The Effect of the Beamspot Size on the Vertex Reconstruction within the Belle II Experiment

The Effect of the Beamspot Size on the Vertex Reconstruction within the Belle II Experiment

Ketevan Parlagashvili

Munich 2019

The Effect of the Beamspot Size on the Vertex Reconstruction within the Belle II Experiment

Ketevan Parlagashvili

Master Thesis

at the Faculty of Physics

of Ludwig–Maximilians–Universit¨ at Munich

submitted by Ketevan Parlagashvili

from Tbilisi, Georgia

Munich, 06.12.2019

Reviewer: Prof. Dr. Christian Kiesling

Der Einfluss der Beamspot Gr¨ oße auf die Vertex Rekonstruktion

im Belle II Experiment

Ketevan Parlagashvili

Masterarbeit

an der Fakult¨ at f¨ ur Physik

der Ludwig–Maximilians–Universit¨ at M¨ unchen

vorgelegt von Ketevan Parlagashvili

aus Tiflis, Georgien

M¨ unchen, den 06.12.2019

Gutachter: Prof. Dr. Christian Kiesling

Contents

Zusammenfassung x

Abstract xi

Introduction xii

1 Physics Motivations 1

1.1 The Standard Model . . . . 1

1.1.1 Open Questions in the Standard Model . . . . 2

1.1.2 Search for New Physics . . . . 2

1.2 CP Violation . . . . 3

1.2.1 CP Transformation . . . . 4

1.2.2 Flavor Mixing . . . . 4

1.2.3 Types of CP Violation . . . . 4

1.2.4 CKM Matrix and the Unitarity Triangle . . . . 7

1.2.5 CP Violation at Belle II . . . . 11

1.3 Other Physics Prospects at Belle II . . . . 13

1.4 Summary . . . . 13

2 The Belle II Experiment 14 2.1 A Short History of e

e

Colliders . . . . 14

2.2 SuperKEKB . . . . 15

2.2.1 Luminosity . . . . 16

2.2.2 The Nanobeam Scheme . . . . 18

2.2.3 Issues with the Nanobeam Scheme . . . . 19

2.3 The Belle II Detector . . . . 20

2.3.1 Vertex Detector . . . . 20

2.3.2 Central Drift Chamber . . . . 21

2.3.3 Particle Identification System . . . . 22

2.3.4 Electromagnetic Calorimeter . . . . 22

2.3.5 K

-Muon Detector . . . . 22

2.4 Data Taking . . . . 22

3 The ∆t Resolution Function 24 3.1 Neutral Meson Mixing . . . . 24

3.2 Time-Dependent Evolution . . . . 26

3.3 Flavor Tagging . . . . 27

3.4 An Event with Signal and Tag Decays . . . . 28

viii Contents

3.5 Detector Effects Impacting the ∆t Distribution . . . . 29

3.6 Analytical Approach to the ∆t Resolution Used at Belle and BaBar . . . 29

3.7 The MPI Concept for Time-Dependent Fits . . . . 30

4 Belle II Software Simulation 32 4.1 Monte Carlo Simultions . . . . 32

4.2 Generators . . . . 33

4.3 Physics Analysis Software . . . . 34

4.4 Beam Parameters . . . . 34

4.5 Roofit . . . . 34

4.6 Track Reconstruction . . . . 35

5 Experimental Results 37 5.1 ParticleGun Studies . . . . 38

5.2 Beamspot Studies . . . . 41

5.3 TagVz for Negative True ∆t . . . . 41

5.4 Privately Produced Samples . . . . 42

5.5 Tag Side Vertexing . . . . 42

5.5.1 Fit Algorithms for Tag Vertex Fitting . . . . 44

5.6 Testing Different TagV Algorithms . . . . 46

5.7 Errors on Tag Side and failing fits . . . . 47

5.8 Centrally Produced Samples . . . . 51

5.8.1 Phase3 vs earlyPhase3, the Effect of Added Background on TagVz Resolution . . . . 51

5.8.2 MC12a Phase3 Samples in More Detail: Background and Different Fitting Algorithms . . . . 51

5.9 More Statistics for Privately Produced Samples . . . . 58

A Beamspot Modification 65 A.1 Beam Parameters at Generator Level . . . . 65

B Signal Side Fitting 69 B.1 The Case for Using RAVE over TreeFitter for Signal-Side Vertex Fitting 69 B.2 RAVE vs TreeFitter Comparison Plots . . . . 70

C Tag Side Fitting 72 C.1 TagVertexModule and “cut” . . . . 72

C.1.1 findConstraintBoost function of TagV . . . . 73

C.1.2 Solution for Updating Beamspot Size in Fitting . . . . 74

C.1.3 The Effect of “cut” on Vertex Fit constraint . . . . 75

C.2 MC12a Samples with Added Background . . . . 78

C.3 The BTube Constraint for Tag Vertex . . . . 80

C.4 Flavor of Tag Side and ∆t . . . . 81

List of Tables 84

Contents ix

Bibliography 85

Acknowledgements 89

Declaration 90

Zusammenfassung

Die beispiellose Verbesserung der Leuchtkraft des asymmetrischen SuperKEKB-Kolliders e

e

erfordert, dass der Interaktionspunkt (IP oder Beamspot) der kollidierenden Strahlen auf eine Mikrometerskala (das sogenannte Nanostrahlschema) reduziert wird, wodurch das IP-Profil kompatibel wird mit der B Meson Zerfallsl¨ ange. Dies bedeutet, dass die B -Mesonen außerhalb des Beamspots zerfallen k¨ onnen, und durch Anwenden der IP- basierten Standardbedingung auf die Tag-Vertex-Anpassung wird der Zerfallspunkt in Richtung des Beamspots vorgespannt. Dies ist insbesondere dann ein Problem, wenn das markierte B-Meson vor dem Zerfall eine lange Strecke von dem IP zur¨ ucklegt. Da- her wird die Verzerrung durch eine Inkompatibilit¨ at des Nanostrahlschemas mit der Art und Weise verursacht, wie die Tag-Vertex-Anpassung derzeit bei Belle II behandelt wird.

Diese Arbeit untersucht die M¨ oglichkeiten, die Verzerrung mit verschiedenen Anpassung-

soptionen f¨ ur den Tag-Vertex zu beseitigen. Es wird gezeigt, dass durch auflockern der

Fit-Einschr¨ ankung auf der Tag-Seite die Vorspannung verschwindet.

