mass eigenstate is not yet known, although the differences in masses squared between them are [9]. Importantly, the observation that neutrinos do have mass requires beyond-SM physics to explain – either in the form of right-handed and extremely-rarely interacting “sterile” neutrinos [13]; or neutrinos must be their own antiparticles (so-called Majorana particles) [14].

6 Neutrinos are electrically-neutral and neither do they carry colour, the charge of the strong force; they therefore only interact via the weak force, meaning they rarely interact with matter [10]. In this thesis we report on our search for decays of the form B−→ Λpνν , which contains two neutrinos in the final state. Since neutrinos so rarely interact with matter, they are never detected in the BABAR and Belle II experiments, which makes searching for events of the form of B−→ Λpνν extremely challenging. We discuss this challenge, and how we overcome it, in Sections 5.1.1 and 6.2.1.

Each matter lepton has an antimatter counterpart which has identical mass but opposite quantum numbers [10]. E.g. in the case of the electron (e−), which is a matter particle, the antimatter counterpart is the anti-electron (e+, also known as a positron), which has electric charge of +1. Neutrinos likewise have antimatter counterparts (unless they are Majorana particles [14], in which case the neutrino is its own antiparticle), e.g. the antimatter counterpart of the νe is the νe. In the case of neutrinos the charge remains zero in both cases but all other quantum numbers, such as lepton number, are flipped, which is significant because neutrino oscillation introduces a process where quantum number (e.g. lepton number) is not conserved.

All fermions (both leptons and quarks) are further classified into three generations according to their mass – fermions with higher mass are placed into higher generations and, apart from differences in mass, they share the same properties as their counterparts in lower generations (although, as previously mentioned, we do not yet know if this is true for neutrinos masses) [10]. A summary of Standard Model fermions, showing their properties and classifications, is shown in Table 2.1.

7 Quarks

The other type of fermion in the Standard Model are the quarks. There are six flavours of quark: up (u), down (d), charm (c), strange (s), top (t) and bottom (b). Like the leptons, the quarks are classified into generations of increasing mass (see Table 2.1). Quarks can interact via the weak, electromagnetic and strong forces, although the relative strength of the strong force means that strong force interactions will dominate where possible [10].

Quarks carry non-integer electric charge of either +2/3 or −1/3. Like the leptons, quarks are also arranged in three generations of weak isospin doublets, although their weak hypercharge of +1/3 is different from that of the leptons which have weak hypercharge −1 [15]. Each quark also has an antimatter counterpart with opposite charge, e.g. the antimatter counterpart to the u quark (charge +2/3) is the u (charge −2/3) [10].

Quarks also carry colour charge associated with the strong force. While colour is not gauge- invariant, we often model quarks as carrying a single colour: red, blue or green for quarks and anti-red, anti-blue or anti-green for antiquarks. Unlike electric charge, the colour charge of a given quark flavour is not constant, a quark can have colour charge of any of red,blue of green, but only one at a time. Changes in colour are mediated by the exchange of gluons, the strong force gauge bosons [10] (see Section 2.1.3 for more details).

A concept known as colour confinement expresses the phenomenon that a quark cannot exist in isolation, nor can combinations of quarks with net colour exist [10]. Thus, quarks must either be grouped together into “colourless” states via the combination of a colour and its anticolour (e.g. red and anti-red), or “white” states which combine all three colours (i.e. red, blue and green mix to make white, and likewise for the anticolours). These quark compounds form particles known as hadrons, where a colourless quark-antiquark pair is known as a meson and a white combination of three (anti)quarks is known as a baryon (see Section 2.1.2 for more details).

8 The SM fermions, both leptons and quarks, are shown in Table 2.1.

Table 2.1: Fermions of the Standard Model [9]. Each fermion also has an antimatter counterpart, see text for details. Particles interact via the strong (S), electromagnetic (EM) or weak (W) forces. All massive particles also interact gravitationally; however, gravity is not included in the Standard Model and its effects are negligible in the context of a typical lab-based, high-energy particle physics experiment. Neutrino mass eigenstates are not flavour eigenstates; the masses given for the neutrino flavour eigenstates are calculated from processes involving the production or decay of the relevant flavour charged lepton; see Ref. [9] for more details. Masses forthe u, d, c, s and b quarks are MS masses, the mass for the t quark is based on direct measurements of tt events; see Ref. [9] for more details.

Leptons Generation Flavour Symbol Electric Mass Interactions charge ( GeV/c2) electron e− −1 0.000511 EM, W 1 e neutrino νe 0 < 0.000002 W muon µ− −1 0.1057 EM, W 2 µ neutrino νµ 0 < 0.00019 W tau τ − −1 1.777 EM, W 3 τ neutrino ντ 0 < 0.0182 W Quarks Generation Flavour Symbol Electric Mass Interactions charge ( GeV/c2) up u +2/3 0.0022 S, EM, W 1 down d −1/3 0.0047 S, EM, W charm c +2/3 1.275 S, EM, W 2 strange s −1/3 0.095 S, EM, W top t +2/3 173 S, EM, W 3 bottom b −1/3 4.18 S, EM, W

2.1.2 Hadrons

Hadrons are composite particles comprising quarks bound together by gluons. With the exception of the proton (which is the lightest baryon), hadrons are unstable and will decay into lighter particles with a given mean lifetime, either producing lighter hadrons, leptons, photons or some combination thereof [9]. The lifetimes of hadrons cover many orders of magnitude, e.g. the B+ meson has a mean lifetime of 1.6 × 10−12 s while the proton is to all

9 intents and purpose stable [9].

Colour confinement has the consequence that hadrons can only have integer electric charge – a qq (i.e. colour + anticolour) meson can only have 0 and 1 electric charge, and a three- quark “white” baryon (red + green + blue, or the corresponding anticolours) can also only be constructed with integer electric charge. The electric charge of a hadron is the sum of the charges of its constituent valence quarks, e.g. a proton with quark content uud has total charge 2/3+2/3−1/3 = 1. An antihadron swaps quarks and antiquarks relative to its hadron counterpart, e.g. an antiproton comprises uud quarks and has electric charge −1. While the electric charge of a hadron is the sum of the electric charges of its constituent quarks, its mass is not simply a sum of the constituent quarks’ masses, but also includes contributions from the internal strong force binding energy which keep the constituent quarks bound inside the hadron [10].

Colour confinement also describes a means of hadron production in certain high-energy particle collision processes. If the q and q in a qq become isolated from one another, the potential energy between the two rapidly increases and soon exceeds the qq rest mass (assuming we are dealing with “light” quarks such as u, d, s), resulting in a new qq pair being produced from the vacuum; these new quarks bind with the preexisting quarks to form hadrons. A quark can become isolated in such instances as the production of a qq pair in a high energy collision between matter and antimatter, as happens at BABAR and Belle II. Conservation of momentum means the q and q will travel in opposite directions and become isolated, and new qq pairs will be produced from the vacuum forming “jets” of hadrons aligned with the trajectory of the original q or q [10].

There are a huge number of mesons and baryons that can be created from the six quarks, only a handful of which are of particular interest with regards to the analyses in the following chapters. The hadrons of interest for this thesis are shown in Table 2.2.

10 Table 2.2: Hadrons relevant to the analyses presented in this thesis [9]. By convention, Λ (without any superscript) is understood to mean the electrically-neutral Λ0.

Name Symbol Quark content Electric charge Mass ( GeV/c2) Upsilon(4S) Υ(4S) bb 0 10.579 B meson B+ ub +1 5.279 Lambda Λ uds 0 1.116 Proton p uud +1 0.938 Pion π+ ud +1 0.140

We note that the Υ(4S) is a type of particle also known as a “resonance”. Resonances are particles created in collisions characterised by a localised increase in the collision cross- section; resonances are also characterised by their extremely short lifetimes of ∼ 10−23 s or less [10].

2.1.3 Bosons

There are two types of bosons on the Standard Model: the spin-1 gauge bosons and the spin-0 Higgs boson.

Gauge bosons are the force carriers for the three SM forces. The number of gauge bosons for each gauge group is equal to the number of generators of that group [15]: a single gauge boson for the U(1) electromagnetic force (the photon); three gauge bosons for the SU(2) weak force (W and Z0); and eight gluons for the SU(3) strong force, where the eight different gluon types are differentiated by their colour states. A summary of gauge boson properties is shown in Table 2.3.

Table 2.3: Standard Model gauge bosons [9].

Gauge boson Symbol Electric charge Mass ( GeV/c2) Force Gluon g 0 0 Strong Photon γ 0 0 Electromagnetic W boson W 1 80.379 Weak Z0 boson Z0 0 91.188 Weak

11 The range of the force carried by a gauge boson is inversely proportional to the boson’s mass, since gauge bosons always appear as virtual particles or on shell when acting as force mediators and the time they can exist for (and thus the range over which they can act) is limited by the Heisenberg uncertainty principle. The electromagnetic force, carried by the massless photon, therefore has an infinite range, while the weak force, carried by massive W and Z0 bosons, has an effective range of approximately 10−18 m [10].

Gluons are also massless, suggesting an infinite range for the strong force. However, self- interactions of the strong force SU(3) gauge field leads to the formation of bonds between quarks (the aforementioned colour confinement), meaning the effective range is approximately 10−15 m. Concretely, quarks can only exist in white or colourless compounds so the exchange of gluons, which carry net colour charge, is not possible over long ranges. In- stead, inter-hadron strong force interactions are mediated by the exchange of colourless or white quark compounds, i.e. massive hadrons (e.g. a pion), which limits the effective range [16].

Uniquely among the fundamental SM forces, the weak force is capable of mediating flavour- changing processes; that is, processes where the flavour of a quark changes. Specifically, the W boson couples between up-type and down-type quarks in weak isospin doublets and across generations of quarks (see Section 2.1.4 for more details).

The Higgs boson was the final SM particle to be discovered, in 2012 at the LHC [11, 12],where it was measured to have a mass of approximately 125 GeV/c2 and zero electric charge.

The Higgs boson is a prediction born out of the necessity for the Higgs field. The Higgs field in turn was motivated by the problem of the mass of the weak force gauge bosons (W and Z0), which the symmetry of the electroweak interaction predicts should be massless. In order to account for the weak gauge boson masses, a field with a non-zero vacuum expectation value was required which would cause spontaneous electroweak symmetry breaking – the

12 Higgs field. This causes spontaneous symmetry breaking of the electroweak SU(2)L×U(1)Y group into the U(1)Q electromagnetic group at low energies (the forces are unified into a single electroweak force at high energies), where the subscripts L, Y and Q refer to left (as in, coupling to left-handed particles only), weak hypercharge and electric charge respectively. The absorption of three of the four components of the Higgs field by the weak gauge bosons gives them their masses (the Higgs mechanism), while the fourth component is the Higgs boson [17, 18, 19].

Quarks and leptons acquire their mass via Yukawa couplings [20] to the Higgs field, and interactions with the Higgs field cause these fermions to flip chirality (i.e. flip between having right-handed and left-handed chirality) [15]. If neutrinos were to acquire mass by the same mechanism there would have to be both left-handed and right-handed chirality neutrinos; however, since we have only observed left-handed chirality neutrinos [10] the origin of neutrino mass remains unexplained.

2.1.4 The weak force and flavour changes

Uniquely among the forces of the Standard Model, the weak force can mediate changes in quark flavour which take place in so-called “flavour-changing” processes. The mostwell- known of these is arguably the flavour-change that occurs during radioactive beta decay where a neutron (quark content udd) decays into a proton (quark content uud), an electron and a neutrino. We see that quark flavour is not conserved –a d quark changes flavour into a u quark. A Feynman diagram for this process is shown in Figure 2.1.1.

We see in Figure 2.1.1 that the W − boson mediates the change in flavour of a d quark into a u quark. Because the d and u have different electric charges (−1/3 and +2/3 respectively), this is known as a flavour changing charged current process (note that overall charge is conserved thanks to the electron). We note also that this process occurs at the tree level,

13 Figure 2.1.1: Beta decay process showing a proton (n) turning into proton (p) thanks to the flavour change of a d quark into a u quark. Figure adapted from [5]. that is, there are no internal loops in the Feynman diagram.

The probability of a given quark flavour change occurring is expressed in the Cabibo-

Kobayashi-Maskawa (CKM) [21, 22] matrix, VCKM :

 

Vud Vus Vub     VCKM = V V V  (2.1)  cd cs cb 

Vtd Vts Vtb where, for example, the probability of a d → u flavour change is proportional to the magnitude squared of Vud.

The elements along the leading diagonal (which relate to flavour-changing processes within the same generation of quarks, e.g. the d → u process seen in beta decay) of VCKM are close to one, but the others (flavour-changing processes across generations) are considerably less than one meaning that, e.g., a d → u transition has a much higher probability of occurring than a b → u transition. The values of the magnitudes of the CKM matrix elements are [9]:

14   0.97446±0.00010 0.22452±0.00044 0.00365±0.00012      VCKM = 0.22438±0.00044 0.97359+0.00010 0.04214±0.00076  (2.2)  −0.00011  +0.00024 0.00896−0.00023 0.04133±0.00074 0.999105±0.000032

Since the W is electrically charged it can only mediate flavour changes that also involve a change in electric charge; e.g. a b → u (electric charges: −1/3 → +2/3) transition can occur thanks to the matrix element Vub but there is no Vsb element and therefore a direct b → s (electric charges: −1/3 → −1/3) transition is not possible. In order to achieve such flavour changing neutral current processes we require two consecutive flavour changes; e.g. a b → s transition could be proceed via b → u and u → s, or b → c and c → s, etc.

Because flavour changing neutral current (FCNC) processes require two flavour changes, they can only happen at the loop level, that is, there must be internal loops in the Feynman diagram (note that non-flavour changing neutral current processes can occur at the tree level, mediated by Z0 bosons and photons, but these conserve lepton flavour). For example, a b → s transition can occur, at the lowest level, as shown in Figure 2.1.2.

Figure 2.1.2: b → s flavour-changing-neutral-current (FCNC) process. Colour confinement means quarks do not exist in isolation – the b and s quarks here would be part of hadrons, but are shown here in isolation to highlight the b → s transition. Figure adapted from [5].

The two consecutive flavour-changes, at least one of which corresponds to an off-diagonal CKM matrix element, means FCNC processes such as b → s are highly suppressed according to the Standard Model, such processes are therefore described as rare.

15 The fact that multiple weak force couplings are required by the lowest level one-loop diagrams in FCNC processes provides further suppression, since each weak force coupling introduces an extra weak force coupling constant into the amplitude for the process occurring. This is further compounded by the GIM mechanism [23], which predicts that the amplitudes for loop-level FCNC processes cancel each other out except for a residual amplitude that remains thanks to the mass differences between the quarks; hence, while loop-level FCNC processes are not completely forbidden by the GIM mechanism, they are highly suppressed.

In the case of the decay of B mesons, the fact that the B is the lightest B meson means it can only decay via the weak force since decay to a lighter state via EM or strong interactions is impossible – a flavour change is required in order for an energetically-favoured decay to take place. So while flavour-changing processes (either neutral- or charged-current) are “rare”, they are in fact universal in the decay of B mesons, although the “rarity” (i.e. low rate) at which they happen causes the B to have a relatively long lifetime of ∼ 10−12 s [9].

The fact that FCNC processes are so heavily suppressed makes them sensitive probes for new physics. If a new physics process provides additional avenues via which an FCNC process can occur, the probability of that process happening may be increased compared to the SM prediction and, given the suppression of such processes in the SM, this increase may be quite drastic and therefore measurable in an experiment. This sensitivity to new physics makes FCNC processes popular, albeit challenging, subjects of analyses searching for new physics, including the topic of this thesis.

16 2.2 Motivation for B−→ Λpνν search

The theory behind the B−→ Λpνν decay was first presented in Ref. [5]. B−→ Λpνν is a rare, flavour-changing-neutral-current (FCNC) decay. That is, it has a small predicted branching fraction (hence “rare”), it requires a change of quark flavour (“flavour-changing”) but this change of flavour is not accompanied by a net change in electric charge of thequarks (“neutral-current”).

B−→ Λpνν has never been experimentally measured before. This thesis documents the world’s first ever search for this mode.

Feynman diagrams for the two leading-order processes by which B−→ Λpνν decays can occur in the Standard Model are shown in Figure 2.2.1. C. Q. GENG AND Y.K. HSIAO PHYSICAL REVIEW D 85, 094019 (2012)

u,c,t u,c,t

(a) (b) Figure 2.2.1: Feynman diagrams for B−→ Λpνν decays in the Standard Model. Adapted from [5]. FIG. 1 (color online). Contributions to the B Ãp## decay from (a) penguin and (b) box diagrams. À ! We see from Figure 2.2.1 that B−→ Λpνν involves the rare, FCNC process b → s. This 2 2 2 invariance, the most general forms of the B BB 0 tran- with ! a; b; c a b c 2ab 2bc 2ca, and sition form factorsdecay are given is therefore by [23 heavily] suppressed! in the Standardt, s Modelðp andpÞ¼ provides2, þ, a sensitive,þ and 0À probeare fiveÀ variablesÀ in the ð # þ # Þ B L for new physics which may contribute# to a higher-than-expectedphase space. As branching seen from fraction Fig. thanks2, the angle B L is BB0 q0"b B iu pB g1" g2i'"#p g3p" ð Þ h j j i ¼ ð Þ½ þ þ between p~ B (p~ #) in the BB0 (##) rest frame and the line to the contribution of beyond-SM weak currents (see Section 2.2.1 for more details). The g4q" g5 pB 0 pB " 5v pB 0 ; of flight of the BB0 (##) system in the rest frame of the B, þ þ ð À Þ −→ð Þ × −7 BB q b B predictediu p branchingf f fractioni' p for# B f pΛpνν iswhile(7.9 the1.9) angle10 0[5],is and between if we measure the BB a0 plane and the ## h 0j 0 " 5 j i ¼ ð BÞ½ 1 " þ 2 "# þ 3 " plane, which are defined by the momenta of the BB branching fraction that is different from this it could be an indication of new physics. 0 f q f p p v p ; pair and the momenta of the ## pair, respectively, in the þ 4 " þ 5ð B0 À BÞ" ð B0 Þ rest frame of B. The ranges of the five variables are B−→ Λpνν decays present several notable(3) features from an experimental analysis point of given by with q p p and p p q, for the vector and B B 0 B 2 2 ¼ þ ¼ À m# m# s mB pt ; axial-vector quark currents, respectively. For the momen- 17 ð þ Þ ð À Þ tum dependences, the form factors f and g (i 2 ffiffi 2 i i mB mB 0 t mB m# m# ; 0 L; 1; 2; ...; 5) are taken to be [19] ¼ ð þ Þ ð À À Þ B %; 0 0 2%: (7) D D f fi ;g gi ; (4) i ¼ t3 i ¼ t3 The decay branching ratio of B BÀ Ãp## depends on the integration in Eqs. (5)–(7), whereð ! we haveÞ to sum over with t q2 m2 , where D and D are constants to be fi gi the three neutrino flavors since they are indistinguishable. BB0 determined by the measured data in B ppM decays. We can also define the integrated angular distribution 3 ! Note that 1=t arises from three hard gluons as the asymmetries, given by propagators to form a baryon pair in the approach of the 1 dB 0 dB perturbative quantum chromodynamics counting rules 0 dcos dcosi 1 dcos dcosi A i À À i ; i B;L : [18,32–34], where two of them attach to valence quarks i 1 dB 0 dB R0 dcos dcosi R 1 dcos dcosi ð ¼ Þ in BB , while the third one kicks and speeds up the i þ À i 0 R R (8) spectator quark in B. It is worth to note that, due to fi, gi 1=t3, the dibaryon invariant mass spectrum peaks at the/ threshold area and flattens out at the large energy region. Hence, this so-called threshold effect measured as a com- III. NUMERICAL RESULTS AND DISCUSSIONS mon feature in B ppM decays should also appear in the For the numerical analysis, we take the values of G , ! F BÀ Ãp#‘#‘ decay. To integrate over the phase space for , sin2 and V V in the PDG [38] as the input ! em W tsÃ tb the amplitude squared A 2, which is obtained by assem- parameters. In the large t limit, the approach of the bling the required elementsj j in Eqs. (2)–(4) and summing over all fermion spins, the knowledge of the kinematics for the four-body decay is needed. For this reason, we use the partial decay width [35–37] A 2 dÀ j j X dsdtd cos d cos d0; (5) ¼ 4 4% 6m3 B L B L ð Þ B where 1=2 1 2 2 X mB s t st ; ¼ 4ð À À Þ À 1 1 1=2 2 2 1=2 2 2 FIG. 2 (color online). Three angles B, L, and 0 in the phase B ! t;mB;m ; L ! s;m#;m# ; (6) ¼ t ð B0 Þ ¼ s ð Þ space for the four-body B BB ## decay. ! 0

094019-2 view.

• The presence of neutrinos in the final state makes analysis especially challenging since a full reconstruction of the decay is not possible. On the other hand, since neutrinos represent missing energy and momentum, this also makes this analysis of this mode sensitive to new physics sources of missing energy and momentum due to weakly- interacting undetectable particles, e.g. dark matter.

• The Λ baryon decays into pπ− approximately 64% of the time, nπ0 approximately 36% of the time, and all other decay modes have branching fractions of 10−3 or less [9]. In contrast to the decay’s other characteristics, these features make B−→ Λpνν very amenable to analysis. If we analyse only the predominant B−→ Λpνν followed by Λ → pπ− mode, then other than the neutrinos the final state consist of three charged tracks: two protons and a pion. Protons and pions are sufficiently long-lived to travel measurable distances in particle detectors and can be identified using high-efficiency particle identification algorithms; in other words, the final state of this decay should be relatively easy to detect.

• The Λ baryon itself is another useful feature of the decay. By identifying the two charged tracks which are the descendants of the Λ, we will be able to reconstruct the Λ mass peak and use this as an extra selection variable to help identify B−→ Λpνν events. Furthermore, the long lifetime of the Λ means its decay vertex is displaced from the point at which the Λ originates; this characteristic can be used to enhance the quality of Λ reconstructions using various fitting algorithms.

The first of these points is perhaps the most important in terms of motivating howwe should conduct a search for B−→ Λpνν decays. Given the high mass of B mesons and the rarity of the decay, searches for B−→ Λpνν must be conducted at a high-energy collider experiment where copious amounts of B mesons can be produced. Furthermore, since a

18 full reconstruction of such an event is not possible, we desire a very clean experimental environment where there is as little as possible background from other processes; ideally, we would like to be able to isolate all other processes happening in a particle collision (a.k.a. an event) such that all we are left with is B−→ Λpνν , so that even if we cannot detect the neutrinos we can calculate how much energy and momentum they carry away by process of elimination. The only type of experiments that meet these criteria are B factories.

In a B factory, e+e− collisions are used to ultimately produce BB meson pairs. Around the point at which the e+e− collision occurs, a particle detector can be used to collect data on the products of the collision. In the case that we wish to search for a signal such as B−→ Λpνν decays, we face the previously discussed challenge of accounting for the missing energy and momentum carried away by the neutrinos. We address this challenge by fully reconstructing one of the two B mesons in the BB pair, and conducting our search among the decay products of the other B meson. By conducting a full reconstruction of one of the B mesons, any missing momentum and energy can be ascribed to the remaining B meson on which we conduct our analysis.

More details on the B factories and detectors (BABAR and Belle II) used for the analyses presented in this thesis can be found in Chapters 3 and 4, and details on the B reconstruction techniques used can be found in Sections 5.1.1 and 6.2.1.

2.2.1 New physics possibilities

The features of B−→ Λpνν decays also motivate our search in terms of the potential for new physics discoveries. The coupling of the νν to quarks makes B−→ Λpνν sensitive to beyond-SM left-handed weak currents (e.g. a non-SM Z′ boson mediating the b → s flavour change), which could provide extra avenues for the coupling to occur; this would manifest in a branching fraction different to that predicted by the SM [24] and has been the subject of

19 − − − previous BABAR studies of related modes, in particular B → K νν decays, of which B → Λpνν is the baryonic equivalent (see Section 2.2.2 for more details).

−→ | ν | Specifically, the branching fraction for B Λpνν decays is sensitive to CL , the Wilson coefficient [24] that expresses short-distance physics in weak interactions if the interactions are modelled using an effective Hamiltonian and expressed using an operator product expansion [25]. Following the parametrisation of Ref. [24], if we assume no right-handed weak currents we can define ϵ:

| ν | | ν SM| ϵ = CL / (CL) (2.3) such that in the SM ϵ has a value of 1, whereas a value other than 1 implies the existence of beyond-SM weak currents. Since new weak currents provide additional avenues via which B−→ Λpνν can occur, non-SM values of ϵ will show up as a branching fraction different to that predicted by the SM, specifically [24]:

− − 2 B(B → Λpνν) = BSM (B → Λpνν) × ϵ . (2.4)

∗ Previous analyses of B+ → K+νν and B0 → K 0νν at BABAR [26] and Belle [27] have set limits on beyond-SM values of ϵ (see Section 5.3.4 for more details), and an analysis of B−→ Λpνν provides a complementary avenue via which we can potentially detect, or set new limits on, new physics of this form.

Specific example of new physics that could alter the branching fraction of B−→ Λpνν decays include beyond-SM quarks, e.g. a fourth generation quark could be added to the “uct” in Figure 2.2.1, providing an extra avenue for the FCNC process to occur [28]. New generations of quarks could also provide avenues via which tree-level Z0-mediated FCNC process could occur [28], a phenomenon which could also be enabled by the existence of a beyond-SM

20 Z′ with flavour-changing couplings [29]. Meanwhile, new loop-level b → s flavour changing processes could also be enabled by a t → c flavour-change as a result of the existence of anomalous tcZ0 couplings (see Figure 2.2.2) [30, 31].

Figure 2.2.2: An anomalous tcZ0 coupling enabling a b → s FCNC transition. Figure from [31].

The νν pair which appear in the final state of the decay also make this mode sensitive to undetectable, weakly-interacting new physics such as dark matter. Concretely, the νν pair shown in Figure 2.2.1 could be replaced by a pair of dark matter particles in a dark matter pair production process (this could potentially also include the replacement of the weak bosons from which the νν pair originate with other particles, e.g. a Higgs boson), providing extra avenues via which B− → Λp + missing momentum can occur and therefore enhancing the branching fraction measured in a search for B−→ Λpνν [32, 33]. Furthermore, flavour- violating couplings of quarks to dark matter could enable tree-level b → s flavour changes, providing yet more avenues for detection of a B−→ Λpνν decay signal [34].

The authors of Ref [5] highlight other interesting features of B−→ Λpνν decays which make it worthy of study: new physics right-handed vector and (psuedo-)scalar currents can be investigated by constructing angular asymmetry observables, and time reversal violation can be tested by constructing T -odd observables. However, these effects, if present, are expected to be too small to observe in the datasets used for the analyses presented in this thesis. Our goal with the analyses presented here will therefore be, in the case of the BABAR analysis (see Chapter 5) to conduct the world’s first experimental search for B−→ Λpνν decays and place an upper limit on the branching fraction, and in the case of the Belle II analysis (see Chapter 6) to perform a sensitivity study to test Belle II’s performance and

21 provide a foundation for future work on this analysis and similar analyses.

2.2.2 Related studies

While B−→ Λpνν has never been experimentally measured before, it is similar to decays which have been the subject of previous experimental analyses.

In particular, the authors of Ref [5] highlight the similarity to B− → K−νν decays, which

− − have been measured at BABAR [26] and Belle [27]. B → K νν involves the same FCNC b → s transition as B−→ Λpνν and features two neutrinos in the final state, it is thus likewise a sensitive probe for new physics both in terms of a branching fraction enhancement and the possibility of undetectable new physics particles carrying away momentum and energy.

The Standard Model prediction for the branching fraction for B− → K−νν decays is (4.0 0.5) × 10−6 [35], while experimental results from B− → K−νν analyses place the upper limit

− − on the branching fraction of 3.7 × 10 5 (BABAR) and 5.5 × 10 5 (Belle). The authors of Ref [5] highlight the fact that the gap between the SM prediction and the measured upper limit leaves room in which new physics could exist. It is also of course possible that future analyses will observe B− → K−νν with the SM-predicted branching fraction, although this also motivates us to continue performing analyses such as these in order to test whether or not the SM predictions are correct.

− → − −→ | ν | B K νν and B Λpνν are also both sensitive to CL , the Wilson coefficient that | ν | describes left-handed weak currents coupling quarks to neutrinos; a non-SM value of CL (i.e. implying the existence of non-SM left-handed weak currents) would show up as an enhanced branching fraction [24]. While the experimental analyses of B− → K−νν have not

| ν | found evidence for beyond-SM values of CL , they have placed limits on it [26].

22 In contrast to B− → K−νν decays, B−→ Λpνν decays offer advantages from an analysis point of view as previously discussed in Section 2.2, namely the presence of three charged tracks in the final state and a Λ baryon which we can reconstruct provide us with additional analysis handles.

23 Chapter 3

The BABAR experiment

The BABAR detector was located at SLAC National Accelerator Laboratory and collected data from 1999 - 2008 [7], with e+e− collisions provided by the PEP-II accelerator. This chapter presents an overview of PEP-II and BABAR.

3.1 The PEP-II accelerator

This section is based on the the description of PEP-II and the end-of-life summary of its performance which can be found in Refs [36, 37], except where otherwise noted.

PEP-II operated from 1999-2008, reaching a peak luminosity of 1.21 × 1034 cm−2 s−1, four

− times its design goal, and delivered an integrated luminosity to BABAR of 557.4 fb 1, with 433 fb−1 of this at the Υ(4S) resonance. The integrated luminosity history of PEP-II is shown in Figure 3.1.1.

Electrons and positrons were first accelerated to the desired energies in a linear accelerator before being injected into PEP-II’s two storage rings [7]: the Low Energy Ring (LER), through which circulated positrons at an energy of 3.1 GeV, and the High Energy Ring

24 Figure 3.1.1: History of PEP-II integrated luminosity. 433 fb−1 was delivered at the Υ(4S) resonance. Figure from [36].

(HER), through which circulated electrons at an energy of 9.0 GeV. The rings were of equal circumference and were constructed in a 2.2 km long tunnel, one atop the other, with the rings being brought together at a single collision point at the centre of the BABAR detector. An illustration of the setup is shown in Figure 3.1.2

The collision energy of the electron and positron beams in the centre-of-mass frame was 10.58 GeV, the threshold for creation of a pair of B mesons via the process e+e− → Υ(4S) → BB, where we take advantage of the fact that Υ(4S) decay almost exclusively to BB [9]. Facilities such as this are thus known as “B factories”.

The low interaction cross-section of electrons and positrons means that at most there will usually only be a single e+e− collision when the bunches of electrons and positrons cross paths. B factories such as PEP-II/BABAR and SuperKEKB/Belle II (see Chapter 4) thus allow us to produce large numbers of B mesons with relatively little background – the ideal e+e− → Υ(4S) → BB process produces nothing other than a pair of B mesons. B mesons

25 Figure 3.1.2: Illustration of PEP-II and BABAR at SLAC National Accelerator Laboratory. Figure from [38]. can be produced and detected at other types of experiments, e.g. hadron collider experiments such as LHCb [39, 40], but the large number of collisions per bunch crossing and the abundance of other particles created in high-energy hadronic decays mean the environment is considerably less clean than at a B factory.

One of the primary design goals of PEP-II and the BABAR experiment was the observation and study of CP-violation in B decays, which lead to the choice of asymmetric beam energies. Had the LER and HER used the same energy, the BB pair descended from the Υ(4S) would have been created almost at rest in the lab frame and, given the short lifetime of the B [9], the separation of the B decay vertices would have been too small to measure. By using asymmetric energies, the BB pair was created in motion in the lab frame, meaning the B mesons travelled further before decaying thus making the distance between the BB decay vertices sufficiently large to be measured. This in turn permitted study ofthetime

26 dependence of B0 and B0 decay rates, and thus of CP violation.

3.2 The BABAR detector

This section is based on the the description of the BABAR detector and its upgrades which can be found in Refs [6, 7], except where otherwise noted.

