Measurement of B → J/ψηK decay branching fraction
and search for narrow resonances in J/ψη final state

2013

School of Interdisciplinary Research of Scientific Phenomena
and Information
Nara Women’s University
Tomoko Iwashita
Doctorial thesis

2
Abstract
We measured branching fractions of B → J/ψηK decay. These results are obtained from a data sample that contains 772×106 B B̄ pairs collected near theΥ(4S) resonance with the Belle detector at the KEKB asymmetric e+ e collider. We get the branching fractions B(B ± → J/ψηK ± ) = (1.3±0.1(stat.)±0.1(syst.)) × 10−4 , B(B 0 → J/ψηKS0 ) = (4.3 ± 0.7(stat.) ± 0.4(syst.)) × 10−5.
And we observed upper limit of B(B ± → X(3872)(→ J/ψη)K ± ) < 3.8 ×
10−6 . X(3872) state is discovered by Belle in 2003 and candidate of exotic
state. We search X(3872)’s C-odd partner in a tetra-quark model using
B → J/ψηK decay system.

3
Acknowledgements
In order to make this thesis, I would like to thank all the people who wereinvolved.
First and foremost, I wish to express my gratitude to my supervisor, Prof.
K. Miyabayashi and Dr. V. Bhardwaj.
And thank you for your help, Prof. H. Hayashii and Prof. S. Noguchi.
Moving on to KEK, Id like to thank Prof. Y. Sakai, Prof. Y. Ushiroda, Prof.
T. Karim, Prof. S. Nishida, Prof. M. Nakao.
I’d like to thank Dr. J. Brodzicka, Dr. A. Zupank, and my Belle Note’s
referees Prof. A. Bondar, Prof. M. C. CHANG, Prof. I. Adach and othercharm group members.
At last, I want to thank my family and friends who have supported me.

Contents
1 Introduction
1.1 Electroweak interactions and B meson decays . . . . . . . . .
1.2 Quark model and formation of hadrons . . . . . . . . . . . . .
1.3 Charmonium . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Multiquarks . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Hybrids . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Threshold effects . . . . . . . . . . . . . . . . . . . . .
1.4 X(3872) state . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
3
4
6
7
8
9
9

2 The Belle experiment
2.1 The KEKB accelerator . . . . . . . . . . . . . . . . . . . . . .
2.2 The Belle detector . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Beampipe . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Silicon Vertex Detector (SVD) . . . . . . . . . . . . . .
2.2.3 Central Drift Chamber (CDC) . . . . . . . . . . . . . .
2.2.4 Aerogel Cerenkov Counter (ACC) . . . . . . . . . . . .
2.2.5 Time of Flight Counter (TOF) . . . . . . . . . . . . .
2.2.6 Electromagnetic Calorimeter (ECL) . . . . . . . . . . .
2.2.7 Solenoid Magnet . . . . . . . . . . . . . . . . . . . . .
2.2.8 KL0 and Muon Detector (KLM) . . . . . . . . . . . . .
2.2.9 Trigger and Data Acquisition . . . . . . . . . . . . . .

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3 Event selection for B → J/ψηK decays
3.1 Data sample . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Reconstruction and identification of particles . . . . . . . . . .
3.2.1 Charged particle detection . . . . . . . . . . . . . . . .
3.2.2 Shower reconstruction and photon selection . . . . . .
3.2.3 B B̄ event selection . . . . . . . . . . . . . . . . . . . .

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CONTENTS
3.2.4 µ, e identicication . . . . . . . . . . . . . . . . . . . . .
3.2.5 Kinematic fit . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 J/ψ reconstruction . . . . . . . . . . . . . . . . . . . .
3.2.7 η reconstruction . . . . . . . . . . . . . . . . . . . . . .
3.2.8 K/π identfication . . . . . . . . . . . . . . . . . . . . .
3.2.9 KS0 reconstruction . . . . . . . . . . . . . . . . . . . . .
3.3 Reconstruction of B → J/ψηK . . . . . . . . . . . . . . . . .
3.4 Detection efficiency of B → J/ψηK decays . . . . . . . . . . .
3.4.1 B ± → J/ψηK ± mode . . . . . . . . . . . . . . . . . . .
3.4.2 B 0 → J/ψηKS0 mode . . . . . . . . . . . . . . . . . . .

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4 Background study
4.1 Continuum background reduction . . . . . . . . . . . . . . . .
4.2 Main backgrounds . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 ψ ′ → J/ψπ + π − and χc1 (χc2 ) → γJ/ψ veto . . . . . . .
4.2.2 Non J/ψ background . . . . . . . . . . . . . . . . . . .
4.3 Optimization of ∆E window . . . . . . . . . . . . . . . . . . .
4.4 Background probability density functions . . . . . . . . . . . .

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5 Results and discussions
5.1 B decay signal extraction . . . . . . . . . . . . . . . . . . . . .
5.2 Resolving intermediate states by MJ/ψη distribution . . . . . .
5.3 Correction and systematic uncertainties . . . . . . . . . . . . .
5.3.1 Tracking efficiency systematic . . . . . . . . . . . . . .
5.3.2 Correction and systematic uncertainty of K ID . . . .
5.3.3 Correction and systematic uncertainty of µ ID . . . . .
5.3.4 Electron ID correction and systematic uncertainty . . .
5.3.5 η detection systematic uncertainty . . . . . . . . . . .
5.3.6 Correction and systematic uncertainty of KS0 π + π − detection . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.7 Signal MC statistics . . . . . . . . . . . . . . . . . . .
5.3.8 Number of B meson pairs . . . . . . . . . . . . . . . .
5.3.9 Branching fraction uncertainties . . . . . . . . . . . . .
5.3.10 PDF systematic uncertainties . . . . . . . . . . . . . .
5.3.11 Summary of systematic uncertainties . . . . . . . . . .
5.4 Upper limit for resonance in J/ψη final state . . . . . . . . . .
5.4.1 X(3872) . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Narrow resonances at other mass points . . . . . . . .

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CONTENTS

7

6 Summary63

Chapter 1
Introduction
The development of particle physics over the past century has led to what iscalled the Standard Model (SM) of particle physics. This framework is basedon the renomalizable quantum field theory and gives descriptions for the fundamental particles of matter, leptons (electrons, muons, taus, and their associated neutrinos) and quarks (with ”flavors” up, down, charm, strange, top,
and bottom), as well as their interactions via the electromagnetic, strong,
and weak forces mediated by photons, gluons, and the W and Z bosons,respectively. Weak interactions are capable of changing quark flavor in thechanged current cases and the couplings between quark flavors are describedby the Cabbibo-Kobayashi-Maskawa (CKM) matrix [1]. The SM also predicts the existence of the Higgs boson that is responsible for the masses of theother particles in the SM, thought to be the consequence of the symmetry
breaking of the electromagnetic and weak forces. In the SM, quarks are massive point-like particles that interact with one another predominantly via thestrong force. The strong force is mediated by gluons and acts between quarks
that have colour, the strong force analogue of electromagnetic charge. The
theory describing these processes is called quantum chromodynamics (QCD).
The QCD predicts the phenomena called ”asymptotic freedom” that means
the coupling gets smaller in higher energy scale, i.e. in shorter distance [2].
It is confirmed by experiments and is recognized as one of the remarkablesuccesses of the SM. It also essentially explains how quarks bind together
to form matter as hadrons. One unsolved question is why hadrons are predominantly formed to be baryons or mesons which contain three constituent
quarks or constituent quark-antiquark, respectively. In spite of the fact there
is no explicit suppression rule to form other constituent quark configurations
1

2

CHAPTER 1. INTRODUCTION

in QCD, the number of candidate states for unusual structure hadrons is still
limited.
From 1999, LEPS experiment at SPring-8 and Belle experiment at KEK
B-factory started physics runs and in 2003 those experiments reported thepentaquark candidate Θ(1540)+ in K + n [5] and the extraordinary narrowcharmonium-like resonance X(3872) in J/ψπ + π − [4], respectively. X(3872)
is an exotic hadron candidate, thought to be a tetra-quark or a meson-meson
molecule state as discussed in more detail later. Since X(3872) was exploredin B ± → J/ψπ + π − K ± decay, other multi-body B meson decays are also
thought to be the place to visit. This work focuses on three-body B meson decays, B ± → J/ψηK ± and B 0 → J/ψηKS0 modes. Measurements ofbranching fraction for these decay modes essentially provide new knowledge
about B meson property. In addition, the J/ψη system in these decays
provide a chance to search for a charmonium or a charmonium-like exotic
hadron. The charmonium-like exotic hadrons are identified by comparing
their characteristics with the ordinary charmonium. The experimental datataken at a B-factory have rich statistics of the hadrons containing heavy
flavored quarks, b or c. Contrary to the case of hadrons comprised by lightquarks (u, d and s) where mixing of neutral mesons plays an important role
because of SU(3) flavor symmetry, c and b quarks are well separated fromother quark flavor due to their large masses of approximately 1.5 GeV/c2
and 5 GeV/c2 , respectively. Therefore the relation between the observed
state and its constituent quarks wave function is pretty straight-forward.
Especially, charmonium (cc̄ ) and bottomonium (bb̄) cases, a QCD potential
model works well to predict their masses including excited states because
their large quark masses are functioning as a kind of good cut off.
The charmonia which are lower than the open charm (D D̄) threshold can
decay only weak, electromagnetic and strong but OZI-suppressed processes,
thus they have narrow decay width. On the other hand, above D D̄ threshold, 3740 MeV/c2 , strong decay to the D meson pair predominantly takes
place and it results in wide decay width. Therefore, when a charmoniumlike hadron has larger mass than the open charm threshold and having oneof the following characteristics, it is to be recognized as an exotic hadroncandidate; (1) decay branching fraction other than D D̄ is large, (2) unusual
narrow decay width, (3) the special decay mode which can not be explained
as cc̄ and (4) mass does not match any predicted states.
In X(3872) case, in spite of the fact that it has larger mass than D D̄ threshold, it decays to J/ψπ + π − , decay width is very narrow and its mass does not1.1. ELECTROWEAK INTERACTIONS AND B MESON DECAYS

3

match with any predicted masses of still unconfirmed charmonium states. After its discovery, search for the decay into J/ψη was attempted in relatively
early stage. BaBar collaboration reported an upper limit on the product ofbranching fractions, B (B → X(3872)K)B (X(3872) → J/ψη) < 7.7 × 10−6
with the data sample corresponding to integrated luminosity of 82 fb−1 [7].
This result is based on limited data statistics and so far no one has revisited
this final state.
In recent a few years, since the radiative decay X(3872) → J/ψγ has been
established [8, 9], the X(3872)’s charge conjugation parity, C, is confirmed
to be even (C = +1). The J/ψη final state has C-odd (C = −1), thus
search for narrow resonance in this final state does not mean an attempt tolook for new X(3872) decay mode but seeking an its C-odd partner state,
which is predicted generally in either tetra-quark or meson-meson molecule
hypothesis. This work is based on a data sample containing 772 × 106 B B̄pairs collected by the Belle detector at the KEKB energy-asymmetric e+ e−
collider by the completion of their operation at 2010 June 30th. It corresponds to nine times larger statistics than that for the BaBar publishedanalysis, therefore we may reveal a signature of X(3872)’s C-odd partner, or
put more stringent constraint for that state.
In this chapter, physics about quarks and hadrons are reviewed in moredetail, including exotic hadrons. After that, experimental apparatus is explained and finally the analysis to get branching fractions for three-body B
decays into J/ψηK as well as to search for narrow resonances in the J/ψη
final state are presented.