Abstract

The unprecedented luminosity upgrade of the SuperKEKB asymmetric e

e

collider

requires squeezing the interaction point (IP or beamspot) of the colliding beams down

to a micrometer scale (the so-called nanobeam scheme), making the IP profile compatible

with the B meson decay length. This means that the B mesons can decay outside of the

beamspot, and applying the default IP-based constraint to the tag vertex fit biases the

decay point toward the beamspot. This is especially a problem for the cases when the

tagged B meson travels a long distance from the IP before decaying. Therefore, the bias

is caused by an incompatibility of the nanobeam scheme with the way the tag vertex

fit is currently handled at Belle II. This thesis investigates the options for getting rid of

the bias with different fit options on the tag vertex. It is shown that by relaxing the fit

constraint on the tag side, the bias disappears.

Introduction

It is widely accepted by physicists today that our universe can be boiled down to a few basic building blocks - the fundamental particles - and the three out of the four fun- damental forces that govern them, described by the Standard Model of particle physics (SM) Section 1.1. Some of the biggest successes of the Standard Model include the prediction of the Higgs, W and Z bosons, as well as the charm, bottom and top quarks.

Despite its many successes, the SM fails to address, for example, the phenomenon of neutrino masses and has no description of gravity, dark matter and dark energy. As a result, the SM has been dubbed a phenomenological description of particle physics;

physicists therefore search for so-called physics Beyond the SM (BSM physics), or New Physics (NP).

Recent efforts by the high-energy physics community focus on the explanation of the asymmetry of matter and antimatter in our observable universe; that is, why much more matter has been observed than antimatter. According to the Big Bang theory, initially equal amounts of matter and antimatter were created, therefore, certain conditions must have been satisfied in order for the imbalance to emerge over time. The Sakharov condi- tions for baryogenesis require the violation of baryon number conservation, interactions out of thermal equilibrium and the violation of charge conjugation (C) symmetry and of the combined charge parity (CP) symmetry[1].

High energy physics experiments aim to address the issues within the SM using com- plementary approaches. At the energy frontier, the high-energy colliders such as the LHC generate high energy collisions to observe new particles that provide information on the makeup of matter and space. At the intensity frontier, the precision experiments such as the B factories, study rare subatomic processes, suppressed in the SM.

One such precision experiment is the Belle II Experiment, which aims to make precise measurements of CP Violation in the B meson sector as well as search for new sources of CP Violation in NP programs. Benefiting from the large cross-section of the pairwise τ-lepton production in e

e

collisions, Belle II has a broad program of τ physics, in par- ticular, searches of lepton flavor and lepton number violations in rare τ-decays forbidden in the SM.

Located in Tsukuba, Japan, Belle II is a second generation B factory, consisting of the high luminosity Belle II detector and the SuperKEKB double ring accelerator.

SuperKEKB is an asymmetric energy e

e

collider, mainly running at a Center of Mass (COM) energy corresponding to the Υ(4S) resonance, where large numbers of B mesons and their antiparticles, boosted in the direction of the high energy electron beam, are produced exclusively. CP violation leads to differences in the decay patterns of B mesons and their antiparticles.

Neutral B mesons are of particular interest for the study of CP violation. The neutral

xiii

B mesons produced by the decay of the Υ(4S) are locked in a quantum-entangled state until one of them decays. Thus identifying the flavor of one of the neutral B mesons at the time of its decay also identifies the flavor of the other B meson at the same time. With one B meson fully reconstructed from a CP-eigenstate (B

) and the other identified from flavor-specific final states (B

), the difference between the particle and the antiparticle can be studied using the shape of the distribution of the difference of their decay times.

The decay processes which are suitable for studying CP violation in B mesons are quite rare. For example, the branching fraction of the process B

→ J/ΨK

is O (10

). This means that extreme luminosity is required to study CP violation in B mesons and other suppressed flavor physics reactions. To increase the precision of relevant measurements, Belle II was designed with an almost two orders of magnitude increase in luminosity from its predecessor experiment Belle. Such a massive increase in luminosity entails drastically increased background, which can cause damage to the electronic components of the detector, as well as make it more challenging to separate the signal from the background. To this end, the Belle II detector has undergone substantial upgrades, most importantly the tracking systems, including a precise silicon pixel vertex detector.

The beam crossing scheme at SuperKEKB has been upgraded from the so-called crab- crossing scheme at KEKB to a so-called nanobeam scheme which drastically squeezes the beams to a few tens of nanometers and constrains the interaction point to a few hundred micrometer scale, meaning that the primary particles originate from a much smaller region compared to KEKB where the beam spot was several millimeters long.

The goal of this thesis is to show that this constraint introduces a bias in decay vertex reconstruction of the flavor-tagged B meson due to the vertex fitting algorithms’ ten- dency to converge the fit of the B meson decay position towards the interaction point.

This bias was not observed at Belle and therefore the methods for determining the ex- perimental resolution functions need to be reconsidered for Belle II. It is shown with Monte Carlo (MC) simulations that, by relaxing or getting rid of this constraint at the origin, the bias disappears, however, relaxing the beamspot constraint results in loss of precision, defeating the intended purpose of the nanobeam scheme. Thus, the trade-off of bias vs. accuracy needs to be investigated in more detail.

The chapters of this thesis are divided as follows: Chapter 1 discusses some of the physics motivations behind the Belle II experiment, Chapter 2 gives an overview of the experiment, describing the SuperKEKB collider and the Belle II detector and their respective upgrades. An overview of ∆t resolution function is given in Chapter 3. Chap- ter 4 describes the role of Belle II software tools used to study time dependent analyses.

The results of this study are summarized in Chapter 5. The detailed plots, tables and

the Belle II software parameters used in this study are given in the Appendix.

1 Physics Motivations

1.1 The Standard Model

The Standard Model of Particle Physics (SM) (Figure 1.1) is a quantum field theory that describes the properties and interactions of fundamental building blocks of matter. The SM includes twelve elementary spin ±

particles called fermions, four gauge bosons with spin 1: the gluon, the photon and the W and Z bosons, and a massive scalar particle, the Higgs boson. The gauge bosons correspond to the fundamental forces. The gluons are the force carriers of the strong interaction, the photons mediate electromagnetic interactions, and W and Z bosons are exchanged in weak interactions. The hypothetical quantum of the gravitational force, the graviton, has not yet been observed, which is one of the several shortcomings of the SM.