The BABAR detector comprises multiple sub-detectors arranged around the interaction region and the PEP-II beam pipe: the silicon vertex tracker (SVT), which measures trajectories of charged particles; the drift chamber (DCH), which measures momentum of charged particles; the detector of internally-reflected Cherenkov light (DIRC), which helps distinguish between pions and kaons; the electromagnetic calorimeter (EMC), which measures electromagnetic showers; and the instrumented flux return (IFR), which helps detect muons and neutral hadrons.

Cross-sectional diagrams showing the arrangement of the sub-detectors are shown in Figure 3.2.1. A more detailed description of each sub-detector follows.

3.2.1 Silicon vertex tracker (SVT)

The SVT measures charged particle positions and angles from which we can infer their trajectories, immediately outside the PEP-II beam pipe, near the interaction region, and at a larger radius immediately inside the DCH. Together with the DCH, it constitutes BABAR’s charged particle tracking system. In addition to allowing us to measure charged particle momenta, charged particle tracking is vital as it allows us to reconstruct decay vertices of short-lived mesons such as the B meson. Particle tracking information from the SVT and DCH is also extrapolated and used to inform measurements in outer sub-detectors.

27 B. Aubert et al. / Nuclear Instruments and Methods in Physics Research A 479 (2002) 1–116 13

Detector C L Instrumented Flux Return (IFR)) 04mScale I.P. Barrel Superconducting BABAR Coordinate System Coil y 1015 1749 x 1149 1149 Electromagnetic Cryogenic 4050 Calorimeter (EMC) z Chimney 370 Drift Chamber (DCH) Cherenkov Detector Silicon Vertex (DIRC) Tracker (SVT)

IFR Magnetic Shield 1225 Endcap for DIRC Forward 3045 End Plug Bucking Coil 1375 Support Tube 810 e– e+

Q4 Q2

Q1 3500 B1

Floor

Fig. 1.(a) BAB LongitudinalAR detector longitudinal view. section. of either the tracking system or the calorimeter material that a high energy particle traverses itself. The forward and backward acceptance before it reaches the first active element of a of the tracking system are constrained by compo- specific detector system. nents of PEP-II, a pair of dipole magnets (B1) followed by a pair of quadrupole magnets (Q1). The vertex detector and these magnets are 2.1. Detector components placed inside a support tube (4:5 m long and 0:217 m inner diameter) that is cantilevered from An overview of the coverage, the segmentation, beamline supports. The central section of this tube and performance of the BABAR detector systems is fabricated from a carbon–fiber composite. is presented in Table 1. Since the average momentum of charged parti- The charged particle tracking system is made of cles produced in B-meson decay is less than two components, the silicon vertex tracker (SVT) 1 GeV=c; the precision of the measured track and the drift chamber (DCH). parameters is heavily influenced by multiple The SVT has been designed to measure angles Coulomb scattering. Similarly, the detection effi- and positions of charged particles just outside the ciency and energy resolution of low energy beam pipe. The SVT is composed of five layers of photons are severely impacted by material in front double-sided silicon strip detectors that are of the calorimeter. Thus, special care has been assembled from modules with readout at each taken to keep material in the active volume of the end, thus reducing the inactive material in the detector to a minimum. Fig. 3 shows the distribu- acceptance volume. The inner three layers primar- tion of material in the various detector systems in ily provide position and angle information for the units of radiation lengths. Each curve indicates the measurement of the vertex position. They are

(b) Transverse view.

Figure 3.2.1: Cross sections of the BABAR detector. Figures from [6].

28 The SVT comprises five layers of double-sided silicon strip sensors arranged in modules around the beam pipe, with radii between 32 mm and 144 mm. Modules at either end of the outer layers are angled towards the interactionB. Aubert et region al. / Nuclear in an Instruments arch shape and in Methods order to in Physicsmaximise Research A 479 (2002) 1–116 35 coverage, with the sensitive areas of the SVT providing polar angular coverage580 mm of 20° to 150° Space Frame in the lab frame. Modules also overlap slightly in order to ensure full azimuthal coverage. Bkwd.

A diagram of theB. layout Aubert et of al. /the Nuclearsupport SVT Instruments strips and is Methods shown in Physics in Figure Research 3.2.2. A 479 (2002) 1–116 35 cone 520 mrad580 mm 350 mrad Space Frame Fwd. support cone Bkwd. e- Front end + support e cone electronics 520 mrad 350 mrad Fwd.Beam support Pipe cone e- Front end e + Fig. 17. Schematic view of SVT:electronics longitudinal section. The roman numerals label the six diﬀerent types of sensors.

Beam Pipe Fig. 17. Schematic view of SVT: longitudinal(a) Longitudinal section. The roman view. numerals label the six diﬀerent types of sensors. Beam Pipe 27.8mm radius

Beam Pipe 27.8mm radius Layer 5a Layer 5a Layer 5b Layer 5b

Layer 4b Layer 4b

Layer 4a Layer 4a

Layer 3 Layer 2 Layer 3

Layer 1 Layer 2

Layer 1 Fig. 18. Schematic view of SVT: tranverse section.

in such a way as to allow for relative motion of the two B1 magnets while ﬁxingFig. the position18. Schematic of the(b) SVT viewRadial of SVT:view. tranverse section. relative to the forward B1 and the orientation relative to theFigure axis of both 3.2.2: B1Cross dipoles. sections The support of the BABAR SVT. Figures from [6]. tube structure is mountedin such on the a PEP-II way as accelerator to allow for relative motion of the supports, independentlytwo of B1 BA magnetsBAR, allowing while for ﬁxingFig. the 19. position Photograph of an the SVT SVT arch module in an assembly jig. movement between the SVT and the rest of TheB SVTABAR is. Precise a solid monitoring staterelative (semiconductor) of to the the beam forward interac- charged B15.4. andparticle SVT components the detector orientation [9] comprising double- tion point is necessary,relative as is described to the in Sectionaxis of 5.5. both B1 dipoles. The support sided silicon strip sensors which form2 p-n junctions. Strips on opposite sides of each sensor The total active silicontube area structure is 0:96 mis mountedand the on theA block PEP-II diagram accelerator of SVT components is shown material traversed by particles is B4% of a in Fig. 20. The basic components ofFig. the detector 19. Photograph of an SVT arch module in an assembly jig. radiation length (seesupports, Section 2). independently The geometrical ofare BA theBAR silicon, allowing sensors, the forfanout circuits, the acceptance of SVT ismovement 90% of the solid between angle in the the29 SVTFront End and Electronics the rest(FEE) of and the data trans- c.m. system, typicallyBA 86%BAR are. usedPrecise in charged monitoringmission of the system. beam Each interac- of these components5.4. SVT is components particle tracking. tion point is necessary, as isdiscussed described below. in Section 5.5. The total active silicon area is 0:96 m2 and the A block diagram of SVT components is shown material traversed by particles is B4% of a in Fig. 20. The basic components of the detector radiation length (see Section 2). The geometrical are the silicon sensors, the fanout circuits, the acceptance of SVT is 90% of the solid angle in the Front End Electronics (FEE) and the data trans- c.m. system, typically 86% are used in charged mission system. Each of these components is particle tracking. discussed below. are orthogonal in order to provide two-dimensional track measurements. When a charged particle passes through the SVT, it imparts energy via ionisation of the semiconductor material, reducing the junction potential and resulting in current creating the signal from which the location at which the charged track hit the strip can be calculated.

Furthermore, the energy loss rate, dE/dx, as a particle traverses the SVT can also be calculated. Combined with dE/dx measurements from the drift chamber, this information can be used to identify what types of charged particles are traversing the detector.

The SVT provides a resolution of 10-15 µm in the inner three layers and 40 µm in the outer two layers, and has a total of approximately 150,000 readout channels. The SVT constitutes ∼ 4% of a radiation length to a charged particle travelling at a right-angle to the beam-line, perpendicular to the z axis, and provides 90% solid angle coverage.

3.2.2 Drift chamber (DCH)

The drift chamber (DCH) forms the second part of BABAR’s charged particle tracking system, together with the SVT. It’s main purposes are, in concert with the SVT, to provide particle identification capability through dE/dx measurements and to provide tracking capability for particle decay reconstruction through trajectory and momentum measurements. Fur-

0 thermore, longer-lived particles (e.g. KS ) can decay outside the SVT, so in these instances the DCH alone must provide sufficiently high-resolution track position measurements for decay vertex reconstruction.

Particle identification capability is provided by measuring energy loss rates, dE/dx, in both the SVT and DCH. Since different particles have different energy loss rates at a givenmo- mentum, as expressed in the Bethe formula [9], this information can be combined with momentum measurements to identify the charged particles passing through the SVT, as shown in Figure 3.2.3.

30 Figure 3.2.3: Energy loss rates (dE/dx) of charged particles in the BABAR drift chamber. Solid lines show predictions from the Bethe formula, dots show real BABAR data. Figure from [6].

The DCH is a gas-filled drift chamber [9]. When charged particles traverse a drift chamber they ionise the gas molecules. Thanks to an applied electric field, these ions will drift towards a charged “sense” wire, causing further ionisations as they travel and creating an “avalanche” of ions. Once the avalanche of ions reaches the sense wires it creates an electronic signal, and by measuring which sense wires send signals and at what times those signals arrive, it is possible to reconstruct the particle’s trajectory through the DCH. Furthermore, the size of the avalanche (and thus the signal) is proportional to the energy lost by the particle in the original ionisation event. By taking data from multiple sense wires we can thus calculate the particle’s energy loss rate as it traverses the drift chamber, which can be used for particle identification.

The BABAR DCH is a hollow cylinder, with its inner radius close to the SVT, while the outer radius is close to the DIRC, in order to facilitate track matching between sub-detectors. The

31 DCH is filled with an 80:20 mix of helium:isobutane, chosen for its long radiation length and good spatial and dE/dx resolution. It is 3 m long and is divided radially into 40 layers of hexagonal cells, with readout electronics in the backward endplate. Each cell comprises a sense wire in the centre kept at ∼ 1900 V, which is surrounded by field wires which are grounded. The cells and wires extend axially, approximately parallel to the beamline.

Cells are further grouped into ten “superlayers”; cells on the edges of superlayers are bordered by guard wires, which help alleviate boundary effects and match the performance of boundary cells to those in the interior. Meanwhile, cells on the inner and outer edges of the DCH are bordered by clearing wires which sweep away charges produced from interactions with the DCH walls.

Longitudinal position information is obtained thanks to 24 of the 40 layers having their sense wires at small angles to the z-axis. Alternating layers are also staggered by half a cell to increase directional resolution and resolve left-right ambiguity.

There are a total of 7,104 cells, each approximately 11.9 mm by 19.0 mm in size in the radial and azimuthal directions respectively. A cross-section of four superlayers is shown in Figure 3.2.4.

Radial-azimuthal directional information is enhanced by performing a fit to the particle’s trajectory through the drift chamber which allows us to estimate the distance of closest approach to the sense wire in each cell. The DCH provides position resolution of 0.1 - 0.4 mm, depending on how close the particle passes to the sense wire, and dE/dx resolution of approximately 7.5%.

32 48 B. Aubert et al. / Nuclear Instruments and Methods in Physics Research A 479 (2002) 1–116

Table 9 The DCH superlayer (SL) structure, specifying the number of cells per layer, radius of the innermost sense wire layer, the cell widths, and wire stereo angles, which vary over the four layers in a superlayer as indicateda

SL # of cells Radius (mm) Width (mm) Angle (mrad)

1 96 260.4 17.0–19.4 0 2 112 312.4 17.5–19.5 45–50 3 128 363.4 17.8–19.6 Àð52257Þ 4 144 422.7 18.4–20.0 0 5 176 476.6 16.9–18.2 56–60 6 192 526.1 17.2–18.3 Àð63257Þ 7 208 585.4 17.7–18.8 0 8 224 636.7 17.8–18.8 65–69 9 240 688.0 18.0–18.9 Àð72276Þ 10 256 747.2 18.3–19.2 0

a The radii and widths are speciﬁed at the mid-length of the chamber.

Table 10 DCH wire speciﬁcations (all wires are gold plated)

Type Material Diameter (mm) Voltage (V) Tension (g) Sense W–Re 20 1960 30 Field Al 120 0 155 Guard Al 80 340 74 Clearing Al 120 825 155

Figure 3.2.4: Cross section of drift chamber cells in the four innermost superlayers, plus interior wall. “Stereo” refers to the angle, in mrad, of the sense wires in that layer. Lines demarcatingtensile yield cell strength of the aluminum wire. For boundaries are for visualisationFig. 31. Schematic purposes layout only. of Figure drift cells from for [6]. the four innermost cells at the inner or outer boundary of a super- superlayers. Lines have been added between field wires to aid in layer, two guard wires are added to improve the visualization of the cell boundaries. The numbers on the right side give the stereo angles (mrad) of sense wires in each layer. electrostatic performance of the cell and to match The 1 mm-thick beryllium inner wall is shown inside of the first the gain of the boundary cells to those of the cells layer. in the inner layers. At the innermost boundary of layer 1 and the outermost boundary of layer 40, two clearing wires have been added per cell to aluminum field wires have matching gravitational collect charges created through photon conver- sag and are tensioned well33 below the elastic limit. sions in the material of the walls. A simulation of the electrostatic forces shows that the cell configuration has no instability problems. At the nominal operating voltage of 1960 V; the 6.3.3. Drift isochrones wires deflect by less then 60 mm: The calculated isochrones and drift paths for The field wires35 are tensioned with 155 g to ions in adjacent cells of layer 3 and 4 of an axial match the gravitational sag of the sense wires to superlayer are presented in Fig. 32. The isochrones within 20 mm: This tension is less than one-half the are circular near the sense wires, but deviate greatly from circles near the field wires. Ions 35 California Fine Wire, Grover Beach, CA, USA. originating in the gap between superlayers are 3.2.3 Detector of internally-reflected Cherenkov light (DIRC)

The DIRC, a type of ring imaging Cherenkov detector [9], is a unique and novel detector whose primary purpose is discrimination between kaons and pions at high momenta (kaon-pion discrimination below 700 MeV/c was done by the SVT and DCH). Kaon-pion discrimination is a vital task because many B decay modes produce kaons and pions, so by identifying them we can correctly reconstruct, and determine the flavour of, the ancestor B mesons.

The DIRC takes advantage of Cherenkov radiation in order to identify particles. When a charged particle passes through a medium at greater than the local speed of light (which is possible in media with a refractive index greater than 1.0), it emits Cherenkov radiation [9]. Cherenkov radiation is emitted at an angle from the particle’s trajectory that depends on the particle’s velocity and the refractive index of the medium. By measuring the angle of the emitted Cherenkov radiation, and with knowledge of the particle’s momentum from the inner tracking sub-detectors, the particle’s mass, and thus identity, can be deduced.

The DIRC comprises a 12-sided barrel of 144 fused silica bars surrounding the central region of the BABAR detector. Each “side” of the barrel comprises a box filled with 12 bars, each bar being 17 mm thick, 35 mm wide and 4.9 m long. The total width of the DIRC in the radial direction in the central region of the BABAR detector is 80 mm. When charged particles pass through the DIRC bars they emit Cherenkov radiation, as described above. Fused silica was chosen due to its resistance to ionising radiation, long attenuation length, and large index of refraction (n = 1.473). Bars within a box are optically isolated by a small air gap.

Cherenkov radiation emitted inside the bars is totally internally reflected along the sides of the bar, with the aim of channeling the light to the backward end of the bar where it exits. The forward end of the bar is coated in a mirror finish so that any light that reaches the forward end is reflected and sent towards the backward end of the bar.

34 Light finally exits the fused silica into a “standoff box” filledwith ∼ 6, 000 litres of purified water, chosen for it’s low cost and similar index of refraction to fused silica, the far inner surface of which is covered in photomultiplier tubes (PMTs).

The interface between the silica bars and the standoff box is a further piece of fused silica of a trapezoidal wedge shape, 91 mm long. Any light that exits a bar at a large angle relative to the bar axis will be reflected off the angled part of the wedge, thus reducing the required photon detection surface in the standoff box and preventing photons being lost to total internal reflection at the boundary between the silica of the bars and the water which fills the standoff box.

Diagrams of the DIRC setup are shown in Figure 3.2.5.

PMTs are light detectors, commonly used in particle physics, which detect and amplify signals from received photons by taking advantage of the photoelectric effect [9]. The standoff box contains a total of 10,751 PMTs, which are approximately 1.2 m from the ends of the bars, each of which is surrounded by a reflective cone in order to maximise the light collection area. The shape and timing of the Cherenkov light cone received at the PMTs is used to calculate the Cherenkov angle of the original radiation event inside the DIRC bars.

The DIRC provides kaon-pion separation of 4.2 σ at a momentum of 3 GeV/c and constituted approximately 17% of a radiation length at normal incidence.

3.2.4 Electromagnetic calorimeter (EMC)

The electromagnetic calorimeter (EMC) is designed to measure the energy and angular position of electromagnetic showers, which are produced by photons and electrons, in the range 20 MeV to 9 GeV. Photon detection is particularly important for the reconstruction of neutral particles that decay to photons (e.g. neutral pions), while electron detection and

35 (a) Longitudinal cross-section of a DIRC bar and standoff box showing total internal reflection of Cherenkov radiation inside the bar and into the standoff box.

(b) 3D view of the DIRC in context. The DIRC bars are held inside bar boxes which form a 12-sided barrel aligned with the beam axis. Cherenkov radiation is emitted into the water-filled standoff box, the inner surface of which is covered in photomultiplier tubes.

Figure 3.2.5: BABAR’s detector of internally-reflected Cherenkov light (DIRC). Figures from [6].

36 identification contributes to B meson flavour tagging.

The EMC takes advantage of electromagnetic showers [9] to measure the energy of photons and electrons. When a high-energy photon enters the calorimeter medium it loses energy primarily by pair production: γ → e+e−. Meanwhile, high-energy electrons in the calorimeter medium (both those created during pair production, and those from other sources) lose energy primarily by Bremsstrahlung: e− → e−γ. For both pair production and Bremsstrahlung a massive nearby nucleus is required to conserve momentum, hence why the processes occur once inside the calorimeter medium but not before. We see that one process can “feed” the other - a photon undergoes pair production and produces an electron and a positron, the electron and positron undergo Bremsstrahlung and produce new photons, the new photons undergo pair production, and so on. As long as the newly-produced electrons/photons have sufficient energy, this process will continue and create a chain reaction, usually referred toas an electromagnetic “shower” or “cascade”. At each stage some energy is lost, and eventually the electrons and photons will enter a low energy regime where energy loss via ionisation and excitation of the calorimeter medium comes to dominate. Ultimately, in a total absorption calorimeter, all the energy of the original photon/electron will be absorbed by the calorimeter medium.

Scintillating materials are often used as calorimeter media, that is, materials that absorb energy via excitation then re-emit the energy in the form of light. Since the light yield from the scintillator is proportional to the energy absorbed, the light emitted by the scintillator can be collected and used to calculate the energy of the original photon/electron that entered the calorimeter.

BABAR’s EMC is a homogeneous, total absorption calorimeter [9], made from scintillating crystals. This means that the entire volume is both an active signal-generator and an absorber, and that it is designed to absorb all the energy of photons and electrons that strike

37 it. Such a design offers the best resolution when measuring the energy of electromagnetic showers.

The crystals in BABAR’s EMC are thallium-doped caesium-iodide (CsI(Tl)). CsI(Tl) offers good energy resolution, a short radiation length and also a small Molière radius which leads to high angular resolution. While pure CsI crystals can be used as a scintillating calorimeter medium, Thallium doping provides an increased light output and the emission wavelength is also better matched to typical photodiode sensitivity [9].

The EMC comprises 6,580 crystals arranged in a hollow cylinder co-linear with the beam axis (5,760 crystals) and in a forward “endcap” (820 crystals), as shown in Figure 3.2.6. There is no backward endcap due to the energy asymmetry of PEP-II, which causes particles produced in collisions to preferentially move in the forward direction. With the barrel and forward endcap, the EMC achieves 90% solid angle coverage in the CM frame.

Figure 3.2.6: Longitudinal cross-section of the top half of the BABAR electromagnetic calorimeter (EMC), showing crystals in the barrel and endcap sections. Figure from [6].

The crystals are trapezoidal, with exact crystal geometry varying along the length of the EMC in order to achieve hermetic coverage. Typically, crystals are approximately 30 cm long, which equates to approximately 16-17 radiation lengths, and have a frontage of 4.7 x 4.7 cm2 and a back face of 6.1 x 6.0 cm2. Light output from the crystals is detected by

38 photodiodes attached to the back face. In order to collect as much light as possible, the crystals are wrapped in a reflective cover in order to maximise reflection of light to theback face of the crystal. A diagram of a single crystal is shown in Figure 3.2.7.

Figure 3.2.7: Diagram of a single calorimeter crystal and associated hardware (not to scale). Figure from [6].

The BABAR EMC achieved an energy resolution from σ(E)/E = (5.0 0.8)%, measured at 6.13 MeV, rising to σ(E)/E = (1.90.07)%, measured at 7.5 GeV; and an angular resolution from 12 mrad at ∼ 100 MeV rising to 3 mrad at ∼ 3 GeV. The reconstructed neutral pion mass of 135.1 MeV varied by less than 1% over the full range of photon energies. Electron ID, which also took advantage of information from the DCH and DIRC, achieved efficiencies of up to 94.8% and a pion mis-ID rate as low as 0.3% at the “tight” level, commonly used in analyses.

39 3.2.5 Instrumented flux return (IFR)

The Instrumented Flux Return (IFR) used the steel flux return of BABAR’s superconducting magnet as an absorber and detector of muons and long-lived neutral hadrons (principally

0 KL mesons and neutrons). Identification of muons and neutral hadrons is important for reconstruction and flavour-tagging of many B meson decay modes, as well as reconstruction of some common intermediate decay products, for example the J/ψ .

The detection capability of the IFR was originally based around resistive plate chambers (RPCs) [9]. An RPC is effectively a planar capacitor where the gap between the electrodes is filled with gas. When a charged particle traverses the gas it causes ionisation ofthe gas molecules and the electric field generated by the electrodes induces further ionisations, which in turn create an “avalanche” of yet more ionisations (in the case of a neutral particle,

0 e.g. a KL, secondary charged particles are produced by the primary neutral particle through interactions with nuclei in the detector material, these interactions produce hadronic showers - a cascade of various charged and neutral particles - which can then be detected). The avalanche eventually makes contact with the electrodes, creating a signal. Due to ageing effects, many of the IFR’s RPCs were later replaced with limited streamer tubes (LSTs) [41]. LSTs have a similar principle of operation, but rather than being a planar capacitor they comprise a central wire anode surrounded by tube- or box-shaped cathode.

The BABAR IFR was embedded in the steel flux return of BABAR’s magnet. The steel was segmented into layers in both the barrel and endcap sections, with RPCs (later LSTs in the barrel) placed between the layers, as shown in Figure 3.2.8. The IFR originally comprised 806 RPCs, although the total number of detectors (RPCs plus LSTs) was later reduced as part of the IFR upgrade.

The IFR RPCs used 2 mm thick bakelite sheets as electrodes, with a resistivity of 1011 − 1012 Ωcm, separated by a 2 mm gap, with one grounded and one held at a ∼ 8 kV potential.

40 Figure 3.2.8: Barrel and endcap sections of the Instrumented Flux Return at BABAR after upgrade. Shown are the six barrel sextants (Sxt) filled with limited streamer tubes (LSTs) and the forward (FW) and backward (BW) endcaps filled with resistive plate chambers (RPCs). Dimensions inmm. Figure from [7].

The gap between the electrodes was filled with a mixture of argon, freon and isobutane. Readout strips were attached to the outside surface of the electrodes and oriented in different directions on either side of the RPC in order to provide 2D positional information in z and ϕ; RPCs in the endcaps likewise had horizontal and vertical readout strips.

The LSTs, introduced in the barrel region of the IFR to replace aged RPCs, comprised anode wires running parallel to the beam in a honeycomb-like structure of long square cells, the walls of which were cathodes. The cells were gastight and were filled with a mixture of carbon-dioxide, isobutane and argon. Signals from avalanches on the anode wires provided ϕ position information while readout strips on the cell walls oriented orthogonal to the anode wire provided z position information.

Muon ID using the IFR was informed by charged particle tracking information from the SVT and DCH - tracks in the inner detectors were extrapolated outwards and associated with hits in the IFR’s RPCs - as well as energy loss measurements from the EMC. Muon ID efficiency was just under 90% in the momentum range 1.5/ -3.0GeV c, with a pion fake rate

41 of approximately 6 - 8%.

The presence of neutral hadrons, meanwhile, could be detected in the form of IFR hits not associated with (extrapolated) charged tracks, but which were associated with showers in

0 the EMC. KL detection efficiency was approximately 20 - 40% in the momentum range1- 4 GeV/c.

42 Chapter 4

The Belle II experiment

The Belle II experiment is located at KEK High Energy Accelerator Research Organization and the full detector is due to start collecting data in 2019 [42], with e+e− collisions provided by the SuperKEKB accelerator. This chapter presents a summary of SuperKEKB and Belle II.

4.1 The SuperKEKB accelerator

This section is based on the description of SuperKEKB which can be found in Refs [43, 44] except where otherwise noted.

SuperKEKB is an upgrade of the KEKB [45, 46] accelerator. Its design luminosity is 8 × 1035 cm−2 s−1, approximately 66 times higher than the peak luminosity reached by PEP- II [7]. Expected to run from 2019 until the mid-2020s [42], SuperKEKB aims to deliver an integrated luminosity of 50 ab−1, approximately 100 times that delivered by PEP-II. A projection of integrated luminosity to be delivered by SuperKEKB is shown in Figure 4.1.1.

43 Figure 4.1.1: Luminosity projections for SuperKEKB. The small amount of luminosity delivered before 2019 is from accelerator testing and commissioning. Figure from [42].

Like PEP-II, SuperKEKB is a e+e− accelerator and collider. Electrons and positrons are first accelerated in a linear accelerator and then injected into SuperKEKB’s twostorage rings: the Low Energy Ring (LER), through which positrons circulate at an energy of 4 GeV, and the High Energy Ring (HER), through which electrons circulate at an energy of 7 GeV. The rings are of equal size and lie in a tunnel approximately 3 km in length . The rings run side-by-side for most of their length, crossing inside the Belle II detector and at a point at the opposite side of the accelerator complex. A diagram of the SuperKEKB setup is shown in Figure 4.1.2.

As at PEP-II, the collision energy of the e+e− pair will, for most of SuperKEKB’s lifetime, be tuned to 10.58 GeV in the centre-of-mass frame to produce B mesons via e+e− → Υ(4S) → BB.

The much larger (integrated) luminosity at SuperKEKB compared to PEP-II will obviously lead to a much larger sample of B mesons. This will allow Belle II, compared to predecessor

B factories such as BABAR and Belle [47, 48], to perform searches for new physics with

44 Figure 4.1.2: Illustration of SuperKEKB and Belle II at KEK High Energy Accelerator Research Organization. The straight sections of the storage rings are named after the local geography, Belle II is in the “Tsukuba” section. Figure from [43]. greater sensitivity and also to improve the precision of existing measurements of Standard Model quantities. Primary targets for Belle II measurements include [42]: searches for CP violation in decays of B mesons via b → s and b → d modes, searches for non-SM Higgs- like particles in decays of τ leptons produced in B meson decays, searches for beyond-SM flavour-changing-neutral-currents through measurements of B meson decays in b → s and b → d modes (e.g. B−→ Λpνν decays), precision measurements of SM quantities such as the CKM matrix elements, and dark matter searches in decays with missing energy. At the time of writing there are also several B meson decays modes which show discrepancies with SM predictions, including the ratio of the branching fractions of B → K+µ+µ− and B → K+e+e− [49], and the ratio of the branching fractions of B → D(∗)τν and B → D(∗)e−ν [50, 51, 52, 53]. These quantities are currently approximately 2.6σ and 4σ [54] respectively away from SM predictions - not significant enough to constitute a detection of non-SM physics but sufficiently large to be worth serious further investigation with larger datasets at more modern experiments, such as Belle II.

45 In order to achieve the much higher luminosity required to obtain the desired Belle II dataset, SuperKEKB relies primarily on two key differences compared to PEP-II: higher beam currents and smaller beam sizes. With an increased number of electrons and positrons flowing through the interaction point (higher current) and by focussing those electrons/positrons into a smaller area (smaller beam sizes), the rate of collisions (luminosity) is increased. Table 4.1 shows a comparison of the key differences between SuperKEKB and PEP-II.

Table 4.1: Comparison of PEP-II [7, 37] and SuperKEKB [43], with beam energies for Υ(4S) running.

PEP-II PEP-II SuperKEKB (design) (best) (design) Beam energy (HER, LER) (GeV) 9.0, 3.1 7, 4 Beam current (HER, LER) (A) 0.75, 2.15 2.07, 3.21 2.60, 3.60 Horizontal beam size (HER, LER) (µm) 155, 155 10.7, 10.1 Vertical beam size (HER, LER) (µm) 6.2, 6.2 0.062, 0.048 Luminosity (1034 cm−2 s−1) 0.3 1.2 80

We note that even though PEP-II exceeded its design luminosity by a factor of four, its peak luminosity is only a small fraction of that targeted by SuperKEKB.

The most significant advantage SuperKEKB holds over PEP-II is its smaller beam sizes which, thanks to the nanometre-scale vertical beam size, are known as “nanobeams”. While the nanobeams allow for much higher luminosity, the high density of electrons and positrons in the beams causes an increase in intra-beam scattering and Touschek scattering [8], which lead to a reduction in luminosity and beam lifetime. These can be counteracted by increasing the energy of the LER, hence why SuperKEKB has more symmetric beam energies than PEP- II (4 GeV and 7 GeV versus 3.1 GeV and 9.0 GeV). The more symmetric beam energies have the additional advantage that events are less forward-biased (that is, more isotropically distributed) in the lab frame which leads to better detector acceptance since detectors usually have (near) hermetic coverage in their central regions but non-hermetic coverage in the extreme forward and backward directions [8]. The disadvantage of more symmetric beam

46 energies is that the separation between B mesons in a BB pair is smaller because the CM system is moving more slowly in the lab frame; however, this can be compensated for with sufficiently high-resolution vertexing sub-detectors [8].

4.2 The Belle II detector

This section is based on the description of the Belle II detector which can be found in Refs [8, 42] except where otherwise noted.

Like BABAR, the Belle-II detector comprises multiple sub-detectors arranged around the interaction region of the SuperKEKB beam pipe: the pixel detector (PXD) and silicon vertex detector (SVD), which both measure the trajectories of charged particles; the central drift chamber (CDC), which measures the trajectories, momenta and energy loss rates of charged particles; the time-of-propagation chamber (TOP) and aerogel ring-imaging Cherenkov detector (ARICH), which provide particle identification capability in the barrel and forward endcap region respectively; the electromagnetic calorimeter (ECL), which measures electro-

0 magnetic showers; and the K-long and muon detector (KLM), which detects KL mesons and muons. Immediately outside the ECL is a superconducting solenoid magnet, the magnetic field of which bends the trajectories of charged particles thus enabling momentum measurements; the flux return of the solenoid hosts the KLM.

A cross-sectional diagram showing the arrangement of the sub-detectors is shown in Figure 4.2.1. A more detailed description of each sub-detector follows.

4.2.1 Pixel detector (PXD)

The PXD together with the SVD forms the inner tracking detector of Belle II, together known as the vertex detector (VXD). As the name implies, the purpose of the VXD is

47 Figure 4.2.1: Cross-section of the Belle II detector. Figure from [42].

48 reconstruction of decay vertices by using positional information from the PXD and SVD, both of which measure the trajectories of charged particles that pass through them. The PXD and SVD are also solely responsible for tracking of low-momentum (∼tens of MeV/c) charged particles that do not escape the VXD.

The PXD is a silicon-based semiconductor detector which uses depleted field effect transistor (DEPFET) technology [55]. The principle of operation is similar to other semiconductor- based charged particle detectors, such as the BABAR SVT (see Section 3.2.1). DEPFET was chosen for Belle II due to the fact that it can be manufactured very thin (75 µm in the case of Belle II), which reduces multiple scatterings of charged particles inside the detector medium thus preserving vertex resolution, which is essential given the lower beam energy asymmetry in SuperKEKB and thus smaller separation between BB pairs compared to PEP- II. It is also radiation hard, a necessary quality given the high-radiation environment near the SuperKEKB beamline.