1.1Electroweak interactions and B meson decays

In the SM, the electromagnetic and the weak interactions are unified as thefield theory based on SU(2) × U(1) gauge symmetry. Between electricallycharged particles, photons (γ) are exchanged to cause electromagnetic interaction phenomena. Among three weak bosons, the Z 0 is responsible forthe neutral current interaction and its mass is 91.19 GeV/c2 . Because of
the electroweak mixing that is denoted as sin θW , the interference between γ
and Z 0 exchange diagrams takes place and the resultant forward-backward

4

CHAPTER 1. INTRODUCTION

asymmetries in charged fermion pair production are well confirmed by thehigh energy e+ e− collision experiments at the center mass energy around
100 GeV. The remained two weak bosons, W + and W − are taking part inthe charged current interaction and thus it changes the flavor of quarks andleptons. Since B meson is the grand state b hadron, all its experimentallyconfirmed decay modes are only caused by the charged current interaction.
The charged current weak interaction in quark sector is described by the
Kobayashi-Maskawa theory [1]. The couplings between different quark flavors are described as a quark-mixing matrix. The quark-mixing matrix iswritten as [3];1 − λ2 /2λAλ3 (ρ − iη)
Vud Vus Vub




2
−λ
1 − λ /2
Aλ2
 . (1.1)
 Vcd Vcs Vcb  = 
3
2
Aλ (1 − ρ − iη) −Aλ1
Vtd Vts Vtb








The B meson decays into the final state with a charmonium is dominantly
caused by b → cc̄s transition in the quark level. Here, since both relevant
couplings Vcb and Vcs are the favored ones, large amount of B meson decay
data contain high statistics charmonium sample in the final states. This
holds not only for two-body B decay modes such as J/ψK (∗) , ψ(2S)K (∗) andso on, but also three-body modes including the J/ψηK which is the target of
this work. Because of relatively heavy B meson mass, the decay daughters
get quickly apart in the two-body decays thus there is very small final stateinteractions. This picture is called ”factorization”. On the other hand there
can be several intermediate states in the three(or more)-body decays andthis fact provides us a possibility to hunt a charmonium-like exotic hadrons
in many-body B decay processes as one of the intermediate states. In thefollowing subsections, the quark model, hadron formation and several exotic
hadron models are discussed.

1.2

Quark model and formation of hadrons

Quarks are acting as building blocks to form composite particles called hadrons.
Because of the strong interaction field, quarks are confined in hadrons and can
not go alone through vacuum. Quarks and gluons have an additional quantum number called colour charge, which characterizes three states, ”red”,”green” and ”blue”. A quark can take one of the three colours, while anantiquark takes an anticolour. Gluons carry both a colour and an anticolour.

1.2. QUARK MODEL AND FORMATION OF HADRONS

5

The colour confinement principle requires hadrons to be colourless. As aconsequence, there are two common types of hadrons, baryons and mesons.
Baryons are hadrons with half-integer spin and contaion three constituent
quarks. Nucleons, proton and neutron are the ground state baryons comprized by u or d quarks only. Note that the bare masses of u and d quarks
are not one third of the nucleon mass. Inside hadron, there is a large effectfrom the many virtual quark-antiquark pairs and gluons that do not give any
net quantum numbers but make hadron more massive than the sum of themasses of the valence quarks which carry the net quantum numbers. Mesons
are hadrons having integer spin and composed of a quark-antiquark pair andthus have zero baryon number. Each meson has a corresponding antimeson,
where quarks are replaced by their corresponding antiquarks and. For example, the B 0 particle is a bottom meson, composed of a down quark anda bottom antiquark. Similarly, the B ± meson is composed of an up quark
and a bottom antiquark. Since mesons have integer spin, some light mesons
can act as the bosons which mediate strong force in relatively long distance,∼ 10−14 m. As well known, π exchange between nucleons can be a good picture to describe nuclear forces to form a nuclei. This is because the pion isa Nambu-Goldstone boson coming from SU(3) symmetry breaking of strong
interaction at low energy. Another example would be the ”Vector Meson
Dominance” that means neutral light vector mesons such as ρ0 , ω and φcan strongly couple with photons. The vector meson dominance is known tolargely contribute to the hadron production in photon-photon collisions especially at relatively low transverse momentum region. These characteristics
for the light mesons are due to the flavor mixing among u, d and s by SU(3)′flavor symmetry. For example,
flaver√ in the case of η and η , using one of the √¯octet ψ8 = (uū + dd − 2ss̄) 6 and the flavor singlet ψ1 = (uū + dd̄ + ss̄) 3 aswell as the mixing angle θ, η = ψ8 cosθ − ψ1 sinθ and eta′ = ψ8 sinθ + ψ1 cosθ.
Therefore we have to solve these relations to understand constituent quarks
wave function in the observed meson states.
As briefly mentioned before, heavy flaxared hadrons are well separated fromlight quark sectors because of the much larger masses. Therefore the relation
between the observed states and its corresponding wavefunction is much morestraight-forward. This really holds well in the case of the quarkonium whichis conposed of a heavy quark and its antiquark. It is called a bottomium
if it is a bb̄ meson, such as the Υ(4S) produced at Belle; or a charmonium
when it is a cc̄ meson like the J/ψ. Charmonium states have masses around
3 GeV/c2 , and bottomium states around 10 GeV/c2 . The toponium doesnt

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CHAPTER 1. INTRODUCTION

exist,because the top quark is so heavy that it decays before a bound state
can form.

1.3

Charmonium

As already explained, a charmonium is a cc̄ meson and the diagram of the
known charmonium and apparently charmonium-related states are shown in
Fig1.1. The quantum numbers and basic properties of most of the states in
the charmonium family can be described within a simple picture of a nonrelativistic quark-antiquark pair cc̄. In this picture the states are characterized
by the orbital angular momentum L, the total spin S of the quark pair, andthe total angular momentum J, which defines the spin of the state viewed
as a particle. As usual, the total angular momentum is given by the vector~ + S.
~ Likewise, the totalsum of the orbital and the spin momenta; J~ = L
spin S is determined by the vector sum of the quark and antiquark spins;~ = ~sc + ~sc̄ . Clearly, S takes the values 0 and 1, thus splitting the fourSpossible spin states of the pair into a singlet and a triplet. Furthermore, theexcitation of the radial motion of the cc̄ pair results in a spectrum of levels
with the same L, S and J, and differing by the radial quantum excitation
number nr . With nr = 0 corresponding to the lowest state. It is therefore
customary to encode the values of these quantum numbers for each state ofcharmonium in the form of the symbol (nr + 1)(2S+1) LJ .
The combination 2S + 1 conveniently indicates the spin multiplicity, while
following the tradition from atomic physics the values of L = 0, 1, 2, 3 are
written as S, P ,D, F . In this notation the lowest state with L = 0, S = 0
and (necessarily) J = 0 is represented as 11 S0 (ηc resonance) while the firstexcited state with the same quantum numbers is 21 S0 (ηc′ ). The value of L
determines the parity (P ) for each of the states; P = (1)L+1 , while L and S
combined also determine the charge conjugation parity; C = (1)L+S . Therefore the previously mentioned 1 S0 states have quantum numbers J P C = 0−+ ,while e.g. 3 S1 states have the same quantum numbers J P C = 1−− as theelectromagnetic current, so that these states for example J/ψ, ψ ′ , ψ(3770)
and so on, can be produced as resonances in e+ e− annihilation. The states
having other quantum numbers than J P C = 1−− have been mostly confirmedby the decay from the higher vector states. For example, S = 1, L = 1 andnr = 0 result in three states called χc0 , χc1 and χc2 according to each own J
and all of them can be found in ψ’s radiative decays. So far, all the states be-1.3. CHARMONIUM

7

low D D̄ threshold (3740 MeV/c2 ) are identified. On the other hand, there
are still unconfirmed states above this threshold and several charmoniumlike states having unusual characteristics have been reported. Here, sometypical ordinary charmonia heavier than D D̄ threshold would be reviewed.
As already mentioned, usually strong decays to open charm mesons become
dominant thus decay widths are wide. Actually ψ(3770) dominantly decays
into D D̄ and its decay width is 27 MeV while J/ψ and ψ’ have widths of
93 keV and 300 keV, respectively. For a charmonium-like hadron, difference
from the typical properties implies a possibility of exotic hadron. For plausible pictures of charmonium-like exotic hadrons are described in the following
subsections.

Figure 1.1: Charmonium spectram. The masses are shown as afunction of
the quantum number, J P C .

1.3.1

Multiquarks

People can say why we have only two quarks (one quark and another antiquark) or three quarks (different colors) to make up the matter. There are
more combinations possible. Multiquark model supports such hypothesis.
Originally, in 1970s, the idea of such a particle known as tetra-quark wasconsidered to explain the properties of light scalar mesons f0 (600), f0 (980),
and a0 (980) as their properties were not well explained by the existing quark
model) [10]. Two types of multiquark states have been considered. The

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CHAPTER 1. INTRODUCTION

first is a molecular state (also known as deuson) which comprises of two
charmed mesons bound together to form a molecule. Molecular states areloosely bound and are expected to bind through two mechanism; quark/color
exchange interactions at short distance and pion exchange at large distance(expected to dominate). Mesons inside the molecule are weakly bound, sothey decay as if they are free. Also, molecular states are not isospin eigenstates which result in distinctive decay patterns. The idea of molecular states
was initially used to explain an excessively large D ∗ D̄ ∗ production cross section compared with the D D̄ and D ∗ D̄ ∗ production cross sections at the peakof ψ(4040) in e− e+ annihilation. It was supposed that ψ(4040) can be a
P -wave molecular resonance in the D ∗ D̄ ∗ system and was forgotten but was
revived in 2003 after the discovery of the X(3872) particle [4].
Multiquark state can also exist in the form of a tightly bound four-quark
state (known as tetra-quark) and they are expected to have properties different from those of a molecular state because size and proper degree of
freedom for the description are different. Maiani et al. [11] suggested thatthe tetra-quark can be described as a diquark-diantiquark structures in which
the quarks group into color-triplet scalar and vector clusters and the interactions are dominated by a simple spin-spin interaction. The strong decays
are expected to proceed via rearrangement processes, followed by disassociation, that give rise to the decays such as X(3872) → ρJ/ψ → ππJ/ψor X(3872) → D D̄ ∗ → D D̄γ for example. A prediction that distinguishes
multiquark states containing a cc̄ pair from conventional charmonia is thepossible existence if multiplets that include members with nonzero charge¯ strangeness (e.g. [cdc̄s̄]), or both (e.g. [cuc̄s̄]). In tetraquark(e.g. [cuc̄d]),picture, Terasaki [12] suggested a C-odd state can decay to J/ψη. It is
important to revisit this final state with high statistics data.