R/G/B2/3

1/2 2.3MeV

up

u

R/G/B−1/3

1/2 4.8MeV

down

d

−1

1/2 511keV

electron

e

1/2

<2eV

eneutrino

ν _e

R/G/B2/3

1/2 1.28GeV

charm

c

R/G/B−1/3

1/2 95MeV

strange

s

−1

1/2 105.7MeV

muon

µ

1/2

<190keV

µneutrino

ν _µ

R/G/B2/3

1/2 173.2GeV

top

t

R/G/B−1/3

1/2 4.7GeV

bottom

b

−1

1/2 1.777GeV

tau

τ

1/2

<18.2MeV

τneutrino

ν _τ

±1

1 80.4GeV

W

1 91.2GeV

Z

photon 1

γ

color

gluon 1

g

0 125.1GeV

Higgs

H

strongnuclearforce(color) electromagneticforce(charge) weaknuclearforce(weakisospin) charge

colors mass spin 6quarks(+6anti-quarks) 6leptons(+6anti-leptons)

12 fermions (+12 anti-fermions)

increasing mass→

5 bosons (+1 opposite chargeW)

standard matter unstable matter force carriers

Goldstone bosons

1

2

3

Figure 1.1: The Standard Model of Elementary Particles [2].

The fermions of the SM are classified into quarks and leptons. There are six quarks

(up, down, charm, strange, top, and bottom), and six leptons (electron, electron neu-

trino, muon, muon neutrino, tau, and tau neutrino). The pairs from each classification

of fermions form generation-wise doublets, with corresponding particles exhibiting same

physical behavior under the weak and strong forces. A distinguishing property of the

quarks is that they carry color charges, and hence interact via the strong interaction. A

2 1. Physics Motivations

phenomenon called color confinement results in quarks being very strongly bound to one another, forming color-neutral composite particles (hadrons) containing either a quark and an antiquark (mesons) or three quarks (baryons). Quarks also carry electric charge and weak isospin, hence they interact with other fermions both electromagnetically and via the weak interaction. Leptons do not carry color charge and therefore don’t partici- pate in the strong interaction. The three neutrinos do not carry electric charge either, so they only interact via the weak interaction, making them notoriously difficult to detect.

The electron, muon, and tau, however, do interact electromagnetically. In the SM, the weak and electromagnetic forces are unified under the electroweak theory.

Each particle in the SM has an associated antiparticle with opposite quantum numbers such as electric charge, baryon number, lepton number and strangeness. The quarks and charged leptons have opposite-charge partners, neutrinos have partners with opposite helicity, photons, Z

and Higgs bosons are their own antiparticles, W

and W

are antiparticles of each other, and gluons, since they not only mediate strong interactions but also carry color charges themselves, form a color octet. Charge conjugating a gluon leads to another gluon or a combination of gluons. Hence the whole color octet is sometimes referred to as its own antiparticle.

All standard (stable) matter is comprised of protons and neutrons, the baryons com- posed of first generation quarks. Second- and third-generation charged particles, on the other hand, decay quickly and are therefore observed only in very high-energy environ- ments of particle accelerators [3].

1.1.1 Open Questions in the Standard Model

The SM is currently one of the best verified physical theories, but despite its tremendous success in describing the basic forces of nature, many fundamental questions still remain unanswered. The problems the SM fails to address include neutrino oscillations, dark matter and dark energy, reconciliation of gravity with other fundamental forces, and asymmetry between matter and antimatter in the observable universe [4]. Considering the open questions that exist in the SM, it is fair to conclude that the present theory is an extremely successful but phenomenological description of subatomic processes at energy scales now experimentally tested up to O (1 TeV).

1.1.2 Search for New Physics

Many new physics (NP) scenarios have been proposed to explain these shortcomings of the SM, where new particles and new processes arise. Experiments in high energy physics are designed to address the above questions through searches of NP using com- plementary approaches. At the energy frontier, the LHC experiments are able to discover new particles produced in proton-proton collisions at a centre-of-mass energy of up to 14 TeV. On the other hand, sensitivity to the direct production of a specific new particle depends on the mass scale of the new particle spectrum and the size of the data sample.

Indirect searches for NP via loop effects require the ability to measure suppressed flavor

1.2 CP Violation 3

physics reactions and deviations from SM predictions. Belle II operates at the inten- sity frontier on energy scales of O (10 GeV), with principal sensitivities to loop effects up to several hundred TeV). The actual sensitivity of Belle II to NP depends on the strength of the flavor violating couplings of the NP. Belle II and SuperKEKB aim to move beyond a simple observation of a NP effect to its detailed characterization through over-constraining measurements in several related flavor physics reactions [5].

1.2 CP Violation

In particle physics, symmetries - and the violation of symmetries - play a fundamental role. According to the famous Noether theorem [6], symmetries are related to conserva- tion laws. For example, the translational symmetry of space leads to the conservation of momentum, the rotational symmetry of space leads to the conservation of angular mo- mentum, finally the symmetry under translation of time leads to energy conservation.

All these symmetries are continuous symmetries. There are also discrete symmetries, such as the inversion of spatial coordinates, which is called “parity transformation” and is denoted by the letter “P”. Conservation of parity (or mirror symmetry) means that a physical state, or particle, with a certain spin direction can also be realized with the opposite spin direction. While P is conserved for the strong and the electromagnetic interactions, it turns out the weak interaction violates P in a maximal way: A neutrino has its spin always against its direction of motion (“left-handed”), while a right-handed neutrino does not exist.

Another discrete symmetry is the charge conjugation, denoted by the letter “C”, which transforms a particle to its antiparticle. Again, the weak interaction violates C in a maximal way: A left-handed neutrino would be transformed to a left-handed antineutrino, which does not exist (Figure 1.2). There is a third fundamental discrete

ν _L ν _R

ν _L ν _R

C

P

CP

Figure 1.2: The effect of C, P, and CP transformations on a left-handed neutrino ν

.

Only the states shown in boxes have been observed in nature.

4 1. Physics Motivations

symmetry, namely time reversal, denoted by “T”. Time reversal means to “run the film backwards”. In the weak interaction, time reversal seems to be conserved: A left- handed neutrino running in +z-direction (the spin of the neutrino points into the − z direction) is transformed under T into a neutrino running into the − z-direction, with its spin pointing into the +z-direction, meaning the neutrino remains left-handed.

1.2.1 CP Transformation

The CP transformation consists of successive C and P transformations, where the C transformation conjugates all internal quantum numbers of a particle and the P trans- formation reverses handedness. Under CP, a left handed neutrino transforms into a right-handed antineutrino (ν

→ ν

), which is allowed in the SM (1.2). Long thought of as an exact symmetry, a CP symmetry is indeed conserved in strong and electromagnetic interactions, but has been shown to be violated in weak interactions.

1.2.2 Flavor Mixing

In particle physics, flavor mixing refers to oscillations of a neutral particle between the particle and antiparticle states. The only hadrons that exhibit mixing with their antiparticles are the mesons K

(sd), B

(bd), B

(bs), D

(cu), and their antiparticles.