There are two PXD layers, each divided into 12 modules, surrounding the beampipe in a barrel shape, at radii of 14 mm and 22 mm, providing detection capability at considerably smaller radii than the BABAR SVT which has a minimum radius of 34 mm. The small radii of PXD layers helps compensate for the smaller separation of BB vertices in Belle II caused by the more symmetric beam energies.

Neighbouring layers overlap slightly to ensure near 100% azimuthal coverage, and the sensitive length of the PXD layers ensures angular coverage from 17° to 150°, slightly better than the 20° - 150° degree coverage of the BABAR SVT. The asymmetry in forward-backward coverage is to account for the forward-bias of events in Belle II caused by the asymmetric beam energies. An illustration of the PXD structure is shown in Figure 4.2.2.

Another key difference between the Belle II PXD and the BABAR SVT is that, while the

BABAR SVT is arranged in strips, the Belle II PXD is segmented into square or rectangular

49 Figure 4.2.2: Belle II pixel detector (PXD). Light grey regions represent sensitive pixel detector areas. Figure from [8]. pixels. By using more output channels (i.e. more pixels than there would be strips if it were a strip detector), the occupancy (the fraction of channels triggered per event) is reduced. The occupancy of a conventional strip detector at the luminosities delivered by Belle II would be so high as to make B vertex reconstruction impossible. While the five-layer BABAR SVT provides a total of 150,000 readout channels, the Belle2 PXD provides 10 million readout channels.

The PXD provides a spatial resolution of 10 µm, comparable to or slightly better than that provided by the inner layers of BABAR SVT’s of 10 - 15 µm. Thanks to the thinness enabled by the use of DEPFET technology, each PXD layer represents only 0.19% of a radition length, which compares favourably with the approximately 4% of a radiation length constituted by the five-layer BABAR SVT.

4.2.2 Silicon vertex detector (SVD)

The SVD forms the second part of the vertex detector (VXD), together with the PXD. Along with the PXD, the SVD records trajectories of charged particles for use in vertex

50 reconstruction. The PXD and SVD are solely responsible for tracking of low-momentum (∼tens of MeV/c) charged particles that do not escape the VXD, additionally, the SVD

0 alone is responsible for vertexing of KS mesons that decay outside the PXD.

The SVD is a double-sided silicon strip detector which operates on the same principle as the

BABAR SVT (see Section 3.2.1 and Figure 4.2.4). It comprises four layers of strips, arranged around the PXD in a barrel shape, at radii of 38 mm - 140 mm, covering the maximum possible radial range between the interior PXD and exterior CDC, allowing data from the SVD to be used to extrapolate tracks all the way from the PXD to the CDC. An illustration of the setup is shown in Figure 4.2.3. The combined radial extent of the PXD and SVD of

14 mm - 140 mm is greater than that of the BABAR SVT (34 mm - 144 mm), which should lead to better resolution on reconstructed vertices and reconstruction of short-lived particles which decay inside the VXD.

Figure 4.2.3: Belle II vertex detector (VXD), comprising the pixel detector (PXD) surrounded by the silicon vertex detector (SVD) (cutaway). The slanted end sections in the forward portion of the three outermost layers of the SVD are visible. Figure from [56].

The SVD uses strips, rather than pixels as used in the PXD, in order to reduce the cost and complexity of the readout electronics - the SVD has a total of 245,000 channels in four layers compared to the 10 million channels in the two-layer PXD. High occupancy, which motivated the choice of pixels for the PXD, does not drive the same requirements for the SVD due to the greater radius of the SVD layers and the fact that radiation intensity drops

51 off with 1/r2, although it does motivate the choice of a much larger inner radius (38 mm) compared to the BaBar SVT (14 mm).

SVD strips on opposite sides of each layer are oriented orthogonally to provide 2D tracking capability - strips on the interior extend in the z directionCHAPTER and strips 5. on SILICON the exterior VERTEX extend DETECTOR (SVD) in the r − ϕ direction, as shown in Figure 4.2.4. SVD modules in the same layer overlap p-side strips, electrons moving towards the n-side induce image currents in the p-side strips. slightly to ensure azimuthal coverage, while those modules at the forward end of the outer Due to their higher mobility, the Hall angle and thus deﬂection of electrons is about three times three SVD layerslarger are than angled that inwards of holes. to ensure Consequently, sufficient the polar tilt of angle the sens coverageor plane while should keeping reduce the electron spread, at the cost of an increased hole spread (right half of Fig. 5.5). This conclusion has been the thicknessconﬁrmed of material by through a numerical which particles simulation must based travel on to Ramo’s a minimum. theorem.

n-side short strips along r-phi e- e- +HV h+ + h p-side long strips along z -HV Particle Particle from IP B||z from IP

Figure 4.2.4: BelleFigure II SVD 5.5: strip Sensor sensors, geometry showing and the orthogonal magnetic orientation field. Left: of the In inner the p andresence outer of a magnetic field, strips. A particleelectrons is illustrated and holes traversing are deflected the sensor by and the liberating Lorentz electrons force. Right and holes,:Theoverallchargespreadcanbe which drift towards the stripsminimized on either by side. a tilt The that signals reduces created the by electron the electrons deflection. and holes when they contact the strips allow us to determine the 2D position of the track. The electrons and holes are deflected by Belle II’s magnetic field, with the electrons spreading out more due to their greater mobility. Figure from [8]. The Origami chip-on-sensor concept (Sec. 5.3.1.1), which will be applied to all sensors except those located at the edge of the acceptance, uses pitch adapters bent around the sensor edge. The SVD providesThese angular bent fanout coverage pieces of 17°can to only 150°, be appliedmatching at that the outer of the side PXDsinawindmillstructure,asshown and slightly schematically in Fig. 5.6. Together with the readout direction, this unambiguously determines exceeding thatthe of the layoutBAB ofAR eachSVT. Origami The resolution, hybrid (Sec. measured 5.4.2). with 0.5 GeV muons, is approximately 2-5 µm in r − ϕ and 7-27 µm in z, depending on layer and angle of incidence. This compares favourably with the 40 µm resolution provided by the outer layers of the BABAR SVT. The SVD’s material constitutes 0.57% of a radiation length per layer, which also compares favourably with the total ∼ 4% of a radiation length constituted by the five-layer B||z BABAR SVT.

Figure 5.6: Schematic cross-section of a windmill structurewithOrigamimodules.Theﬂex pitch adapters, which are bent around the sensor edges, can only be placed on the outer edge of each sensor.

Further details on the mechanical layout and the cooling pipes attached to the Origami modules are provided in Sec. 5.3.

144 4.2.3 Central drift chamber (CDC)

The central drift chamber (CDC) provides track reconstruction capability by measuring the trajectories and momenta of charged particles, and provides PID capability by measuring the energy loss rates of charged particles that pass through it. For low-momentum particles which do not survive to be detected in the TOP and ARICH sub-detectors, the CDC alone is responsible for PID.

The Belle II CDC is a cylindrical, gas-filled drift chamber operating on a similar principle to the BABAR DCH (see Section 3.2.2). It is filled with a 50:50 mixture of helium and ethane, chosen for its high resolution in both position and energy loss, low radiation length, and proven performance in the Belle detector.

The CDC forms a cylinder around the VXD and has inner and outer radii of 160 mm and 1130 mm. The CDC volume is divided into 14,336 cells, approximately twice as many as the

BABAR DCH, each with a sense wire running through the middle and delineated by 42,240 field wires. The cells are grouped into nine “superlayers” each comprising six layers, except the innermost superlayer which comprises eight layers, for a total of 56 layers, as shown in Figure 4.2.5.

Figure 4.2.5: Belle II central drift chamber (CDC) sense wires. Visible are the eight outer superlayers, each comprising six layers, and the the inner superlayer comprising eight layers and which has smaller cells. Figure from [8].

The cells in the inner superlayer are smaller than those in the other layers (with a radial size of approximately 10 mm versus 18 mm) in order to cope with the high background and

53 event rates at Belle II, and in order to prevent occupancy becoming too high.

Like the BABAR DCH, the Belle II CDC uses wires at stereo angles to provide 3D measurement capability. Superlayers alternate between axial and stereo wire angles; the magnitude of the stereo angle is between approximately 45 and 74 mrad.

The CDC has a polar angle acceptance of 17° - 150°, matching that of the VXD. Position resolution is approximately 0.1 mm, competitive with the BABAR DCH’s position resolution of 0.1 - 0.4 mm, and the dE/dx resolution of approximately 8% - 12% (depending on angle of incidence) is comparable to the ∼ 7.5% resolution of the BABAR DCH.

4.2.4 Time-of-propagation counter (TOP)

The time-of-propagation counter (TOP) sub-detector is a Cherenkov detector designed to provide PID information in the barrel region of Belle II, particularly discrimination between pions and kaon. Its function is analogous to that of the DIRC in BABAR (see Section 3.2.3).

Like the BABAR DIRC, the Belle II TOP takes advantage of Cherenkov emissions by charged particles as they traverse the TOP detector material to identify particles. The TOP radiation medium comprises 16 quartz bars arranged around the Belle II barrel section in a barrel shape, as shown in Figure 4.2.6. Each bar is 2.6 m long, 45 cm wide and 2 cm thick.

The TOP relies on total internal reflection of Cherenkov photons to collect the light emitted by charged particles as they traverse the bars; in order to achieve this the bars have a mirror at one end and are highly-polished to ensure minimum loss - for a 100-bounce photon the setup achieves 97% reflectivity. The bars, however, do not overlap so azimuthal coverage is 93%. At the non-mirrored end of each bar are 32 PMTs, each with 16 readout channels for a total of 512 pixels on each of the 16 modules, with a pixel size of 5 mm [57]. The PMTs

54 Figure 4.2.6: Belle II time-of-propagation counter (TOP) (grey), surrounding the CDC (purple). Figure from [8]. provide x and y positional information for the detected photons. The PMTs additionally provide precise timing information, allowing the measurement of photon arrival time with a resolution better than 50 ps, where the photon arrival time is the time from the e+e− collision to the detection of the Cherenkov photons in the TOP detector [57].

For a given momentum, particles of different masses take different times to arrive atthe TOP; additionally they will produce photons at a different Cherenkov angle. Additionally, for a given trajectory through the TOP module, the Cherenkov photons they produce will have different path lengths (i.e. travel time) through the quartz bar and will be detectedby the PMTs at different positions, as shown in Figure 4.2.7.

Thus, by combining the timing and x − y position information, it is possible to discriminate between different particles, as shown in Figure 4.2.8. Specifically, the timingand position information from the PMTs is compared to probability density functions for various charged particles (e, µ, π, K, p) and a PID likelihood is calculated for each particle hypothesis [57].

The TOP provides polar coverage of 31° - 128° and a total of approximately 8,000 readout

55 Figure 4.2.7: Principle of operation of a Belle II TOP module, showing a charged particle traversing the module and emitting Cherenkov radiation. For a given momentum, the Cherenkov angle (and thus photon travel time and detection position) will be different. Figure from [8].

Figure 4.2.8: Particle identification at Belle II TOP. By plotting channel number (i.e. detection position of Cherenkov photons) versus photon arrival time, we can discriminate between different types of particles. Figure from [58].

56 channels. Kaon-pion separation of 4.3 σ is achieved for particles with momentum 4 GeV/c

[59], competitive with the BABAR DIRC which achieved 4.2 σ at 3 GeV/c.

4.2.5 Aerogel ring-imaging Cherenkov detector (ARICH)

The Aerogel ring-imaging Cherenkov detector (ARICH) provides PID capability in the forward end-cap region of Belle II, and is specifically aimed at providing kaon-pion separation.

Like the BABAR DIRC, ARICH uses Cherenkov ring images to provide PID capability. The radiation medium in the case of ARICH is a double layer of aerogel, each layer being 2 cm thick. On the outer side of the aerogel layers is a 20 cm long expansion area which provides volume for sufficiently large Cherenkov rings to form. On the far side of the expansion area is a wall of photon detectors which provide positional information and allow us to image Cherenkov rings.

In general, the thicker the radiation medium, the more Cherenkov photons produced and therefore the better ring image. However, increasing the thickness of the radiation medium degrades the resolution of the Cherenkov angle measurement because there is greater uncertainty in the origin of any given photon. In order to achieve a high photon yield without sacrificing detector effectiveness, Belle II uses a novel approach of a double-layer radiation medium. The two layers of aerogel in the ARICH have different refractive indices (1.055 and 1.065), meaning that Cherenkov photons are emitted at slightly different angles in the two layers. The double-layer of aerogel therefore acts as a primitive lens, focussing the photons emitted at different points onto the same area of the distant photon detection screen, as shown in Figure 4.2.9.

The two-layer focussing design of the ARICH motivates the choice of aerogel as a radiation medium because aerogel can be manufactured with a variety of refractive indices. Compared

57 Figure 4.2.9: Focussing effect of the ARICH aerogel layers. The different refractive indices(n1, n2) of the two aerogel layers focus photons emitted at different depths onto the detection screen on the right. Figure from [8]. to a single-layer aerogel design, the double-layer focussing design increases kaon PID efficiency by approximately 10-20% for kaons of momentum 4-5 GeV/c while pion mis-ID rate is kept constant at 1%.

The detection screen comprises 540 hybrid avalanche photon detectors (HAPDs), which are conventional PMTs combined with silicon sensors, providing both the high gain of a PMT with the positional resolution of a silicon detector [9]. The HAPDs provide a gain of ∼ 105 and detection is provided by 144 square pixels per HAPD, with pixel dimension of 4.9 mm. An example Cherenkov ring image is shown in Figure 4.2.10.

The ARICH provides single-photon angular resolution of approximately 14 - 17 mrad, which results in a Cherenkov angle resolution of 3.1 mrad. This in turn provides pion-kaon separation of 5.5 - 5.8σ at 4 GeV/c, as well as pion-electron separation of 4σ up to 1 GeV/c. The ARICH provides 14° - 30° polar coverage. The ARICH and TOP together provide Cherenkov-based PID capability for the barrel and forward end-cap regions of Belle II, whereas BABAR’s DIRC covered only the barrel region.

58 Figure 4.2.10: Cherenkov ring image in the ARICH from a cosmic muon. Figure from [42].

4.2.6 Electromagnetic calorimeter (ECL)

The electromagnetic calorimeter’s (ECL) primary purpose is to detect photons from neutral particle decays (e.g. π0 → γγ), including both their energy and position. Aproximately one third of products from B meson decays are neutral particles that ultimately decay to photons over a wide energy range, so high-resolution electromagnetic calorimetry is essential for a B

0 factory. The ECL also provides electron and, together with the KLM, KL ID capability.

The Belle II ECL operates on the same principle as the EMC in BABAR (see Section 3.2.4), including using the same type of scintillating crystal - thallium-doped caesium-iodide (CsI(Tl)).

The ECL comprises 8,736 crystals divided into three sections covering the backward end-cap, barrel and forward end-cap, as shown in Figure 4.2.11. The barrel section is 3 m long and extends from 1.25 m to 1.62 m in radius, while the backward and forward end-cap sections are positioned at -1.02 m and 1.96 m respectively. The ECL crystals have a face of approximately 6x6 cm with a depth of approximately 30 cm, equivalent to about 16 radiation lengths; they produce on average 5,000 photoelectrons of every MeV of deposited energy. On the rear of each crystal are two 10 mm x 20 mm photodiodes which produce detection signals.

CsI(Tl) was chosen for similar reasons to those at BABAR, namely good energy resolution,

59 Figure 4.2.11: Belle II electromagnetic calorimeter (ECL). Figure adapted from [60].

60 high light output and short radiation length. The added benefit in the case of Belle II was that the crystals and support structure used in the Belle calorimeter could be reused, significantly reducing the cost. The challenge is that Belle II has a much higher luminosity than Belle or BABAR which, combined with the relatively long decay time of CsI(Tl) crystals, can lead to a phenomenon known as “pile-up”, where signals from one event overlap with those from a subsequent event because the emission from the crystals does not have enough time to drop to zero before another particle enters the crystals and causes more scintillation. In order to counteract this, new, faster readout electronics are used in the Belle II ECL which incorporate waveform sampling, whereby the shape of potential signals are fit using timing information to ensure only signals that are in time with e+e− collision are kept. This is done in a shaping time of just 0.5 µs, half the ∼ 1µs scintillation decay time of CsI(Tl).

The ECL provides 90% solid angle coverage in the CM frame and polar coverage of 12.4° - 155.1°, with ∼ 1° gaps between end-cap and barrel section. For photons of energies 100 MeV and 8 GeV, expected energy resolution is 4% and 1.6% and angular resolution is 13 mrad and 3 mrad, respectively, competitive with the performance of the BABAR EMC.

4.2.7 K-long and muon detector (KLM)

0 As the name suggests, the K-long and muon detector’s (KLM) purpose is to detect KL mesons and muons.

Like the BABAR IFR (see Section 3.2.5), the KLM is embedded in the flux return of Belle II’s solenoid magnet, with the 4.7 cm thick iron plates of the flux return serving as a nucleus- rich shower-inducing medium. Layers of detectors are sandwiched between layers of iron plates of the magnetic flux return, with the barrel comprising 14 detection layers andthe

0 end-caps 12. KL mesons are identified based on clusters in the KLM and/or ECL which are not associated with a charged track originating from near the interaction point (IP), while

61 0 CHAPTER 10. KL AND µ DETECTION (KLM) muons are identified based on charged tracks extrapolated from the CDC through theKLM. The layout of the KLM is shown in Figure 4.2.12.

0 1 2 3 m

Magnet Yoke

Barrel KLM Backward Forward Nikko Endcap Endcap Oho KLM KLM Side Side Solenoid

Barrel ECL

Backward Forward Pole Tip Pole Tip ECL ECL

Figure 4.2.12:Figure Belle 10.1: II Side K-long view of and the KLM, muon located detector outside (KLM), the ECL and withsolenoid. ECL The crystals gray lines also mark shown on the interior. Greythe lines nominal indicate polar angular the nominal acceptance angular of Belle II. acceptance of Belle II. Figure from [8].

The 12 outermost layers of the barrel section of the KLM use resistive plate chambers (RPCs), 314 the same technology used in the BABAR IFR. The RPCs are recycled from the Belle detector and are equipped with pickup strips oriented to provide z and ϕ positional information. However, an RPC’s capacitor-like design works on the principle that it discharges when it detects charged particles passing through and must recharge before it can make another

62 detection. The time taken to recharge is dead time – time during which the RPC cannot be used for detection. With the higher luminosity and background event rates of Belle II, the dead time of an RPC is too long for it to be an efficient detector technology except in the outer layers of the barrel section where event rates are lower. Therefore, in the inner two layers of the barrel section of the KLM, and in all layers of the end-cap sections, scintillation detectors are used instead.

The scintillation detectors are formed of scintillating polystyrene strips covered in a reflective coating. Each strip has a cross-section of 7 mm x 40 mm, with lengths varying from 0.5 m to 2.8 m. In each detection layer (i.e. in each gap between the iron flux return plates) strips are arranged in two orthogonal planes, as shown in Figure 4.2.13. There are a total of 16,800 scintillator strips in the KLM.

Figure 4.2.13: Layout of scintillating strips in the Belle II K-long and muon detector (KLM). The two orthogonal layers of strips are sandwiched between the iron flux return plates of Belle II’s solenoid magnet. Figure from [61].

Inside each strip is an optical fibre, mirrored at one end, through which scintillation light is transmitted out of the scintillator and to photodiodes which ultimately produce the detection signal. The fibre also acts as a wavelength shifter, transforming the blue scintillation light to a green wavelength in which the photodiodes have greater efficiency [61]. A diagram of the principle of operation is shown in Figure 4.2.14.

63 Figure 4.2.14: Belle II K-long and muon detector (KLM) scintillator. The scintillator as well as the optical fibre are mirrored at one end, and the scintillator is also covered in a reflective coating, to ensure light is collected and transported to the photodetector. Figure from [8].

The KLM provides polar angle coverage of 25° - 155° and approximately 49,000 readout channels. Muon ID efficiency for particles of momentum > 1 GeV/c is 89% (competitive with BABAR) with a hadron fake rate of approximately 1.3% (favourable compared to the

0 6% - 8% pion fake rate in the BABAR IFR). KL efficiency reaches a maximum of 80% at3

GeV/c, considerably better than the 20% - 40% seen in the BABAR IFR.

64 Chapter 5

Analysis at BABAR

− The decay B → Λpνν is first analysed using data from the BABAR experiment.

− The analysis of B → Λpνν at BABAR presented in this chapter builds on a previous study by the same author [62], henceforth referred to as the sensitivity study. The sensitivity study was based primarily on Monte Carlo simulations (i.e. no final result based on data was obtained) and examined the feasibility of performing a full, data-based search for B−→

Λpνν decays at BABAR.

The analysis presented in this chapter is that full, data-based search which has been approved by the BABAR collaboration and the results presented in public [63]. In this analysis we introduce new analysis techniques and improve various aspects of the sensitivity study and, importantly, obtain a final result based on real data. Where techniques or results that were first introduced in the sensitivity study have been used unmodified, or largely unmodified, this is noted in the relevant section.

This analysis is the world’s first experimental result in the search for B−→ Λpνν and sets a benchmark against which the results of future B-factories, such as Belle II, will be measured.

65 5.1 Analysis tools

5.1.1 Hadronic Btag reconstruction

One of the great advantages of B factories compared to hadron colliders is the extremely clean experimental environment that allows us to use analysis techniques not possible at other experiments. The e+e− → Υ(4S) → BB process produces a BB pair and nothing else - the high mass of the B mesons means there is no energy left for the production of other particles, and the small e+e− interaction cross-section means there will usually be at most one pair of BB mesons produced per e+e− bunch crossing (by comparison, in a hadron collider the large hadron − hadron cross-section means there are usually many hadron − hadron collisions per bunch crossing, leading to a much more complicated environment). With no other spectator particles to pollute the event, it is possible to fully reconstruct one of the B mesons and conduct a search for our signal (in this case B−→ Λpνν , although such techniques are generally applicable to analyses of other B meson decay modes) among the rest of the event (i.e. among the decay products of the second B meson).

For this analysis we use a technique called hadronic Btag reconstruction [64]. Hadronic

Btag reconstruction has been successfully used in previous similar BABAR analyses (e.g. Refs [26, 65, 66]), and was also used in the sensitivity study [62] for this analysis.

In a Υ(4S) → BB decay the B mesons decay almost immediately due to their short lifetime of ∼ 1 × 10−12 s [9]. The B mesons decay via various hadronic and (semi)-leptonic decay modes, many of which are known and can be reconstructed.

Hadronic tag reconstruction, as the name suggests, reconstructs known hadronic decay modes of B mesons. Only B meson decay modes that can be fully reconstructed are accepted, meaning we retain only reconstructed B meson candidates with fully determined kinematics

(four-momenta). The B meson reconstructed via this process is called the Btag.

66 Fully determining the kinematics of the Btag is important because we can use this to determine the kinematics of the other B meson (known as the Bsig) in the BB pair. In an e+e− → Υ(4S) → BB event, conservation of momentum means that in the CM frame the three-momentum of the Bsig is opposite-and-equal to that of the Btag, and since we know the CM e+e− collision energy we also know what energy each B meson should have; the four- momentum of the Bsig can thus be calculated without having to reconstruct the Bsig itself.

This is particularly useful because it means that even if the Bsig decays via a mode that involves “missing” energy or momentum (that is, energy or momentum we cannot detect because it is carried away by undetectable particles, e.g. neutrinos) we still know the Bsig’s four-momentum, and we can therefore even calculate how much energy and momentum are missing from an event. In summary, since the Btag is fully reconstructed, we know that anything else detected in the event (e.g. charged tracks, neutral clusters), and anything not detected in the event (e.g. missing energy or momentum) must originate from the Bsig. We search for our signal in the decay of the Bsig, hence the name.

In principle we could skip the Btag reconstruction process and attempt a more direct search for B−→ Λpνν decays. While a full reconstruction of the parent B meson in a B−→ Λpνν event is impossible, because neutrinos cannot be detected, we could conduct an analysis based on a partial reconstruction by searching for the three charged tracks which are the telltale signs of the B meson’s descendants in this mode. However, the commonness of charged tracks in BB event means it would be difficult to isolate charged tracks originating from B−→ Λpνν decays from those originating from other processes. Furthermore, without a full reconstruction of at least one of the B mesons in the BB pair, it would also be very challenging to preferentially pick charged tracks descended from only one of the B mesons; in other words, we would likely have a lot of crossover between the descendants of the two B mesons in the BB pair. Also, without a full reconstruction of either of the B mesons, it would be difficult to isolate BB events from other types of events, since certain characteristic

67 features of BB events (e.g. a reconstructed B meson mass, see later in this section for more details) would be absent.

Hadronic tag reconstruction is therefore particularly suited to B meson decay modes such as B−→ Λpνν which have missing energy in the form of neutrinos – thanks to the fully- determined kinematics of the Btag we can quantify how much energy has been carried away in the event in the form of the neutrinos, and we can also fully determine the kinematics of the

Bsig (conservation of momentum means we can simply take the negative of the Btag’s three- momentum) despite the fact that we cannot fully reconstruct the Bsig itself. Hadronic tag reconstruction has the additional advantage of significantly reducing non-BB backgrounds, which tends not to survive the hadronic tag reconstruction process (while non-BB events do not, of course, contain actual B mesons, the decay products of such events can be reconstructed such that they mimic B decays and some of these events will therefore survive hadronic Btag reconstruction). The principal disadvantage is the extremely low efficiency, usually below 1%, due to the fact that only a fraction of B meson decay modes can be fully reconstructed and attempted reconstructions of these modes are not guaranteed to be successful.

The hadronic tag reconstruction process reconstructs the Btag through decay modes of the → (∗) → (∗)0 → form B D(s) X, B D X and B J/ψ X, where X is a combination of up to (∗) (∗)0 five pions and kaons, and where the D(s) , D and J/ψ mesons are reconstructed as [67, 68]:

+ → 0 + 0 + 0 0 + − + − + + − + + 0 + − + + − + 0 • D KS π , KS π π , KS π π π , K π π , K π π π , K K π , K K π π ;

0 → − + − + 0 − + − + 0 + − 0 + − 0 + − + − + − 0 • D K π , K π π , K π π π , KS π π , KS π π π , K K , π π , π π π ,

0 0 KS π ;

• D∗+ → D0π+, D+π0;

• D∗0 → D0π0, D0γ;

68 ∗+ → + + → + 0 + • Ds Ds γ followed by Ds ϕπ , KS K ;

• J/ψ → e+e−, µ+µ−;

0 → 0 → + − → + − and where in the above decays π γγ, KS π π , and ϕ K K are reconstructed.

A cartoon of the concept is shown in Figure 5.1.1.

Figure 5.1.1: An idealised illustration of hadronic Btag reconstruction where the Bsig decays via the B−→ Λpνν mode.

Once Btag candidates have been reconstructed, some preliminary cuts are applied to remove low quality reconstructions; the same or similar sets of cuts were previously used in Refs

[69, 70]. Specifically, we calculate the “energy-substituted mass”, mES, of the Btag candidate as

√ m = E2 − ⃗p 2 , (5.1) ES beam Btag

+ − 2 where Ebeam is half the energy of the e e system and ⃗pBtag is the three-momentum of the 2 Btag, both defined in the CM frame. mES is required to satisfy the criteria 5.20 GeV/c <

2 + − mES < 5.30 GeV/c . Note that the energy of the e e system is used since this is known

with better precision than EBtag , the energy of the Btag itself.

69 We also define

E∗ ∆E = CM − E∗ , (5.2) 2 Btag

∗ where superscript asterisk represents a quantity in the CM system and where ECM is the energy of the CM system. We require −0.12 GeV < ∆E < 0.12 GeV.

If more than one Btag candidate in an event survives these cuts we choose the candidate which decays via the mode which has the highest B-mode purity, where B-mode purity is the probability of a given B meson decay mode being correctly reconstructed and is calculated from MC studies. If there is more than one candidate with an equally high purity, the candidate with the lowest value of |∆E| is chosen.

Apart from performing the Btag reconstruction itself, the Btag reconstruction process also outputs various reconstructed detector objects that are vital to the rest of the analysis. Lists of reconstructed charged tracks and neutral clusters, as well as their association with either the Btag or Bsig, are output; these objects are accompanied by measurements of their kinematic properties as well as more sophisticated information such as particle ID pass/fail information (see Section 5.2.7 for more information on particle ID).

From such information, more complex selection variables can be constructed, e.g. extra energy, a measurement of total neutral energy (see Section 5.2.6 for more details); or whole- event shape variables, which can be used to suppress certain types of background (see Section 5.2.5).

Composite particle candidates, other than the Btag, are also provided; of particular relevance to this analysis are the Λ candidates which are returned with useful information such as their mass and reconstruction quality information (see Section 5.2.9 for more details on Λ reconstruction).

70 5.1.2 BABAR dataset

This analysis uses BABAR data collected at the Υ(4S) resonance, which corresponds 471 million BB pairs and 424 fb−1 integrated luminosity (while PEP-II delivered 433 fb−1 at the Υ(4S) energy, not all of it was collected).

The data are divided into six “runs” corresponding to different sets of conditions in the

BABAR detector at the time of data taking. Details of the dataset used in this analysis are shown in Table 5.1.

Table 5.1: Integrated luminosity [71] and B-count [64] (number of BB pairs) values for the BABAR dataset at the Υ(4S) resonance. Uncertainties are statistical only.

Run Integrated luminosity ( pb−1) B-count (×106) 1 20373 22.557 0.138 2 61322 68.439 0.413 3 32279 35.751 0.217 4 99606 111.430 0.671 5 132366 147.613 0.888 6 78308 85.173 0.513 Total 424254 470.963 2.840

5.1.3 Background Monte Carlo

In addition to the “real” data collected at BABAR discussed in Section 5.1.2, we also use a simulated dataset known as background Monte Carlo (MC).

Background MC is a simulation of the BABAR dataset created using Monte Carlo random number generation techniques which aims to replicate what we see in real BABAR data. The benefit of running an analysis on background MC is that we have control over andknowledge of the simulated physics processes in any given event. For example, in real data it can be difficult to discriminate between an event that isan e+e− → Υ(4S) → BB event and an event that is some other process but which looks very similar to an e+e− → Υ(4S) → BB

71 event when viewed through the reconstruction provided by the BABAR detector. In contrast, with background MC we can explicitly simulate and label an e+e− → Υ(4S) → BB event, as well as similar-looking but physically different events, and use this to study how different types of events are expected to appear in real BABAR data.

− In BABAR, background MC is classified in five types: B+B , B0B0, qq (q = u, d, s), cc and τ +τ −. B+B− and B0B0 MC are used for e+e− → Υ(4S) → BB events which have been discussed previously (see Section 5.1.1). qq and cc events represent e+e− → qq and e+e− → cc events; these are known as “continuum” events; cc events are considered separately from other types of qq events because charm quarks are constituents of D mesons which are used

+ − in many reconstructions in the hadronic Btag reconstruction process. τ τ MC represents e+e− → τ +τ − events; other e+e− → l+l− events are not considered since leptons other than the tau are not massive enough to decay hadronically and will therefore not be picked up by the hadronic Btag reconstruction process because there are usually not enough tracks in such events for them to be mistaken for B decays. Note that the contribution of τ +τ − events is so small that it is not visible in most of the histograms in this document.

BB events are generated using EvtGen [72], continuum events with JETSET [73] with EvtGen simulating decays, and τ +τ − with KK [74] with Tauola [75] simulating decays. All background MC events are then passed through a simulation of the BABAR detector created using the GEANT4 toolkit [76].

In order to provide abundant statistics, background MC is produced in multiples of real data (i.e., for every one event in data we simulate multiple events in MC so that our simulations are not as statistically limited as our data; specifically, we simulate B+B−, B0B0 and cc MC at ten times data, and all other event types at four times data) and then down-weighted to match the luminosity of real data. In order to mimic data as closely as possible, the MC is also simulated in six runs matching detector conditions corresponding to the six data

72 collection periods, with MC luminosity also proportional to data luminosity on a run-by-run basis. Details of the background MC used in this analysis are shown in Table 5.2.