1.3.2

Hybrids

Hybrid mesons are states which has an excited gluon degree of freedom. Suchstates are discussed in many different models and calculation schemes. In lattice QCD, the quarks are viewed as moving in adiabatic potentials produced
by gluons in analogy to the atomic nuclei in molecules moving in the adiabatic potentials caused by electrons. Conventional charmonium spectrum is
produced by lowest adiabatic surfaces while excited adiabatic surfaces leadto an octet of the lightest hybrids. These excitations introduces an additional degree of freedom related to gluons and add the spin and the angular1.4. X(3872) STATE

9momentum [13, 14]. In the flux-tube model[15], the lowest excited adiabatic
surfaces corresponds to transverse excitations of the flux tube and leads to adoubly degenerate octet of the lowest mass hybrids with quantum numbers
J P C = 0+− , 0−+ , 1+− , 1−+ , 2+− , 2−+ , 1++ , and 1−− . Some of the octet
component having quantum numbers 0+− , 1−+ , and 2+− are not possible forcc̄ bound states in the usual quark model. If these states are observed, they
will confirm the existence of an unconventional states. Lattice QCD predicts
the lowest charmonium hybrid state to be roughly 4200 MeV/c2 in mass [16].

1.3.3

Threshold effects

In addition to these states, threshold can also give rise to the structuresin cross sections and kinematics distributions. The possible thresholds include the DD ∗ , D ∗ D ∗ , DD1 and D ∗ D1 at Ecm ∼ 3872, 4020, 4287 and 4430
MeV, respectively. S-wave (L = 0) scattering dominates the cross section
at the threshold, however in few cases higher waves also become important.
States in a relative S-wave with little relative momentum can live long on thetimescale of strong interactions, then have enough time to exchange pions tointeract each other [17]. Here, molecular state is possible to be produced
due to the possible binding via an attractive π exchange which could occurs
through couplings such as Dπ 0 ↔ D ∗ . It should be noted that there could
also be a repulsive interaction which arises due to some strong interaction
effects and it can result in a virtual state above threshold. Thus, near the
kinematical threshold there can be a structure in the cross section which
may or may not be a simple real resonance. In addition, if there are cc̄ states
which are near a threshold, they can interact with the threshold and will
result in a mass shifts of both the cc̄ resonance and the threshold-related
enhancement. This effects could be quite significant in the observed crosssection, particularly for the cc̄ states close to the thresholds [17, 18].

1.4

X(3872) state

In 2003, the Belle Collaboration discovered a narrow charmonium-like stateX(3872) → J/ψπ + π − having width less than 2.3 MeV/c2 (90% C.L.) and amass of 3872.0±0.6±0.5 MeV/c2 in the charged B decay to X(3872) and K[6]. Later on it was confirmed by CDF [19], D0 [20], LHCb [21] and BaBar [22]Collaborations. Figure 1.2 shows observation of X(3872) at Belle. At present

10

CHAPTER 1. INTRODUCTION

the world average width and mass are Γ < 1.2 MeV/c2 and 3871.7±0.2
MeV/c2 in which Belle experiment is dominating [26]. Since X(3872) →J/ψπ + π − , it is quite obvious to identify X(3872) as the new charmonium
state. The X(3872) displays some characteristics of a charmonium-like state,but its narrow width above the D D̄ threshold and quantum numbers limit its
possible assignment within the charmonium model. Its mass near mD0 +m0D̄∗
has led to speculation that the X(3872) may be the bound state of thesetwo charged mesons. Other more exotic interpretations include a tetraquark(tightly bound state of four quarks) model, or charmonium-gluon hybrid
bound states.
In order to identify what is the X(3872) state, experimentalists can makeseveral attempts. First of all, determination of the quantum numbers suchas spin (J), parity (P ) and charge conjugation (C) gives very important information. As already mentioned, the radiative decay of X(3872) to J/ψγ
final state determines C = +1 (C-even) [8, 9]. The J/ψπ + π − mode enables
us to assess other quantum numbers by the angular distribution analysis of
the decay products. According to the Belle [26] and CDF [27] studies, stillallowed quantum number assignments are J P C = 1++ or 2−+ . A next generation higher statistics experiment is necessary to identify one of these two.
Second approach is search for the hypothesis-oriented decay mode. Motivated by the assumption that X(3872) is a D 0 D̄ ∗0 molecule, B → D 0 D̄ ∗0 K
modes are reconstructed and X(3872) → D 0 D̄ ∗0 has been confirmed. This
decay mode’s branching fraction is found to be approximately 10 times larger
than J/ψπ + π − mode [28].
This result seems to support the interpretation as a molecular state, however there are several unsolved question assuming that it has J P C = 1++ .
Difference between the observed mass and D 0 D̄ ∗0 threshold is representing
the binding energy and it is found to be small, 0.1 ± 0.35 MeV. This binding
energy can be translated into the distance between D 0 and D̄ ∗0 under the
Yukawa-type potential with pion exchange. That distance corresponds to thesize of X(3872) and is found to be about 5 fm, comparable spacial spreadingwith the lead nuclei [29]. On the other hand, the size of J/ψ meson is about
0.4 fm, therefore volume difference is so large, O(103 ), that the probability
for c and c̄ quarks to meet each other to form J/ψ can not be one tenth
but should be much smaller, then contradicting with the observed facts. In
addition, such very loosely bound object can hardly be produced by the highenergy pp̄ collisions at Tevatron, thus it would not be easy to explain theX(3872) production cross section measured by CDF experiment [30].

1.4. X(3872) STATE

11

Under such situation, search for the partner states of X(3872) will give us
independent information to test interpretation of it. So far, though the search
for X(3872)’s charged partner in J/ψπ ± π 0 gave negative results [26, 31], thecharged partner might be so broad that we can not get a proper signaturein the current statistics and the X(3872)’s C-odd partner state can havemoderately narrow decay width and may decay into the J/ψη final state
in a tetraquark model [32]. In more general argument, the C-odd partner
can exist in either molecule or tetraquark pictures and the photon energyin η → γγ is well above the energy threshold to be detected in B-factories
even in the case such resonance is just above J/ψη mass threshold. Thus theJ/ψη system in the three-body B → J/ψηK decay is an important subject
to discuss about the missing C-odd X(3872) partner.

Figure 1.2: Observation of X(3872). In (a), narrow peak around 3.872
GeV/c2 .

Chapter 2
The Belle experiment
The Belle experiment is one of two dedicated B physics experiments in theworld and it is located the High Energy Accelerator Research Organization(KEK), Tsukuba, Japan. Another B-factory experiment, BaBar is performedat the Stanford Linear Accelerator Center (SLAC), california, USA. The
B−factory at KEK consists of two separate entities, the KEKB e+ e− collider
and the Belle detector.

2.1

The KEKB accelerator

The KEKB accelerator [23], which was commissioned in December 1998, isdesigned to produce large number of B B̄ pairs by colliding electrons andpositrons of asymmetric energy. It consists of two storage rings, an 8 GeVelectron high energy ring (HER) and a 3.5 GeV positron low energy ring(LER). The two storage rings are located side by side in the acceleretor tunnel originally built for the TRISTAN e+ e− collider project. The accelerator is
located11 m underground and have a circumference of roughly 3 km. Thereis only one beam crossing point where the e+ e− collision takes place, known
as the interaction point (IP). A linear accelerator (Linac) accelerates theelectrons and positrons to their required energies and inject them into theirrespective storage rings. Figure 2.1 shows a schematic of the KEKB collider.
Electrons and positrons are kept in bunches around the storage rings. There
are approximately 1000 bunches in each ring which corresponds to a bunch
separation of around 3.0 m. The electrons and positrons collide with a finite
crossing angle of ±11 mrad to avoid the parasitic interactions of bunches13

14

CHAPTER 2. THE BELLE EXPERIMENT

near but not at the IP.
√
The centre-of-mass energy at the collision point is nominally s = 10.58
GeV, which coincides with the peak of the cross section to produce the Υ(4S)
resonance. This is the optimized choice to get B meson data as much as possible because the Υ(4S) decays to a B B̄ pair more than 96%. The mass of
the B meson is almost half the Υ(4S) mass, thus it will be produced roughly
at rest in the Υ(4S) rest frame.
The advantage of the asymmetric collider is that the B mesons receive a
Lorentz boost, βγ = 0.425, in the laboratory frame along the direction of thebeam line (z coordinate), thus simplifying the kinematics of the B B̄ pair to
one-dimension. The boost also gives the B mesons a mean flight length ofabout 200 µm in the laboratory frame making it feasible with current technology to measure a separation between the decay points of the B B̄ pair in z
direction, ∆z. This allows the time difference between two B meson decays
to be calculated as ∆t ≃ ∆z/βγc. It is an indispensable future of the experimental apparatus to realize time-dependent CP violation measurement in
B meson system.
The KEKB collider and the Belle detector were operated not only on theΥ(4S) resonance but also on Υ(1S), Υ(2S), Υ(3S) and Υ(5S) as well as
60 MeV below Υ(4S) for understanding of continuum background. The design luminosity of the KEKB collider was L = 1.0 × 1034 cm−2 s−1 , whichcorresponds to an approximate production rate of 10 B B̄ pairs per second.
By the completsion of the operation at 2010, we have well exceeded thisdesign luminosity with the world record of L = 2.11 × 1034 cm−2 s−1 , andour accumulated luminosity is now greater than 1000 fb−1 . Out of those, anintegrated luminosity of 703 fb−1 was recorded at Υ(4S). The number of B B̄pairs recorded in that data sample is 772 × 106 .