The meson states are flavor eigenstates and the corresponding antimesons have op- posite flavor quantum numbers. The mesons are eigenstates of the strong interactions, and in the absence of weak interaction, they are also mass eigenstates. In the SM all interaction vertices conserve flavor, except for the couplings of W bosons to fermions.

Meson-antimeson mixings belong to the class of flavor-changing neutral current (FCNC) processes, which involve different flavors with the same electric charge. In the SM such processes are forbidden at tree level, but are allowed at loop level (Figure 1.3). Time evolution and mixing of neutral mesons are discussed in more detail in Chapter 3.

Figure 1.3: Dominant box diagrams for the B

→ B

transitions (q = d or s). Similar diagrams exist where one or both t quarks are replaced with c or u quarks.

1.2.3 Types of CP Violation

CP violation can occur via different mechanisms and can thus be classified into three

types. For the purpose of such classification, it is useful to consider four pure quantum

1.2 CP Violation 5

mechanical states: the meson | M i and its charge conjugate state (antiparticle) | M i , as well as a final state particle | f i and its CP conjugate | f i . We have the following quantities of interest:

A

≡ A ( | M i → | f i ), A

≡ A ( | M i → | f i ), A

≡ A ( | M i → | f i ), A

≡ A ( | M i → | f i ),

(1.1)

Here, the symbol A denotes the amplitude of the respective process.

Indirect CP Violation

This type of CP violation manifests itself in processes where flavor mixing is involved.

It means that a transformation does not occur with exactly the same probability in both directions, for example, h B

| B

i 6 = h B

| B

i . In this case, CP violation arises as a consequence of an asymmetry in the flavor oscillation | M i → | M i → | M i , meaning that physical mass eigenstates are not CP eigenstates.

Violation of the CP symmetry in weak interactions due to mixing was first observed in neutral K mesons in 1964 [7]. In 1964, Christenson, Cronin, Fitch and Turlay designed an experiment to search for 2π decays of the K

meson. To conserve CP symmetry, K

should only decay to three pions. The observed O (10

) branching fraction of K

mesons decaying to two-pion final states could not be explained away as it would require highly unphysical behavior in three-pion decays, which proved that K

is not a pure CP eigenstate, hence there is mixing in the K-meson system.

For neutral B mesons mixing was first observed in late 1980’s at UA1 experiment at CERN [8], where the rates of muon pairs with same(++ or −− ) and opposite(+ − ) charges were studied in final states of reactions where bb states decayed to

1. (+ − ): b → c µ

ν

and b → c µ

ν

.

2. (++): b → c µ

ν

and b → cX, where c → s µ

ν

, or ( −− ): b → c µ

ν

and b → cX where c → s µ

ν

.

The ratio of same to opposite charged muon pairs was found to be substantially larger than the prediction,

R

= N (++) + N ( −− )

N (+ − ) = 0.42 ± 0.07(stat) ± 0.03(syst) (1.2)

R

= 0.26 ± 0.03, (1.3)

and this difference was interpreted as evidence for B

B

oscillation. The same year, the

ARGUS collaboration also published the first observation of the B

− B

oscillations [9].

6 1. Physics Motivations

These papers led to the realization that a precise measurement of this phenomenon could pin down the Unitarity Triangle [Section 1.2.4] and perhaps explain the excess of matter over antimatter in the universe. To this end, the construction of the first generation B-factories Belle and BaBar ensued, which over a decade of operation amassed over 1.5 ab

of data, corresponding to roughly 1.2 billion B

B

pairs [10]. This resulted in an experimental confirmation of CKM mechanism as source of CP violation in the SM.

For neutral D mesons mixing was observed in 2007 [11]. The CDF II detector at the Fermilab Tevatron measured the time dependence of the ratio of decay rates for the rare decay D

→ K

π

to the Cabibbo-favored decay D

→ K

π

, and found the data to be inconsistent with the no-mixing hypothesis with a probability equivalent to 3.8σ.

Direct CP Violation

Direct CP violation, also called CP violation in decay, is related to asymmetry in decays of charge-conjugate processes, meaning that a meson decay to a final state | f i does not occur with the same probability as an antimeson decay to the charge conjugate state

| f i . In terms of the amplitudes defined in Eqn. 1.1, this means

A

A

6

= 1 or

A

A

6

= 1. (1.4)

This is the only kind of CP violation that is possible for both, neutral mesons and charged mesons. Other types of CP violation exclude charged mesons, since they do not mix with their antiparticles.

The first attempt to prove the existence of direct CP violation was executed at CERN by the NA31 experiment. The experiment was proposed in 1982 with the explicit goal of establishing whether the ratio of direct and indirect CPV parameters,

/, was nonzero.

If the mixing parameter were the only source of CP violation, the fraction of K

decays with a two-pion final state normalized to K

would be independent of whether the two pions were π

π

or a π

π

. Any observed difference between the amplitude ratios with charged and neutral pions as final states would be evidence for direct CP violation.

Therefore, to make a measurement of the direct CP violation parameter, all four decay rates of K

and K

to π

π

and π

π

had to be measured.

Because

/ is of the order of 10

, the measurements were particularly difficult. In 1988, NA31 found the first evidence for direct CP violation, with a result that was about three standard deviations from zero. However, shortly after this the E731 experiment at Fermilab reported a measurement that was consistent with zero. These conflicting results prompted the design of a new generation of detectors, both at CERN (NA48) and at Fermilab (kTeV), which were able to, through a significant increase in beam intensity and event rates, confirm direct CP violation in K mesons in 1999 [12, 13].

For the B meson sector, direct CP violation wasn’t observed until 2004, when the

BaBar collaboration published their study of B

→ K

π

and B

→ K

π

decays. If

CP symmetry were conserved in these processes, then the two decays would be equally

likely to occur, and by starting with equal numbers of B

and B

the experiment would

1.2 CP Violation 7

end up with equal numbers of K

π

and K

π

pairs. However, BaBar found more K

π

pairs than K

π

pairs in a total of about 1600 events. The resulting asymmetry

A

= N (K

π

) − N (K

π

)

N (K

π

) + N (K

π

) = − 0.133 ± 0.030(stat) ± 0.009(syst) (1.5) established direct CP violation in the B

-meson system at the level of 4.2σ [14]. That same year, Belle reported A

= − 0.101 ± 0.025(stat) ± 0.005(syst) in about 2140 events, corresponding to a significance of 3.9σ [15]. As expected theoretically, both experiments confirmed that the CP violation is large in the B meson sector. At 10-13% asymmetry, the effect is about 10

times larger in neutral B mesons than in K mesons.