73 Table 5.2: Background Monte Carlo used in BABAR analysis. For information on skimming, see Section 5.2.1.

Run Generated Skimmed Skim efficiency Cross-section Weight events (×106) events ( %) ( nb) B+B− Monte Carlo 1 113.877 42851548 37.63 0.5536 0.099 2 334.464 125051492 37.39 0.5580 0.102 3 176.806 67104199 37.95 0.5538 0.101 4 556.454 210706801 37.87 0.5594 0.100 5 724.256 270883359 37.40 0.5576 0.102 6 431.176 163900008 38.01 0.5438 0.099 B0B0 Monte Carlo 1 108.105 38068048 35.21 0.5536 0.104 2 347.176 121290427 34.94 0.5580 0.099 3 180.262 64089470 35.55 0.5538 0.099 4 553.458 195903930 35.40 0.5594 0.101 5 761.070 265477026 34.88 0.5576 0.097 6 429.680 152373995 35.46 0.5438 0.099 cc Monte Carlo 1 256.312 66845940 26.08 1.3 0.103 2 778.982 203371202 26.11 1.3 0.102 3 413.797 109203059 26.39 1.3 0.101 4 1266.48 338137571 26.70 1.3 0.102 5 1677.53 445755971 26.57 1.3 0.103 6 1017.42 278228302 27.35 1.3 0.100 uds Monte Carlo 1 176.404 30845293 17.49 2.09 0.241 2 524.856 92343997 17.59 2.09 0.244 3 276.381 49077341 17.76 2.09 0.244 4 845.699 153075722 18.10 2.09 0.246 5 1109.38 201103577 18.13 2.09 0.249 6 654.992 123250409 18.82 2.09 0.250 τ +τ − Monte Carlo 1 74.665 59325 0.07945 0.94 0.256 2 227.690 192581 0.08458 0.94 0.253 3 117.694 100824 0.08567 0.94 0.258 4 360.242 335622 0.09317 0.94 0.260 5 474.008 469996 0.09915 0.94 0.262 6 363.346 384601 0.1058 0.94 0.203

74 5.1.4 Signal Monte Carlo

As with background MC, which simulates what we expect to see in generic events in BABAR, we also produce an MC simulation of the expected behaviour of the specific signal decay mode B−→ Λpνν .

Our signal MC comprises 4,053,000 events, all of which contain the process Υ(4S) → B+B− where one B meson decays as B−→ Λpνν (or the charge conjugated equivalent) while the other B meson decays generically. For the B mesons which decays via B−→ Λpνν , this is followed by Λ → pπ− with a 100% branching fraction (note that the Λ baryon only decays to pπ− approximately 65% of the time [9]; however, since we only search for this decay mode of the Λ we simulate it with a 100% branching fraction).

The signal MC, which is generated using a simple phase space model, is also reweighted to match the theoretically predicted mΛp distribution given in Ref. [5]. The reweighting procedure was first presented in the sensitivity study [62] and is used here without modification (the details and results of the reweighting procedure are reproduced in Appendix A).

5.1.5 Blinding

In order to avoid experiment bias, this analysis was performed “blind”. That is, the analysis was performed on MC rather than data, with data being completely hidden from the analyst at later stages of the signal selection. Specifically, data in the mES signal region

2 2 (5.27 GeV/c < mES < 5.29 GeV/c ) is hidden for all stages of the signal selection beyond the

Eextra cut (see Section 5.2 for definition of mES and details of the signal selection stages). Note that the rarity of the signal we are searching for means that at early stages of the signal selection there is no chance of the signal being visible in data and potentially biasing the analyst, so histograms from early stages of the analysis include data.

75 After the analysis was reviewed by the BABAR collaboration, data were unblinded and we obtained the final results discussed in Section 5.3.3.

5.2 Signal selection

The signal selection is a multi-stage process, each stage of which is designed to facilitate discrimination between B−→ Λpνν events and all other types of event.

The first stage of the signal selection is the skim (Section 5.2.1), which comprises “common sense” selection criteria and considerably reduces the amount of data we have to process. This is followed by the implementation Btag mES (Section 5.2.3) and B-mode purity (Section 5.2.4) selection criteria, relatively generic properties that we use to preserve well-reconstructed Btag candidates. We then preferentially select events that are BB-like in shape (Section 5.2.5) and events with a low level of neutral energy (Section 5.2.6), both characteristics of B−→ Λpνν decays. The final steps in the signal selection are the most specific to asearchfor B−→ Λpνν decays, and involve selecting events based on the ID (Section 5.2.7) and topology of the charged tracks in the event (Section 5.2.8), as well as reconstructing and selecting Λ candidates (Section 5.2.9).

5.2.1 Skim

In addition to the reconstruction criteria imposed on our data (and background and signal MC) discussed in Section 5.1.1, we apply a subsequent set of loose selection criteria in order to significantly reduce the size of our dataset (here, “dataset” refers to both dataandMC). This is known as a “skim”. The selection criteria used in the skim are [62, 69, 70]:

• one Btag candidate per event (to exclude events where the Btag reconstruction process is not able to reconstruct a candidate, such events have zero candidates),

76 • Btag charge must be 1 (to exclude neutral Btag candidates, which are not relevant to this analysis),

• the sum of the charges of the Bsig descendants (i.e. those particles which are assumed

to originate from the decay of the Bsig) must be equal-and-opposite to the charge of

the Btag (to ensure charge consistency across the entire event),

• missing energy > 0, where missing energy is calculated as half the energy of the e+e− system less the total energy of all detected tracks and clusters that are assigned to

− the Bsig (the presence of neutrinos in B → Λpνν decays means we expect missing energy),

• three charged tracks assigned to the Bsig (to match the three charged tracks expected from B−→ Λpνν followed by Λ → pπ−).

5.2.2 Explanation of histograms

The majority of histograms in the remainder of this chapter will be of the form shown in Figure 5.2.1.

Important points to note here are that the background MC (stacked, solid colours) have been weighted to match data (black points with error bars) luminosity on a run-by-run basis (see Table 5.2 for more details).

Signal MC (red line, right-hand y-axis) has been weighted to an assumed branching fraction of 1 × 10−4. The assumed branching fraction is chosen primarily for convenience and ease of presentation rather than for any physical reason.

77 5.2.3 Btag mES cut

The hadronic Btag reconstruction process outputs both correctly- and incorrectly-reconstructed

Btag candidates. Incorrectly-reconstructed (or “misreconstructed”) candidates appear in both B+B− events and other types of events. In the case of B+B− events, misreconstructions can occur because the hadronic tag reconstruction process does not assign the correct tracks and clusters to the Btag candidate (i.e. it mixes up tracks and clusters from the two BB mesons in an event, rather than accurately assigning them to their true ancestor) but still produces a viable candidate that is sufficiently B-like that it passes the reconstruction

0 0 process. In other types of events, no true Btag exists (in the case of B B events, the hadronic

Btag reconstruction process reconstructs both charged and neutral B meson candidates, but

0 0 as part of our skim cuts only charged Btag candidates are kept, so in the case of B B events no true charged Btag exists, although one may be mistakenly reconstructed and survive the skim cuts). In these cases, Btag candidates are the result of the hadronic Btag reconstruction process finding combinations of tracks and clusters that look sufficiently B-like that they survive the reconstruction and skim cuts. Both these types of events are known as combinatorial background.

When we reconstruct a Btag candidate we should, assuming the reconstruction has been successful, obtain the four-momentum of a real B meson that existed in the event, which means that the mass component of that four-momentum should agree with the known mass of the B meson (5.28 GeV/c2 [9]) within the limitations imposed by detector resolution. As explained in Section 5.1.1, we can improve our measurement of the B mesons mass by using the energy-substituted mass (mES, see Equation 5.1). We can therefore remove some misrecontructed Btag candidates by cutting on the mES of the candidates, a technique commonly used in analyses of B meson decays. The mES of the Btag candidate in an event that passes hadronic Btag reconstruction is calculated as shown in equation 5.1 and is plotted,

78 after skim cuts, in Figure 5.2.1.

Figure 5.2.1: Btag mES after hadronic Btag reconstruction and skim cuts.

In Figure 5.2.1 we can see the behaviour of the different types of MC. B+B− MC (in light blue) has a modest peaking component around the B meson mass of 5.28 GeV/c2, but at this early stage of the signal selection most of it is combinatorial background (i.e. misreconstructed) which shows a relatively flat distribution across the whole of the mES range shown in the histogram before dropping off to zero at 5.29/ GeV c2, the highest mass permitted by the hadronic Btag reconstruction. All other types of background MC are combinatorial in origin, both the B0B0 MC and the various continuum MC types.

Signal MC, on the other hand, shows a strong peaking behaviour with a clear B meson mass visible at approximately 5.28 GeV/c2, and a relatively small combinatorial misreconstruction component.

The data, which contains both B+B− events and non-B+B− events (in theory, a similar mix of events to that in the background MC), shows a slight peak at the B-meson mass due to correctly-reconstructed B+B− events and a large combinatorial component from all other event types.

79 2 2 We retain events with a Btag mES that satisfies 5.27 GeV/c < mES < 5.29 GeV/c .

It is notable in Figure 5.2.1, and in many other histograms in this document, that the background MC overestimates the data, despite the MC having been weighted to match data luminosity. This effect has been seen in previous similar BABAR analyses (e.g. [26, 65, 66]) and is due to a combination of factors including poorly-known Btag decay-mode branching fractions and inconsistencies in reconstruction between data and MC. We correct for this using a method detailed in Section 5.2.10.

5.2.4 B-mode purity cut

We define B-mode purity as the fraction of Btag candidates that are correctly reconstructed in a given decay mode by our hadronic Btag reconstruction process. The B-mode purity definition used here was used previously in Ref. [70].

B-mode purity is calculated using BB events which satisfy [70]:

2 • mES > 5.273 GeV/c ,

• 1-3 charged tracks assigned to the Bsig,

• sum of charges of tracks assigned to the Bsig is equal and opposite to the charge of the

Btag,

0 0 + − • Btag is neutral in a B B event or charged in a B B event,

• fewer than 13 clusters assigned to the Bsig,

• Emiss > 0, where Emiss is defined as:

80 − − Emiss = EBsig Etracks Eclusters (5.3)

where EX is the energy of X and where tracks and clusters refers only to those tracks and clusters assigned to the Bsig (i.e. not used in the reconstruction of the Btag). As the name

+ − suggests, Emiss represents “missing” energy, it being half the energy of the e e system (i.e. the expected energy of the Bsig) minus the energy of all the tracks and clusters that are assigned to the Bsig.

The fraction of Btag mesons for a given decay mode that pass these requirements is the purity of that mode, hence the name B-mode purity. Figure 5.2.2 shows the B-mode purity after hadronic Btag reconstruction and skim cuts.

Figure 5.2.2: B-mode purity after hadronic Btag reconstruction and skim cuts.

Note that while B-mode purity is calculated based on studies of B+B− and B0B0 MC, all event types (i.e. including non-BB events) are assigned a B-mode purity based on the mode via which the Btag candidate in that event is reconstructed. For example, a qq event obviously does not contain a real BB pair, but if the qq event is misreconstructed such that it has a Btag candidate, the B-mode purity of that Btag candidate is assigned as the B-mode

81 purity of that qq event.

In this analysis we optimise our cut on B-mode purity by implementing a nominal signal selection and using the expected final branching fraction upper limit as the figure of merit(for BaBar_PurityOpt Purity cut detailsoptimisation, on calculation of the branching Barlow fraction upper method limit see Section 5.3.2), consistent with

the method used for the optimisation of other cuts such as Eextra and continuum suppression (see Sections 5.2.6 and 5.2.5).

To optimise the value of the cut we test different possible values of cut on B-mode purity and see how this affects the final expected branching fraction upper limit, shown inFigure 5.2.3. ) -5

-5 2.5⋅10 2.5

-5 2⋅10 2

-5 1.5⋅10 1.5 Branching fraction upper limit -5 1⋅10 1

-6 5⋅10 0.5 Branching fraction upper limit (10 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 B-mode purity cut 0 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 1.04 1.12 Figure 5.2.3: Expected branching fraction upper limit according to Barlow calculation [77] after a full signal selection as a function of B-modeB-mode purity purity cut. Forcut details on branching limit calculation techniques see Section 5.3.2.

We can see from Figure 5.2.3 that the best result (lowest expected branching fraction upper limit) is achieved when we retain events with a purity > 0.5, we therefore use this as our cut value on B-mode purity.

82 5.2.5 Continuum suppression

Continuum (qq) events and BB events have different and characteristic distributions of particles and energy within the BABAR detector, and we can exploit this to suppress continuum backgrounds. The continuum suppression technique used here was used previously in Ref. [70].

The mass of a BB pair is only slightly below the mass of the Υ(4S) resonance. Thus, in Υ(4S) → BB events the B mesons are produced almost at rest, and their decay products are distributed almost isotropically, with no strongly-preferred direction in the CM frame; such events are known as “spherical” in shape. In continuum events, the qq is very light and thus when created from the e+e− collision they will have a strong directionality in the forward and backward directions due to conservation of momentum, which is inherited by their descendants; such events are known as “jet-like” in shape. A cartoon of the difference between BB and continuum event shapes is shown in Figure 5.2.4.

B B q q

Figure 5.2.4: Cartoon of BB (left) and continuum (right) event shapes. Arrows indicate the trajectory of decay products. Figure from [62].

To suppress continuum backgrounds, we build a multivariate likelihood called BB likelihood from six variables in the CM frame, all of which measure the shape of an event:

• R2All: the ratio of the 2nd and 0th Fox-Wolfram moments [78] calculated using all tracks and clusters in the event. A measure of event sphericity, spherical events have a R2All value of 0 and jet-like events 1, as shown in Figure 5.2.5a.

83 • Thrust magnitude: the sum of the magnitudes of track and cluster momenta projected onto the thrust axis, where the thrust axis is the axis that maximises their total momentum, divided by the magnitude of their total momentum. Spherical events have lower thrust magnitude than jet-like events, as shown in Figure 5.2.5b.

• |cosθthrust|: the magnitude of the cosine of the angle between the thrust vectors of

the Btag and Bsig descendants. Jet-like events’ forward-backward directionality means

they have |cosθthrust| values near 1, whereas spherical events’ lack of directionality give them a relatively flat distribution of values, as shown in Figure 5.2.5c.

• Thrustz: the magnitude of the projection of the event thrust axis onto the z-axis. Due to the forward-backward directionality of jet-like events, they tend to have higher

thrustz values than spherical events, as shown in Figure 5.2.5d.

• cosθB: cosine of the angle between the Btag three-momentum and the z-axis. Because

the BABAR detector is elongated in the z direction, spherical events are preferentially

detected perpendicular to the beam, causing them to prefer cosθB values near 0, while jet-like events are more evenly distributed, as shown in Figure 5.2.5e.

• cosθpmiss : cosine of the angle between the missing momentum in an event and the z-axis. Due to inferior detector acceptance at angles close to the z-axis, jet-like events will peak more strongly at 1 than spherical events, as shown in Figure 5.2.5f.

We then calculate our continuum suppression variable:

∏ P (x ) BB likelihood = ∏ i BB∏ i (5.4) i PBB(xi) + i Pcont(xi) where the index i iterates over the six event-shape variables described above, and where

PBB(xi) and Pcont(xi) are probability density functions for BB and continuum events for event-shape variable xi. The output of BB likelihood is shown in Figure 5.2.6.

84 (a) R2All (b) Thrust magnitude

(f) Cosine of angle between missing momen- (e) Cosine of angle between B and z-axis tag tum and z-axis.

Figure 5.2.5: Event-shape variables used in continuum suppression, after hadronic Btag reconstruction, skim and Btag mES cuts.

85 Figure 5.2.6: BB likelihood for events passing hadronic Btag reconstruction, skim and Btag mES cuts.

We can see that BB likelihood provides powerful separation between BB events (including signal events) and continuum events.

The expected final branching fraction upper limit after a nominal signal selection isusedas the figure of merit for optimising the cut value. We vary the BB likelihood cut value and see how this affects the branching fraction upper limit, as shown in Figure 5.2.7. As wecansee, the value of the BB likelihood cut has little impact on estimated final branching fraction upper limit for cuts between ∼ 0.3 and ∼ 0.7. We therefore choose to cut conservatively and keep events with BB likelihood > 0.35.

5.2.6 Extra energy

Background event types often include neutral particles assigned to the Bsig. These particles will leave neutral energy deposits in the ECL known as extra energy, or Eextra. Events of the

− type B → Λpνν , however, ideally contain no neutral particles assigned to the Bsig and will therefore leave no deposits in the ECL and should have an Eextra value of zero. This difference in expected Eextra can be used to discriminate between signal and background.

86 BaBar_BBbarLHOptcontLH cut optimisation, Barlow method ) -5

-5 2.5⋅10 2.5

-5 2⋅10 2

-5 1.5⋅10 1.5 Branching fraction upper limit

-5 1⋅10 1

-6 Branching fraction upper limit (10 5⋅10 0.5 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96

0 0.08 0.16 0.24 0.32 BB0.4 likelihood0.48 0.56 cut 0.64 0.72 0.8 0.88 0.96

Figure 5.2.7: Expected branching fractionContinuum upper likelihood limit accordingcut to Barlow calculation [77] after a nominal signal selection as a function of BB lieklihood cut. For details on branching limit calculation techniques see Section 5.3.2.

Using Eextra (or a similar quantity) in this way is a common technique in analyses of relevant B-meson decay modes. The exact technique we use here was adapted from that used in a

previous BABAR study [70].

We calculate Eextra by summing energy deposits in the ECL that are associated with the Bsig

(i.e. they are not used in the reconstruction of the Btag) and which are also not associated with charged tracks (i.e. they are assumed to originate from neutral particles). Comparisons

of Eextra distributions in MC and data were performed as part of the sensitivity study

[62], as a result of which we implement corrections to the Eextra distribution in MC in order to increase agreement with data; details of these corrections are given in Appendix B (reproduced from Ref. [62]) and are applied throughout this analysis.

In ideal conditions Eextra would represent energy from neutral particles originating from the

Bsig. In reality there are several other contributions, including:

• showers of neutral energy deposits from charged particles, if these showers are distributed far from the ancestor particle’s trajectory they will be considered as having originated from a neutral particle,

87 • energy deposits from beam background processes, and

• neutral particles that originate from the Btag but are misassigned to the Bsig, often low-mass particles such as π0 mesons.

The sources listed above tend to leave low-energy deposits in the ECL, whereas real neutral particles originating from B meson decay processes often leave much higher-energy deposits. In order to remove contamination from the items listed above we place an additional requirement that only energy deposits of 50 MeV or more are counted when calculating Eextra.

The output of Eextra is shown in Figure 5.2.8.

Figure 5.2.8: Eextra after hadronic Btag reconstruction, skim and Btag mES cuts.

We see that signal events peak at Eextra = 0, as we would ideally expect, but also have a significant non-zero component from the sources described above. Background events generally have higher, non-zero values of Eextra thanks to real neutral particles.

The expected final branching fraction upper limit after a nominal signal selection isusedas the figure of merit for optimising the cut value. We vary the Eextra cut value and see how this affects the branching fraction upper limit, as shown in Figure 5.2.9. We see that thepredicted final branching fraction upper limit is lowest between Eextra values of approximately 0.3 GeV

88 BaBar_EextraOpt.pdfEextra cut optimisation, Barlow method

and 0.5 GeV. We therefore choose to retain events with Eextra < 0.4 GeV. ) -5

-5 2.5⋅10 2.5

-5 2⋅10 2

-5 1.5⋅10 1.5 Branching fraction upper limit

-5 1⋅10 1

-6 5⋅10 Branching fraction upper limit (10 0.5 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96

0 0.08 0.16 0.24 0.32 0.4 Eextra0.48 cut0.56 0.64 0.72 0.8 0.88 0.96

Figure 5.2.9: Expected branching fraction upperEextra limit cut according to Barlow calculation [77] after a full signal selection as a function of Eextra cut. For details on branching limit calculation techniques see Section 5.3.2.

5.2.7 Particle identification

An event of the form B−→ Λpνν followed Λ → pπ− is expected to contain three charged tracks - two protons and one pion. Using particle identification (PID) selectors, we can further suppress background events while retaining signal events by selecting events conforming to the expected PID characteristics.

The PID cut in this analysis uses BABAR’s KMTightProton selector (a pion selector is not

used because charged tracks in BABAR are assumed to be pions by default). The KMTight- Proton selector is based on error correcting output codes [79] and utilises 36 detector inputs including a particle’s momentum, charge, and energy loss rate [7]; at a typical momentum of 1 GeV/c it has an efficiency of approximately 95% [7].

To pass the PID cut, an event is required to have two oppositely-charged tracks that pass the KMTightProton PID selector, i.e. one proton and one antiproton. The third track is

assumed to be the pion and is required to have the same charge as the Bsig. The two ID’ed

89 protons are hypothesised to be descendant-of-the-Λ and descendant-of-the-Btag based on their charge relative to that of the Btag. Knowledge of their charge is used for the evaluation of the systematic uncertainty on the PID cut (see Section 5.3.1), and their hypothesised ancestries are used in the evaluation of the systematic uncertainty on the Λ reconstruction (see Section 5.3.1).

5.2.8 Distance of closest approach

In addition to the PID criteria discussed in the previous section, we also expect the three tracks in a signal event to conform to a particular ordering of distance of closest approach (DOCA) to the interaction point (IP). We can therefore additionally use DOCA requirements to enhance our signal selection. The usage of DOCA requirements in this way was originally demonstrated in the sensitivity study for this analysis [62].

While tracks may originate from very close to the IP, there is no tracking subdetector in the immediate vicinity of the IP, the closest tracking subdetector being the SVT with an inner radius of 32 mm (see Section 3.2.1 for more details). A track that originates near the IP will traverse the BABAR detector leaving “hits” in the SVT and possibly the DCH (which lies immediately outside the SVT). Hits represent the points in space where a track is detected interacting with a subdetector. From these hits the trajectory of the track can be extrapolated back into the region near the IP.

From this extrapolated trajectory we can calculate DOCA – the extrapolated distance of closest approach of a track to the IP. DOCA is not the actual distance of closest approach but rather how close a track would come to the IP if it were extrapolated backwards in the direction of the IP (see Figure 5.2.10 for a visual representation of the concept).

For events of the type B−→ Λpνν , we expect a DOCA ordering of:

90 • Lowest DOCA: the p that is the descendant of the Bsig. The Bsig decays almost instantly, very close to the IP. The extrapolated trajectory of its immediate descendant, the p, will therefore have a very small DOCA.

• Middle DOCA: the p that is the descendant of the Λ. The Λ decays as Λ → pπ−. Of its two descendants, the p is by far the most massive and will therefore carry most of the Λ’s momentum and its extrapolated trajectory is more likely to approach close to the IP than that of the π−.

• Highest DOCA: the π− that is the descendant of the Λ.

A cartoon illustrating the expected DOCA ordering is shown in Figure 5.2.10.

Figure 5.2.10: Cartoon of expected distance of closest approach (DOCA) order in a B−→ Λpνν event. Solid lines represent the trajectories of particles, broken lines the extrapolation of those trajectories back to the IP, black dots represent decay vertices. The DOCA of a particle is the minimum distance between the IP and that particle’s extrapolated trajectory.

By using the PID tags we determined for the three tracks in an event (see Section 5.2.7) we can see that the DOCA ordering we expect is, in general, reproduced in signal MC, as shown in Figure 5.2.11.

We include the DOCA requirements detailed in this section by requiring that tracks passing the PID cuts detailed in the previous section also conform to the expected DOCA order.

Imposing these DOCA requirements after the hadronic Btag reconstruction, skim, mES and PID cuts increases the proportion of MC background events that contain a real Λ (determined

91 DOCANewPIDTwoPIDBDaughtProtonDOCANewPIDTwoPIDLambdaDaughterProton

hDOCANewPIDTwoPIDBDaughtProton hDOCANewPIDTwoPIDLambdaDaughtProton Entries 5948 Entries 5948 Mean 0.07446 Mean 0.5439 hDOCANewPIDTwoPIDBDaughtProton RMS 0.24 hDOCANewPIDTwoPIDLambdaDaughtProton RMS 0.5429

60 8

7 50 6 40 5

DOCANewPIDTwoPIDLambdaDaughterPion30 4

3 Number of events (per 0.05 cm) 20 Number of events (per 0.05 cm) 2 10 1

0 0 −1 0 1 2 3 4 5 −1 0 1 2 3 4 5 DOCA (cm) DOCA (cm)

hDOCANewPIDTwoPIDLambdaDaughtPion Entries 5948 Mean 1.578 (a) p that is the descendant of thehDOCANewPIDTwoPIDLambdaDaughtPionB−. (b) p that isRMS the descendant 1.331 of the Λ.

2.5

1.5

1 Number of events (per 0.05 cm)

0.5

0 −1 0 1 2 3 4 5 DOCA (cm) (c) π− that is the descendant of the Λ.

Figure 5.2.11: Distance of closest approach (DOCA) for ID-tagged charged tracks in signal MC after hadronic Btag reconstruction, skim, mES and PID cuts. ID-tagging is described in Section 5.2.7.

92 from MC truth) from approximately 15% to approximately 27%, decreases background by approximately 77% and decreases signal efficiency by approximately 10%. The corresponding numbers for the end of the analysis (i.e. comparing the full signal selection with and without the DOCA requirements) are: increase in real Λ backgrounds from approximately 94% to approximately 96%, decrease in background yield of approximately 24%, and decrease in signal efficiency of approximately 10%.

5.2.9 Λ reconstruction

The final step in our signal selection is Λ reconstruction, whereby we reconstruct possible Λ candidates from the charged tracks in an event and choose a single best Λ candidate per event. This provides us with a powerful discriminator between signal and background.

To reconstruct the Λ we use TreeFitter [80], a fitting algorithm based on a Kalman Filter [81]. TreeFitter performs fits over an entire decay tree using constraints on, in ourcase:

• 4-momentum conservation, incorporating proton and pion mass assumptions for the Λ descendants,

• a common production vertex position for decay products,

• mass of the reconstructed Λ being consistent with the PDG Λ mass 40 MeV/c2, and

• production vertex of the Λ being within the flight length of its ancestor B meson, plus an allowance for variation in location of the beamspot (i.e. the point at which the B is produced).

We also introduce some “common sense” constraints, namely that the Λ must have exactly two descendants, the descendants of the Λ must be oppositely-charged tracks, and each event must have at least one reconstructed Λ candidate.

93 The resulting reconstructed Λ mass is shown in Figure 5.2.12. We see that in Figure 5.2.12a there is a clear peak in signal MC around the known Λ mass of 1.116 GeV/c2. However, there is a considerable amount of background both within and outwith the region in which the signal MC peaks.

(b) Reconstructed Λ mass after hadronic (a) Reconstructed Λ mass after hadronic B reconstruction, skim, m , PID and B reconstruction, skim and m cuts. tag ES tag ES DOCA cuts.

Figure 5.2.12: Reconstructed Λ mass.

The background events we see in Figure 5.2.12a are mostly combinatorial background - events where no Λ baryons are present but where a viable Λ candidate can be reconstructed or where a Λ candidate does exist but has been misreconstructed. There are additionally some events in background MC which contain real Λ baryons and which have been correctly reconstructed which create the peak in B+B− MC which can be seen at the known Λ mass.

The background events on either side of the peak in Figure 5.2.12a are due the Λ reconstruction having fairly generous constraints which allow many possible candidates to be reconstructed which do not necessarily share many properties with decays of the form B−→ Λpνν . By implementing the PID and DOCA cuts (see Sections 5.2.7, 5.2.8) we select events that conform more closely to the expected Λ decay in a B−→ Λpνν event and, as we can see in Figure 5.2.12b, this leads to a sharply-defined peak in background MC around the PDG Λ mass and much smaller combinatorial background tails on either side of the peak.

94 The remaining background events outside the peak region are clearly misreconstructions and

2 2 are excluded by implementing a cut on the Λ mass of 1.112 GeV/c < mΛ < 1.120 GeV/c .

The Λ reconstruction process presented here can produce more than one Λ candidate per event. In the case that there is more than one candidate in an event that survives to this point we choose the Λ candidate with the highest decay-length significance (that is, the flight length of the Λ before it decays, divided by the uncertainty on the flight length), because we expect the relatively long-lived Λ to have an appreciable flight distance. For events in

MC that pass local-skim, mES, PID+DOCA and Λ reconstruction cuts, the proportion of events with more than one viable Λ candidate (that is, a Λ candidate that meets all the aforementioned Λ reconstruction requirements) is approximately 0.3%.

5.2.10 MC correction

In many of the histograms presented in the this chapter thus far there has been a noticeable discrepancy between the number of events in MC and in data, despite the MC being weighted to match data luminosity. The MC consistently overestimates the data, an effect seen in previous similar BABAR analyses (e.g. Refs [26, 65, 66]). This can be corrected using a process known as an mES sideband substitution.

The mES sideband substitution was originally developed in Ref [82]. The mES sideband substitution presented in this document is a slightly modified version of the original; the modified version was first presented in Ref [69].

For the purposes of the mES sideband substitution, we divide the mES range into two regions:

2 2 the “sideband region” defined as 5.20/ GeV c < mES < 5.26 GeV/c and the “signal region”

2 2 defined as 5.27/ GeV c < mES < 5.29 GeV/c . We also conceptually divide our background events into two categories: “peaking” background represents B+B− events which are correctly reconstructed by the hadronic Btag reconstruction process resulting in a Btag four-momentum

95 with an invariant mass consistent with that of a B meson mass; these events therefore peak in the signal region. All other events are combinatorial background – i.e. misreconstructed

+ − B B events plus all other background event types; the Btag in such events is reconstructed from a random combination of reconstructed particles and thus the invariant mass has no preferred value.

The mES sideband substitution is a technique for making a data-driven background estimation, rather than relying solely on MC. We achieve this by extrapolating data in the mES sideband region into the mES signal region in order to calculate the expected amount of combinatorial background in the mES signal region; our combinatorial background estimation is thus based on data rather than solely on MC, and in the process we eliminate the problem of data/MC disagreement for combinatorial events. Any remaining discrepancy between data and MC in the mES signal region (i.e. in peaking events) is accounted for by scaling the

+ − peaking portion of the B B MC in the mES signal region such that it matches the peaking portion of the data in the mES signal region; again meaning that our background estimation is data-driven rather than solely reliant on MC, and in the process correcting any remaining MC/data disagreement.

The MC correction procedure is done in two steps: first, we estimate the level of combinatorial background in the signal region; second, we estimate the level of peaking background in the signal region; the total level of background in the signal region being the sum of the two.

Combinatorial background in the signal region

To estimate the combinatorial background in the signal region we extrapolate the data in the sideband region into the signal region.

We first calculate the ratio, Ri, of events in the signal region to those in the sideband region for each type of background i:

96 sig Ni Ri = side (5.5) Ni

sig side where Ni is the number of MC background events of type i in the signal region and Ni is the number of MC background events of type i in the sideband region.

+ − Note that for all event types other than B B , Ri is a ratio of combinatorial events in the signal and sideband regions, which is what we need in order to calculate the combinatorial background in the signal region based on an extrapolation of the (combinatorial) data in the sideband region. B+B− events in the signal region, however, comprise both peaking and

+ − combinatorial events, so for B B events RB+B− does not have the required meaning. We therefore assume that the signal:sideband ratio for B+B− events is the same as that for B0B0

0 0 + − events and use RB0B0 for both B B events and for B B events.

We now calculate the fraction, Fi, that each event type i constitutes of the total background MC in the sideband region:

side Ni Fi = side (5.6) NMC

side where Ni is the number of MC background events of type i in the sideband region and

side NMC is the total number of all MC background events in the sideband region.