2.2

The Belle detector

The Belle detector is a large solid-angle magnetic spectrometer that can detect the following final state particles (K ± , π ± , e± , µ± , p(p̄), γ and KL0 ). Sincea B meson will eventually decay to some combination of these final state particles most of the time, it is important that these particles can be detected
and identified with high efficiency. The Belle detector was designed to achieve
this task with many sub-detectors as shown in Fig 2.2, and is placed asymmetrically around the IP because of the direction of the boost. The following

2.2. THE BELLE DETECTOR

15

Figure 2.1: The KEKB collider.

sections describe the various sub-detectors and further details can be foundin Ref. [24].
Now we describe the Belle coordinate systems used in this thesis. In Cartesian coordinates, z is defined as being the direction opposite the positron
beam line, y is vertically upwards,and x is in the direction of the crossproduct,√ 2 x =2 y × z. Cylindrical coordinates are also used. The radius,r = x + y , is defined in the x-y plane, θ is the polar angle from the zaxis, and φ is the azimuthal angle around the z-axis. Further details of thehandware components are to be described.

2.2.1

Beampipe

Although not active component of the Belle detector, the beampipe aroundthe IP is the first piece of material through which particles must traverse
before reaching the detector. Since Coulomb scattering affects track resolution, it is important to minimise the impact of the beampipe on particle

16

CHAPTER 2. THE BELLE EXPERIMENT

Figure 2.2: Cut-away view of the Belle detector.

trajectories by choosing a thin material with low atomic number. In addition, track quality is reduced as the detector is further removed from the IP.
So the diameter of the beampipe must also be as small as possible.
With these considerations in mind, a beryllium beampipe was chosen. The
beampipe is a dual layer cylinder whose radii are 20.0 mm and 23.0 mm
respectively, where each cylinder has a 0.5 mm thickness. The 2.5 mm gap
between the cylinders is used as a helium gas channel which acts as a coolant.
This prevents overheating induced by the beam and minimally interferes withtracks due to its low atomic number. The outer layer is covered with a 20 µm
thick gold sheet to reduce low energy X-ray background from the HER. The
total thickness of the beampipe corresponds to 0.9% of a radiation length.
After the first 152 × 106 B B̄ pairs were accumulated, the innermost detector
was redesigned to accomodate new 4-layer SVD having an improved acceptence and to get closer to the IP. The radius of the inner cylinder of the new
beampipe is now 15.0 mm. Fig 2.3 shows the design of the original beampipe.
The new beampipe has almost same structure except for the radius and newly2.2. THE BELLE DETECTOR

17

introduced paraffin coolant.

Figure 2.3: Side view and cross section of the beampipe used for accumulation
the first 152 × 106 B B̄ pairs.

2.2.2

Silicon Vertex Detector (SVD)

The Silicon Vertex Detector is the most important detector in the timedependent CP analysis as it is responsible for precise measurement of B
vertex positions. This is achieved via the high spatial resolution of the SVD.
The SVD is the innermost detector and consists of three concentric cylindrical layers of silicon sensors which cover the polar angle, 23◦ < θ < 139◦ . This
corresponds to 86% of the solid angle. The radii of the innermost, middle,
and outermost layers are 30.0, 45.5 and 60.5 mm, consisting of 8, 10 and 14
ladders, respectively. Each ladder is made up of two half-ladders that are
joined by a support structure but are electrically independent of each other.
A long half-ladder contains two double sided silicon strip detectors (DSSD)
and a hybrid unit which processes signals from the DSSD. A short half-laddercontains a DSSD and a hybrid unit. The innermost layer consists of two shorthalf-ladders, the middle layer consists of a short and long half-ladder and theoutermost-layer ladder consists of two long half-ladders.
The DSSD, manufactured by Hamamatsu Photonics, was originally developed for the DELPHI detector [25]. Its dimensions are 57.5 × 33.5 mm2 witha thickness of 300 µm. Each DSSD consists of 1280 sense strips and 640

18

CHAPTER 2. THE BELLE EXPERIMENT

readout pads on both sides. One side of the DSSD (n-side) has its n+ sense
strips, each separated by 42 µm, oriented perpendicular to the beam direction to measure the z coordinate. The p+ sense strips, each separated by 25µm, on the other side (p-side) are oriented longitudinally which allows ther-φ position to be measured. A DSSD is basically a pn junction. A bias of
75V is supplied to the n-side, while the p-side is grounded. The n+ strips areinterleaved by p+ implants (p-stops) to electrically separate the consecutive
strips. A charged particle passing through the n bulk silicon creates electronhole pairs. The electrons and holes drift to their corresponding biased side of
the DSSD making a 2-dimensional hit signal. On the n-side, adjacent strips
are read out by a single channel, giving an effective strip separation of 84 µm.
On the p-side, every other strip is connected to a readout channel. Chargecollected by the floating strips in between is read from adjacent strips bycapacitive charge division. A schematic of the DSSD is shown in Fig 2.4.
A redesigned SVD was installed after 152 × 106 B B̄ pairs were accumulated.
The SVD already described is called SVD1 and was replaced with the 4-layer
SVD2. Among the several improvements were that the angular acceptanceof SVD2 was increased to 17◦ < θ < 150◦ , and the innermost layer was
moved 1.0 cm closer to the IP to a radius of 2.0 cm. The fourth layer isaccommodated by redesigning the inner region of the CDC. Fig 2.5 shows
the geometry of the SVD. We estimate the performance of the SVD with twoquantities. One is the SVD-CDC track matching efficiency which is definedas the probability that a CDC track passing through the SVD acceptancehas associated SVD hits in at least two layers, and at least one 2-D hit. The
CDC is the next innermost detector after the SVD and will be describedlater. The average matching efficiency is better than 98.7%.

2.2.3

Central Drift Chamber (CDC)

The Central Drift Chamber is a charged particle tracking system that measures track momenta from their curvature in the magnetic field induced by thesolenoid magnet. The CDC also measures dE/dx of charged tracks to provide particle identification information. A charged particle moving througha constant magnetic field will follow the path of a helix which is defined by
five parameters. The first is the curvature of the helix which gives the transverse momentum, pT , and the second gives the pitch which is related to thelongitudinal momentum, pL . The other three give the impact parameters.
The inner side of the CDC is not encased with aluminium like the outer19

2.2. THE BELLE DETECTOR

n+ stripp- stophole

n bulkelectronp+ stripFigure 2.4: DSSD schematic.

SVD sideview
SVD endview

CDC

Heat pipe
45.5
60.5
30
unit:mm139°
Be beam pipe

23°

k

at

IP

He

sin

BN ribs with CFRP
HybridVA1p-sideDSSDn-sideFigure 2.5: The schematic shows the SVD1 geometry.

parameters with respect to the IP. By minimising the amount of passive material in the way, good tracking efficiency can be maintained even for low
pT tracks. The CDC coverage is 17◦ < θ < 150◦ which corresponds to 92%

20

CHAPTER 2. THE BELLE EXPERIMENTof the solid-angle. Figure 2.6 shows the geometry of the CDC. The CDC
is filled with a gas consisting of 50% helium and 50% ethane. The low-Z
gas mixture is useful for minimising multiple Coulomb scattering to ensure agood momentum resolution, especially for low momentum tracks. The CDC
contains a total of 8400 drift cells. A drift cell is made up of eight grounded
wires providing an electric field which surrounds a positively biased sense
wire. The CDC cell structure is shown in Fig 2.7.
When a charged particle passes through a drift cell, electrons are dislodged
from the gas and drift towards the sense wire. In the final 1 mm, the electric field increases as 1/r. This accelerates the electrons sufficiently to cause
secondary ionisation which, in turn, cause further ionisation resulting in acascade of charge. This process, called gas amplification, increases the signal
by a factor a few 104 . Before amplification, the electrons have a specific drift
velocity, so the measured pulse height and drift time are related to the energy
deposit, dE/dx, and distance from the sense wire. Roughly half the wires areoriented parallel to the z-direction (axial) to provide pT information while theremaining wires are oriented at a small angle, ±50 mrad, to the z-direction(stereo) to give pL . Figure 2.8 shows a scatter plot of the measured dE/dx
as a function of the particle momentum. Separation between pions, kaons,protons and electrons can clearly be seen with particle momenta below 1
GeV/c. Now that the behaviour of particles with different mass have shown
distinct characteristics in dE/dx, we can perform particle identification on
an unknown track that traverses the CDC.

2.2.4

Aerogel Cerenkov Counter (ACC)

The role of the Aerogel Cerenkov Counter is to provide particle identification
information to distinguish charged kaons from charged pions in the momentum range of 1.0 to 4.0 GeV/c. Cerenkov radiation is emitted when thevelocity of a charged particle in a medium exceeds the speed of light in thesame medium,
s
m
1
(2.1)
n > = 1 + ( )2βpwhere m and p are the mass and momentum of the particle, and n is the refractive index of the material. Therefore, we can distinguish kaons frompions, muons and electrons by selecting a material in which pions emit
Cerenkov light, but heavier kaons do not.

21

2.2. THE BELLE DETECTOR
Belle Central Drift Chamber
2204
702.2

1501.8
5

790.0

r

880

150°

1589.6

17°

83

294

747.0

e-

+

e
Interaction Point

10

Cathode part
Backwardyz
100mm

Forwardyx
100mm

Inner part
Main part

Figure 2.6: CDC geometry.

The ACC can be divided into two regions, the barrel and the forward endcap. The barrel consists of 960 counter modules separated into sets of 60 in
the φ direction. There are 228 modules that occupy the forward endcap in
5 concentric layers. Each counter is arranged in the way to points towards
the direction of the IP. Fig 2.9 and 2.10 show the geometry of the ACC and
ACC modules of barrel part and endcap part.
A counter module consists of silica aerogel blocks encased in an aluminium
box of roughly 12 × 12 × 12 cm3 in size. One or two photomultiplier tubes
capable of operating in the 1.5 T magnetic field are attached to the sidesof each box to detect Cerenkov photons. The refractive indices of the silica
aerogel blocks are selected to maintain good kaon/pion separation over the
kinematic range stated earlier. For the barrel modules, silica aerogel withfive different refractive indices, n =1.010, 1.013, 1.015, 1.020 and 1.028 areused depending on the polar angle. Silica aerogel with n = 1.030 is used in
the forward endcap modules, to encompass lower momentum particles. Thisis because the TOF, designed for particle identification with low momentum
particles and the next sub-detector in line, is not present in the endcap.