The size of CP violation in charm decays is tiny in the SM, with asymmetries typically of the order of 10

to 10

. Decades of experimental searches for CP violation in D

→ K

K

and D

→ π

π

modes by the BaBar, Belle, CDF, and LHCb collaborations reported values of CP asymmetries consistent with zero within a precision of a few per mille. In 2019, the LHCb collaboration managed to measure CP violation in charm decays with a precision 5.3σ [16].

Mixing-Induced CP Violation

Mixing-induced CP violation, which occurs due to interference of mixing and decay can be observed when the neutral mesons | M i and | M i have a common final state | f i , preferentially a pure CP eigenstate | f

i . Even if there is no CP violation in mixing and decay separately, i.e. if |A

/ A

| = 1, the sum of the decay and the mixing phases can give rise to a total phase difference and thus to an interference between these two processes, violating the CP symmetry.

In 2001, Belle presented a measurement of the Standard Model mixing-induced CP violation parameter sin(2φ

) based on a 29.1f b

data sample collected at the Υ(4S) resonance using signal channels J/ψK

, ψ(2S)K

, χ

K

, η

K

, J/ψK

, and J/ψK

. From the asymmetry in the distribution of the time intervals between the two B meson decays sin(2φ

) = 0.99 ± 0.14(stat) ± 0.06(syst) was determined, which was an indication for an observed mixing-induced CP violation in the neutral B meson system [17].

1.2.4 CKM Matrix and the Unitarity Triangle

In the SM quarks can only change flavor through emission of a W boson. For example, a top quark can decay to a bottom, strange or down quark: These decays are not equally likely. The labels V

, V

, V

in Figure 1.4 represent the relative probabilities of these transitions, which are encoded in the so-called CKM matrix:

V

=





| V

| | V

| | V

|

| V

| | V

| | V

|

| V

| | V

| | V

|





=





0.97427 ± 0.00015 0.22534 ± 0.00065 0.00351

0.22520 ± 0.00065 0.97344 ± 0.00016 0.0412

0.00867

0.0404

0.999146



 [18].

(1.6)

8 1. Physics Motivations

Figure 1.4: Top quark decaying to bottom, strange and down quarks by emitting a W

boson.

It can be seen from the CKM matrix that the probability of t → b is much higher (V

≈ 0.999146) than of t → s (V

≈ 0.0404) and t → d (V

≈ 0.00867). In general, the magnitude of the matrix elements follows a decreasing order, transitions within the same generation having the highest strength, followed by the transitions from first to second generation, then second to third generation and lastly, first to third generation.

This hierarchy is visualized in Figure 1.5.

Figure 1.5: Relative sizes of the CKM matrix elements [19]

The CKM matrix is named after the Italian physicist Nicola Cabibbo, who postulated weak universality in 1963, and the Japanese physicists Makoto Kobayashi and Toshihide Maskawa, who, a decade after, established a method to keep track of the weak decays of three generations of quarks that is still widely used today.

Quarks had not yet been theorized when Cabbibo published his major work on weak

interaction in 1963. His concept of weak universality [20] involves a similarity in weak

interaction coupling strength between different generations of particles. Cabbibo was

trying to explain, comparing the decays of charged pions and kaons, why the transitions

1.2 CP Violation 9

with a change in strangeness (∆S = 1) had a likelihood equal to one fourth of those with no change in strangeness (∆S = 0).

To explain this discrepancy, he introduced a mixing angle, now called the Cabibbo angle (Figure 1.6), which is related to the relative probability that down and strange quarks decay into up quarks ( | V

|

and | V

|

respectively). The object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks, here denoted by d

. Mathematically this is

| d

i = V

| d i + V

| s i = cos θ

| d i + sin θ

| s i . (1.7) Using the currently accepted values for | V

| and | V

| , the Cabibbo angle can be calculated using

tan θ

= | V

|

| V

| = 0.22534

0.97427 ⇒ θ

= 13.02

. (1.8) When the charm quark was theorized [21], it was noticed that the down and strange quark could decay into either the up or charm quark, leading to a 2x2 Cabbibo matrix:

d

s

=

V

V

V

V

d s

=

cos θ

sin θ

− sin θ

cos θ

d s

, (1.9)

where | V

|

represent the probability that the quark j decays into a quark i.

In 1973, observing that CP-violation could not be explained in a four-quark model, Kobayashi and Maskawa generalized the Cabibbo matrix to keep track of the weak decays of three generations of quarks, a year before the charm quark was discovered.

θc

θc

Figure 1.6: The Cabbibo Angle.

Thus, the Cabibbo-Kobayashi-Maskawa matrix (V

) is a unitary matrix (V

V

= 1) containing strengths of flavor-changing weak interactions for the quark sector. It is usually written as



 d

s

b



 =





V

V

V

V

V

V

V

V

V







 d s b



. (1.10)

10 1. Physics Motivations

The choice of usage of down-type quarks in the definition is a convention, and does not represent a physically preferred asymmetry between up-type and down-type quarks.

The CKM matrix can be parametrized by three mixing angles and the CP-violating phase. A ”standard” parameterization (Eqn. 1.11) uses three Euler angles (θ

, θ

, θ

) and one CP-violating phase (δ).

V

=





c

c

s

c

s

e

− s

c

− c

s

s

e

c

c

− s

s

s

e

s

c

s

s

− c

c

s

e

− c

s

− s

c

s

e

c

c



 , (1.11)

Here, s

= sin θ

, c

= cos θ

and δ is the CP-violating phase. Couplings between quark generation i and j vanish if θ

= 0. θ

is the Cabibbo angle.

The CKM matrix can be written using a conventient Wolfenstein parametrization [22]

that shows the sizes of matrix elements, with s

≡ λ, s

≡ Aλ

, s

e

≡ Aλ

(ρ + iη).

The parameters λ, A, ρ, η are all real and of order 1.

λ = 0.2257

, A = 0.814

,

ρ = 0.135

, η = 0.349

[18]. (1.12) The CKM matrix then becomes

V

=





1 − λ

/2 λ λ

A(ρ − iη)

− λ 1 − λ

/2 λ

A λ

A(1 − ρ − iη) − λ

A 1



 + O (λ

). (1.13) The CKM matrix elements are fundamental parameters of the SM, so their precise determination is important. In general, a unitary N × N matrix has (N − 1)

free variables. The unitarity of the CKM matrix imposes Σ

V

V

= δ

and Σ

V

V

= δ

. The six vanishing combinations can be represented as triangles in a complex plane. All these triangles have equal areas, A = J/2, with J corresponding to Jarlskog invariant:

J = c

c

c

s

s

s

sin δ ∼ 4 × 10

. (1.14) In the matrix element notation,

| J | = Im(V

V

V

V

) (for any ijkl, i 6 = k, j 6 = l). (1.15) The most commonly used unitarity triangle, relevant for B physics, is determined by

V

V

+ V

V

+ V

V

= 0, (1.16) divided by V

V

, this is equivalent to

1 + V

V

V

V

+ V

V

V

V

= 0. (1.17)

Introducing the parametrization ρ + iη ≡ −

cdV_cb

gives a nice graphical representation

of the matrix in the form of the Unitarity Triangle, where the horizontal axis is real and

the vertical axis is imaginary (Figure 1.7).