Using Ri and Fi we can now calculate the ratio, RMC , of combinatorial MC background events in the signal region and sideband region:

− × − × − × × RMC = ((FB+B + FB0B0 ) RB0B0 ) + (Fτ +τ Rτ +τ ) + (Fqq Rqq) + (Fcc Rcc). (5.7)

97 side We can now use RMC to extrapolate the data in the sideband region, NData, into the signal region to provide us with a more accurate estimate of the number of combinatorial

comb background events in the signal region, Nbkgd :

comb × side Nbkgd = RMC NData. (5.8)

Peaking background in the signal region

Now that we have accounted for the combinatorial part of the background in the signal region, we must also obtain an estimate of the peaking background in the signal region.

peak We first calculate the number of data events which peak in the signal region, NData:

( ) peak sig − side × NData = NData NData RMC (5.9)

sig where we have taken the total number of data events in the signal region, NData, and subtracted from it the estimated number of combinatorial background events in the signal region,

side × NData RMC .

We then calculate the number of B+B− background MC events which peak in the signal

peak region, NB+B− :

( ) side peak sig sig NB+B− N − = N − − N × . (5.10) B+B B+B B0B0 N side B0B0

+ − sig where we have taken the total number of B B events in the signal region, NB+B− , and subtracted from it the estimated number of combinatorial B+B− events in the signal region, which has been calculated by scaling the number of B0B0 MC background events in the signal region (N sig , which are all combinatorial) by the ratio of B+B− to B0B0 MC background B0B0

98 events in the sideband region.

peak peak From NData and NB+B− we calculate a scaling factor, Cpeak:

peak NData Cpeak = peak (5.11) NB+B− which is the ratio of data events which peak in the signal region to B+B− MC background events which peak in the signal region.

We note that in order to calculate Cpeak using equation 5.11, we are required to observe the number of data events in the signal region. We therefore have to calculate Cpeak at a stage of the signal selection where the events in the mES signal region are dominated by background (rather than any signal that might be present), this is discussed later in this section.

Additionally, there is the risk that even by calculating Cpeak earlier in the signal selection, the presence of signal in real data (that is B−→ Λpνν events in data rather than signal

− MC), could bias the calculation of Cpeak. However, given that B → Λpνν has an expected branching fraction of ∼ 8 × 10−7, we can avoid any significant bias from real signal events by ensuring we have sufficient statistics such that any contribution from real signal events becomes negligible. As discussed later in this section, we calculate Cpeak at at point in the signal selection where we have ∼ 5 × 104 events, more than enough to mask any possible contribution from signal events.

peak Finally, we estimate the number of peaking events in the signal region, Nbkgd , by scaling peak down the NB+B− by Cpeak:

peak × peak Nbkgd = Cpeak NB+B− (5.12)

peak where NB+B− is calculated according to equation 5.10.

99 peak peak We note that ideally it would be preferable to replace NB+B− in equation 5.12 with NData, as this would allow us to calculate an estimate based on data rather than MC. However, at the end of the signal selection (i.e. the point at which we wish to actually calculate the background in the signal region), we cannot observe how many data events exist in the signal

peak region because they have been blinded. We therefore use NB+B− instead.

Calculation of total background

total The total background in the signal region, Nbkgd , is simply the sum of the combinatorial and peaking components:

total comb peak Nbkgd = Nbkgd + Nbkgd . (5.13)

The more complex issue which arises in the calculation of the background using the mES sideband substitution method is the point at which we evaluate RMC and Cpeak; as explained above, Cpeak must be calculated at some sufficiently early stage of the analysis where weare unblinded and have high statistics. Furthermore, RMC and Cpeak are anti-correlated and, by design, force a numerical match between data and MC only when calculated at the same point of the signal selection; we should therefore aim to calculate them under the same conditions, so the point at which we choose to evaluate Cpeak affects the point at which we evaluate RMC .

Figure 5.2.13 shows RMC and Cpeak as a function of sequential cut in the signal selection.

Note that Cpeak is not evaluated for cuts after the Eextra cut since at that point we enter a low statistics regime where the data are blinded (as evidence by the much larger statistically errors on RMC when it is evaluated beyond the Eextra cut). We also show mES after each of the cuts in Figure 5.2.14, where we can also see the drastic drop in statistics after the Eextra cut.

100 R_MC C_peak

Ratio for B->Lambda Pbar Nu Nubar signal selection Correction Factor for B->Lambda Pbar Nu Nubar signal selection

0.22

0.85 0.2

0.84 0.18 MC peak R 0.16 C 0.83

0.14 0.82

0.12 0.81

Local skim Purity ContLH E_extra PID (with DOCA) Lambda reco Local skim Purity ContLH E_extra Cut Cut

(a) RMC as a function of signal selection (b) Cpeak as a function of signal selection cut. cut.

Figure 5.2.13: MC correction variables RMC and Cpeak (see text for definitions) as a function of sequential signal selection cut.

We note that RMC is expected to vary as a function of cut because different sets of cuts

change the background composition which will obviously lead to a change in the value of RMC

(see Equation 5.7), and this is indeed that we see in Figure 5.2.13a. Cpeak, on the other hand, effectively represents a correction to B meson branching fractions and/or the reconstruction

efficiencies of the B mesons decays modes used in the hadronic Btag reconstruction process. Its value is therefore expected to remain relatively stable, as shown in Figure 5.2.13b. The

variation in RMC and Cpeak, and the different final background estimates their different values could lead to, are accounted for in a systematic uncertainty (see Section 5.3.1).

In an ideal situation we would evaluate RMC and Cpeak at the end of the signal selection

but for the reasons already discussed this is not possible for Cpeak and therefore also not

desirable for RMC . We therefore choose to evaluate them as late as possible in the signal selection, where we have a set of cuts as close as possible to the final signal selection before

data become blinded, i.e. we evaluate them immediately after the Eextra cut.

Evaluating RMC and Cpeak immediately after the Eextra cut we obtain values of RMC =

0.2150.001 and Cpeak = 0.8190.006, where the uncertainties are statistical only (systematic uncertainties are discussed and evaluated in Section 5.3.1), and where the associated

101 (a) Btag mES hadronic Btag reconstruction (b) Btag mES after hadronic Btag recon- and skim cuts. struction, skim and B-mode purity cuts.

(c) Btag mES after hadronic Btag recon- (d) Btag mES after hadronic Btag reconstruction, skim, B-mode purity and BB struction, skim, B-mode purity, BB like- likelihood cuts. lihood and Eextra cuts.

(e) Btag mES after hadronic Btag recon- (f) Btag mES after hadronic Btag reconstruction, skim, B-mode purity, BB likeli- struction, skim, B-mode purity, BB likelihood, Eextra and particle identification (in- hood, Eextra, particle identification (incor- corporating DOCA) cuts. porating DOCA) and Λ reconstruction cuts.

Figure 5.2.14: Btag mES as a function of signal selection cut.

102 values of Ri (see Equation 5.5) and Fi (see Equation 5.6) are shown in Table 5.3.

Table 5.3: Values of Ri (see Equation 5.5) and Fi (see Equation 5.6) corresponding to RMC = 0.215 0.001 and Cpeak = 0.819 0.006. Note that we do not calculate a value for RB+B− (see text for explanaton). Uncertainties are statistical only.

Event type (i) Ri Fi B+B− - 0.297 0.001 B0B0 0.278 0.002 0.168 0.000 qq 0.162 0.001 0.280 0.001 cc 0.160 0.001 0.256 0.001 τ +τ − 0.229 0.042 0.000 0.000

Any residual disagreement between MC and data after the MC correction is applied, plus the uncertainty associated with the choice of the stage of the signal selection at which we evaluate RMC and Cpeak, are accounted for by a systematic uncertainty which is discussed in Section 5.3.1.

Correction to signal MC

The discrepancy between background MC and data is believed to be due to various deficiencies with our MC simulation and reconstruction. We must therefore assume that our signal MC, which goes through similar simulation and reconstruction, also requires correction. Since the signal MC is overwhelmingly peaking, rather than combinatorial, we apply only the Cpeak correction, i.e. we simply multiply our final signal efficiency by Cpeak. The numerical effects of this are shown in Table 5.4.

5.2.11 Summary of signal selection

The sharp peak around the Λ mass visible in Figure 5.2.12b, as well as the extremely low combinatorial background under it, indicates that our background is now dominated by real Λ decays. Combined with the other cuts presented in the preceding sections, which select for events matching the expected characteristics of events of the form B−→ Λpνν , we are

103 now at a point where nothing more can be done to suppress background – the remaining background now so strongly mimics our signal that any further cuts would adversely affect our signal efficiency and have little-to-no benefit to our final result.

With the issue of the discrepancy in the number of MC and data events now accounted for with the MC correction, we are now at the end of the signal selection cuts for the BABAR analysis of B−→ Λpνν . At this point of the signal selection, with all cuts implemented, there are now estimated to be only 2.43 background events surviving and our signal efficiency is 0.065%; a summary of the sequential and marginal effects of our signal selection cuts are shown in Tables 5.4 and 5.5.

Table 5.4: Summary of sequential background yield and signal efficiency as a function of signal selection cut. Uncertainties are statistical only.

Cut Events in background MC Signal efficiency [after MC correction] [after MC correction] Skim (1.7355 0.0002) × 107 (0.552 0.004)% 6 Btag mES (2.5086 0.0006) × 10 (0.311 0.003)% B-mode purity (1.3780 0.0005) × 106 (0.261 0.003)% BB likelihood (5.8585 0.0028) × 105 (0.213 0.002)% Eextra 55, 969 79 [46, 879 250] (0.137 0.002)%[(0.112 0.002)%] PID (with DOCA) 25.12 1.91 [17.91 2.09] (0.0798 0.0014)%[(0.0654 0.0012)%] Λ reconstruction 2.43 0.50 [2.34 0.70] (0.0654 0.0013)%[(0.0536 0.0011)%]

Table 5.5: Summary of marginal background yield and signal efficiency as a function of signal selection cut (i.e. the background yield and signal efficiency if the specified cut were removed). Note that removal of the PID cut necessitates the removal of the DOCA cut, since DOCA can only be performed on PID’ed tracks. Uncertainties are statistical only.

Cut Events in background MC Signal efficiency Btag mES 14.7 1.4 (0.0686 0.0013)% B-mode purity 5.04 0.76 (0.0739 0.0014)% Continuum suppression 10.4 1.3 (0.0786 0.0014)% Eextra 79.0 3.3 (0.100 0.002)% PID+DOCA 764 9 (0.105 0.002)% DOCA 3.18 0.60 (0.0718 0.0013)% Λ reconstruction 25.2 1.9 (0.0798 0.0014)%

104 5.3 Results

5.3.1 Systematic uncertainties

There are systematic uncertainties associated with both the signal MC model, the MC correction and the signal selection cuts used in this analysis. An evaluation of these uncertainties, in addition to purely statistical uncertainties, is necessary in order to calculate a final result.

Of the methods used to evaluate systematic uncertainties described in this section, the methods used for the signal MC model, the B-mode purity cut, the continuum suppression cut and the Eextra cut are the same as those used in the sensitivity study [62] for this analysis.

Signal MC model

As discussed in Section 5.1.4 and Appendix A, the signal MC is reweighted to match the mΛp distribution given in Ref. [5]. Ref. [5] also provides predictions for three other distributions to which we could have reweighted the signal MC but which, alone, did not produce a significant change in the final signal efficiency. In this section we evaluate a systematic uncertainty on the signal MC model reweighing based on the effects of rewetighting simultaneously to more than one distribution.

We evaluate a systematic by reweighting the signal MC simultaneously to mΛp and one other variable in turn, and measuring the signal efficiency at the end of the signal selection ineach case. The results are shown in Table 5.6.

The helicity angle θL should be independent of mΛp and, looking at Table 5.6, we see that the reweighting to mΛp and θL agrees with the reweighting to mΛp alone within statistical

105 Table 5.6: Signal efficiency for different MC reweightings. Uncertainties are statistical only.

Variable(s) to reweight to Signal efficiency after full signal selection mΛp (0.0654 0.0013)% mΛp and θL (0.0630 0.0012)% mΛp and mνν (0.0597 0.0012)% mΛp and θB (0.0628 0.0012)%

uncertainties. We therefore ignore the reweighting to mΛp and θL when calculating this systematic uncertainty.

To calculate the systematic we conservatively take the change in final signal efficiency between the reweighting to mΛp alone and each of the remaining two cases, and sum these in quadrature to obtain a systematic uncertainty of 9.59%.

B-mode purity cut

Any systematic disagreement between MC and data associated with the B-mode purity cut is accounted for either when we implement the MC correction, or in the systematic on the MC correction.

As we can see from Figure 5.2.2, the vast majority of events that survive the cut on B- mode purity are continuum events. Most of the other, BB, events will be combinatorial, rather than peaking. In short, most of the events that survive the cut on B-mode purity are combinatorial events. Since the MC correction process, which is implemented after the cut on B-mode purity, estimates combinatorial background from data, rather than MC, there is no need to calculate a systematic uncertainty related to data/MC disagreement for such events.

In the remainder of the events (the small number of peaking B+B− events that pass the cut), any remaining data/MC discrepancy is accounted for by the Cpeak factor in the MC correction process and the systematic uncertainty on it (see Sections 5.2.10 and 5.3.1).

106 Continuum suppression cut

Similarly to the case with B-mode purity, any systematic disagreement between MC and data associated with the continuum suppression cut is accounted for either when we implement the MC correction, or in the systematic on the MC correction.

As we can see from Figure 5.2.6, despite the power of continuum suppression cut in discriminating between continuum and non-continuum events, a large proportion of the events that survive the cut are continuum events. Most of the other, BB, events will be combinatorial, rather than peaking. In short, most of the events that survive the continuum suppression cut are combinatorial events. Since the MC correction process, which is implemented after the continuum suppression cut, estimates combinatorial background from data, rather than MC, there is no need to calculate a systematic uncertainty related to data/MC disagreement for such events.

MC correction

The MC correction procedure, discussed in Section 5.2.10, fixes the discrepancy between data and MC by forcing numerical agreement between the two at the stage of the signal selection at which it is implemented (immediately following the Eextra cut). However, while there is exact numerical agreement (by design), there is still room for systematic uncertainty arising from the way in which we reach this numerical agreement.

The MC correction procedure splits MC in the mES signal region into two types, combinatorial and peaking, and scales these separately by RMC and Cpeak respectively. At the

107 stage at which we evaluate RMC and Cpeak the ratio of these values is not important, we obtain exact numerical agreement regardless. However, different ratios of RMC and Cpeak (in other words, different assumptions about the shape of combinatorial events under the peak) lead to different estimated total background numbers at later stages of the analysis (see Equations 5.8, 5.12 and 5.13). So, any uncertainty in our assumption of the shape of the combinatorial events in the mES signal region is an uncertainty on our values of RMC and

Cpeak, which in turn create an uncertainty in our final background estimate as well as our final signal efficiency (in the latter case, because signal efficiency isscaledby Cpeak).

Furthermore, we note from Figure 5.2.13 that the values of RMC and Cpeak change as a function of cut. In other words, the aforementioned shape assumed by the mES sideband substitution process changes as the cuts change. Taking our values of RMC and Cpeak at an earlier stage than we do would result in a different final background estimate and signal efficiency. Thus there is an uncertainty associated with the stage at which we chooseour values which is, again, an uncertainty associated with the shape of the combinatorial events in the mES signal region assumed by the mES sideband substitution process.

So, both of the aforementioned uncertainties are uncertainties associated with the shape of the combinatorial events in the mES signal region assumed by the MC correction procedure. The way we measure this shape is expressed in Equation 5.7. We can split the background into two components: continuum background and BB background. These types of background are qualitatively different because the continuum background is expected to smoothly drop off under the peak in an Argus-like [83] shape. However, BB background can contain pseudo-peaking events which are almost, but not entirely, correctly reconstructed (for example due to a single particle being missing or assigned to the wrong side of the reconstruction) which, rather than falling away in a smooth Argus-like fashion, can in fact increase in number within the mES signal region.

108 We can thus conservatively estimate the value of the systematic uncertainty due to the mES sideband substitution process by applying Equation 5.7 under two different assumptions: that the background is entirely continuum, and that the background is entirely BB. In other words, under the first assumption we use a modified version of Equation 5.7 thatdoes

− × not include the ((FB+B + FB0B0 ) RB0B0 ) term, and under the second assumption we use a

− × modified version of Equation 5.7 that contains only the ((FB+B +FB0B0 ) RB0B0 ) term.

Using these two assumptions we obtain values of RMC and Cpeak immediately after Eextra cut of RMC = 0.161, Cpeak = 0.935 assuming continuum only, and RMC = 0.278, Cpeak =

0.685 assuming BB only (compare regular values of RMC = 0.215, Cpeak = 0.819).

Applying these two sets of values of RMC and Cpeak, we obtain the final background and signal efficiency values shown in Table 5.7.

Table 5.7: Final background and signal efficiency estimates at the end of the signal selection using an unadjusted MC correction procedure, and using an MC correction procedure under two different assumptions of background composition (see text for details). Changes are with respect to the Unadjusted column. Uncertainties are statistical only.

Unadjusted Continuum only BB only RMC 0.215 0.001 0.161 0.001 0.278 0.001 Cpeak 0.819 0.006 0.935 0.006 0.685 0.006 Background 2.34 0.70 1.99 0.60 2.74 0.84 Change in background N.A. −15.0% +17.1% Signal efficiency (3.42 0.08) × 10−6 (3.91 0.09) × 10−6 (2.86 0.07) × 10−6 Change in signal efficiency N.A. +14.2% −16.3%

We conservatively take the maximum changes in the final background estimate and the final signal efficiency estimate to evaluate a systematic uncertainty due to the MC correction procedure on background yield of 17.1% and on signal efficiency of 16.3%.

109 Particle ID

The PID selectors used in this analysis (see Section 5.2.7) introduce a systematic uncertainty due to their different performance on MC and data.

To evaluate a systematic uncertainty on the PID step of our analysis we examine the PID performance plots for the TightKMProton PID selector (the PID selector we use), which are shown in Figure 5.3.1.

Figure 5.3.1: PID performance of BABAR’s TightKMProton selector. Note that the values for the p in the 3.2-3.4 GeV/c bin and the 4.0-4.2 GeV/c bin are not visible in the right plot because they are below the minimum value on the y-axis; however, they can be computed from the data shown in the middle plot. Figure from [84].

Looking at the right plot in Figure 5.3.1 we see that the PID selector’s efficiency differs for MC and data as a function of proton momentum and of proton charge. We thus plot the momentum of the tracks ID’ed as protons in our selection, as shown in Figure 5.3.2.

To evaluate a systematic we calculate weighted averages of the values in the right plot of Figure 5.3.1 for both p+ and p−, with the weights proportional to the number of tracks in each momentum bin in Figure 5.3.2; this is done separately for background MC and signal MC. This produces two values each for background MC and signal MC (one value for each charge). Since each event that passes the PID stage contains one p+ and one p−, we linearly add the p+ and p− values to find the total uncertainty to produce final systematics of1.28% for background and 1.44% for signal.

110 (a) p+ (b) p−

Figure 5.3.2: Momentum distributions for tracks ID’ed as protons after hadronic Btag reconstruction, skim and PID+DOCA cuts. Binning matches that in Figure 5.3.1.

Distance of closest approach and Λ reconstruction

It is possible to create reconstructed Λ candidates using only PID information, as we will show later in this section. These Λ candidates can then be refined by implementing our subsequent selections based on DOCA (see Section 5.2.8) and Λ reconstruction (see Section 5.2.9). To evaluate a systematic on the the DOCA and Λ reconstruction steps of the analysis we therefore examine the effect of these steps on the Λ candidates we can reconstruct from PID alone.

Figure 5.3.3 shows the mass of Λ candidates reconstructed using PID information only, for events in a control sample comprising the mES sideband region. To obtain these Λ candidates we combine the four-momenta of the Λ descendants (the track ID’ed as a proton and which has charge oppose that of the Bsig, and the track presumed to be the pion, see Section 5.2.7 for details) to recreate the four-momentum of the Λ, from which we extract the Λ mass.

We define a Λ peak region as 1.081 GeV/c2 to 1.151 GeV/c2 and a Λ sideband region as anything outside the peak region, as shown in Figure 5.3.3. The data/MC ratios in these regions are 1.022 0.015 and 0.791 0.005 respectively.

111 (a) Λ peak region. (b) Λ sideband region.

Figure 5.3.3: Mass of Λ candidates reconstructed using PID information only in a control sample comprising the mES sideband region after hadronic Btag reconstruction and skim cuts.

We now implement the DOCA and Λ reconstructions steps. We know from Section 5.2.9 that the Λ reconstruction process produces a much narrower Λ mass peak than that which we see in Figure 5.3.4, we therefore define a new Λ peak region as 1.112 GeV/c2 to 1.120 GeV/c2 and a new Λ sideband region as anything outside the peak region. The mass of the resulting Λ candidates is shown in Figure 5.3.4. These Λ candidates have thus been through PID, DOCA and Λ reconstruction and are, again, taken from a control sample comprising events in the mES sideband region.

(a) Λ peak region. (b) Λ sideband region.

Figure 5.3.4: Mass of Λ candidates selected using PID, DOCA and Λ reconstruction in a control sample comprising the mES sideband region after hadronic Btag reconstruction and skim cuts.

112 The data/MC ratios in these regions are 1.158 0.026 and 0.892 0.029 respectively. Com- paring with the data/MC ratios for Λ candidates from PID only, the change in the data/MC ratio in the lambda peak region is 13.3% and the change in the lambda sideband region is 12.7%. Since only events in the peak region survive further into the analysis, we evaluate a systematic due to DOCA and Λ reconstruction of 13.3% on both background yield and signal efficiency.

Eextra cut

As discussed in Section 5.2.6 and Appendix B, we altered the definition of Eextra in MC by subtracting 5 MeV from the ECL deposit energies. This, however, means that we are no longer using the “default” definition of Eextra and introduces a source of systematic uncertainty, which we will evaluate in this section.

The cut on Eextra has a large impact on both the number of background MC events and on signal efficiency. We therefore evaluate a systematic for each.

To evaluate a systematic on signal efficiency originating from the definition of Eextra, we measure the signal efficiency at the end of the signal selection using three different definitions of Eextra: unadjusted Eextra (no changes to the energy of ECL deposits), Eextra adjusted by

-5 MeV per ECL deposit (the definition we use in the signal selection), and Eextra adjusted by -10 MeV per ECL deposit. In other words, we adjust Eextra by 5 MeV compared to the definition we use in the signal selection; definitions of Eextra outside this window show such large discrepancies between MC and data that they are not considered viable. The results are shown in Table 5.8.

To evaluate the systematic uncertainty, we take the average of the change in signal efficiency relative to that given by the Eextra definition we use in the signal selection, resulting ina systematic uncertainty on signal efficiency of 1.91%.

113 Table 5.8: Signal efficiency at the end of the signal selection with different definitions of Eextra (see text for details). Uncertainties are statistical only.

Eextra definition Signal efficiency after Difference from median full signal selection Unadjusted (0.0644 0.0013)% −1.53% −5 MeV (0.0654 0.0013)% n.a. −10 MeV (0.0669 0.0014)% +2.29%

For the uncertainty on background, we use the same approach, except here we measure the change in data/MC ratio rather than the change in signal efficiency. Because data is blinded for stages of the signal selection beyond the Eextra cut, we measure the data/MC ratio immediately after the Eextra cut rather than at the end of the signal selection. The results are shown in Table 5.9.

Table 5.9: Data/MC ratio after hadronic Btag reconstruction, Btag mES, B-mode purity, continuum suppression and Eextra cuts, with different definitions of Eextra. Uncertainties are statistical only.

Eextra definition Data/MC ratio immediately Difference from median after Eextra cut Unadjusted 0.9611 0.0027 +11.56% −5 MeV 0.8615 0.0024 n.a. −10 MeV 0.7766 0.0022 −9.85%

Taking the average change in data/MC ratio with respect to that given by definition of Eextra that we use, we evaluate a systematic uncertainty on background of 10.71%.

Summary of systematic uncertainties

A summary of systematic uncertainties is shown in Table 5.10.

5.3.2 Calculation of branching fraction limit

To calculate a branching fraction limit for our analysis we must first use the results of the signal selection and systematic uncertainty evaluation, plus the MC correction procedure, to

114 Table 5.10: Summary of systematic uncertainties.

Source Signal efficiency Background Signal MC model 9.6% N.A. MC correction 16% 17% Particle ID 1.4% 1.3% DOCA and Λ reconstruction 13% 13% Eextra 1.9% 11% calculate our final background yield and signal efficiency. These figures can then beusedto calculate both a branching fraction and a branching fraction limit.

As explained in Section 5.2.10, we calculate our final background yield using an mES side-

total band substitution. The total background, Nbkgd , is simply the sum of the combinatorial

comb peak and peaking backgrounds, Nbkgd and Nbkgd respectively, which are calculated according to equations 5.8 and 5.12, reproduced here:

comb × side Nbkgd = RMC NData (5.8)

peak × peak Nbkgd = Cpeak NB+B− (5.12)

peak where NB+B− is calculated according to equation 5.10, reproduced here:

( ) side peak sig sig NB+B− N − = N − − N × . (5.10) B+B B+B B0B0 N side B0B0

As discussed in Section 5.2.10, RMC and Cpeak are already evaluated as RMC = 0.2150.001 and Cpeak = 0.819 0.006, where the uncertainties are statistical only. The remaining quantities required for the background calculation are measured at the end of our signal selection and are presented in Table 5.11.

115 Table 5.11: Numbers of events required to calculate final background yield using the MC correction procedure. See text for details. Uncertainties are statistical only.

Event type Number of events sig NB+B− 1.01 0.32 N sig 0.10 0.10 B0B0 side NB+B− 2.62 0.51 N side 0.99 0.31 B0B0 side NData 8.00 2.83

Inputting these numbers into the above equations, we obtain the final background yields shown in Table 5.12, where we have incorporated the statistical uncertainties shown in Table

5.11 as well as those associated with RMC and Cpeak and the systematic uncertainties shown in Table 5.10.

Table 5.12: Final background estimates after the full signal selection. See text for details.

Background type Number of events comb Nbkgd 1.72 0.61(stat.) peak Nbkgd 0.62 0.34(stat.) total Nbkgd 2.34 0.70(stat.) 0.57(sys.)

Second, we calculate our final signal efficiency. As explained in Section 5.2.10, wetake signal efficiency at the end of the signal selection, (0.0654 0.0013)%, and multiply by

− Cpeak = 0.8190.006. We also multiply by the branching fraction of Λ → pπ , 0.6390.005 [9], to account for the fact that this analysis only searched for this B−→ Λpνν via this channel. Finally, we incorporate the systematic uncertainties shown in Table 5.10 to obtain

final a final signal efficiency, ϵsig , of:

final × −4 ϵsig = (3.42 0.08(stat.) 0.80(sys.)) 10 . (5.14)

116 The branching fraction, B, for B−→ Λpνν is calculated as:

N obs − N total B = Data bkgd (5.15) final × initial ϵsig NB+/−

obs initial where NData is the number of events in data observed upon unblinding and where NB+/− is the number of charged B-mesons in the dataset (see Section 5.1.2). However, since this

obs analysis was conducted blinded (i.e. we did not know NData until we received approval to unblind), we calculated a range of possible values for B based on a range of likely values for

obs NData, as shown in Table 5.13. In the absence of new physics contributions, the extremely low predicted branching fraction of B−→ Λpνν of (7.91.9)×10−7 is below the sensitivity of this analysis and we would therefore expect to see zero signal events (i.e. no excess of events in data). We also calculate upper limits on the branching fraction at the 90% confidence level using the Barlow method, as explained below.

Barlow method

The Barlow method [77] is a confidence interval calculator designed for measuring branching ratios of rare particle physics decay modes. It uses a frequentist method of interval estimation incorporating Gaussian uncertainties on signal efficiency and background yield.

The Barlow method first generates a trial value for the branching fraction B, which is then multiplied by a “sensitivity” S. In the case of this analysis, the value for S is drawn from

final × initial a Gaussian with mean ϵsig NB+/− and a standard deviation equal to the uncertainty on final × initial ϵsig NB+/− .

We then add to (B × S) a number of background events, b, where in the case of this analysis

total the value of b is drawn from a Gaussian with mean Nbkgd and a standard deviation equal to

total the uncertainty on Nbkgd .

We now define µ ≡ B × S + b, and µ is used as the mean of a Poisson distribution from

117 which a number of events, n, is drawn.

The above recipe is repeated many times for each trial value of B and the 90% confidence level upper limit on B is the value of B for which 10% of trials generate a value of n equal

obs to or less than our assumed value of NData.

5.3.3 Final results

The branching fraction and branching fraction upper limits figures for a range of possible

obs values of NData are shown in Table 5.13.

Table 5.13: Branching fraction central values and upper limits at the 90% confidence level for a obs range of possible values of NData. Central value Upper limit N obs Data (×10−5) (×10−5) 0 −1.45 0(stat.) 0.65(sys.) 0.21 1 −0.83 0.62(stat.) 0.59(sys.) 1.17 2 −0.21 0.89(stat.) 0.56(sys.) 2.10 3 0.41 1.08(stat.) 0.57(sys.) 3.02 4 1.03 1.24(stat.) 0.61(sys.) 3.92 5 1.65 1.39(stat.) 0.68(sys.) 4.80

The expected background based on the analysis of MC is 2.34 0.70(stat.) 0.57(sys.) and, on unblinding the data, we see three events, consistent with our expectation.

We thus evaluate a branching fraction central value of (0.411.08(stat.)0.57(sys.))×10−5, i.e. consistent with zero. An upper limit on the branching fraction at the 90% confidence level is evaluated using the Barlow method of 3.02 × 10−5. For comparison, the Standard Model prediction for the branching fraction is (7.9 1.9) × 10−7 [5].

118 5.3.4 New physics implications

A comparison of the branching fraction limit and its SM-predicted value allows us to place

| ν | a constraint on beyond-SM values of CL , the Wilson coefficient that describes left-handed weak currents [85]. Using the parametrization of Ref. [24], and assuming the SM value of

ν CR = 0 (that is, there are no right-handed weak currents), we can place an upper-limit on | ν | | ν SM| ϵ = CL / (CL) of 7.4 at the 90% confidence level. The same calculation for the related b → sνν modes B → K(∗)νν, using measured and predicted branching fraction values from Refs. [26, 27, 35], yields upper limits on ϵ of 2.2 for B+ → K+νν and 2.7 for B0 → K∗0νν at the 90% confidence level.

We also provide a plot of signal efficiency versus q2, where signal efficiency has been measured relative to the number of signal events which pass the local skim cuts and after they have been reweighted, and where the plot has been normalised to unity, see Figure 5.3.5. Since q2 represents undetected physics, and because undetectable New Physics may contribute to the B−→ Λpνν signature, knowledge of signal efficiency as a function of q2 can be valuable for theorists constructing possible New Physics models.

2 y = 0.22, dof = 0.61, p-value = 0.65 0.250

0.225

0.200 Reltaive efficiency 0.175

0.150

0.125

0.100

0.075

0 2 4 6 8 10 q2 (GeV/c2)

Figure 5.3.5: Signal efficiency at the end of the signal selection as a function of q2, normalised to unity. See text for details.

119 Since high q2 means less momentum is available for the final state charged tracks, we would expect higher q2 to correlate with lower signal efficiency, since lower-momentum charged tracks are more difficult to detect and identify. We see in Figure 5.3.5 that visually the correlation between q2 and signal efficiency matches our intuition. The correlation, however, is weak and a χ2 goodness-of-fit test to the uncertainty-weighted mean of the points returns χ2/d.o.f. = 0.61 with a p-value of 0.65. In other words, the data can be fit with a straight, horizontal line.

120 Chapter 6

Analysis at Belle II

This chapter describes a sensitivity study for a search for B−→ Λpνν at the Belle II experiment. The description of the analysis provided in this document is the first time it has been presented publicly.

6.1 Motivation

− The analysis of B → Λpνν at BABAR presented in the previous chapter represents the first experimental measurement of this decay mode. It thus acts as a benchmark for analyses at future experiments such as Belle II.

While some limits on new physics can be drawn from the result at BABAR, as described in Section 5.3.4, they are not competitive with those from other analyses and the branching fraction limit is compatible with Standard Model predictions. However, there is a considerable gap between the upper limit we obtained of 3.02 × 10−5 and the Standard Model prediction of (7.9 1.9) × 10−7. It is possible that in this gap lies new physics, and by performing analyses on future experiments with more data and better software and hard-

121 ware capabilities we may be able to discover new physics hiding in the gap, or obtain a lower branching fraction limit and thus place tighter limits on where new physics could exist.