22

CHAPTER 2. THE BELLE EXPERIMENT

0
3.0
10

Layer 2

Sense wire
.00
83
0
5.0

Field wire
11.25°

45°

unit: mm

16mm

Layer 011.25°

17mm

Layer 1
Field Wire Al 126µmφ
Sense Wire Au plated W 30µmφ

Figure 2.7: CDC cell structure.

2.2.5

Time of Flight Counter (TOF)

The Time of Flight Counter gives particle identification information to distinguish charged kaons from pions in the low momentum region, below 1.2
GeV/c. The particle mass (m), can be determined from its relation to themeasured elapsed time from collision at the IP, and is expressed as,
s

L
L
m
T =
=
1 + ( )2
cβ
c
p

(2.2)

where p is the momentum of the track and L is the flight length. The
TOF sub-detector consists of plastic scintillation counters attached to thefine-mesh type photomultiplier tubes and has a timing resolution of 100 ps.
The TOF also provides fast timing signals for the data acquisition and thetrigger system. To sustain a fast trigger rate in any beam background condition, thin trigger scintillation counters (TSC) are placed just before the
TOF counter. A TOF module consists of two TOF counters and one TSC
counter, a schematic of which is shown in Fig 2.11.
In total, there are 64 TOF modules located in the barrel region at a radius

23

dE/dx

2.2. THE BELLE DETECTOR

4

π

3.5

K

P

3

2.5

2

e

1.5

1

0.5
-1.5

-1

-0.5

0

0.5

1

log10(p)dE/dx vs log10(p)Figure 2.8: dE/dx vs momentum taken from collision data.

of 1.2 m from the IP, covering a polar angle of 34◦ < θ < 120◦ . Figure 2.12
shows the mass distribution obtained from TOF measurements. The data
points are consistent with the simulation that assumes a time resolution of
100 ps.

2.2.6

Electromagnetic Calorimeter (ECL)The Electromagnetic Calorimeter serves to identify electrons and photons bymeasuring electromagnetic showers. Electrons in this analysis are required
for J/ψ reconstruction while photons are needed for the reconstruction of η.
The ECL consists of 8736 thallium-doped CsI crystal (CsI(Tl)) counters. The
CsI(Tl) crystal has a tower shape and is 30 cm long, which corresponds to16.2 radiation lengths. Each CsI(Tl) crystal is arranged so that it points
towards the IP. The barrel component has 6624 crystals divided into 46 in θand 144 in φ. The forward (backward) endcap has 1152 (960) crystals divided
into 13 (10) in θ and 48- 144 (6-1 144) iφ depending onθ. The geometry of
the ECL is shown in Fig 2.13.

24

CHAPTER 2. THE BELLE EXPERIMENTBELLE Aerogel Cherenkov Counter
120.7°
1950

1670(EACC/outside)(EACC/inside)

TOF

Barrel ACC n=1.013
854(BACC)

1622(BACC)

34.2°

B

n=1.028I

n=1.010A

n=1.020 n=1.015
HGF
EDC

150.0°

Endcap ACC
17.0°

R 885

(BACC/inner)

B (1.5Tesla)

R 1165 (BACC/outer)n=1.030
FW
3" FM-PMT
2.5" FM-PMT
2" FM-PMTR 1145 (EACC/outer)

CDC

3.0m

2.5m

2.0m

1.5m

1.0m

0.5m

0.0m

Figure 2.9: ACC geometry.

When an electron or photon hits a crystal, most of its energy is depositedin electromagnetic showers produced by bremsstrahlung and pair production. Other charged particles deposit a small amount of energy by ionisation.
Therefore, the ratio of the cluster energy measured by the ECL to the momentum of the charged track momentum as measured by the CDC, E/p, isclose to unity for electrons and lower for other particles. In this way, electron
identification can be performed. The energy resolution of the ECL is givenbyσE
0.066 0.81
(2.3)
= (1.34 ⊕⊕ 1/4 )%
E
E
E
where, E in GeV.

2.2.7

Solenoid Magnet

The superconducting solenoid provides a magnetic field of 1.5 T, that bends
charged particles in a helix to enable track momentum measurement in the
CDC. The superconducting coil consists of a single layer niobium-titaniumcopper alloy embedded in a high purity aluminium stabiliser. The coil is25

2.2. THE BELLE DETECTORa) Barrel ACC Module
Finemesh PMT

Aluminum container(0.2mm thick)

AerogelGoretex
Finemesh PMT
120 mm

120 mmb) Endcap ACC Module

Base & Amplifier
FM-Phototube

Air light guide (CFRP)
Aerogel

CFRP(0.5mm thick)
Goretex Reflector

Figure 2.10: ACC modules. The top is barrel part modele, bottom is endcap
part module.

wound around the inner surface of an aluminium support cylinder of 3.4 m
in diameter and 4.4 m in length. Cooling is provided by circulating liquid
helium through a tube on the inner surface of the aluminium cylinder.

2.2.8

KL0 and Muon Detector (KLM)

The KL0 and muon detector (KLM) provides muon identification for charged
particles with enough momentum to reach the KLM, PT > 0.6 GeV/c. It
can also detect the neutral KL0 . Since these are highly penetrative particles,
a lot of material is needed to identify them efficiently.
The KLM consists of alternating layers of charged particle detectors and 4.7
cm thick iron plates. There are 15 resistive plate counter (RPC) superlayers
and 14 iron layers in the barrel region and 14 RPC superlayers in each endcap, covering the polar region, 20◦ < θ < 155◦ . The iron layers also serve as areturn yoke for the magnetic flux provided by the superconducting solenoid.
The KLM barrel part of the iron yoke is shown in Figure 2.14. Each RPC

26

CHAPTER 2. THE BELLE EXPERIMENT

ForwardBackward
I.P (Z=0)- 91.5- 80.5182. 5- 72.5190. 5

1. 0

PMT

PMT

4. 0

TOF

4.0 t x 6.0 W x 255.0 L

TSC

0.5 t x 12.0 W x 263.0 L

PMT

122.0

1. 5
R= 117. 5282. 0287. 0Light guide

PMT

R=120. 05

PMT

R=117. 5

R= 122. 0
R= 117. 5

08

w

× 60

0t
C4

BC4
L
0
5
× 25

TS

2" FM-PMT

12

TS

t×
C5

w

120

BC4
L
0
3
× 26

TOF/TSC Module

Figure 2.11: TOF module geometry.

superlayer consists of two RPC modules to provide 2-dimensional θ-φ information. The cross section of an RPC superlayer is shown in Figure 2.15.
Hadrons interacting with the iron plates produce a shower of ionising particles that are detected by the RPC layers. The result is a cluster of hits
deposited in the KLM. A KL0 candidate can be distinguished from anothercharged hadron because it will not leave an associated track in the CDC. A
muon, on the other hand, does leave a charged track in the CDC. However,muons can still be distinguished from charged and neutral hadrons because
they do not feel the strong interaction. Hadrons are more rapidly absorbed
and deflected by strong interactions with iron resulting in wide clusters and2.2. THE BELLE DETECTOR

27

Figure 2.12: Mass distribution from TOF measurements for particle momenta below 1.2GeV/c.

Figure 2.13: ECL geometry.

are stopped within a few layers of iron. Muons only experience electromagnetic multiple scattering and energy loss, so their clusters tend to be thinner
and they have far greater penetration depth.

28

CHAPTER 2. THE BELLE EXPERIMENT

Figure 2.14: KLM geometry in units of mm.

Figure 2.15: Cross section of an RPC superlayer.

2.2.9

Trigger and Data Acquisition

The role of the trigger system is to distinguish and record the interesting
physics events from the enormous amount of background that enters the de-2.2. THE BELLE DETECTOR

29

tector, using fast signals from the sub-detectors. Because of the high beam
current of the KEKB accelerator, the trigger suffers severe beam background,and since the rates of beam background are very sensitive to real-time accelerator conditions, it is difficult to estimate reliably. For this reason, thetrigger system is required to be flexible so that background rates can be kept
within the tolerance of the data acquisition system. Redundant triggers arealso needed to keep the high trigger efficiency for interesting physics events.
The Belle trigger system consists of the Level-1 hardware trigger and theLevel-3 software trigger which operate in real-time. The Level-4 trigger andevent reconstruction and classification is performed offline. A flow diagramof the Belle trigger system is shown in Figure 2.16.
The Level-1 trigger consists of the sub-detector trigger systems and the central trigger system called the Global Decision Logic (GDL). The sub-detector
trigger systems are categorised into two: track triggers and energy triggers.
The CDC and TOF are responsible for charged track trigger signals while the
ECL provides triggers based on the total energy deposit. The KLM provides
additional trigger signals for muons. A schematic of the Belle Level-1 trigger
system is shown in Figure 2.17. These are four main sub-triggers in the GDL,
the two track trigger, the three track trigger, the cluster number trigger andthe energy sum trigger. The two track trigger requires twotracks with an
opening angle greater than 135◦ . At least one track must have z information
and a minimum of 2 hits in the TOF. The three track trigger is similar to
the two track trigger, but no opening angle condition is required. At least
three hits in the inner tracking sub-detectors are required. The cluster number trigger requires at least 4 isolated clusters in the ECL. The energy sum
trigger requires at least 1 GeV of energy deposited in the ECL.
The GDL combines the sub-detector trigger signals and makes the final decision to initiate a Belle-wide data acquisition (DAQ) within 2.2 µs of thebeam crossing. The typical trigger rate is 200-250 Hz. With redundant triggers in place, the trigger efficiency for B B̄ events is greater than 99.5%.
The performance goal of the DAQ is to be operational at a maximum trigger
rate of 500 Hz, while keeping the dead time fraction to less than 10%. In order to achieve this, the entire DAQ system is divided into seven sub-systems
running in parallel. An event builder combines the signals from sub-detectors
into a single event and passes it to an online computer farm. The online computer performs a basic track and cluster reconstruction and further rejects
unwanted events with the Level-3 trigger. The remaining events are sent to acomputer centre for offline processing. A schematic of the Belle DAQ system

30

CHAPTER 2. THE BELLE EXPERIMENT

is shown in Figure 2.18.
The Level-4 trigger is applied first during offline processing. Events musthave at least one track originating from the IP, dr < 1.0 cm and |dz| <4.0 cm, with pT > 300 MeV/c. Events passing the Level-4 trigger undergofull event reconstruction. Tracks are reconstructed with hits in the CDC,
then these tracks are extrapolated towards the IP to search for associatedSVD hits. They are also extrapolated outwards to search for hits in theouter detectors. Thus, 4-vectors and particle identification likelihoods canbe assigned. Clusters in the ECL are also reconstructed to form photons.
This information along with many other calculated variables are stored in aformat available to collaborators for analysis.
Belle Detector

Electronic Hut

Level 1
Trigger

Online Farm
Rawdata
Level 3
Trigger

OnlineOnlineBelle Computing System
Level
4
Trigger

DST

Reconstruction

Figure 2.16: An overview of the Belle trigger system.