1.2 CP Violation 11

VudV∗

V ub cdV∗

cb

VtdV∗

V tb cdV∗

cb

γ= φ3 β =φ1

α=φ2

(0, 0) (1, 0)

(ρ, η)

Figure 1.7: The Unitarity Triangle

The area of the triangle can be thought of as a qualitative measure of the CP violation:

a vanishing complex phase (no CP violation) would cause the triangle to collapse into a zero-area line, while a non-vanishing phase (CP violation) is required to have a non- zero area triangle. Since the triangle in Figure 1.7 has sides and angles of comparable magnitude, more so than other unitarity triangles stemming from the constraints of CKM matrix, an equivalent statement is that CP violation is largest in the B sector, which is indeed what has been observed [17, 14].

1.2.5 CP Violation at Belle II

The general strategy for CP violation measurements is to take advantage of the entangled production of the B

B

meson pair through the reaction e

e

→ Υ(4S) → B

B

. The B meson pair evolves in a coherent state, with exactly one B

and one B

at any given time, until one of the mesons decays. When one of the B mesons decays, the other B meson continues to propagate and oscillate between a B

and a B

state until its own decay. Identifying the flavor of one B meson, the tagging B, as B

or B

, defines the flavor of the other B meson at the same time. The time dependent asymmetry for the decay of the other B meson, the signal B, to a CP eigenstate, can be written as

a

= Γ(B

(∆t)) − Γ(B

(∆t)) Γ(B

(∆t)) + Γ(B

(∆t))

= S sin (∆m∆t) − C cos (∆m∆t), (1.18) where ∆t is the difference in decay time between the moment the flavor of the B meson is observed and the moment the other meson decays into a CP eigenstate, and

∆m is the mass difference. The difference in decay time can be calculated measuring the decay length through ∆t = ∆z/βγc. The coefficients S and C are proportional to different types of CP violation: C accounts for “direct” CP violation while S accounts for the “mixing induced” CP violation.

The best way to measure φ

at B-factories is the time-dependent CP violation analysis

of b → ccs and b → qqs transitions. While the tree-level process b → ccs results in a

12 1. Physics Motivations

more precise measurement, especially using the golden mode B

→ J/ψK

, b → ccs, being a loop process, is also sensitive to NP contributions.

In this kind of measurement the main source of systematic uncertainty comes from the resolution on the vertex of the tagging B meson and the performance of the flavor tagging algorithm. The new flavor tagger of Belle II developed by F. Abudin´ en has already shown about 10% improvement in flavor tagging efficiency when used on the Belle data [23].

Because the B meson pair is produced almost at rest in the Υ(4S) COM frame, the boost is required to increase the separation and and thereby allow for time-dependent CP violation measurements. The boost factor has been reduced from about 0.43 at KEKB to about 0.28 at SuperKEKB in order to provide better hermeticity for missing energy decays, which reduces the separation between the B mesons from 200 µ m to 130 µ m . This would make it more challenging to separate the vertices, but the improved vertex detector is expected to not only compensate for the reduced B-vertex separation, but also improve the resolution. For the benchmark channel B → J/ψK

, the resolution on

∆t is expected to improve from 0.92 ps to 0.77 ps (Figure 1.8).

Figure 1.8: Tag vertex fit residuals (left): bias = 6 µm, resolution= 53 µm, and ∆t resid- uals(right): bias=-0.03 ps, resolution = 0.77 ps, of the fully reconstructed B

→ (J/ψ → µ

µ

)(K

→ π

π

). Both fits are performed using the sum of three Gaussian functions [24].

The measured distribution of ∆t includes a physics contribution arising from time

evolution of a neutral meson pair, and a contribution due to the detector effects, which

has a smearing effect on the true physics distribution. The detector effects are modeled

as the ∆t resolution function, which is to the first order, a Gaussian distribution. In

practice, the deviations from the Gaussian are important since precise determination

of the resolution on ∆t is crucial for carrying out time-dependent measurements, such

as determining the B meson lifetimes, BB oscillation frequency, and time-dependent

CP-asymmetries [25]. The upgrades to Belle II and SuperKEKB have made it impos-

sible to fully separate the experimental resolution and dilution effects from the physics

distribution. The interpretation of the observed ∆t distribution will be one of the major

challenges for the collaboration (Chapter 3).

1.3 Other Physics Prospects at Belle II 13

1.3 Other Physics Prospects at Belle II

In addition to searching for CP violation in the B-meson sector and other B-physics analyses, Belle II has an extensive NP program that aims to over-confine SM parameters and search for hints of Physics Beyond the Standard Model (BSM). The experiment will provide possibilities to study a wide range of areas in b-quark, c-quark, τ -lepton, two- photon, quarkonium and exotic physics, as well as searches for lepton flavor violation, dark matter, and axion-like particles. Since the sides of the triangles are products of CKM matrix elements, their sides and angles can be quantified by measuring proper decay rates. This definition of the UT with three sides and three angles seems to be too constraining, since any triangle can be defined by three of its six parameters, as long as at least one side is known. However, these measurements offer an excellent test of the SM: if the SM fully describes the mechanism for the CP violation, the unitarity of the CKM matrix would require each unitarity triangle to close, and the deviation from this condition would suggest a source of NP. Thus, an important goal of flavor physics is to overconstrain the CKM elements, and either close the unitarity triangle, or show the contrary with sufficient certainty.

1.4 Summary

The results of the first generation B factories Belle and BaBar confirmed the theory for the origin of CP violation by Kobayashi and Maskawa, who received the Nobel Prize for their theory in 2008 [26]. Until now, all measurements of CP violation in the meson sector agree with the CKM mixing mechanism of the SM, however, recent years have shown great progress in experiments that refine the measured parameters. Belle II is projected to greatly improve the accuracy of the angles and sides of the Unitarity Triangle, as shown in Figure 1.9. Belle II has a clear advantage over its competitor LHCb for measuring decays with missing energy, and searches for dark sector particles will happen in a mass window that is complementary to the searches at ATLAS and CMS [27]. It remains to be seen whether a significant deviation from the SM will be observed.