As the only next-generation B-factory, Belle II is the natural place at which to conduct a new search for the B−→ Λpνν decay. At the time of writing Belle II has not commenced full data taking and therefore it is not yet possible to conduct an analysis and obtain a result based on data. However, an analysis based purely on MC (i.e. a sensitivity study) can be conducted. This has value for several reasons:

• First, as an early analysis it acts as a way of testing the analysis framework of the experiment. The analysis described in this chapter was performed using early Belle II MC simulations and analysis software (see Sections 6.2.2 and 6.2.4). Such early analyses, performed in the initial stages of an experiment’s life, have great value because they act as trial runs for future analyses of all types by pulling together and testing the software, simulation and general analysis setup in a single project. This is particularly important in a large collaboration such as Belle II, where many disparate groups are responsible for different parts of the analysis setup since it is only once an analyst puts all the parts into action together that problems (and their solutions) become apparent. In concrete terms, early analyses such as this one contribute to finding bugs in analysis software, identifying missing features in analysis software, identifying missing or lacking technical documentation, highlighting usability issues, etc.

• Second, it allows us to compare the expected performance of Belle II with its prede-

cessors such as BABAR and identify comparative strengths and weaknesses. Despite the lack of data at Belle II at the time this analysis was conducted, the results of the MC-driven sensitivity study can give us an indication as to how Belle II is expected

to perform, once data arrives, compared to predecessor experiments such as BABAR. While we would expect, due to the superior capabilities of Belle II, that performance

122 would be better, it is possible that due to the infancy of the analysis tools being used

that our performance may in fact be comparable or even inferior to BABAR when using a comparably-sized dataset. It is also possible that there are deficiencies in the detector itself, such as a subdetector not performing as expected, and an early analysis such as this can highlight such issues. Somewhat related to the first point, results such as these help highlight areas that require improvement if Belle II is to be a competitive experiment in its coming years of operation. In light of this motivation, we have scaled the MC we use for this Belle II analysis to the same integrated luminosity as

the dataset used for the BABAR analysis in the previous chapter (see Section 6.2.2 for more details). We have also, as far as possible and sensible, used the same or similar

analysis techniques as the BABAR analysis (compare Sections 5.2 and 6.3). These two

measures ensure that the BABAR and Belle II results are as like-for-like comparable as possible and that any differences should be due to inherent differences between the experiments (as opposed to being due to, for example, a completely different analysis strategy).

• Third, it provides a foundation on which future Belle II analysts can build when performing future analyses of B−→ Λpνν or similar modes. The long operating lifetime of an experiment such as Belle II, combined with the high turnover of students and young researchers, mean that an early analysis may be started by one person and continued by another at a later date. Even in cases where it is not the exact same mode that is analysed, it is common for analysts to adapt and build on work done by their predecessors when performing similar analyses. In light of this motivation we have, as far as possible and sensible, used default Belle II analysis software and functionality with the aim of ensuring usability and ease of comprehension for future analysts who might wish to continue, or adapt elements of, this analysis.

A detailed description of the analysis at Belle II follows.

123 6.2 Analysis tools

6.2.1 Full event interpretation

Full event interpretation (FEI) is Belle II’s equivalent of the hadronic Btag reconstruction

(which we will henceforth refer to as “HTR” for brevity’s sake) we used in the BABAR analysis of B−→ Λpνν decays. This section is based on the description of the FEI algorithm given in Ref. [86], except where otherwise noted.

Belle II’s FEI shares the same objective as BABAR’s HTR: the reconstruction Btag candidates from exclusive decay modes in e+e− → Υ(4S) → BB events, for the purposes of analysing B meson decays.

FEI reconstructs B mesons from on the order of 10,000 decay chains, a significant increase on the 1,768 [64] used in BABAR’s HTR. FEI starts from final state particles detected by Belle II and, like HTR, progresses up the decay chain via J/ψ , kaon and D-meson reconstructions. A diagram of the concept is shown in Figure 6.2.1.

Figure 6.2.1: B-meson reconstruction by FEI. Figure from [86].

124 Like BABAR’s HTR, FEI provides both B+ and B0 tagging capability although, as before, the B0 mode is not of interest for this analysis. FEI also provides semileptonic tagging capability, reconstructing B-mesons through B → D(∗)lν decays. Semileptonic tagging offers a higher efficiency than hadronic tagging, mostly thanks to the higher inclusive branching fraction for semileptonic decays, but also due to the high-momentum lepton which can be easily identified. However, we do not use it for this analysis partly to maintain comparability with the BABAR analysis, and partly because it relies on tagging modes which contain a neutrino and therefore cannot fully reconstruct a Btag which means that kinematic information will inevitably be lost.

FEI’s candidate selection and reconstruction is based around several layers of multivariate classifiers. At each stage of reconstructing a Btag candidate (i.e. from selecting final state particles, to reconstructing intermediate particles such as D mesons, through to selection of a final B meson candidate), a machine learning-based multivariate classifier is used to calculate a signal probability for all candidates at that stage. The classifier uses inputs such as PID likelihoods (for final state particles), kinematic information and vertex fit parameters and (for composite particles) inherited signal probability values from their constituent descendants to calculate the signal probability of the candidate in question. Candidates are then ranked based on their signal probability and the best 10-20 candidates are kept for the next (higher) level of reconstruction in the decay chain. Finally, reconstructed Btag candidates are returned with their associated signal probability values, allowing the analyst to either pick the best (highest signal probability) candidate or even to perform an analysis with multiple candidates.

We see that FEI’s most distinctive difference from BABAR’s HTR, other than the huge increase in the number of decay chains, is that HTR selects candidates based on physically- meaningful quantities such as mES and ∆E. While FEI does employ some basic cuts on physical quantities in the pre-selection of candidates, its actual candidate selection is based

125 on signal probability, the numerical but non-physical output of its multivariate classifiers.

Signal probability can be thought of as analogous to the purity measure used in the BABAR analysis (see Section 5.2.4) in that they are both figures of merit that serve the purpose ofre- moving low quality reconstructions. However, they are slightly different in execution: purity is a relatively straightforward measure – the probability that an event has been reconstructed in the correct decay mode; whereas signal probability is a multivariate calculation based on (some) non-physical quantities (e.g. inherited signal probability) making the process less intuitive and the output less straightforward to interpret.

FEI claims to offer better tagging efficiency (the fraction of events that can be tagged)and tag-side efficiency (the fraction of events with a correct tag) than previous tagging methods such as BABAR’s HTR or Belle’s [47, 48] Full Reconstruction [87], thanks to an increased number of decay chains used for tag reconstruction and an improved tag selection process.

While BABAR’s HTR had a maximum tag-side efficiency of 0.4% for B reconstructions, FEI obtains a tag-side efficiency of 0.76% for hadronic B reconstructions on Belle MC converted to Belle II format. However, despite these claimed performance improvements, the FEI faces challenges due to being in the early stages of development and also from the relative infancy of the Belle II analysis software and MC (hence why, in many cases, performance of the FEI was measured on Belle, rather than Belle II MC, since Belle is a more mature experiment where the MC is is better understood and is believed to be more accurate).

Performance studies on the FEI using converted Belle data and MC show that the data/MC tag-side efficiency ratio is below unity in most cases, generally in the range 0.6 - 0.9,with

+0.014 an average for charged Btag reconstruction of 0.74−0.013(stat.) 0.050(sys.). This study was, however, limited in scope: it examined only ten modes where the Bsig could be reconstructed via semileptonic modes and, as already mentioned, was based on Belle data converted to Belle II format. While a data/MC ratio in tag-side reconstruction efficiency of less than unity is not unexpected (we observed the same effect at BABAR, see Section 5.2.10), early

126 indications are that the discrepancy using FEI is large. A detailed study of the FEI using Belle II MC and data is required and eagerly awaited so that we can better understand its performance.

6.2.2 Background Monte Carlo

As in the BABAR analysis discussed in the previous chapter, the Belle II analysis uses background Monte Carlo to simulate the expected behaviour of generic background processes in the Belle II detector.

In the case of Belle II, background processes are classified in seven types: B+B−, B0B0, cc, uu, ss, dd, τ +τ −. The event types represented by these MC types are the same as those represented by the corresponding BABAR MC types (see Section 5.1.3), although the MC itself is new and generated specifically for the Belle II experiment.

BB events are generated using EvtGen [72]. Continuum (qq and τ +τ −) events are simulated using KK [74], with qq hadronisation handled by Pythia [88, 89] and τ decays by Tauola [75]. The Belle II detector geometry and the interactions of particles with the detector are simulated using GEANT4 [76].

The relative infancy of the Belle II experiment means that large-scale MC production has not yet occurred and the best and most recent background MC available to us has an integrated

− − luminosity of only 0.8 ab 1. While this is more than the entire BABAR dataset (0.424 ab 1), it is obviously dwarfed by the targeted Belle II integrated luminosity of 50 ab−1. In time, larger background MC samples for Belle II will become available.

For this early study, where we are aiming to provide comparability between this Belle II

− sensitivity study and the BABAR analysis, we use the 0.8 ab 1 of background MC available

− to us and down-weight it to match the 0.424 ab 1 integrated luminosity of the BABAR ex-

127 periment’s dataset. Details of the background MC used in this analysis are shown in Table 6.1.

Table 6.1: Background Monte Carlo used in the Belle II sensitivity study. For information on skimming, see Section 6.3.1.

Type Generated events Skimmed events Skim efficiency Cross-section Weight (106) (106) (%) (nb) B+B− 452.32 37.759406 8.3480 0.5654 0.530 B0B0 427.68 24.019193 5.6162 0.5346 0.530 uu 1284.00 88.125714 6.86337 1.605 0.530 dd 320.80 23.084031 7.1958 0.401 0.530 cc 1063.20 128.112738 12.0497 1.329 0.530 ss 306.40 18.778530 6.1288 0.383 0.530 τ +τ − 735.20 1.151058 0.15656 0.919 0.530

6.2.3 Signal Monte Carlo

The signal MC used for the Belle II analysis comprises the same type of events as that used

− for the BABAR analysis (see Section 5.1.4), namely Υ(4S) → B+B where one B meson decays as B−→ Λpνν while the other B meson decays generically, and for the B meson which decays via B−→ Λpνν , this is followed by Λ → pπ− with a 100% branching fraction. The physics of the events simulated in the signal MC used in this analysis are identical to that used in the BABAR analysis, although the signal MC we use here is generated specifically for this analysis and is run through a simulation of the Belle II detector. We generate 10 million signal MC events, compared to approximately 4 million which we generated for the

BABAR analysis.

For the histograms in this chapter, signal MC has been plotted with an assumed branching fraction of 1 × 10−4, as in the previous chapter.

The signal MC has also been reweighted to account for the predicted phase space distributions given in Ref. [5], which are explained in more detail in Appendix A. As discussed in

128 Appendix A, in the case of the signal MC used in the BABAR analysis we reweighted only to the Λp invariant mass, as reweighting to the other variables given in Ref. [5] made no significant difference to the final signal efficiency.

In the case of the signal MC used in this Belle II analysis, the only reweightings that make a significant difference to the final signal efficiency aretothe Λp invariant mass and to the νν invariant mass. The final signal efficiency in both cases agree within statistical uncertainties therefore, and in order to maintain comparability with the BABAR analysis, we reweight only to the Λp invariant mass.

6.2.4 Belle II Analysis Software Framework

The Belle II collaboration uses a custom software framework for analyses known as the Belle II Analysis Software Framework (basf2) [90].

The BABAR analysis described in the previous chapter was performed primarily using “vanilla” ROOT [91], a commonly-used particle physics software toolkit. While ROOT provides many capabilities specifically tailored for particle physics analyses it is not, in it’s vanilla form, targeted at a specific experiment or even a specific type of experiment. Consequently, a considerable amount of custom analysis code had to be used in order to perform the analysis described in the previous chapter, and several other pieces of software and other languages also had to be employed for different stages of the analysis. basf2, on the other hand, provides simulation, reconstruction and analysis capabilities specifically tailored for Belle II within a single software framework. As with many aspects of Belle II, basf2 is still in its infancy. At the time this analysis started, basf2 has not even reached release-01* and we therefore worked using the latest available release-00-09*. By the time the analysis was finished release-01* was available and was used to run the analysis from start to finish, although limitations and bugs were still present in the software.

129 In line with our aim of making a future-compatible analysis that later analysts can use and build from, we use wherever possible default basf2 functionality for this analysis. Due to some limitations still present in basf2, we also conducted a small portion of the analysis in ROOT.

6.3 Signal selection

6.3.1 Skim

Within the Belle II collaboration, skims are centrally produced by a dedicated skimming group and made available to individual analysts to perform analyses on. For this analysis we use the FEIHadronicBPlus skim which, as the name suggests, is a skim comprising hadronic B+B− candidates created using FEI (see Section 6.2.1 for details on FEI). The cuts used in this skim are:

2 • Mbc > 5.24 GeV/c

• |∆E| < 0.20 GeV

• signal probability > 0.001 where:

Mbc is the beam-constrained mass (the equivalent of mES in the BABAR analysis) and is defined as:

√ M = (E /2)2 − ⃗p 2 (6.1) bc CM Btag

and ECM is the energy of the centre-of-mass system,

130 ∆E has a similar definition as in BABAR:

E∗ ∆E = E∗ − CM , (6.2) Btag 2 and signal probability is the non-physical output of the FEI multivariate classifiers described in Section 6.2.1.

We see that these skim cuts are similar to the cuts used in the hadronic Btag reconstruction stage of the BABAR analysis (see Section 5.1.1) but are considerably looser than those used in the skim stage (see Section 5.2.1). Furthermore, unlike the cuts used in the hadronic

Btag reconstruction stage of the BABAR analysis, these cuts do not require only a single Btag candidate per event - if the FEI returns multiple candidates which survive these cuts then multiple candidates will be provided to the analyst.

In order to maintain comparability with the BABAR analysis as far as possible, and also in order to reduce the amount of data we are required to work with for the rest of the signal selection, we additionally implement the following selection criteria:

• there must be exactly three charge tracks remaining in the event after Btag reconstruction,

• if there is still more than one Btag candidate, we choose the candidate with the highest signal probability.

Most of the cuts used in the BABAR skim are now accounted for, the exceptions are:

• missing energy > 0, and

• the sum of the charges of the Bsig descendants must be equal-and-opposite to the

charge of the Btag.

Regarding the first requirement, missing energy is a default variable provided by basf2and

131 therefore could easily be incorporated into the analysis. However, it is known to be poorly- defined and buggy in release-01* of basf2, problems that we confirmed as part of this analysis. We therefore chose not to include it. In any case, the cut on missing energy was used in the BABAR analysis largely as a so-called “sanity check”, since it is almost impossible to fully account for every particle in an event reconstruction almost all events have missing energy >0. The fact that this cut is not present in the Belle II analysis is therefore of little consequence.

Regarding the second requirement, charge consistency is of course important and is, in fact, implemented as part of this analysis. However, the analysis paradigm employed by basf2 means it is not possible to implement this requirement at an early stage of the signal selection (e.g. during the skim), and it instead must be implemented later (see Section 6.3.4). basf2 is based around a bottom-up analysis paradigm where the analyst starts by selecting final- state-particle candidates and works up the decay tree of their chosen signal to create a Bsig candidate. Once this is done, the Bsig candidate can be combined with the Btag candidate to create a Υ(4S) candidate, and it is only once this is done that charge consistency can be imposed. This analysis model also means that some quite general tasks such as continuum suppression and an extra energy cut can only be done later in the analysis, after signal-specific steps of the signal selection have been performed. Thus, the rest of the signal selection for this Belle II analysis is done in a rather different order than the BABAR analysis presented in the previous chapter.

6.3.2 Particle identification

As explained in the previous section, analyses at Belle II using basf2 begin by selecting final-state-particle candidates. In the case of B−→ Λpνν followed by Λ → pπ−, our final state particles (FSPs) of interest are two protons (of opposite charge) and a pion.

132 To select our FSPs we use two PID selectors: one for the protons and one for the pion. In both cases we use PID selectors that have a 95% efficiency, where the efficiency is calculated based on MC studies for tracks with momentum of between 1 GeV/c and 4 GeV/c with trajectories inside Belle II’s barrel region and originating from near the IP.

Particle ID hypotheses are based on input from all Belle II tracking sub-detectors where a track leaves a signal, and discrimination of one particle type from another is based on the discriminating power of these sub-detectors as described in Section 4.2. For charged particles, particle ID is based primarily on energy loss rate measurements from the PXD and CDC; and for charged hadrons time-of-flight and Cherenkov ring-imaging information from the TOP and AIRCH also play an important role [42].

Unlike the low-level analysis possible using vanilla ROOT that we did for the BABAR analysis, basf2’s high-level approach does not, at this point in the signal selection, allow us to specify that we require two oppositely-charged protons in an event. We likewise are not able to tag

(or even require) charged tracks as originating from the Λ or the Bsig; this means a cut on DOCA is also not yet possible. This stage of the signal selection simply selects all protons and pions (including their antimatter counterparts) that pass the PID requirements.

Note that the charged FSPs we have selected include proton and pions from the entire event, both those used in the reconstruction of the Btag and those originating from the Bsig. The bottom-up approach of basf2 means we have not yet made any relation between the Btag candidate and the analysis that we are performing of B−→ Λpνν which will ultimately be restricted to the Bsig side of the event. It is only later in the signal selection, after we have worked our way up to recontructing a Bsig and relating it to the Btag by reconstructing an Υ(4S), that we can impose separation of the Btag and Bsig descendants (see Section 6.3.4).

133 6.3.3 Λ reconstruction

Once the charged FSPs that we expect from B−→ Λpνν have been identified, we move to the next stage up in reconstructing the decay chain: reconstructing the Λ.

We take the charged FSPs that pass the PID selectors and from them create all possible Λ candidates that meet the requirements of charge consistency (i.e. that the proton and pion that are the descendants of the Λ have opposite charged) and that the reconstructed Λ has an invariant mass within 40 MeV of the world average mass of the Λ [9].

Note that because the FSPs we collected in the previous stage of the signal selection can originate from anywhere in the event, the Λ candidates we reconstruct at this stage cannot be limited to being reconstructed from descendants of the Bsig. In fact, basf2 will reconstruct all possible Λ candidates that have charge consistency and pass the cut on the Λ mass, including candidates built from descendants of the Btag, and even candidates built from a mix of Btag and Bsig descendants. Clearly, such a list of Λ candidates will include many misreconstructions and candidates that are not of interest to us.

The reconstructed Λ masses that result from this process are shown in Figure 6.3.1. As expected, we see a significant combinatorial background contribution, both in background and signal MC events. Note that at this stage it is possible for a single event to contain multiple Λ candidates, which will further increase the combinatorial background.

Many irrelevant candidates will be removed later in the signal selection when we work our way up the decay chain to reconstructing the entire event (see Section 6.3.4); until then we can slightly improve our Λ selection by using a vertex fitter.

The Λ candidates are fitted using KFit [92], which performs a fit based on kinematic, mass and vertex constraints using a least-squares minimisation method; Λ candidates for which a viable fit cannot be achieved are discarded. This is less sophisticated than TreeFitter

134 Figure 6.3.1: Reconstructed Λ candidates after FEI, skim, particle ID and Λ reconstruction cuts. used in the BABAR analysis (see Section 5.2.9) which additionally utilised a constraint on the production vertex of the Λ being within the flight length of the ancestor B meson. Furthermore, TreeFitter fits an entire decay chain, with the aim of providing improved results by sharing fit information across the entire chain [80]; KFit, on the other hand, fits only a single vertex. However, at the time this analysis was performed, TreeFitter had not been implemented in basf2 and KFit was the most capable fitting algorithm available.

It should also be noted that early studies [93] performed on Belle II phase 2 data have highlighted a large systematic disagreement between Λ reconstruction in MC and in data. Specifically, the efficiency for Λ reconstruction in data is approximately 51% of that in MC even when using a later basf2 release (release-02-00-01) and newer MC than used in the analysis presented in this chapter. The Λ reconstruction results presented in this chapter should therefore be interpreted with caution. Further studies into Belle II’s Λ reconstruction performance are clearly vital to the future performance of the experiment.

The reconstructed Λ mass after the application of KFit is shown in Figure 6.3.2. As we can see, the Λ peak is now better-defined and a considerable amount of combinatorial background has been eliminated. Note that it is still possible at this stage for a single event to contain

135 multiple Λ candidates, and Λ candidates can still be reconstructed using FSPs from anywhere in the event (i.e. Λ candidates are not restricted to being reconstructed only from descendants of the Bsig). Our Λ candidate selection will be further refined in the following stages ofthe signal selection.

Figure 6.3.2: Reconstructed Λ candidates after FEI, skim, particle ID, Λ reconstruction and KFit cuts.

6.3.4 Event reconstruction

We now move up to the highest levels of the decay chain reconstruction: the Bsig and Υ(4S) candidates.

In the BABAR analysis no attempt was made to reconstruct a Bsig or Υ(4S). Due to the

− missing energy in a B → Λpνν decay, any attempt at reconstructing a Bsig (and thus an Υ(4S)) candidate is bound to end in an incomplete reconstruction since the neutrinos cannot be detected. Furthermore, the full reconstruction of the Btag via HTR means that the kinematics of our Bsig are fully defined, rendering a reconstruction of the Bsig and Υ(4S) unnecessary.

136 In the case of the Belle II analysis, however, a reconstruction of the full event (that is, all the way up to the Υ(4S)) is necessitated by basf2’s bottom-up analysis model. As we have discussed in previous sections, our signal selection thus far has been conducted based ultimately on FSPs in the entire event, as we do not have a way at the lowest levels of the analysis to discriminate between FSPs that descend from the Btag and those that descend from the Bsig. Once we reconstruct the full event, we create a relation between the Btag and Bsig (specifically, we demand that they are distinct and do not share any descendants) and we can then reach back down the decay chain and examine variables (e.g. the mass of reconstructed Λ candidates) relating only to descendants of the Bsig.

The “reconstruction” of the Bsig and Υ(4S) is principally a logical, rather than physical, exercise. The missing energy in B−→ Λpνν events means our reconstructions have little physical meaning, they serve instead only to separate the Btag and Bsig descendants. The requirements for the full event reconstruction are thus relatively simple and straightforward:

• Bsig candidates are reconstructed by combining Λ candidates from the Λ reconstruction stage of the signal selection (see Section 6.3.3) with an proton ID’ed during the PID stage of the signal selection (see Section 6.3.2) (specifically, anti-protons are combined with Λ candidates, and protons with anti-Λ candidates). The lone proton must not be a descendant of the Λ candidate it is combined with, and the charge of the proton

must be the same as the Bsig candidate.

• Bsig candidates from the above stage are combined with Btag candidates provided by

the FEI (see Section 6.2.1). Combined Bsig and Btag candidates must not share any descendants, and must be of opposite charge.

In summary, by reconstructing the event we impose separation between the Btag and Bsig and impose charge consistency. This has the natural consequence of removing a considerable

137 amount of candidates which had survived our signal selection up till this point, as we can see by comparing Figure 6.3.2 with Figures 6.3.3, where the former shows Λ candidates before event reconstruction and latter after event reconstruction.

Figure 6.3.3: Reconstructed Λ candidates after FEI, skim, particle ID, Λ reconstruction, KFit and event reconstruction cuts.

The Λ peak in Figure 6.3.3 has a very similar shape to that in 6.3.2, which is expected as we have not performed any selection on the Λ candidates themselves; however, the number of candidates is much reduced as Λ candidates are now required to comprise only FSPs which are descended from the Bsig.

6.3.5 Distance of closest approach

With the event reconstruction now complete, we can reach back down the Bsig decay chain and conduct further signal selection exclusively among the descendants of the Bsig, including selecting a single best Λ candidate per event.

In the Λ reconstruction and selection steps taken so far, it is possible for us to reconstruct multiple Λ candidates per event. We would, of course, like to pick the Λ candidates with the best reconstruction, but until and unless we have conducted the event reconstruction,

138 we cannot guarantee that any best Λ candidate that we select is descended from the Bsig. Now that the event reconstruction has occurred, and we can limit ourselves to descendants of the Bsig, we can select Λ candidates with the best reconstructions.

The first variable we use to do this is distance of closest approach (DOCA), which was explained in Section 5.2.8. The physics of a B−→ Λpνν event are the same in Belle II as they are in BABAR, so we expect to see the same DOCA order, namely:

− • lowest DOCA: the p that is the descendant of the B (Bsig),

• middle DOCA: the p that is the descendant of the Λ, and

• highest DOCA: the π− that is the descendant of the Λ, where we utilise the PID tags assigned in the PID stage of the signal selection (see Section 6.3.2).

The expected DOCA ordering is clearly visible in signal MC, as shown in Figure 6.3.4.

We therefore impose the DOCA requirements on the Λ candidates, any Λ candidates that do not conform to the expected DOCA ordering are discarded. The surviving Λ candidates are shown in Figure 6.3.5.

We see that, compared to Figure 6.3.3, the numbers of both signal and background MC candidates have been reduced; however, the reduction in the number of Λ candidates in background MC is much greater than the reduction in those in signal MC, demonstrating the value of the DOCA cut in retaining signal while rejecting background. A calculation of the marginal efficiency of the DOCA cut (see Section 6.3.11) shows that it retains approximately 83% of signal events while rejecting approximately 56% of background events.

139 Belle2_BsigdaughtP_DOCA Belle2_Lambda0daughtP_DOCA

h_Bsig_daughtP_DOCA Entries 7065 Mean 0.2033 Std Dev 0.7795

h_Lambda0_daughtP_DOCA h_Bsig_daughtP_DOCA Entries 7065 Mean 0.6958 h_Lambda0_daughtP_DOCA Std Dev 0.8196 24

22 7 20 6 18 16 5 14 12 4 Belle2_Lambda0daughtPi_DOCA10 Number of tracks (per 0.2 cm) 3

8 Number of tracks (per 0.2 cm) 6 2 4

2 1 0 0 1 2 3 4 5 6 7 8 9 10 0 DOCA (cm) 0 1 2 3 4 5 6 7 8 9 10 DOCA (cm) (a) Proton that is the descendant of the

(b) Proton that is descendanth_Lambda0_daughtPi_DOCA of the Λ. Entries 7065 Mean 2.39 Bsig. h_Lambda0_daughtPi_DOCA Std Dev 2.122

1.8

1.6

1.4

1.2

0.8 Number of tracks (per 0.2 cm)

0.6

0.4

0.2

0 0 1 2 3 4 5 6 7 8 9 10 DOCA (cm) (c) Pion that is descendant of the Λ.

Figure 6.3.4: Distance of closest approach (DOCA) for tracks identified as descendants of the Bsig.

Figure 6.3.5: Reconstructed Λ candidates after FEI, skim, particle ID, Λ reconstruction, KFit, event reconstruction and DOCA cuts.

140 6.3.6 Best Λ selection

Even after the cut on DOCA order described in the previous section, it is possible that there remain multiple Λ candidates per event - with three FSPs per event there are two possible combinations which have the necessary charges to produce a neutral reconstructed Λ candidate (although the selection we have implemented thus far make it unlikely that two Λ candidates will survive to this point). The second, and last, step in selecting Λ candidates is therefore to select the single-best remaining candidate in an event.

To select the best Λ, we rank all surviving Λ candidates based on their significance of flight distance, defined as the distance of the particle from the IP divided by the uncertainty on that distance, and pick the candidate in each event with the highest significance of distance. The surviving Λ candidates are shown in Figure 6.3.6.

Figure 6.3.6: Reconstructed Λ candidates after FEI, skim, particle ID, Λ reconstruction, event reconstruction, DOCA and best Λ selection cuts.

We see that Figure 6.3.6 is visually identical to Figure 6.3.5, indicating that in fact there were no cases of multiple Λ candidates per event surviving the DOCA cut; a check of the numerical output of the signal selection confirms that this is the case. While, in the specific case of this early sensitivity study, the best Λ selection is redundant, we include it because

141 this will not necessarily be the case in future studies of B−→ Λpνν at Belle II using higher statistics, as well as newer MC and software.

6.3.7 Continuum suppression basf2 contains some default continuum suppression tools; however, these mostly involve cutting on a single continuum-related variable and offer inferior performance compared to the multivariate technique we used in our BABAR analysis (see Section 5.2.5). It is likely that as Belle II evolves, more sophisticated techniques will be incorporated into basf2, and/or the Belle II collaboration will make recommendations for more effective continuum suppression techniques.

In the meantime, in order to preserve comparability with the BABAR analysis and in order to avoid sacrificing performance, we opt to implement the same multivariate likelihood technique that we used in the BABAR analysis. However, in order to also use as much default basf2 machinery as possible (and thus make it easier for future Belle II analysts to continue or adapt this analysis), we restrict ourselves to using continuum-related variables that are available by default in basf2 or which can be easily defined by the analyst using basf2.

The variables used (all calculated in the CM frame) are:

• R2: the ratio of the 2nd and 0th Fox-Wolfram moments [78] (also used in BABAR continuum suppression under the name R2All), see Figure 6.3.7a.

• |cos(TBTO)|: the magnitude of the cosine of the angle between the thrust axis of

the Btag and the thrust axis of the rest of the event (also used in BABAR continuum

suppression under the name |cosθthrust|), see Figure 6.3.7b.

• |cos(TBz)|: the magnitude of the cosine of the angle between the thrust axis of the Btag

and the z-axis (also used in BABAR continuum suppression under the name Thrustz),

142 see Figure 6.3.7c.

• thrustBm: magnitude of the Btag thrust axis (similar, but not identical to, the “thrust

magnitude” variable used in the BABAR continuum suppression which measured the

thrust of the entire event, rather than just the Btag), see Figure 6.3.7d.

• cosθpmiss : the cosine of the angle between missing momentum and the z-axis in the

CM frame (also used in BABAR continuum suppression), see Figure 6.3.7e.

• cosθB: the cosine of the angle between the Btag three-momentum and the z-axis in the

CM frame (also used in BABAR continuum suppression), see Figure 6.3.7f. and where thrust and thrust axis are defined in Section 5.2.5.

These variables are combined into a multivariate likelihood according to Formula 5.4 to produce our continuum suppression variable, BB likelihood, which is shown in Figure 6.3.8.

We can see that, as was the case in the BABAR analysis, BB likelihood provides excellent discrimination between continuum and non-continuum events.

The value of the cut BB likelihood is optimised using the branching fraction upper limit after a nominal signal selection as the figure of merit. We vary the BB likelihood cut value and see how this affects the branching fraction upper limit, as shown in Figure 6.3.9. Aswe can see, the value of the BB likelihood cut has little impact on estimated final branching fraction upper limit for cuts below ∼ 0.5, above which we see a clear trend of increasing branching fraction upper limit.

Given the wide range of possible cut values, our next priority is to maintain comparability with the BABAR analysis. We do this by choosing a cut value whose marginal change in signal efficiency matches that of the BABAR cut (marginal change in signal efficiency is defined as the change in signal efficiency that occurs when a single cut is removed from an otherwise

143 (a) R2 (b) cos|(TBTO)|

(e) cos(θpmiss ) (f) cos(θB)

Figure 6.3.7: Event-shape variables used to calculate BB likelihood, after FEI, skim, and Mbc cuts. Charge consistency is also imposed (i.e. the charge of the Btag must be equal-and-opposite to that of all remaining tracks in the event).

144 Figure 6.3.8: BB likelihood for events passing FEI, skim, and Mbc cuts. Charge consistency is also imposed (i.e. the charge of the Btag must be equal-and-opposite to that of all remaining tracks in the event). ) -5 Branching fraction upper limit (x10

BB likelihood

Figure 6.3.9: Expected branching fraction upper limit according to the Barlow calculation after a nominal signal selection as a function of BB lieklihood cut. For details on branching limit calculation techniques see Section 5.3.2

145 complete signal selection). That is, we check the marginal change in signal efficiency of the BB likelihood cut in the BABAR analysis and, if possible within the range of cut values available to use in the case of Belle II, choose a cut value for the BB likelihood in the Belle II analysis that has the same marginal change in signal efficiency.