31

2.2. THE BELLE DETECTOR

Cathode Pads

CDC

Z finderz track countTrack Segmentr-φ track countStereo Wires
Axial Wires

Hit

topology
timingCluster count

ECL

Trigger Cell
4x4 Sum
Energy Sum

TimingHigh Threshold
Low Threshold
Bhabha

KLM

Hit

µ hit

EFC

Trigger Cell

Threshold

Global Decision Logic

multiplicity

TSC

Trigger Signal
Gate/Stop

BhabhaTwo photon

2.2 µsec after event crossing
Beam Crossing

Figure 2.17: The Belle Level-1 trigger system.

Figure 2.18: The Belle DAQ system.

Chapter 3
Event selection for B → J/ψηK
decays
The target B meson decay modes, B ± → J/ψηK ± and B 0 → J/ψηKS0
are reconstructed by combining these daughter particle candidates, J/ψ, η
and K ± or KS0 mesons. K ± is stable but all other daughters are unstable,
therefore we need to reconstruct them by the proper final states for each.
The analysis procedure to carry out that task is described in this chapter.

3.1

Data sample

After the first physics run in 1999, Belle experiment accumulated e+ e− beamcollision data mostly on the Υ(4S) resonance. Operation of KEKB accelerator and Belle detector at that energy continued until 2008. In total anintegrated luminosity of 703 fb−1 are recorded and there are 772 × 106 BB
pairs in this high statistics data sample. It is the basis of this work.
In order to understand acceptance and performance of the detector to estimate detection efficiency for B → J/ψηK decay signal and possible background contamination, an appropriate Monte Carlo simulation (MC) has tobe used. In order to generate B → J/ψηK decay signal events as well asprobable background events, the EvtGen program [33] is used. This program is capable to treat the key kinematics and resultant decay products
angular distributions, not only distributing according to the available phasespace but also isotropic angular distribution in the B meson decays into two
pseudoscalar mesons, or the final state becomes linear combination of relative33

34

CHAPTER 3. EVENT SELECTION FOR B → J/ψηK DECAYS

angular momentum of S-, P - and D-waves in the case into two vector mesons
for example. This software can also handle the time-dependent CP violationin the neutral B meson decays into a CP eigenstate. For the description andmodeling of the detector material and particles’ interaction during their passage, the GEANT3 [34] software is used. Based on the particle’s energy loss
in the active material, the detector response including the readout electronics
as well as digitization effect is simulated by the hand-made codes composedby Belle collaborators.
In order to estimate reconstruction efficiencies for B ± → J/ψηK ± and
B 0 → J/ψηKS0 modes, 5 × 105 events for each are generated with the threebody distribution obeying the available phase space, sometimes denoted as
PHSP hereafter. B ± → ψ ′ K ± and B 0 → ψ ′ KS0 are well established decay
modes and these can be a part of signal when ψ ′ → J/ψη decay occurs.
Therefore these B decay modes are also simulated up to the same amount as
the PHSP using the corresponding chain of two-body decays. In this study,
main backgrounds come from B B̄ events in which one of the B decays tothe final state containing a real J/ψ → e+ e− or µ+ µ−, i.e. the B → J/ψX
processes. In order for understanding of these backgrounds, a large amountof MC simulation sample for the B → J/ψX is prepared by including themost up-to-date B meson decay modes information as of 2010 April. We callthis MC sample as the inclusive J/ψ MC throughout this thesis.

3.2

Reconstruction and identification of particles

At first, charged particle reconstruction in CDC with SVD and shower reconstruction in ECL are done. After those, more detailed information isnecessary to be obtained to pick up the B decay daughter particles in the
final state correctly as much as possible. Among the daughter particles coming from the target B decays, lepton identification and photon detection arenecessary to reconstruct J/ψ → e+ e− or µ+ µ− and η → γγ decays. Selection
procedures for charged and neutral Kaons are described later in the proper
subsections.

3.2. RECONSTRUCTION AND IDENTIFICATION OF PARTICLES 35

3.2.1

Charged particle detection

The first step of charged particle reconstruction is finding track-segment-hitpatterns in the CDC. The tracks projected onto the r − φ plane are searched
for with axial wire hits, then hits of the streo wires are used to determine
z positions of the track. Track parameters (momentum and position) of thefound track are obtained by the fitting based on the Kalman filter technique,which minimizes the effects of the multiple Coloumb scattering and nonuniformity of the magnetic field in the CDC in the determination of the trackparameters. Then, all of the hit points are connected and fitted to a helix toobtain the particle momentum and position. Finally, the reconstructed tracks
are connected to the SVD hits to improve the resolution of track parameters.
Here, the track parameters are computed again with combinationof the hitson the CDC and SVD.

3.2.2

Shower reconstruction and photon selection

The γ is a neutral particle, hence they can not be identified directly. In Belle
detector, the γ candidate identification is based upon their electromagnetic
interactions inside the ECL by a shower production mechanism of γ. In order to reconstruct showers, at first the seed crystals that have higher energy
than sorrounding crystals and exceeding 10 MeV are picked up. The 5×5
crystal matrix centered at the seed crystal is looked for. The crystals’ energy
deposit more than the proper threshold, typically 0.5 MeV, are summed toobtain the incident particle energy. The incident position is estimated by theenergy-weighted center of gravity of the included crystals’ energies. Finite
shower leakage effect and possible bias of the estimated incident position are
corrected by the knowledge obtained by large statistics single-γ MC event
sample.
Reconstructed charged particle tracks are extrapolated to the ECL. The
shower that does not have any associated changed track are recognized as γ
candidate.

3.2.3

B B̄ event selection

Electron-positron colliders operated at the Υ(4S) resonance do not always
produce B B̄ events. In fact, non-B B̄ events have larger cross section and themost common are in the Bhabha reaction which is e+ e− elastic scattering.

36

CHAPTER 3. EVENT SELECTION FOR B → J/ψηK DECAYS

Also present are radiative Bhabha, other lepton pair production, e+ e → l+ l,
where l = µ, τ , two-photon events, e+ e → γγ, and beam-gas interactions.
Non-B B̄ hadronic events may also be produced and occur when, e+ e → qq
where q = u, d, s, c represent the light quarks and is known as continuum.
Hadronic events including B B̄ pair production are selected if they satisfy
the following citeria: at least three reconstructed charged tracks; a total
reconstructed√ in the√center of mass (cms) frame in the range√ ECL energy
between 0.1 s and 0.8 s, where, s is the total cms energy; an average ECL
cluster energy below 1 GeV;at least one ECL shower in the region -0.7√< cos θ< 0.9 in the laboratory frame; a total visible energy, exceeding 0.2 s, andreconstructed primary vertex that is consistent with the known interaction
point. After imposing these requirements, the efficiency for selecting B meson
pairs that include a J/ψ meson is estimated by Monte Carlo (MC) simulation
to be 99%.

3.2.4µ, e identicication

Muons are identified on the basis of track penetration depth and hit scatterpattern in the KLM system. These informations are arranged into a likelihood to be a muon, Lµ . The track is identified as muon if the criteria of
Lµ > 0.1 is satisfied. While, electrons are identified on the basis of electron
likelihood Le > 0.01, which uses dE/dx in CDC, E/p ratio (E is the energy
deposited in the ECL and p is the momentum measured in CDC and SVD),
shower shape in the ECL, distence between the experimented track and thereconstructed shower center and number of Cerenkov phton in the ACC.

3.2.5

Kinematic fit

Kinematic fitting reduces the effects of detector resolution to improve themass or momentum resolutions and determine the decay vertex of a candidate particle. There are two types of kinematic fitting used in this analysis: mass-constrained fitting and vertex-constrained fitting. In the massconstrained fitting, the invariant mass of the candidate, Mcand , is set to the
known mass and the momentum of its daughters are re-calculated. This approach is applicable when the reconstructed state has narrow width and theobserved invariant mass distribution is dominated by the detector resolution.
The underlying motivation for vertex-constrained fitting is that the tracks
used to reconstruct a candidate may not pass through the same point. The3.2. RECONSTRUCTION AND IDENTIFICATION OF PARTICLES 37
Mcand decay vertex is obtained by tuning the momentum and position ofeach daughter according to its measurement errors so that all tracks passthrough a single point. These tuning of momentum or position are done byminimization of the χ2 based on the involved particles momentum, position
and their estimated errors. The minimization procedure is carried out by a
Lagrange mutiplier approach.

3.2.6

J/ψ reconstruction

J/ψ is reconstructed using its dileptonic decay, J/ψ → ℓ+ ℓ− where ℓ corresponds to e or µ. The branching fraction of J/ψ → ℓ+ ℓ− is (11.87 ±0.08) × 10−2 (combine J/ψ → e+ e− : (5.94 ± 0.06) × 10−2 and J/ψ →µ+ µ− : (5.93 ± 0.06) × 10−2 ). Electron and muon pairs are selected from thecharged tracks after applying electron likelihood (Le ) larger than 0.01 andmuon likelihood (Lµ ) larger than 0.1, respectively. In order to include thebremsstrahlung photon emitted by either electron or positron, γs within 50
mrad of the initial momentum are added, in order to reduce the lower side tailof invariant mass distriubution. Figure 3.1 shows invariant mass of J/ψ ofsignal MC and data. As we can still miss some photons, we apply asymmetric
cut on the invariant mass of Me+ e− (γ) , -0.150 GeV/c2 < Me+ e− (γ) − MJ/ψ <0.036 GeV/c2 . For muon, invariant mass of Mµµ is required to satisfy -0.06
GeV/c2 < Mµµ − MJ/ψ < 0.036 GeV/c2 . Here MJ/ψ mass denotes the nomial J/ψ mass and invariant mass requirements are indicated by the vertical
red lines in Figure 3.1. Then, we used vertex fit and mass constraint fit toimprove the momentum resolution for the reconstructed J/ψ candidates.