Figure 1.9: Constraints on the UT (a) 2016 (b) Projected: after 50ab

from Belle II.

2 The Belle II Experiment

The Belle II experiment consists of the 3 km SuperKEKB accelerator ring and the high luminosity Belle II detector. While the Belle II experiment has a rich physics program aiming at a number of exotic BSM scenarios, it is first and foremost a B factory: a facility where large quantities of B mesons are produced alongside their antiparticles to study CP violation in the B meson sector. The e

e

colliders are advantageous for this purpose because of the relatively clean environments they harness, typically producing only a few tracks in each event. In contrast, at hadron colliders such as the LHC the processes of interest are harder to identify due to the omnipresent QCD background [28].

This chapter will outline main features of the SuperKEKB accelerator and the Belle II detector, and discuss some of the main upgrades that are most relevant for precise vertexing and consequently the ∆t resolution measurements.

Figure 2.1: (a) Luminosities of past, ongoing and scheduled e

e

colliders over the years [29] (b) Luminosity vs. COM energy of e

e

colliders [30]

2.1 A Short History of e ⁺ e ⁻ Colliders

The circular electron-positron colliders date back over 50 years (Figure 2.1.a). The first e

e

collider, the storage ring AdA (Anello di Accumulazione in Italian, meaning the accumulation ring), was built in Frascati, Italy, in 1960 and the first observation of electron-positron collisions took place in a laboratory, in Orsay, France, in 1963.

Following this first proof of feasibility, new particle colliders were planned and built,

leading to milestone discoveries such as the 1974 observation made independently at the

SLAC and Brookhaven laboratories of the J/ψ meson. These earlier machines opened

2.2 SuperKEKB 15

the way to the large particle accelerators of the 1980’s, and to more discoveries that established the Standard Model of elementary particles as a well-tested physics theory.

In 1976, in light of the discovery of J/ψ and other heavy particles, B. Richter argued that an e

e

machine with several hundred GeV COM energy would enable one to

“understand the structure of the weak force itself by a study of reactions that involve only leptons in the initial and final states in an energy region where the weak interac- tions dominate”, and that such a machine would be “the most useful project on the horizon” [31]. An accelerator meeting these requirements, the Large Electron-Positron Collider (LEP) with a maximum COM energy of 209 GeV, was built at CERN. It ran from 1989 to 2000, and to this day it’s the most powerful e

e

accelerator ever built. In 1996, LEP produced its first pair of fundamental particles known as W

and W

today, taking particle physics research into new and unexplored territory.

A further important step forward was made by the two B factories, PEP-II and KEKB.

They established collider operation at very high beam current (well above 1 A per beam), world record luminosities, and top-up injection as a routine mode of operation. Another machine, DAΦNE, demonstrated the merits of crab-waist collisions, with a small vertical beta function β

at the interaction point (IP), and a large vertical beam-beam tune shift [32].

The next big step in luminosity upgrades has been the SuperKEKB, whose beam commissioning started in 2016. SuperKEKB was designed to operate with a “nanobeam collision scheme” (Section 2.2.2), which is similar to the crab waist, but without any crab- waist sextupoles. It features a β

of only 0.3 mm, and aims to achieve a 40-fold increase in luminosity compared to the previous world record achieved by its own predecessor, KEKB.

2.2 SuperKEKB

At SuperKEKB, electrons and positrons collide to create a COM energy in the region of the Υ-resonances. The Υ meson is comprised of a b and a b quark in a bound state, similar to a hydrogen atom. It has a mass of about 9.46 GeV in the ground state, but several excited states can also be produced. Figure 2.2 shows hadronic cross section for e

e

collisions as a function of e

e

COM energy close to the Υ-range. At the first three resonances, the Υ meson can only decay by the annihilation of b and a b quark, but at the fourth resonance, called the Υ(4S), there is enough energy in the excited stated to create a light quark/anti-quark pair, which results in production of a pair of B mesons.

Most data at Belle II is taken at Υ(4S) resonance, which is just enough energy for a B-meson pair production where no fragmentation particles are produced, however, the SuperKEKB accelerator has the capacity to deliver collisions in the COM energy range from just below the Υ(1S) (9.46 GeV) to just above the Υ(6S) (11.24 GeV) by tuning the energies of the colliding beams [5].

The SuperKEKB accelerator consists of two main storage rings, called the high energy

ring (HER) for the 7 GeV-electrons, and the low energy ring (LER) for the 4 GeV-

positrons. The positrons and electrons to be injected into their respective rings, are

16 2. The Belle II Experiment

Figure 2.2: Υ resonances cross sections [33]

provided by the linear accelerator (LINAC) and the 1 GeV positron Damping Ring (DR). The LINAC accelerates bunches of e

/e

to their target energies before they are injected into the main rings. Positrons need to be passed through the DR first since they are produced with too large an emittance for the nanobeam scheme (Section 2.2.2).

The electron and positron bunches collide at the center of the detector, at the so-called interaction point (IP) or the beamspot, at an angle of 83 mrad, allowing for ease of beam separation before and after collisions.

Figure 2.3: Projected luminosity of Belle II [34]

2.2.1 Luminosity

The target luminosity of SuperKEKB is a factor 40 larger than that of KEKB (Fig- ure 2.3), requiring a substantial upgrade to the accelerator complex. The essential elements in the increase of the luminosity are a reduction in the the beam size at the collision point by a factor of 20, from about 1 µ m to 50 nm, and an increase in the beam currents by a factor of 2 compared to the KEKB values.

This is known as a nanobeam scheme, and was invented by P. Raimondi for the

2.2 SuperKEKB 17

Figure 2.4: The SuperKEKB Schematic

Italian Super B Factory. Compared to KEKB, the two beams collide at an even larger angle of 83 mrad (22 mrad in KEKB). A somewhat lower beam energy asymmetry of 7 GeV (electrons) and 4 GeV (positrons), instead of 8 GeV and 3.5 GeV, was chosen to reduce the beam losses due to Touschek scattering in the lower energy beam. This leads to slight improvements in solid angle acceptance for missing energy decays, but it also reduces the spatial separation between the B mesons. Because of the reduced separation it is even more important to understand the vertex resolution in order to carry out time-dependent CP violation measurements.