We use this method in order to ensure equivalence between the two analyses. While BB likelihood in Belle II and BB likelihood in BABAR are conceptually similar, the details of their implementations are slightly different, so simply “copying” the BB likelihood cut value used in the BABAR analysis and using it in the Belle II analysis does not necessarily mean that the cuts are equivalent in effect. By matching marginal changes in signal efficiency, we achieve equivalence of effect and thus comparability between the two analyses.

The marginal change in signal efficiency when the BB likelihood cut is removed from the

BABAR analysis is 1.20 (i.e. signal efficiency increases by 20%). We can achieve a similar (1.19) marginal change in signal efficiency in the Belle II analysis by choosing to retain events with a BB likelihood value of >0.35, which meets our requirement of being below ∼ 0.5 and which happens to be the same cut value as that used in the BABAR analysis.

6.3.8 Extra energy

As in the BABAR analysis, Eextra is an important and powerful variable for discriminating between signal and background. The physics concerning the production of extra energy is largely the same in BABAR and Belle II (see Section 5.2.6 for more details). However, the higher beam backgrounds at Belle II present us with extra challenges.

In the BABAR analysis, the only requirement we imposed to help discriminate between (lower energy) background sources of Eextra and (higher energy) real sources of Eextra was a minimum energy of 50 MeV per EMC deposit. In Belle II, the much higher rate of beam background processes, plus the increased coverage of the Belle II ECL compared to the

146 BABAR EMC, means a more sophisticated approach is required.

Photons from real physics processes will generally have higher energy than those from beam background processes. Additionally, photons from real physics processes will arrive approximately in time with each e+e− collision, whereas beam background photons constitute a relatively time-invariant background. We can therefore use cuts on both photon energy and photon arrival time to help discriminate between these two sources of photons.

The selection can be further enhanced by treating each section of the ECL (forward, barrel and backward) separately. The geometry of the ECL combined with the forward bias of Belle II’s collisions mean that in general photons in the forward region will be more energetic and arrive sooner than photons in the barrel, and likewise for barrel versus backward.

Based on standard Belle II photon selection procedures [94], we therefore implement the cuts shown in Table 6.2 when calculating Eextra.

Table 6.2: ECL cuts for Eextra calculation. ECL region forward barrel backward Minimum energy ( MeV) 62 60 56 |cluster timing| (ns) <18 <20 <44

Our resulting Eextra is shown in Figure 6.3.10. We can see that, like in the case of BABAR, signal events peak at Eextra = 0, as we would ideally expect, but they also have a significant non-zero component from beam background and other sources as described in Section 5.2.6.

Background events, meanwhile, have generally much higher values of Eextra, thanks mainly to contributions from real neutral particles.

The value of the cut on Eextra is optimised using the branching fraction upper limit after a nominal signal selection as the figure of merit. We vary the Eextra cut value and see how this affects the branching fraction upper limit, as shown in Figure 6.3.11. As we cansee,the value of the Eextra cut has little impact on estimated final branching fraction upper limit for

147 Figure 6.3.10: Eextra after FEI, skim, particle ID, Λ reconstruction, event reconstruction, DOCA and best Λ selection cuts. cuts above ∼ 0.35 GeV. ) -5 Branching fraction upper limit (x10

Eextra cut (GeV)

Figure 6.3.11: Expected branching fraction upper limit according to the Barlow calculation after a nominal signal selection as a function of Eextra cut. For details on branching limit calculation techniques see Section 5.3.2

We now use the same technique as described in the previous section to choose a cut value, by comparing marginal changes in signal efficiency between the BABAR and Belle II analyses.

The marginal change in signal efficiency in the BABAR analysis when the Eextra cut is removed is 1.50. We obtain a similar (1.52) marginal change in signal efficiency in the Belle II analysis

148 by choosing to retain events with a Eextra value of <0.5 GeV, which meets our requirement of being above ∼ 0.35 GeV. The Eextra cut value used at BABAR was Eextra <0.4 GeV; the slightly different value arrived at for our Belle II analysis is likely due to the higher beam background contributions at Belle II which lead to generally higher levels of Eextra.

6.3.9 Btag Mbc cut

As in the BABAR analysis, we make a cut on the reconstructed mass of the Btag candidate, Mbc

2 (known as mES at BABAR). The range of Mbc available to us after the skim (5.24−5.29 GeV/c )

2 is smaller than in the BABAR analysis (5.20 − 5.29 GeV/c ) due to the value of the Mbc cut chosen by the skimming group for the FEIHadronicBPlus skim; however, it is still wide enough such that a peak around the known B-meson mass is clearly distinguishable from the surrounding combinatorial background.

The reconstructed Btag mass, Mbc, is shown in Figure 6.3.12. We retain events with Mbc

>5.27 GeV/c2, the same value as used in the BABAR analysis.

Figure 6.3.12: Mbc after FEI, skim, particle ID, Λ reconstruction, event reconstruction, DOCA and best Λ selection cuts.

149 6.3.10 mΛ cut

The final stage in our signal selection is a tighter cut on the reconstructed Λ mass. The cut on the Λ mass implemented earlier in the selection, during the Λ reconstruction step (see Section 6.3.3), is relatively loose, we can clearly see that by the time our Λ selection has been refined (see Figure 6.3.6) the cutof 40 MeV/c2 around the known Λ mass still allows through combinatorial background on either side of the Λ mass peak. We therefore now implement another cut on Λ mass, retaining events with a reconstructed mass within 25 MeV/c2 of the known Λ mass of 1.116 MeV/c2 [9]. The Λ mass at the end of the signal selection is shown in Figure 6.3.13.

Figure 6.3.13: Λ mass after FEI, skim, particle ID, Λ reconstruction, event reconstruction, DOCA and best Λ selection, Eextra, BB likelihood and Mbc cuts.

6.3.11 Summary of signal selection

The extremely low background and clear Λ peak shown in Figure 6.3.13 indicate that we are now at the end of the signal selection. The remaining background is within our Λ mass window and any attempts at further background suppression are likely to adversely affect our signal efficiency.

150 Furthermore, one of our aims (see Section 6.1) with this Belle II sensitivity study is to provide comparability with our BABAR analysis as far as possible and sensible. Our signal selection for this sensitivity study is now a close analogue of that used in the BABAR analysis, while working within the restrictions of the Belle II analysis framework and also taking advantage of its capabilities.

At the end of our signal selection the signal efficiency is (2.26 0.11(stat.)) × 10−4 and the remaining background amounts to 10.62.4(stat.) events. A summary of the marginal effect of each signal selection cut is shown in Table 6.3.

Table 6.3: Summary of marginal background yield and signal efficiency as a function of signal selection cut (i.e. the background yield and signal efficiency if the specified cut is removed). Uncertainties are statistical only. See text for further details.

Cut Events in background MC Signal efficiency (×10−4) PID + DOCA 1429.7 27.5 4.46 0.16 Λ reconstruction 14.3 2.8 2.48 0.12 KFit 22.8 3.5 2.77 0.12 DOCA 24.34 3.6 2.71 0.12 Continuum suppression 38.2 4.5 2.68 0.12 Eextra 208.4 10.5 3.39 0.14 Mbc 26.5 3.7 2.61 0.12 mΛ 11.7 2.5 2.36 0.11

Regarding Table 6.3 we note that:

• Removal of the PID cut also necessitates removal of the DOCA cut, since DOCA can only be performed on PID’ed tracks.

• “Λ reconstruction” refers only to the removal of the PDG 40 MeV cut on the reconstructed Λ mass. The bottom-up analysis process required by basf2 means we have to reconstruct Λ candidates if we want to implement the rest of the signal selection. By removing the cut on Λ mass we come as close as possible to removing the Λ reconstruction cut - any Λ candidate which has descendants of appropriate charge is permitted regardless of its mass.

151 • “mΛ” refers to the tighter cut on the reconstructed Λ mass which we discuss in Section 6.3.10.

• A marginal efficiency is not calculated for the best Λ selection step of the signal selection (see Section 6.3.6) since it does not change the number of events, it only selects the single best Λ candidate within an event.

• A marginal efficiency is not calculated for event reconstruction (see Section 6.3.4). While it is a vital part of the analysis, it makes little sense to attempt a signal selection without it - the processing and storage requirements of performing a signal selection

on an entire event (rather than just the Bsig side) would be huge and the results would not be instructive. Event reconstruction is better thought of as a prerequisite for a signal selection rather than as a part of the signal selection itself, it was only due to basf2’s analysis model that we were forced to do it in the middle of the signal selection

rather than before, as was the case with BABAR.

Comparing with the same Table for the BABAR analysis (Table 5.5) we see that the marginal effect of a cut in the Belle II analysis is generally within order-of-magnitude agreementor better with the marginal effect of the cut on the same or similar variable inthe BABAR analysis. We would not expect exact numerical agreement - we are using different MC in a different experiment with different analysis software, the definition of signal selection variables is often similar but rarely identical, and the range of values permitted when we remove a cut also differs (e.g. in the case of the BABAR analysis removing the mES cut

2 2 additionally permits events with 5.20 GeV/c < mES < 5.27 GeV/c , whereas in the case of

2 the Belle II analysis removing the Mbc cut additionally permits events with 5.24 GeV/c <

2 Mbc < 5.27 GeV/c ). Given these differences, agreement to within an order-of-magnitude or better is an encouraging sign that we have succeeded in providing comparability with the BABAR analysis as far as sensible and practicable; it also indicates that there are no

152 significant (i.e. greater than order-of-magnitude level) systematic uncertainties onanyof the Belle II signal selection steps in this sensitivity study.

6.4 Results

6.4.1 Systematic uncertainties

As discussed in Section 6.1, among the purposes of this sensitivity study are to provide a performance benchmark for Belle II and to act as an early test of the Belle II analysis framework, and in doing so highlight areas where the framework requires improvement. The very early versions of the tools and software used for this sensitivity study mean that any exact numerical results (e.g. detailed calculations of systematic uncertainties) will soon be outdated due to Belle II’s rapid development, whereas issues this analysis raises relating to deficiencies and areas for improvement in the analysis framework are far more important and enduring. We have already commented on some such issues in earlier sections of this chapter, and a more detailed discussion follows in Section 6.4.3. Another aim of this analysis is to provide a foundation on which future analysts can build and, once Belle II data arrives in sufficient quantities, can ultimately perform a full analysis of B−→ Λpνν at Belle II. Given the rapid development of Belle II software and other parts of the analysis framework, any systematic uncertainties we might be able to evaluate will be rendered obsolete by the time an analysis on data is performed. We therefore do not calculate any systematic uncertainties for this analysis.

We further note that even if we wanted to calculate systematic uncertainties for this analysis, this would be impossible and/or of limited use for the following reasons:

• This analysis is a sensitivity study, that is, it is conducted entirely on MC with no data available. Without data, many systematics simply cannot be calculated.

153 • This analysis was conducted using early Belle II software and MC. Even during the course of this analysis, basf2 and Belle II MC production procedures have both gone through multiple upgrades. An evaluation of systematics for this analysis would therefore not be representative of the current capabilities of Belle II.

• The relative immaturity of Belle II means that systematics for many pieces of standard Belle II analysis machinery have not yet been evaluated by the Belle II collaboration; without such measurements it is impossible to evaluate the systematic uncertainties from these sources on the result of this analysis. For example, the charged PID algorithms used by Belle II are still under development and until the Belle II PID group evaluates the systematic uncertainties associated with Belle II’s PID selectors, it is not possible (even with real data) to evaluate the systematic uncertainties associated with our use of the PID selectors in this analysis.

6.4.2 Final results

Our final signal efficiency for the Belle II sensitivity study (incorporating the Λ → pπ− branching fraction of 0.639 0.005 [9]) is:

final × −4 ϵsig = (1.44 0.07(stat.)) 10 (6.3) which compares unfavourably with that at BABAR of (3.42 0.08(stat.) 0.80(sys.)) × 10−4).

Our final background estimate is:

total Nbkgd = 10.6 2.4(stat.) (6.4)

154 which likewise compares unfavourably with the result of our BABAR analysis of 2.34 0.70(stat.) 0.57(sys.).

Assuming the absence of excess events in data, we take the branching fraction central value to be zero for the purposes of comparing the results of this Belle II analysis and the BABAR analysis. In order to provide a further comparison of the Belle II and BABAR result, we can also calculate an upper limit on the branching fraction under the assumption that no excess of events in data is observed. We do this using the Barlow method (described in Section 5.3.2). The result is a branching fraction upper limit at the 90% confidence level of

− − 1.2 × 10 4, approximately four times higher than the equivalent BABAR result of 0.30 × 10 4 and considerably higher than the Standard Model prediction of (7.9 1.9) × 10−7.

6.4.3 Implications for Belle II

We can see from the results presented in Sections 5.3.2 and 6.4.2 that our Belle II sensitivity study indicates an inferior performance at Belle II compared to BABAR: our final signal efficiency is less than half that at BABAR, our final background estimate is approximately four times as high, and our estimated branching fraction upper limit also approximately four times higher. This relatively poor performance comes despite the fact that Belle II is a next-generation B-factory aiming to outperform its predecessors such as BABAR.

A comparison of matching signal selection stages from the BABAR and Belle II analyses can help us understand what parts of the Belle II analysis framework require improvement if

Belle II is to compete with, and ultimately surpass, BABAR.

Λ reconstruction

Differences in the Λ reconstruction performance are clearly evident from a comparison of the reconstructed Λ masses produced by each analysis, which we can see in Figures 6.4.1

155 below.

(b) Reconstructed Λ mass at Belle II after (a) Reconstructed Λ mass at BABAR after FEI, skim, particle ID, Λ reconstruction, hadronic B reconstruction, skim, m , tag ES event reconstruction, DOCA and best Λ se- PID and DOCA cuts. lection cuts.

Figure 6.4.1: Comparison of reconstructed Λ masses at BABAR and Belle II.

The Λ candidates shown are plotted at similar points in the two analyses (as similar as can reasonably be achieved given the inherent differences between the two experiments). The absolute number of events (i.e. a comparison of the numbers on the y-axes of the two histograms) is not relevant since differences between the two analyses mean we do not expect these to match. However, what is of importance is the clear difference in quality of the reconstructed Λ mass. The Λ reconstruction performed in the the BABAR analysis is clearly of much higher quality, as demonstrated by the much higher resolution on the Λ mass peak; this sharper peak in turn allows us to achieve better signal retention and background rejection since we are able to cut tightly around the peak shown in Figure 6.4.1a whereas we can see in Figure 6.4.1b that tightening the mass window leads to the loss of a similar proportion of events in signal MC as it does in background MC.

They key difference between the way that Λ candidates are reconstructed in the two analyses is the fitting algorithm. As discussed in Section 5.2.9, forthe BABAR analysis we used TreeFitter while, as discussed in Section 6.3.3, for the Belle II analysis we use KFit. As we

156 note in Section 6.3.3, KFit is known to be inferior to TreeFitter for this task but was chosen because TreeFitter has not yet been implemented in basf2 and KFit is the best tool available. The Belle II collaboration is currently in the process of adding TreeFitter to basf2, and once available this should lead to a significant improvement in the quality of Λ candidates that Belle II analysts are able to produce.

PID and DOCA

A comparison of the effect of the PID and DOCA cuts used in each analysis can be obtained by comparing the marginal effects of the cuts. Based on the data in Tables 5.5 and6.3, we calculate the background rejection and signal retention of these cuts in an otherwise complete signal selection, where background rejection is the percentage of background MC events rejected by the cut, and signal retention is the percentage of signal MC events retained by the cut, i.e. in both cases higher numbers are better. Recall that PID cuts cannot be removed from the analysis in isolation – the removal of PID cuts also necessitates the removal of DOCA cuts. The results are shown in Table 6.4.

Table 6.4: Comparison of PID and DOCA cuts at BABAR and Belle II, see text for details.

Analysis PID+DOCA DOCA Background Signal Background Signal rejection retention rejection retention BABAR 99.7% 62.3% 23.6% 91.1% Belle II 99.3% 50.7% 56.5% 83.4%

We can see from Table 6.4 that BABAR generally outperforms Belle II. When we look at PID and DOCA combined, the signal retention performance at the two analyses is similar, however at the BABAR analysis we are able to reject more background than at Belle II.

Looking at DOCA alone, we see that BABAR retains more signal while Belle II rejects more background.

The much higher background rejection figure for Belle II with regards to the DOCA cuts would appear to be an endorsement of Belle II’s tracking capabilities; however, it is important

157 to understand these numbers in the context of the analysis as a whole. We have seen from our final results that Belle II significantly underperforms BABAR, including the survival of approximately four times as many background events as at BABAR; it is therefore possible that the apparently superior performance of the Belle II DOCA cuts shown here is in fact a symptom of the poor performance of the rest of the Belle II signal selection, in other words, the Belle II DOCA cuts could be rejecting more background simply because there is more background to reject. In order to endorse the Belle II DOCA selection we would also expect to see a better performance in terms of signal retention when in fact we see the opposite.

In summary, the DOCA performance results, when compared to BABAR, suggest that extra work is needed both on Belle II tracking itself and, as we already knew, on Belle II’s analysis framework as a whole.

The PID+DOCA results show similar background rejection rates, so we can compare their performance based on signal retention alone. Additionally, while removal of the PID cuts also necessitates the removal of the DOCA cuts, we can see from Tables 5.5 and 6.3 that the signal retention effect of the DOCA cuts alone is much smaller than that of the PID+DOCA cuts, so the performance figures for PID+DOCA cuts can be approximated as representing the performance of the PID cuts alone. Based on the performance figures in Table 6.4 it is apparent that Belle II’s PID is underperforming compared to BABAR’s, pointing to the need to improve Belle II’s PID algorithms. This comparatively poor performance is not surprising since the PID selectors available in the basf2 version used for the Belle II sensitivity study in this thesis are in the very early stages of development, so competitive performance was not expected.

Extra energy

A comparison of the Eextra cuts in both analyses can likewise be obtained by comparing the marginal effects of the cuts in the same way as the preceding section. The results areshown

158 in Table 6.5.

Table 6.5: Comparison of Eextra cuts at BABAR and Belle II. Analysis Background Signal rejection retention BABAR 96.9% 65.4% Belle II 94.9% 66.7%

As explained in Section 6.3.8, the signal retention rates of the Eextra cuts used in the two analyses are closely matched by design to ensure comparability, and we find that the background rejection rates also happen to approximately agree. This suggests that the Eextra selections used in the two analyses are approximately equally effective, which is pleasing given the much higher background rates (i.e. sources of extra energy) that Belle II must en- dure. It is likely that such comparatively equal performance was only obtained thanks to the more sophisticated Eextra selection used in Belle II, where we used cluster energy and timing cuts specific to each region of the ECL in order to ensure a good signal:background separation (see Section 6.3.8 for more details), and this highlights the need for careful treatment of Eextra at Belle II.

Continuum suppression

A comparison of the continuum suppression cuts in both analyses can be obtained by comparing the marginal effects of the cuts in the same way as described above. The resultsare shown in Table 6.6.

Table 6.6: Comparison of continuum suppression cuts at BABAR and Belle II.

Analysis Background Signal rejection retention BABAR 76.6% 83.2% Belle II 72.3% 84.3%

As explained in Section 6.3.7, the signal retention rates of the continuum suppression cuts used in the two analyses are closely matched by design to ensure comparability, and we

159 find that the background rejection rates also happen to approximately agree. Thisisnot surprising given the very similar definitions of BB likelihood used in the two continuum suppression techniques (see Sections 5.2.5 and 6.3.7) and the fact that the continuum suppression technique we use relies on event shape variables. The event shape variables we employ are relatively straightforward to measure in any modern B factory detector such as BABAR or Belle II, and a large discrepancy in the performance between the two would have been surprising. It is likely that scope for improvement by Belle II in this specific case is therefore limited; however, more powerful continuum suppression could potentially be achieved by inputting more and/or different variables into the multivariate likelihood that we use. Another approach that could also be investigated is the use a more modern multivariate discriminator utilising machine learning.

We note that the Belle II collaboration’s continuum suppression plan is to use deep learning algorithms with many more variables than used here [42]. In comparison to the six event- shape variables used here, Belle II has investigated the use of up to 30 event-shape variables plus 500 detector-level and vertex-related variables variables (e.g. track momentum, track fit quality, cluster energies, BB vertex separation, etc). Early studies [42] on Belle II MC show that using this much larger and more varied selection of variables provides powerful continuum suppression, with background rejection of 95% or higher at a signal retention rate of 98%. These studies were, however, based on a model trained on only a single signal

0 → 0 0 sample (B KS π ) and using only continuum MC (as opposed to continuum MC and BB MC) as the background sample; it remains to be seen how effective the techniques are in more realistic scenarios and how generally applicable they are to the many and varied signal modes that Belle II will search for.

In summary, Belle II’s continuum suppression capabilities are roughly comparable to those at

BABAR when using a near-identical technique, as expected. The outlook for continuum suppression at Belle II using more variables and more sophisticated techniques appear promis-

160 ing, although further investigation is required into the efficacy of these techniques in more realistic scenarios.

Other considerations

The numerical results of the Belle II sensitivity study (and thus any numerical comparison with the results of the BABAR analysis, such as those presented above) should be treated with caution. In particular, there are two components of the Belle II analysis framework used in this sensitivity study that stand out as areas in need of attention:

• First is the efficiency of the FEI process – as discussed in Section 6.2.1, early studies of the FEI using Belle (rather than Belle II) data suggest that its efficiency in data

versus MC is between approximately 0.6 and 0.9, with an average for charged Btag re- +0.014 construction (i.e. the reconstruction type relevant to this analysis) of 0.74−0.013(stat.) 0.050(sys.). Furthermore, these results were based on a very limited analysis examin-

ing only ten modes where a semileptonic Bsig reconstruction was possible. The true efficiency of FEI for analyses such as the one presented in this chapter therefore remains largely unknown, but we have reason to believe that our MC-driven results significantly overestimate the performance of the current FEI if it were applied toreal data. More detailed studies of the FEI using Belle II data are clearly vital to a good understanding of FEI’s performance and if, as early results suggest, there is a large discrepancy between FEI’s efficiency on data and on MC then it will be vital toun- derstand and correct for this. In terms of the implications for this sensitivity study, it is likely that a large but unknown uncertainty has been introduced into our MC yield as a result of using FEI which propagates through the entire analysis.

• Second is basf2’s Λ reconstruction performance – as discussed in Section 6.3.3, early studies of Λ reconstruction efficiency on Belle II data show that the Λ reconstruction efficiency in data is barely half that of MC. Given the fact that said studywasper-

161 formed using Belle II (not Belle) data, and a later baf2 release (release-02-00-01) and a later MC production than the sensitivity study presented in this chapter, this is especially concerning. More investigation of this problem is clearly urgent if Belle II is to produce reliable physics results in the near future, particularly if it proves to be a problem affecting not just Λ reconstruction specifically but basf2’s reconstruction algorithms in general. In terms of the implications for this sensitivity study, our Λ reconstruction results should be treated with scepticism in terms of their ability to accurately model basf2’s performance on real data, and one should bear in mind that any uncerainty introduced as a result of the Λ reconstruction will propagate through the rest of the results.

The above two items are evidently in urgent need of further investigation and remediation. The anticipated widespread use of FEI and basf2’s particle reconstruction algorithms in many future Belle II analyses means that the implications of these issues spread far beyond the sensitivity study presented in this chapter.

Summary

We see from our final result that Belle II significantly underperforms BABAR when performing a similar analysis. A cut-by-cut comparison shows that while Belle II performs competitively with regards to relatively simple selection procedures such as Eextra and continuum suppression, in more complex areas such as PID and Λ reconstruction there is a significant deficit that Belle II needs to make up if it is to match, and eventually outperform, BABAR. While there are some promising signs from early studies of certain selection procedures, such as the planned continuum suppression technique, there is clearly much work to do. Furthermore, the comparisons we have performed are done in the shadow of two potentially serious issues – the data versus MC efficiency of FEI and of Λ reconstruction, both of which potentially point to problems with Belle II’s particle reconstruction. These are large and fundamental

162 problems that urgently need to be studied in more detail, understood and rectified if Belle II is to perform high-quality, competitive physics.

We do, however, note that the inferior performance of Belle II compared to BABAR indicated by this very early sensitivity study is not surprising. The BABAR analysis described in

Chapter 5 was started when BABAR had already been running and collecting data for almost a decade. BABAR at the time was a mature experiment with a thoroughly-tested, well- understood and highly-optimised analysis framework. The analysis we performed at BABAR

− represents the very upper limit of what BABAR is capable of in an analysis of the B → Λpνν decay.

Belle II, by comparison, is still in the early stages of its life. The Belle II sensitivity study presented in this chapter was started when Belle II’s analysis software had not yet even reached version 1 and while Belle II itself was still under construction. Several necessary pieces of the analysis framework only became available after the sensitivity study had been started. The sensitivity study we have performed therefore represents the very lower limit of Belle II’s capabilities in the search for B−→ Λpνν decays.

Belle II’s analysis framework is undergoing rapid development and improvement, particularly as Belle II approaches the beginning of data-taking in mid-2019 and as more analysts start using, and helping to improve, the analysis machinery. The results of this analysis will be made available to the Belle II collaboration in order to contribute to this effort. These factors, combined with the superior Belle II detector, should ensure that Belle II will ultimately outperform previous-generation B-factories. With the inevitable improvements that Belle II will experience over the coming years, it will eventually outperform BABAR given an equivalent integrated luminosity. Furthermore, the much larger integrated luminosity that Belle

II will collect compared to BABAR will only add to Belle II’s competitive advantages.

163 Chapter 7

Conclusion

We have presented the world’s first experimental search for the rare, flavour-changing-

− − neutral-current B → Λpνν decay, using 424 fb 1 of data from the BABAR experiment. We measure a branching fraction central limit consistent with zero and a branching fraction upper limit at the 90% confidence level of 3.02 × 10−5. The Standard Model prediction for the branching fraction of B−→ Λpνν is (7.9 1.9) × 10−7.

It is possible that in the gap between our measured branching fraction and the Standard Model prediction, there lies new physics. Furthermore, a tighter upper limit, even in the absence of a new physics discovery, will allow us to place tighter constraints on new physics models. A new search for B−→ Λpνν , using a superior experiment and more data, is therefore well-motivated.

Belle II, the world’s only next-generation B-factory, provides the ideal setting in which a future search for B−→ Λpνν decays can be conducted. Belle II offers a superior detector, improved analysis software and a much larger dataset compared to BABAR. A search for B−→ Λpνν at Belle II should therefore be able to achieve a better result than our analysis at BABAR.

164 At the time of writing, Belle II has not started collecting data; a data-driven analysis of B−→ Λpνν at Belle II is therefore not possible. We instead conduct an early sensitivity study based on Monte Carlo simulations to demonstrate the viability of the analysis at Belle II and to provide a basis on which future analysts can work from. Furthermore, by conducting such an early sensitivity study, we have also “test-driven” the Belle II analysis framework and contributed to its ongoing improvement.

Our sensitivity study at Belle II obtains an expected branching fraction upper limit at the 90% confidence level of 1.2 × 10−4, assuming 424 fb−1 of data and that no excess of events is observed. While this limit is approximately four times higher than that which we obtained at BABAR, the sensitivity study was conducted using very early versions of Belle II’s analysis machinery. We expect significant improvements in Belle II’s capabilities in the near future and that Belle II will eventually outperform BABAR.

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172 Appendix A

Signal MC reweighting

As discussed in Section 5.1.4, the signal MC used in the BABAR study is reweighted according to the mΛp distribution given in Ref. [5]. This reweighting was first introduced in the sensitivity study [62]; the relevant part of the sensitivity study, as originally presented, is reproduced below, with minor changes to match the presentational style of the present document.

The signal MC simulations were generated using a phase space model. However, there are theoretical predictions (see Ref. [5]) for the distributions of four kinematic variables for the decay B−→ Λpνν :

• The invariant mass of the Λp pair.

• The invariant mass of the νν pair.

• The helicity angle between the baryon (i.e. the Λ in a B− decay or the p in a B+ decay) trajectory in the rest frame of the baryon-antibaryon system and the trajectory of the baryon-antibaryon system in the B meson rest frame.

• The helicity angle between the neutrino (as opposed to the antineutrino) trajectory in

173 C. Q. GENG AND Y.K. HSIAO PHYSICAL REVIEW D 85, 094019 (2012)

(a) (b)

FIG. 1 (color online). Contributions to the B Ãp## decay from (a) penguin and (b) box diagrams. À !