3.2.7

η reconstruction

We use η → γγ decay to reconstruct η because it has the large branching fraction of (39.31 ± 0.20) × 10−2 . In order to reduce the background coming fromlow energy γs, we require of Eγ > 100 MeV where Eγ is the reconstructed
photon energy. Also, the photon pair having large energy asymmetry is rejected using energy balance AE , that is defined as follows
AE =|E1 − E2 |E1 + E2(3.1)

where, E1 (E2 ) is the energy of γ1 (γ2 ), to reduce combinational background.
We require AE < 0.8. To remove the background coming from π 0 s, if a

38

CHAPTER 3. EVENT SELECTION FOR B → J/ψηK DECAYS

M(ee)

M(mumu)
80000

50000

40000

(a)

70000

Signal MC

60000

(b)
Signal MC

50000
30000
40000
30000

20000

20000
10000
10000
0
2.8 2.85 2.9 2.95

3

3.05 3.1 3.15 3.2 3.25 3.3
M ee γ GeV/c 2

M(ee) 30
2.8 2.85 2.9 2.95

3

3.05 3.1 3.15 3.2 3.25 3.3
M µ µ GeV/c 2

3

3.05 3.1 3.15 3.2 3.25 3.3
M µ µ GeV/c 2

M(mumu)3

220 × 10300 × 10

200
180
160

250

(c)
Data

(d)
Data

200

140
120

150
100
80

100

60
40

50

20
0
2.8 2.85 2.9 2.95

3

3.05 3.1 3.15 3.2 3.25 3.3
M ee γ GeV/c 2

0
2.8 2.85 2.9 2.95

Figure 3.1: These are MJ/ψ distribution of signal MC and data. (a) is reconstructed from ee(γ) of signal MC. (b) is reconstructed from µµ of signal MC.
(c) is reconstructed from ee(γ) of data. (d) is reconstructed from µµ of data.
Red lines show invariant mass window boundaries to accept J/ψ candidates.

reconstructed γ is found to form the π 0 candidate that is defined as 0.117
GeV/c2 < Mγγ < 0.153 GeV/c2 by combining with any other photon, thenthis photon is rejected to from η candidates. And we determine η mass
window as 0.510 GeV/c2 < Mγγ < 0.575 GeV/c2 as indicated by vertical red

3.2. RECONSTRUCTION AND IDENTIFICATION OF PARTICLES 39
lines in Figure 3.2. Finally, in order to improve the momentum resolution ofthe η, mass constraint fit is applied.
M(gamgam)M(gamgam)
10000 × 10

50000

3

9000

Signal MC

8000

40000

Data

7000
6000

30000
5000
4000

20000

3000
2000

10000

1000
0
0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65 0.7
M γ γ GeV/c 2

0
0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65 0.7
M γ γ GeV/c 2

Figure 3.2: Mass distribution of η reconstructed from γγ. Red lines show
invariant mass window boundaries to accept η candidates.

3.2.8

K/π identfication

In order to distinguish charged kaons from pions, the sub-detectors of theBelle are able to provide information to compose a likelihood that a charged
track is a kaon hypothesised or to be a pion. Then we can get the likelihood
ratio asLK
P (K : π) =(3.2)
LK + Lπ
where Li (i = K, π) is the product of the likelihoods that the particle is oftype i and is calculated as,
Li = LCDC
× LTOF
× LACC
i
i
i

(3.3)

For the reconstruction of B ± → J/ψηK ± , K likelihood ratio is required to belarger than 0.4. And for the reconstruction of ψ ′ → J/ψπ + π − , we required π
likelihood ratio to be larger than 0.4, which is used fo ψ ′ veto, it is explainedin Section §4.2.1

40

CHAPTER 3. EVENT SELECTION FOR B → J/ψηK DECAYS

3.2.9

KS0 reconstruction

For B 0 → J/ψηKS0 candidate reconstruction, KS0 is reconstructed by combining two oppositely charged pions. The two charged pion tracks are fittedwith constraint to come from common vertex, and the pion pair invariant
mass, Mπ+ π− , calculated at the obtained vertex is required to satisfy 482
MeV/c2 < Mπ+ π− < 514 MeV/c2 . The resultant momentum gotten by amass- and vertex- fit is assigned to be the one for the reconstructed KS0 .

3.3

Reconstruction of B → J/ψηK

To reconstruct B meson, the 2-body kinematics in the Υ(4S) →B B̄ is fully
utilized. For the signal, the energy of reconstructed B in the centre-of-masssystem (CMS), EBCMS , must be half the total energy of the e+ e system in the
CMS
same frame, Ebeam. With this constraint, the B meson candidate is identified
by two kinematic variables defined as,
Mbc =

q

CMS 2
(Ebeam) − (pCMS)2
B

CMS∆E = EBCMS − Ebeam

(3.4)
(3.5)

The variable, Mbc , is known as the beam-constrained mass and peaks at thenominal B mass for correcty reconstructed case. The Mbc has much better
resolution than the reconstructed B mass, thus providing better separation of
signal and background. The energy difference, ∆E , should peak around zerofor correctly reconstructed B mesons. The B candidates satisfying Mbc >5.2 GeV/c2 and -0.2 GeV < ∆E < 0.2 GeV are retained for further analysis.
By the reconstruction procedure described so far, we find that 29% of thereconstructed events found in the region of Mbc > 5.2 GeV/c2 and -0.2 GeV <∆E < 0.2 GeV have multiple B candidates. Most of the multiple candidates
come from the different combination of γγ when we reconstruct η. Smaller
portion of multiple candidates come from lepton pair’s combination at J/ψ
reconstruction. Mistake of K ± or KS0 selection would be more rare. The best
candidate is selected when J/ψ and η are closest to the known candidate
having least χ2 is selected as best B, where χ2 is defined as
χ2 = (

Mℓℓ − MJ/ψ 2
Mγγ − Mη 2
) +(
)
σJ/ψ
ση

(3.6)

3.3. RECONSTRUCTION OF B → J/ψηK

41

where, Mℓℓ (Mγγ ) is invariant mass which before the mass constraint is applied. MJ/ψ (Mη ) is the mass of J/ψ (η) and σJ/ψ (ση ) is mass resolution ofJ/ψ (η). Where, each value is summarized as fallows.
• MJ/ψ = 3096.916 MeV/c2• Mη = 547.853 MeV/c2• σJ/ψ (J/ψ → e+ e− ) = 11.09 MeV• σJ/ψ (J/ψ → µ+ µ− ) = 8.9 MeV• ση (η → γγ) = 13.8 MeV
In very rare case, different K ± tracks can result in multiple candidates eventhough the J/ψ and the η candidates are identical. When it happens, weselect the charged kaon having higher K likelihood ratio. In the same casefor KS0 , the one having the closest Mπ+ π− to the nominal KS0 mass is chosen.

Mbc

hmbc1

16000

∆E

hde1

Entries

60843

Entries

Mean

5.276

Mean

-0.006822

RMS

0.01112RMS

0.0454

70069

14000
14000
12000
12000

Signal MC

Signal MC
10000

10000
8000

8000

6000

6000
4000

4000

2000

2000

0
5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3

Mbc

0-0.2 -0.15 -0.1 -0.05

0

0.05

0.1 0.15

0.2∆ E(GeV)Figure 3.3: Mbc distribution in ∆E signal region (-0.035 GeV < ∆E < 0.03
GeV) and ∆E distribution in Mbc signal region (Mbc > 5.27 GeV/c2 ) for
B ± → J/ψηK ± PHSP MC sample.

42

CHAPTER 3. EVENT SELECTION FOR B → J/ψηK DECAYS

12000

12000

10000

10000

8000

8000

6000

6000

4000

4000

2000

2000

0
5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3

Mbc

0-0.2 -0.15 -0.1 -0.05

0

0.05

0.1 0.15

0.2∆ E(GeV)Figure 3.4: Mbc distribution in ∆E signal region (-0.035 GeV < ∆E < 0.03
GeV) and ∆E distribution in Mbc signal region (Mbc > 5.27 GeV/c2 ) forB 0 → J/ψηKS0 PHSP MC sample.

3.4

Detection efficiency of B → J/ψηK decays

Based on the obtained Mbc and ∆E distributions for the signal MC sample,
we can estimate the detection efficiency by applying the same procedure to
extract signal. We use unbinned maximum kikelihood fit to ∆E distribution,
In order to perform it, an approriate formula of the Probability Density
Function (PDF) has to be found. Here, the ψ ′ veto, that is discussed in thenext chaper for background reduction, is introduced.

3.4.1

B ± → J/ψηK ± mode

Since B ± → J/ψηK ± mode is expected to have enough statistics to attempt
to resolve intermediate states, two MC samples are used to compose proper
PDF for each, B ± → J/ψηK ± PHSP and B ± → ψ ′ (→ J/ψη)K ± processes.
In both cases, ∆E distribution is found to be well described by the double
Gaussian which is sum of two Gaussians. In the PHSP case, the signal yield
is found to be 49593 ± 239 events in -0.2 GeV < ∆E < 0.2 GeV out of 0.5
Million generated events. Integration of the obtained PDF in the range of-0.035 GeV < ∆E < 0.030 GeV result in 45624±220 events to discuss about

3.4. DETECTION EFFICIENCY OF B → J/ψηK DECAYS

43

the yield in B signal enhanced region to resolve intermediate states. Thus
MC determined detection efficiency is 9.9% for -0.2 GeV < ∆E < 0.2 GeV
and 9.1% for -0.035 GeV < ∆E < 0.03 GeV. Figure 3.5 shows fit to ∆E
distribution for signal PHSP MC. Here, small outlier conponent (green line
in Figure 3.5) is introduced to fit large statistics signal MC sample. We
omit this contribution from detection efficiency, because it is absorbed inbackground fluctuation.
Same procedure is repeated for B ± → ψ ′ (→ J/ψη)K ± . ∆E distribution is
obtained as shown in Figure 3.6. The MC determined detection efficiency of
B ± → ψ ′ K ± is estimated to be 9.4% at -0.2 GeV < ∆E < 0.2 GeV and 8.5% at -0.035 GeV < ∆E < 0.030 GeV. Note that in order to get the branching
fraction from experimental data, the particle identification related correction
factors must be multiplied to the MC determined efficyency to be discussed
in Chapter 5.

Events / ( 0.005 )a2a = 0.2811 ± 0.0077
bkg = 5969 ± 117
delm = -0.007705 ± 0.00042
mean = -0.0004696 ± 0.000071

8000
7000
6000

s2s1 = 3.052 ± 0.048
sig = 49593 ± 239

5000

sigma1 = 0.009719 ± 0.000096
slope1 = -0.4674 ± 0.023

4000
3000
2000
1000
0
-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2
∆E

Figure 3.5: Fit to ∆E (GeV) distribution for signal PHSP MC sample. The
signal diescribed by sum of two Gaussian and small outlier component (green
dash line) are superimposed.