The first generation B factories, KEKB and PEP-II achieved peak luminosities of 2.1 × 10

cm

s

and 1.2 × 10

cm

s

, respectively. To understand how the SuperKEKB design accounted for an almost two orders of magnitude increase, one must consider the factors determining the luminosity of a ring collider. The instantaneous luminosity achieved by ring colliders, including asymmetric ones, can be written as

L = γ

2er

1 + σ

σ

Iξ

β

±

R

R

. (2.1)

Here, L is the luminosity, γ the Lorentz factor, e the elementary charge, r

the classical electron radius, σ

and σ

beam sizes at IP along the x and y axes, I the beam current stored in the ring, ξ

the beam-beam tune-shift parameter, β

is the beta function at the IP, denoting the aperture of the beam. The suffix ± denotes each beam. R

, R

are the correction coefficients. The Expression 2.1 can be obtained from the beam-beam tune-shift parameter

ξ

= r

2πγ

N

β

σ

(σ

+ σ

)R

(2.2) and the definition of luminosity

L = N

N

f

4πσ

σ

R

, (2.3)

18 2. The Belle II Experiment

where N and f are the number of particles per bunch and the collision frequency (I = N ef), respectively, and the sizes of the two beams are assumed to be the same. The factors R

are the geometric reduction factors due to the hourglass effect and the crossing angle.

Parameters KEKB SuperKEKB Units

LER HER LER HER

Beam Energy E

3.5 8 4 7.007 GeV

Half Crossing Angle φ 11 41.5 mrad

Number of Bunches N 1584 2500

Horizontal Emittance ε

18 24 3.2 5.3 nm

Beta Functions at IP β

/β

1200/5.9 3.2/0.27 2.5/0.30 mm

Beam Currents I

1.64 1.19 3.6 2.6 A

Vertical Beam Size σ

0.94 0.048 0.062 µm

Luminosity L 2.1 × 10

8 × 10

cm

s

Table 2.1: Beam Parameters, KEKB vs SuperKEKB [5]

To boost the luminosity, the most essential parameters are in the ratio (Iξ

)/β

in Eqn. 2.1. This ratio can be maximized in different ways.

A head-on collision scheme was once considered for SuperKEKB, hoping to achieve a very high ξ

∼ 0.3 and ξ

∼ 0.5. Such a scenario assumed gains of × 5 in ξ

, × 4 in I, × 2 in 1/β

to achieve × 40 in the luminosity. The head-on scheme had a number of problems, including the very high synchroton ratiation due to large dynamic β functions and short bunch length in z (σ

. β

), required to avoid the hourglass effect. The coherent synchrotron radiation would in turn cause severe longitudinal instability and make such a short bunch impossible. Additionally, the experience from KEKB showed that the ξ

projected in simulations was never realized in three years of operation with the crab-crossing scheme, even with sophisticated machine tuning [35]. Thus the head-on scheme had to be replaced eventually with an alternative, called the nanobeam scheme, proposed by P. Raimondi.

2.2.2 The Nanobeam Scheme

The idea of the nanobeam scheme consists of

1. A relatively large beam crossing angle, with θ

σ

/σ

1, where θ

is the half horizontal crossing angle.

2. A very small vertical beta function, β

σ

.

3. Small horizontal and vertical emittances.

2.2 SuperKEKB 19

The formula for the luminosity, Eqn. 2.1 is still valid in the nano-beam scheme. The major gain of the luminosity comes from a very short β

. Unlike a head-on scheme, the bunches intersect one another only at the central part close to the IP in the nano-beam scheme due to the large crossing angle as shown in Figure 2.5.

As the length of the intersecting region is σ

σ

, the condition to avoid an hourglass effect becomes β

. σ

σ

. In the case of SuperKEKB, it is possible to choose β

∼ 0.3 mm, which gives × 20 gain compared to KEKB. Then the bunch length σ

does not need to be very short, making it possible to avoid the coherent synchrotron radiation. This scheme does not require a very large tune-shift parameter: ξ

∼ 0.09 is enough. The nano-beam crossing is similar to a collision with many micro-bunches with a very short bunch length σ

/θ

σ

.

2.2.3 Issues with the Nanobeam Scheme

The nanobeam scheme theoretically has no fatal issues but a number of technical and beam dynamics issues should be considered. The tiny beamspot size, especially in ver- tical direction, requires the stability of the orbit at the IP at a nanometer level, and the stability of final focus quadrupole magnets at a few µ m level to keep the vertical emittance relatively constant. Even small deviations would cause beam blowup due to the collision offset. The large crossing angle which is central to nanobeam scheme makes beam-beam effects less trivial, and introduces strong nonlinearities around the IP. The increased intrabeam scattering and space charge effects will also need to be taken into account, and the injection efficiency could suffer due to a smaller Touschek lifetime, which comes from a small dynamic aperture (β

). In addition, this extreme precision requires all power supplies, beam diagnostics and feedbacks to have a higher precision stability and a quicker response.

Figure 2.5: Beam Crossing in the Nanobeam Scheme [5]

Another issue, indirectly related to the nanobeam scheme, that affects time-dependent

analyses at Belle II, was presented by V. Chekelian at the 32nd Belle II Collaboration

General Meeting [36, 37]. The issue is the incompatibility of the tiny beamspot size

at SuperKEKB, provided by the nanobeam scheme, with the current time-dependent

analysis methods, resulting in a bias in the primary vertex reconstruction. This issue is

described in detail in Chapters 3 and 5.

20 2. The Belle II Experiment

2.3 The Belle II Detector

The Belle II detector surrounds the collision point of the SuperKEKB collider. While it fits the same shell as the Belle detector, most of the subdetectors have either been completely replaced or considerably upgraded due to the fact Belle II has to be able to operate at 40 times higher event rates than Belle, as well as with background rates higher by a factor of 10 to 20 [5].

Figure 2.6: The Belle II Detector [38]

To maintain the excellent performance of the spectrometer, the critical issue will be to mitigate the effects of higher background levels, which lead to an increase in occupancy and radiation damage, as well as to fake hits and pile-up noise in the electromagnetic calorimeter, and to neutron induced hits in the muon detection system. Higher event rates also require modifications to the trigger scheme, data acquisition system (DAQ) and computing [24]. The following modifications have been made to the detector:

2.3.1 Vertex Detector

The Belle vertex detector has been completely replaced by a new generation vertex de- tector (VXD), and is now comprised of two devices, two layers of silicon Pixel Detector (PXD), based on the novel DEPleted p-channel Field Effect Transistor (DEPFET) tech- nology, and four layers of the Silicon Vertex Detector (SVD) with double-sided silicon strip sensors. Altogether, the VXD consists of six layers distributed at radii ranging from 14mm to 14cm around the center of the detector (Figure 2.7).

Compared to the Belle vertex detector, the beam pipe and the PXD layers are closer

to the interaction point, while the outermost SVD layer is further away. The design was

chosen for optimally fulfill requirements for time-dependent CP-violation analyses and

to cope with the anticipated large background. It allows for a significant improvement