2 2 2 invariance, the most general forms of the B BB 0 tran- with ! a; b; c a b c 2ab 2bc 2ca, and sition form factors are given by [23] ! t, s ðp pÞ¼2, þ, ,þ and 0À are fiveÀ variablesÀ in the ð # þ # Þ B L # phase space. As seen from Fig. 2, the angle B L is BB0 q0"b B iu pB g1" g2i'"#p g3p" ð Þ h j j i ¼ ð Þ½ þ þ between p~ B (p~ #) in the BB0 (##) rest frame and the line g4q" g5 pB pB " 5v pB ; of flight of the BB 0 (##) system in the rest frame of the B, þ þ ð 0 À Þ ð 0 Þ # while the angle 0 is between the BB0 plane and the ## BB0 q0"5b B iu pB f1" f2i'"#p f3p" h j j i ¼ ð Þ½ þ þ plane, which are defined by the momenta of the BB 0 f4q" f5 pB 0 pB " v pB 0 ; pair and the momenta of the ## pair, respectively, in the þ þ ð À Þ ð Þ (3) rest frame of B. The ranges of the five variables are given by with q pB pB and p pB q, for the vector and 2 2 ¼ þ 0 ¼ À m m s m pt ; axial-vector quark currents, respectively. For the momen- ð # þ # Þ ð B À Þ tum dependences, the form factors f and g (i 2 ffiffi 2 i i mB mB 0 t mB m# m# ; 0 L; 1; 2; ...; 5) are taken to be [19] ¼ ð þ Þ ð À À Þ B %; 0 0 2%: (7) D D f fi ;g gi ; (4) i ¼ t3 i ¼ t3 The decay branching ratio of B BÀ Ãp## depends on the integration in Eqs. (5)–(7), whereð ! we haveÞ to sum over with t q2 m2 , where D and D are constants to be fi gi the three neutrino flavors since they are indistinguishable. BB0 determined by the measured data in B ppM decays. We can also define the integrated angular distribution 3 ! Note that 1=t arises from three hard gluons as the asymmetries, given by propagators to form a baryon pair in the approach of the 1 dB 0 dB perturbative quantum chromodynamics counting rules 0 dcos dcosi 1 dcos dcosi A i À À i ; i B;L : [18,32–34], where two of them attach to valence quarks i 1 dB 0 dB R0 dcos dcosi R 1 dcos dcosi ð ¼ Þ in BB , while the third one kicks and speeds up the i þ À i 0 R R (8) spectator quark in B. It is worth to note that, due to fi, gi 1=t3, the dibaryon invariant mass spectrum peaksthe at rest the/ frame of the neutrino-antineutrino system and the trajectory of the neutrino- threshold area and flattens out at the large energyantineutrino region. system in the B meson rest frame. Hence, this so-called threshold effect measured as a com- III. NUMERICAL RESULTS AND DISCUSSIONS mon feature in B ppM decays should also appear in the For the numerical analysis, we take the values of GF, ! The definitions of the2 angular variables are shown graphically in Figure A.0.1 andthepre- BÀ Ãp#‘#‘ decay. To integrate over the phase space for em, sin W and VtsÃ Vtb in the PDG [38] as the input ! 2 the amplitude squared A , which is obtaineddicted by distributionsassem- parameters. for all four In variables the large in Figuret limit, A.0.2. the approach of the bling the required elementsj j in Eqs. (2)–(4) and summing over all fermion spins, the knowledge of the kinematics for the four-body decay is needed. For this reason, we use the partial decay width [35–37] A 2 dÀ j j X dsdtd cos d cos d0; (5) ¼ 4 4% 6m3 B L B L ð Þ B where 1=2 1 2 2 X mB s t st ; ¼ 4ð À À Þ À 1 1 ′ 1=2 2 2 1=2 Figure2 A.0.1:2 DefinitionsFIG. 2 (color of angles online). used Three in anglesFigure A.0.2B, L, andwhere: B is0 thein the baryon, phaseB¯ is the antibaryon B ! t;m ;m ; L ! s;m#;m# ; (6) B B0 ¼ t ð Þ ¼ s ð and B¯ isÞ the B meson.space Figure for the from four-body [5]. B BB0## decay. ! RARE B Ãp DECAY PHYSICAL REVIEW D 85, 094019 (2012) À ! 30 10 perturbative quantum chromodynamics counting rules al- 094019-2(a) (b) L 25 7 8 lows the vector and axial-vector currents to be incorporated GeV 20 10 7 as two chiral currents. As a result, Dg and Df from the 6 i i 15 m m p vector currents can be related by the another set of con- 10 4 10 B stants D and DD from the chiral currents, and the 10 m m 2 5 dB dcos jj jj dB dm constants for BÀ Ãp are reduced as [23] 0 0 ! 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1.0 0.5 0.0 0.5 1.0 m GeV cos 3 3 j Dg Df D ;Dg Df D ; −→ 1 ¼ 1 ¼Às2ffiffiffi jj j ¼À j ¼Às2ffiffiffi FigureFIG. A.0.2: 3 Predicted (color distributionsonline). of Invariant invariant masses mass and spectra angles for asB functionsΛpνν . Grey of areas jj represent theoretical uncertainties. Figure from [5]. (9) the invariant masses mÃp and m and angular distributions as functions of cosB;L for BÀ Ãp, respectively, where the By reweighting our signal MC it is possible! to match these variables’ distributions in signal with j 2; 3; ...; 5. We note that the reduction is first shaded areas represent the theoretical uncertainties from the ¼ MC to the theoretically-predicted distributions. It was not possible to satisfactorily match developed in Refs. [32–34] for the spacelike B B0 bar- form factors and CKM mixings. yonic form factors, and extended to deal with the! timelike all four variables’ distributions to their theoretical predictions simultaneously. However, 0 BB 0 baryonic form factors and the B BB 0 transi- by reweighting each variable independently (i.e. reweighing the signal MC to match the ! ! contrast, the curve in the m spectrum is associated with tion form factors in the studies of the B BB 0M decays ! the total energy of the pair.174 This is due to the helicity j j [18–23,39–43]. For Dð Þ and Dð Þ, we adopt the values, structure of 1 5 in the amplitude, formed as jj jj ð À Þ given by [23] E E " p with " p the left-handed polarization. ðMoreover,þ Þ theÀð factÞ that À"ð Þp couples to the left-handed 5 Àð Þ D ;D 67:7 16:3; 280:0 35:9 GeV ; helicity state of the virtual Z boson results in a factor of ð jj Þ¼ð Æ À Æ Þ jj 1 cos 2 to explain the angular distribution for D2 ;D3 ;D4 ;D5 187:3 26:6; 840:1 132:1; ð þ LÞ ¼ L ð jj jj jj jjÞ ¼ ðÀ Æ À Æ in Fig. 3(b). As a duplicate case, BÀ ppe Àe has the 10:1 10:8; 157:0 27:1 GeV4; same helicity structure for the lepton pair! to couple to the À Æ À Æ Þ left-handed helicity state of the virtual weak boson W . (10) ÃÀ As a result, it is reasonable to have A B Ãp L ð À ! Þ ’ A B ppe in Table I. On the other hand, since extracted from the measured data of the total branching L ð À ! À eÞ ratios, invariant mass spectra, and angular distributions in B BÀ Ãp can be traced back to the tensor terms ð ! Þ the B ppM decays. By using the various inputs, we f2 g2 in the BÀ Ãp transition, which give the main ! ð Þ ! obtain the numerical results for the branching ratio and contributions, f1u 5 and g1u are too small to pro- angular distribution asymmetries of B Ãp in vide factors of 1 cos 2 as apparent angular dependent À ð Æ BÞ Table I, where the values of B ppe ! are taken terms, as given in Fig. 3(b) for and Table I for A . À À e ¼ B B from Ref. [9]. The invariant mass spectra! and angular dis- The domination of the tensor terms f g in the B 2ð 2Þ À ! tributions for BÀ Ãp are shown in Fig. 3, where the Ãp transition can be realized. The terms f3 g3 disappear ! ð Þ shaded areas represent the theoretical uncertainties from the due to " p with p p p , leading to the coupling of form factors and Cabibbo-Kobayashi-Maskawa (CKM) " p Àð0.Þ Because¼ of theþ relatively small value of D4 À Á ¼ j j’ mixings. Note that the errors of the integrated angular 10 GeV4, the terms f g are negligible. The suppressionjj 4ð 4Þ asymmetries A in Table I are relatively small compared B;L for f5 g5 is in accordance with the limit of pp pÃ to those in Fig. 3(b). The reason is that A depend on the ð Þ ð À Þ ¼ B;L E E ; p~ p~ 0; 0~ as the invariant mass m ð p À Ã p À ÃÞ ! ð Þ Ãp ratios as shown in Eq. (8), which reduce the uncertainties. approaches the threshold area to receive the main contri- From Fig. 3(a), we see that B BÀ Ãp receives the ð ! Þ bution for B BÀ Ãp (see Fig. 3(a)). Moreover, with dominant contribution near the threshold of mÃp mÃ an additionalð p in!f g Þ p, the ratio of f g p 2 to ! þ 2ð 2Þ j 2ð 2Þ j mp , when the curve sharply peaks in the invariant mass f g 2, which is equal to D2 p 2=D2 8 p 2, can 3 1 1 f2 g2 f1 g2 spectrum. This reflects the fact of 1=t as the momentum j ð Þj ð Þj j ð Þ ’ j j be enhanced by p mB mÃ mp around the dependence in the BÀ Ãp transition form factors. In j j! Àð þ Þ ! threshold area. This explains why f g prevail over the 2ð 2Þ other terms in the BÀ Ãp decay. Since the decays of TABLE I. Numerical results for B and A (i B, L) for ! i ¼ BÀ ppe Àe and BÀ Ãp are similar four-body BÀ Ãp and BÀ ppe Àe [9], respectively, where the decays,! we suggest a relation,! given by theoretical! errors are mainly! from the uncertainties in the form factors and CKM mixings. 2 12 A BÀ Ãp 1=mpp R A 2 j ð ! Þj 3R Const2 ; 2 12 B Ãp B ppe [9] ðj j Þ A BÀ ppe À ¼ ð Þ 1=m À ! À ! À e j ð ! eÞj Ãp B 7:9 1:9 10 7 1:04 0:29 10 4 (11) ð Æ ÞÂ À ð Æ ÞÂ À A 0:01 0:02 0:06 0:02 B Æ Æ where the factor 3 comes from the three neutrino flavors A 0:56 0:02 0:59 0:02 L Æ Æ and R Const2 0:012 is due to the constants of their own ð Þ¼

094019-3 theory distribution of one variable without regard to the distributions of the remaining three variables) we could measure the effect of reweighting to each of the four variables by passing the signal MC through a nominal signal selection process (see Section 5.2) and calculating the final signal efficiency.

It was observed that the signal efficiency only showed a significant change after reweighting the signal MC to match the theoretically-predicted distribution of the Λp invariant mass (see Figure A.0.3). We believe this is due to the fact that the reweighing to the Λp invariant mass TruthLambdaPbarMassReweighted hTruthLambdaPbarMassExtendedAxisdistribution alters the momenta distribution of the two protons in a signal event (one proton

from the Λ, the other from the Bsig), as shown in Figure A.0.4. BABAR’s PID selectors are more efficient at lower momenta [7], thus leading to a change (increase) in signal efficiency after running reweighted events through a nominal signal selection. hTruthLambdaPbarMassReweighted hTruthLambdaPbarMassExtendedAxis Entries 22396 Entries 22524 Mean 2.315 Mean 3.169 RMS 0.1965 hTruthLambdaPbarMassExtendedAxis RMS 0.6103 hTruthLambdaPbarMassReweighted ) 16 ) 2 2

70 14

60 12

10 50

8 40

6 30 Number of events (per 0.1 GeV/c Number of events (per 0.1 GeV/c 4 20

2 10

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Mass (GeV/c2) Mass (GeV/c2) (a) Before signal reweighting. (b) After signal reweighting.

Figure A.0.3: mΛp before and after signal MC reweighting, determined from MC Truth information.

We thus chose to reweight our signal MC only to this variable. Simultaneous reweighting to the Λp invariant mass and one other variable (for each of the three remaining variables in turn) caused only a small change in signal efficiency compared to reweighting to Λp invariant mass alone. This discrepancy is accounted for as a systematic error (see Section 5.3.1).

175 TruthProtonPairSumMmtm TruthProtonPairSummMmtmRweighted

hTruthProtonPairSumMmtm hTruthProtonPairSumMmtmRweighted Entries 22524 Entries 22396 Mean 2.964 Mean 2.184 hTruthProtonPairSumMmtm RMS 0.7818 hTruthProtonPairSumMmtmRweighted RMS 0.6696

6 7

5 6

5 4

4 3 3

2 Number of events (per 0.05 GeV/c) Number of events (per 0.05 GeV/c) 2

1 1

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Momentum (GeV/c) Momentum (GeV/c) (a) Before signal reweighting. (b) After signal reweighting.

Figure A.0.4: Sum of proton momenta before and after signal MC reweighting, determined from MC Truth information.

176 Appendix B

Eextra adjustment

As discussed in Section 5.2.6, a study undertaken as part of the sensitivity study [62] for the

BABAR analysis demonstrated improved data/MC agreement when the energy of each ECL cluster in MC was reduced by −5 MeV. The study as presented in Ref. [62] is reproduced below for reference, with minor changes to match the presentational style of the present document.

Eextra is defined in this analysis using cluster energies in MC adjusted by −5 MeV (with a minimum permitted cluster energy of 0 MeV). Ordinarily one would use unadjusted cluster energies to calculate Eextra. The reasons for our choice of adjusted cluster energies will be explained in this appendix.

Figure B.0.1a shows Eextra when calculated using unadjusted cluster energies (which we will refer to as “unadjusted Eextra” for the remainder of this appendix), while Figure B.0.1b shows Eextra when calculated using clusters adjusted by −5 MeV (“adjusted Eextra”).

Any differences between the two definitions of Eextra are, at this stage, difficult to see, although a higher number of events in lower bins is visible in adjusted Eextra compared with unadjusted Eextra. The reason for concern is that when unadjusted Eextra is plotted after an

177 BRIEF ARTICLE

THE AUTHOR

B ⇤p¯⌫⌫¯ !BRIEF ARTICLE EMC_Eextra_Less05Clus_sig B K⌫⌫¯ ! ( ) B¯ pp¯(THEK¯ ⇤ AUTHOR, ⇡, ⇢) 0! ( )0 B¯ ppD¯ ⇤ ! (B ⇤p¯⌫⌫¯) B ⇤p¯⌫⌫¯ B !6 ! 1/m ¯ B K⌫⌫¯ / BB ! ( ) ¯ B¯ pp¯(K¯ ⇤ , ⇡, ⇢) BB 0! ( )0 ¯ B¯ ppD¯ ⇤ BB ! + stackh_PIDCount_Passstackh_PIDCount_Pass (B ⇤p¯⌫⌫¯) B B B !6 0 ¯0 1/mBB¯ B B / ¯ stackh_PIDCount_Pass BB Btag ¯ BB Bsig + B B ⇤ p¯ ⌫ ⌫¯ B0B¯0 p⇡ Signal Region Data Sideband scaled data + Corrected MC peak ccbar stackhEMC_Eextra_Less05Clus_sigBtag b¯b 30000 Bsig µuds⌫¯ccbarµ ⇤ p¯ ⌫ ⌫¯ stackh_PIDCount_Pass 25000 2 (1 + cos✓ ) ccbar ccbar L uds p⇡ tautau tautau 100 B0B0bar uds 20000 / BpBm uds data Signal tautau ¯ 60000 hello! B bb ccbar B0B0bar 15000 100 B0B0bar BpBm hello! 80 µ⌫¯µ 50000 stackh_PIDCount_Pass data

Number of events tautau 10000 2 + Signal stackh_RBmes_q2Cutccbar uds sideband-scaled(1 + cos✓L) B BpBmB tautau uds 100 B0B0bar BpBm 40000 data 25 / 60 Signal 50000 5000 60000 0 ¯0 100data plushello! B B BB0B0bar data 80 ccbar 0 30000 -0.1 0 corrected0.1 0.2hello! 0.3 0.4 50000 0.5 uds Number of events ⌧⌧¯ tautau 40 + tautau 0.9 peaking B B Signal B0B0bar 20000 40000 qq¯ (BpBmq = u, d, s) 60 3.5 0 ¯0 BpBm B B 20 Signal 100data 10000 30000 cc¯ B0B0bar 40 Number of events 40000 ⌧⌧¯ data 20 60000 0.8 20000 signal 0 0 qq¯ (q = u, d, s) Pass BpBm 20 3 cc¯ 10000 dataSignal 0 0 0.7 signal Pass data data 30000 15 2.5 60000 Number of events 0.6 Signal 60000 0.5 2 20000 10

Number of events (per 0.05 GeV) 80 1 0.4 1.5 1 50000 0.3 10000 5 1 Number of events 800.2 0.5 0 0.1 0 0 1 2 3 4 5 0 0 50000 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 80Eextra (GeV) mES (GeV/c2) Number of events 50000 40000 (a) Unadjusted Eextra, calculated using un- (b) Adjusted Eextra,60 calculated using cluster adjusted cluster energies. energies adjusted by −5 MeV Number of events

Figure B.0.1: Unadjusted and adjusted Eextra after local-skim and Btag mES cuts. 40000 30000 60 m sideband substitution (see Section 5.2.10 for details), it becomes clear that the shapes 40000 ES 6040 of the data and MC Eextra distributions do not match. As we can see from Figure B.0.2a, it 20000 appears that the MC is offset slightly to the right (higher energy) of data, suggesting that 30000 the MC systematically overestimates the value of Eextra. 30000 4020 10000 mES sideband substitutions work best when there is an mES distribution with a flat com- 20000 binatorial tail, a prominent B meson peak and a small proportion40 of combinatorial events. Other than the Btag mES cut itself the only other cuts used in FigureB.0.1a are the skim 0 0 20000 cuts, thereforePass the corresponding Btag mES distribution is that shown in FigureB.0.2b; this is clearly not ideal. 20 10000 In order to provide a more well-behaved Btag mES distribution20 we plot unadjusted Eextra 10000 again, but after skim, B-mode purity and BB likelihood cuts. The relevant Btag mES distribution is shown in FigureB.0.3c. Although the combinatorial tail is far from flat, the 0 B meson peak is considerably more prominent and the cut on0BB likelihood has reduced Pass the proportion of combinatorial events relative to peaking events. 0 0 Pass Unadjusted Eextra after local-skim, B-mode purity and BB likelihood cuts and before and

after mES sideband substitution are shown in Figure B.0.3a and Figure B.0.3b. In terms

178 BRIEF ARTICLE EMC_EExtra THE AUTHOR B BRIEF⇤p¯⌫⌫¯ ARTICLE Desktop/tempWork/output_babar/archive/B ! K ⌫⌫¯ ! ( ) B¯ pp¯(THEK¯ ⇤ AUTHOR, ⇡, ⇢) 0! ( )0 B¯ ppD¯ ⇤ ! stackFileNew-2018-01-25.root(B ⇤p¯⌫⌫¯) B ⇤p¯⌫⌫¯ B !6 BRIEF ARTICLE ! 1/m ¯ B K⌫⌫¯ / BB ! ( ) ¯ B¯ pp¯(K¯ ⇤ , ⇡, ⇢) BB 0! ( )0 ¯ THE AUTHOR B¯ ppD¯ ⇤ BB ! + (B ⇤p¯⌫⌫¯) B B B 1/m!6 B0B¯0 / BB¯ B BRIEF⇤p¯⌫⌫¯ ARTICLE BB¯ B ! tag B K⌫⌫¯ BB¯ Bsig B¯ !pp¯(K¯ ( ), ⇡, ⇢) stackh_LTDA_RBmes_GoodTruthCutB+B THE⇤ AUTHOR ⇤ p¯ ⌫ ⌫¯ B¯0! ppD¯ ( )0 B0B¯0 ⇤ p⇡ ! Signal Region Data Sideband scaled data + Corrected MC peak (B ⇤p¯⌫⌫¯) Btag B¯ ⇤p¯⌫⌫¯ B !6 bb ! 1/m ¯ 30000 B BB sig Signal Region Data Bµ ⌫¯ K⌫⌫¯ / ⇤ p¯ ⌫ ⌫¯ Sideband scaled data + Corrected MC¯ peak !µ ¯ ( ) BB¯ 25000 B pp¯(K ⇤ , ⇡,2⇢) 0!(1 + cos( )0✓L) ¯ p⇡ B¯ ppD¯ ⇤ BB 20000 / ¯ hello!! B + stackh_PIDCount_Passstackh_PIDCount_Pass bb (B ⇤p¯⌫⌫¯) B B 15000 B !6 0 stackh_LTDA_RBmes_GoodTruthCut0 µ⌫¯ hello!1/m ¯ µ BB¯ 3 B B 50000 10000 2 stackh_RBmes_q2Cut/ + sideband-scaled(1 + cos✓ ) B¯ B ×10 L B) B B stackh_PIDCount_Pass tag ccbar / 2 0 500 uds 5000 data plushello! B BB¯ ¯0 B B Bsig 35 tautau + ccbar B0B0bar 0 corrected uds -0.1 0 0.1 0.2hello!0.3 0.4 0.5 B⌧⌧¯B ⇤ p¯ ⌫ ⌫¯ BpBm + 0 ¯0 tautau data 0.9 peaking B B B B B0B0bar Signal qq¯ (q = u, d, s) p⇡ 3.5 Signal Region Data BpBm 0 ¯0 Sideband scaled data + Corrected MC peak B B Btag ccbar Signal 40000 data cc¯ b¯b 30 ⌧⌧¯ 30000 Bsig 0.8 signal µuds⌫¯ccbarµ ⇤ p¯ ⌫400⌫¯ stackh_PIDCount_Pass qq¯ 25000(q = u, d, s) 2 (1 + cos✓ ) ccbar 3 data L uds p⇡ tautau tautau cc¯ 100 B0B0bar 20000 / BpBm uds data b¯b 60000 hello!ccbarB Signal 0.7 signal Number of events 15000 100 B0B0bar 25 hello! 80 data µ⌫¯µ 50000 stackh_PIDCount_Pass

Number of events tautau 10000 2 + 30000 stackh_RBmes_q2Cutccbar uds sideband-scaled(1 + cos✓L) B BpBmB tautau 2.5 uds 100 B0B0bar BpBm Number of events 40000 data / 60 Signal 0.6 5000 300 60000 0 ¯0 100data plushello! B B BB0B0bar ccbar 30000 data 80 0 50000 uds 20 -0.1 0 corrected0.1 0.2hello! 0.3 0.4 0.5 Number of events ⌧⌧¯ tautau 40 + tautau 0.9 peaking B B Signal B0B0bar 0.5 20000 40000 qq¯ (BpBmq = u, d, s) 60 2 3.5 0 ¯0 BpBm B B 20 Signal 100data 10000 30000 cc¯ B0B0bar 20000 ⌧⌧¯ data 40 60000 0.8 20000 signal 1 0 0 15 0.4 qq¯ (q200= u, d, s) Pass Number of events (per 0.05 GeV) BpBm 20 1.5 3 10000 data cc¯ 1 Signal 0 0 0.7 signalNumber of events (per 2 MeV/c Pass 0.3 data data 10 1 2.5 60000 10000 Number of events 0.6 0.2 100 Signal 0.5 0.5 2 5 60000 0.1 80 0 1 0 1 2 3 4 0.45 0 0 0 1.5 0 50000 5.2 5.21 5.22 5.23 5.24 5.25.25 5.215.26 5.275.22 5.285.231 5.295.24 5.35.25 5.26 5.27 5.28 5.29 5.3 Eextra (GeV) 0.3 mES (GeV/c2) mES (GeV/c2) 1

Number of events 0.2 (a) Unadjusted Eextra after mES sideband80 0.5 0.1 (b) Corresponding Btag mES distribution, substitution and after local-skim and Btag 0 0 50000 5.2 5.21 after5.22 5.23 local-skim5.24 5.25 5.26 cuts5.27 only.5.28 5.29 5.3 m cuts. 80 ES mES (GeV/c2) 50000Number of events 40000 60 Figure B.0.2: Unadjusted Eextra after mES sideband substitution and corresponding Btag mES

Number of events distribution.

40000 30000 of magnitude the agreement between data60 and MC in Figure B.0.3b is not much different 40000 than in Figure B.0.2a; however, the fact60 that40 MC now underestimates data in lower bins but overestimates in higher bins suggests that the overall data/MC discrepancy has been 20000 30000 compensated for and that the sideband substitution is now working. The remaining prob- 30000 lem is that the shapes of the MC and data4020 distributions do not match across the Eextra 10000 spectrum.

40 − − 20000 To correct for this we adjust cluster energies when calculating Eextra by 5 MeV and 10 MeV. 0 The results, along with sideband-substituted0 versions, are shown in Figure B.0.4. 20000 Pass − Figure B.0.4b shows that adjusted (by 205 MeV) Eextra, after a sideband substitution, ame- 10000 liorates the underestimation by MC seen in the lower bins (≲ 1 GeV) of Figure B.0.3b while maintaining a relatively good agreement20 over the rest of the distribution. The agreement 10000 is not perfect, and there is a small overestimation by MC in some of the lowest-energy 0 bins. Adjusting by −10 MeV, shown in Figure0 B.0.4d, overcompensates for the corrections Pass needed to Figure B.0.2a, as can be seen in the most of the bins below ∼ 1 GeV, where MC 0 considerably overestimates data. 0 Pass 179 BRIEF ARTICLE

BRIEF ARTICLE THE AUTHOR

THE AUTHOR EMC_EExtraPurityContLHCut_sigEMC_EExtraPurityContLHCut B BRIEF⇤p¯⌫⌫¯ ARTICLE ! B K⌫⌫¯ ¯ ! ¯ ( ) B BRIEF⇤p¯⌫⌫¯ ARTICLE B pp¯(THEK ⇤ AUTHOR, ⇡, ⇢) ! 0! ( )0 B K⌫⌫¯ B¯ ppD¯ ⇤ ¯ ! ¯ ( ) ! B pp¯(THEK ⇤ AUTHOR, ⇡, ⇢) (B ⇤p¯⌫⌫¯) ¯0! ( )0 B ⇤p¯⌫⌫¯ B !6 B ppD¯ ⇤ ! 1/m ¯ ! B K⌫⌫¯ / BB (B ⇤p¯⌫⌫¯) ¯ ! ¯ ( ) BB¯ B ⇤p¯⌫⌫¯ B !6 B pp¯(K ⇤ , ⇡, ⇢) ! 1/m ¯ ¯0! ( )0 ¯ B K⌫⌫¯ / BB B ppD¯ ⇤ BB ¯ ! ¯ ( ) BB¯ ! + B pp¯(K ⇤ , ⇡, ⇢) (B ⇤p¯⌫⌫¯) B B ¯0! ( )0 BB¯ B !6 0 ¯0 B ppD¯ ⇤ 1/m ¯ B B ! + / BB stackh_PIDCount_Pass (B ⇤p¯⌫⌫¯) B B BB¯ stackh_PIDCount_Pass B tag B !6 0 ¯0 1/m ¯ B B ¯ BB BB Bsig / ¯ + stackh_PIDCount_Pass BB Btag B B ⇤ p¯ ⌫ ⌫¯ ¯ 0 0 BB Bsig B B¯ + p⇡ Signal Region Data B B Sideband scaled data + Corrected MC peak ⇤ p¯ ⌫ ⌫¯ Btag ¯ B0B¯0 bb p⇡ 30000 Bsig Signal Region Data Signal Region Data Sideband scaled data + Corrected MC peak ccbar Sideband scaled data + Corrected MC peak µ ⌫¯ Btag ¯ ⇤ p¯ ⌫ ⌫¯ µ stackhEMC_EextraPurityContLHCut_sigbb 25000 stackh_LTDA_RBmes_ContLHCut2 30000 Bsig (1 + cos✓L) udsccbar p⇡ µ⌫¯µ 20000 stackh_PIDCount_Pass / 25000 ⇤ p¯ ⌫ ⌫¯ ¯ hello! B 2 bb ccbar (1 + cos✓ ) ccbar ccbar L uds 15000 p⇡ tautau tautau uds 100 B0B0bar uds 14000 20000 / BpBm 50000 hello! uds data µ⌫¯µ tautau Signal 18 tautau ¯ 60000 hello! B bb 10000 + B0B0bar ccbar B0B0bar 12000 2 stackh_RBmes_q2Cut BpBm 15000 100 B0B0bar BpBm sideband-scaled(1 + cos✓L) B B hello! 80 data µ⌫¯µ 50000 stackh_PIDCount_Pass data / 12 5000 0 ¯0 Signal Number of events tautau 10000 2 + Signal data plushello! B B B stackh_RBmes_q2Cutccbar uds ccbar sideband-scaled(1 + cos✓L) B BpBmB tautau uds 100 B0B0bar BpBm 0 40000 data correctedhello! uds / 60 Signal 16 -0.1 0 0.1 0.2 0.3 0.4 0.5 5000 60000 0 ¯0 ⌧⌧¯ 12000 100data plushello! B B BB0B0bar + tautau data 80 ccbar 0.9 peaking B B B0B0bar 0 30000 qq¯ (q = u, d, s) 3.5 -0.1 0 corrected0.1 0.2hello! 0.3 0.4 50000 0.5 uds BpBm Number of events ⌧⌧¯ tautau 40 0 ¯0 + 10000 tautau 40000 B B Signal 0.9 peaking B B Signal B0B0bar data cc¯ 20000 40000 qq¯ (BpBmq = u, d, s) 60 14 3.5 10 0 ¯0 BpBm ⌧⌧¯ B B 20 Signal 0.8 signal 100data 10000 30000 cc¯ B0B0bar qq¯ (q = u, d, s)

40 Number of events Number of events 10000 ⌧⌧¯ data data 3 60000 0.8 20000 signal 0 0 cc¯ qq¯ (q = u, d, s) Pass BpBm 20 12 3 cc¯ 10000 dataSignal 8000 0.7 signal 8 0 0 30000 data 0.7 signal Pass 8000 data 2.5 data Number of events 10 2.5 0.6 60000 Number of events 0.6 Signal 6000 6 2 6000 8 0.5 0.5 2 20000 60000 1 0.4 Number of events (per 0.05 GeV) Number of events (per 0.05 GeV) 80 1.5 0.4 6 1 4000 4 4000 1.5 1 1 0.3 50000 LTDA_RBmes_ContLHCut0.3 4 10000 1 1 2000 2000 0.2 2 Number of events 0.2 2 0.5 80 0.1 0.5 0.1 0 0 0 0 0 0 1 2 3 4 5 0 1 2 3 5.2 5.210 4 5.22 5.235 5.24 5.25 5.26 5.27 5.28 5.29 5.3 0 0 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 50000 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28BRIEF5.29 ARTICLE5.3 80Eextra (GeV) Eextra (GeV) 2 mES (GeV/c ) mES (GeV/c2) THE AUTHOR Number of events 50000 40000 (a) Unadjusted Eextra60after local-skim, Btag (b) Unadjusted Eextra after mES sideband B ⇤p¯⌫⌫¯ !BRIEF ARTICLE B K⌫⌫¯ mES, B-mode purity and BB likelihood! ( ) substitution and after local-skim, B m , B¯ pp¯(THEK¯ ⇤ AUTHOR, ⇡, ⇢) tag ES Number of events 0! ( )0 B¯ ppD¯ ⇤ ! cuts. (B ⇤p¯⌫⌫¯) B-mode purity and BB likelihood cuts. B ⇤p¯⌫⌫¯ B stackh_LTDA_RBmes_ContLHCut!6 ! 1/m ¯ B ×K10⌫3⌫¯ / BB

) ¯ ¯ ! ¯ ( ) BB ccbar

2 B pp¯(K , ⇡, ⇢) 100 ⇤ uds B¯0! ppD¯ ( )0 BB¯ tautau ⇤ 25 B0B0bar ! + BpBm B B stackh_PIDCount_Passstackh_PIDCount_Pass (B ⇤p¯⌫⌫¯) data B 1/m!6 B0B¯0 Signal 40000 BB¯ / 30000 BB¯ stackh_PIDCount_Pass 60 Btag ¯ BB80 Bsig + B B ⇤ p¯ ⌫ ⌫¯ 20 B0B¯0 p⇡ Number of events Signal Region Data Sideband scaled data + Corrected MC peak ccbar 40 Btag b¯b B 40000 30000 sig udsccbar µ⌫¯µ ⇤ p¯ ⌫ ⌫¯ stackh_PIDCount_Pass 25000 60 2 (1 + cos✓ ) ccbar L uds 60 tautau p⇡ tautau 15 100 B0B0bar 20000 / BpBm uds data b¯b 60000 hello!ccbarB Signal 15000 100 B0B0bar hello! 80 µ⌫¯µ 50000 stackh_PIDCount_Pass

Number of events tautau 10000 2 + stackh_RBmes_q2Cutccbar uds sideband-scaled(1 + cos✓L) B BpBmB tautau uds 100 B0B0bar BpBm 40000 data / 60 Signal 5000 60000 0 ¯0 100data plushello! 40 B B BB0B0bar data 80 ccbar 0 30000 10 -0.1 0 corrected0.1 0.2hello! 0.3 0.4 50000 0.5 uds 20000 Number of events ⌧⌧¯ tautau 40 + tautau 0.9 peaking B B Signal B0B0bar 20000 40000 60 3.5

Number of events (per 2 MeV/c qq¯ (BpBmq = u, d, s) 0 ¯0 BpBm B B 20 Signal 100data 10000 30000 cc¯ B0B0bar 30000 ⌧⌧¯ data 40 60000 0.8 20000 signal 0 0 qq¯ (q = u, d, s) Pass 20 BpBm 20 3 cc¯ 10000 dataSignal 5 0 0 0.7 signal Pass data data 2.5 60000 Number of events 0.620 Signal 40 0 0 30000 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 60000 0.5 2 10000 80 mES (GeV/c2) 1 0.4 1.5 50000 1 400.3 (c) Btag mES after local-skim, B-mode pu- 1 20000 Number of events 800.2 rity and BB likelihood cuts. 0.5 0.1

0 0 50000 0 Figure B.0.3: Unadjusted8005.2 5.21Eextra5.22 ,5.23 after5.24 5.25 local-skim,5.26 5.27 5.28Btag5.29 m5.3ES, B-mode purity and BB likelihood Pass mES (GeV/c2) 20000Number of events cuts, before and after mES sideband substitution; and corresponding Btag mES distribution. 50000 40000 2060 Number of events 10000 40000 30000 2060 1000040000 6040 0 0 20000 Pass 30000 180 0 0 20 30000 Pass 40 10000 20000 40 0 0 20000 Pass 20 10000 20 10000 0 0 Pass 0 0 Pass (b) E adjusted by −5 MeV after m (a) E adjusted by −5 MeV after local- extra ES extra sideband substitution and after local-skim, skim, B m , B-mode purity and BB tag ES B m , B-mode purity and BB likelihood likelihood cuts. tag ES cuts.

(d) E adjusted by −10 MeV after m (c) E adjusted by −10 MeV after local- extra ES extra sideband substitution and after local-skim, skim, B m , B-mode purity and BB tag ES B m , B-mode purity and BB likelihood likelihood cuts. tag ES cuts.

Figure B.0.4: Eextra adjusted by −5 MeV and −10 MeV, and mES sideband-substituted versions.

181 We therefore consider adjusted (by −5 MeV) Eextra to be the best estimation of the three op- tions presented here (unadjusted, adjusted by −5 MeV, and adjusted by −10 MeV), allowing us to achieve the best agreement between MC and data. We therefore use adjusted Eextra in our analysis. Differences between Eextra adjusted by −5 MeV and unadjusted Eextra, and between Eextra adjusted by −5 MeV and Eextra adjusted by −10 MeV are used to determine a systematic error on our Eextra cut (see Section 5.3.1).

182