3.4.2

B 0 → J/ψηKS0 mode

Because of smaller expected statistics in B 0 → J/ψηKS0 case, the study
is performed only for the PHSP sample. We estimate the MC determinedCHAPTER 3. EVENT SELECTION FOR B → J/ψηK DECAYS
a2a = 0.7999 ± 0.0031
bkg = 3329 ± 118

Events / ( 0.005 )44delm = -0.003630 ± 0.00061

10000

mean = 0.00349 ± 0.00060

8000

s2s1 = 0.1639 ± 0.0032
sig = 47033 ± 240

6000

slope1 = 0.763 ± 0.028

sigma1 = 0.04278 ± 0.00091

4000

2000

0
-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2
∆E

Figure 3.6: Fit to ∆E (GeV) distribution of B ± → ψ ′ (→ J/ψη)K ± MC
sample. Notation of the superimposed lines is same as Figure 3.5.

detection efficiensy likewise charged mode. Figure 3.7 shows fit to ∆E distribution for signal MC. The obtained MC determined efficiency is 8.1% for
the B 0 → J/ψηKS0 PHSP sample.
Events / ( 0.005 )a2a = 0.6997 ± 0.0089
bkg = 4408 ± 101

7000

delm = 0.00764 ± 0.00044

6000

mean1 = -0.009283 ± 0.00043

5000

s2s1 = 0.3278 ± 0.0052
sig = 40499 ± 215
sigma1 = 0.02930 ± 0.00063

4000

slope1 = -0.5298 ± 0.026

3000
2000
1000
0
-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2
∆E

Figure 3.7: Fit to ∆E (GeV) distribution of B 0 → J/ψηKS0 PHSP MC
sample. Notation of the superimposed lines is same as Figure 3.5.

Chapter 4
Background study
4.1

Continuum background reduction

To suppres the background coming from the continuum relative to B B̄ events,
we use ratio of second to the zeroth Fox-Wolfram moments (R2 ). R2 is 0 for
perfect spherical event.
H2
,
R2 =
H0

Ht =

P

pi ||p~j |Pt (cosθij )ij |~P( i Ei )2(4.1)

Here, Pt is the Legendre Polynomial and p~i , p~j represent the four momentumPof the particles while i Ei represents the visible energy of the particles inthe event. The B B̄ mesons are produced almost at rest and their decay axis
are uncorrelated. So, B B̄ events are almost spherical in shape and can be
distinguished from the jet like continuum events of u, d, s or c. To reducethe continuum background R2 is chosen to be less than 0.5.

4.2

Main backgrounds

For background study, we use the inclusive J/ψ MC sample corresponding
to 100 times data larger statistics with respect to the used experiment data.
Figure 4.1 (4.2) shows ∆E distribution of the expected background alongwith the probable signal for B ± → J/ψηK ± (B 0 → J/ψηKS0 ).
45

46

CHAPTER 4. BACKGROUND STUDY∆E w/o veto

ψ ’ K± (J/ ψ η)
J/ψ X su(η K)
χc1 K±
ψ ’ K± (others)
J/ψ K± π0 π0 0
J/ψ K (1270)
1
J/ψ K1(1270)+*
J/ψ K*(892)+
0
J/ψ K (892)J/ψ X sd
ψ ’ Xsd
χc1 X su*
χc1 K
χc2 X sdothers

14000
12000
10000
8000
6000
4000
2000
0
-0.2 -0.15 -0.1 -0.05

00.05 0.1 0.15 0.2∆E[GeV]

Figure 4.1: Expected ∆E distribution of B ± → J/ψηK ± candidates for the
inclusive J/ψ MC sample.

4.2.1

ψ ′ → J/ψπ + π − and χc1(χc2 ) → γJ/ψ vetoWe find B ± → J/ψηK ± (ψ ′ 6→ J/ψη) (light blue region in Figure 4.1) can beone of the backgrounds. Among ψ ′ decay modes into a J/ψ, ψ ′ → J/ψπ + π −has relatively large branching fraction, 33.6% and it is clearly identified.
Therefore, we reject the J/ψ which come from ψ ′ → J/ψπ + π − using massdifference cut 0.58 GeV/c2 < MJ/ψπ+ π− − MJ/ψ < 0.60 GeV/c2 . Also, we
found B ± → χc1 K ± results in background above +0.1 GeV in ∆E (yellow
region in Figure 4.1), as this decay include χc1 → J/ψγ. So, we try to
reject the J/ψ which coming from χc1 → J/ψγ using mass different cut 0.39
GeV/c2 < MJ/ψγ − MJ/ψ < 0.43 GeV/c2 . Figure 4.3 shows mass differenceof MJ/ψπ+ π− − MJ/ψ and MJ/ψγ − MJ/ψ . We can see one more peak in
MJ/ψγ − MJ/ψ distribution next to χc1 → J/ψγ. It is χc2 → J/ψγ and, we
try to reject it also using mass difference cut 0.45 GeV/c2 < MJ/ψγ − MJ/ψ

47

4.2. MAIN BACKGROUNDS∆E
J/ ψ X (X ->ηK0 )sd sd
ψ ’K0 (ψ ->J/ ψ η)
S
0
ψ ’K
S
χ K0S
J/c1ψ X
sd
χ Xsu

3500
3000

c1

*

0

J/ ψ K (892)J/ ψ K (1270)0* 1
ψ ’K (892)+*
χ K*+
c1
J/ ψ K (1270)+1*
J/ ψ K (892)+
Others

2500
2000
1500
1000
500
0
-0.2 -0.15 -0.1 -0.05

00.05 0.1 0.15 0.2

Figure 4.2: Expected ∆E distribution of B 0 → J/ψηKS0 candidates for the
inclusive J/ψ MC sample. (After applying the ψ ′ → J/ψπ + π − veto, that is
to be mentioned in the text.)< 0.48 GeV/c2 . Whether these vetos are effective is judged by the figure of
merit (F.O.M.) defined as
NS
NS + NB(4.2)

NS = ǫ × B × NBB̄

(4.3)

F.O.M. = √where, NS is the number of expected signal events and, NB is the number of
expected background. B is the product of the branching fractions of B ± →J/ψηK ± , J/ψ → ℓ+ ℓ− and η → γγ decay chain. ǫ is the detection efficiency
of B ± → J/ψηK ± . Table 4.1 summerizes the F.O.M. study based on thementioned vetos. Signal loss is found to be unacceptably large in χc1,c2 veto,and result in deterioration of the F.O.M. On the other hand, ψ ′ veto gives

48

CHAPTER 4. BACKGROUND STUDY

almost some F.O.M. as the case without any veto and it will make the ψ ′background related uncertainty small. Thus, only ψ ′ veto is to be applied.
M(llpipi)-M(ll)M(llgam)-M(ll)100 ×10300 ×10

3

3

90
250

80
70

200

60
50

150

40
100

30
20

50

10
0
0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7
Mllππ-Mll[GeV/c2]0
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
Mllγ -Mll[GeV/c2]

Figure 4.3: Mass difference of MJ/ψππ − MJ/ψ for ψ ′ → J/ψπ + π − veto (left).
MγJ/ψ − MJ/ψ for χc1 (χc2 ) → J/ψγ vetos (right). The vertical lines show thewindow to apply vetos.

Mode
Without veto
All veto
ψ ′ veto
χc1 veto
χc2 vetoχc1 and χc2 veto
χc1 and ψ ′ vetoNS
448.79288.31422.01356.38386.68304.11335.87NB
NS /NB
759.250.59
345.380.83
649.070.65
649.07
0.71
632.3
0.61
411.430.74
425.790.79

F.O.M.
12.91
11.45
12.89
12.16
12.11
11.37
12.16

Table 4.1: F.O.M. study for each veto.

4.2.2

Non J/ψ backgroundWe checked non-J/ψ background, i.e. due to fake J/ψ, using e+ e− (γ) orµ+ µ− mass sideband of the J/ψ signal region (Figure 3.1) in the experimental
data.

4.3. OPTIMIZATION OF ∆E WINDOW

49• Mee(γ) : 2.80 GeV/c2 < Mee(γ) < 2.95 GeV/c2 and 3.13 GeV/c2 <Mee(γ) < 3.30 GeV/c2 .
• Mµµ : 2.80 GeV/c2 < Mµµ < 3.03 GeV/c2 and 3.13 GeV/c2 < Mee(γ)< 3.30 GeV/c2 .
As shown in Figure 4.4, non-J/ψ background is small and has flat distribution in ∆E projection. Here, the inclusive J/ψ MC is normalized to data,and sideband data is normalized to the signal region. Non-J/ψ backgroundis found to be enough small and to be treated as apart of combinatrial background.
∆E
140

Inclusive J/ ψ MC

120

J/ ψ sidebande data

100
80
60
40
20
0
-0.2 -0.15 -0.1 -0.05

0

0.05

0.1

0.15

∆E

0.2

Figure 4.4: Comparing between inclusive J/ψ MC (black) and non-J/ψ background (red).

4.3

Optimization of ∆E window

After extracting the B decay signal, the J/ψη invariant mass distribution
is to be visited. In order to have the proper B candidate sample for thispurpose, the ∆E window should be optimized. The optimum window isjudged by the F.O.M. using the signal PHSP MC and the inclusibe J/ψ
MC sample. It shows optimum for ∆E lower and upper bounds at -0.025
GeV and +0.020 GeV respectively. F.O.M. plots are shown in Figure 4.5.
However, concerning the possible ∆E resolution difference between data andMC, -0.035 GeV < ∆E < +0.030 GeV is to be used.

50

CHAPTER 4. BACKGROUND STUDY∆ E upper bound = 0.04

∆E lower bound = -0.03
14.5

14

14
13

13.5
13

12
12.5
12

11

11.5
10

11
10.5

9
-0.1

-0.08

-0.06

-0.04

-0.02

0

10
0

0.02

0.04

0.06

0.08

0.1

Figure 4.5: F.O.M. is shown as a function of ∆E lower bound with fixing∆E upper bound = 0.04 GeV (left) and ∆E upper found with ∆E lower
bound = -0.03 GeV (right).

4.4

Background probability density functions

As seen in Figure 4.1, B ± → χc1 K ± and B ± → ψ ′ K ± have nontrivial structure in ∆E distribution in B ± → J/ψηK ± case. Same things happen also inthe case of B 0 → J/ψηKS0 as shown in Figure 4.2. In order to parameterize
them, we used biffurcated Gaussian as shown in Figure 4.6. Since rest of backgrounds are featureless, we used 2nd order polynomial for B ± → J/ψηK ±candidates and 1st order polynomial for B 0 → J/ψηKS0 . The treatment of
the latter case is to have stable fit even in the limited statistics.

B±→χ K±

B±→ψ’(not decay to J/ψη)K ±Events / ( 0.005 )Events / ( 0.005 )4.4. BACKGROUND PROBABILITY DENSITY FUNCTIONS

c1

1200
1000

600

mean = 0.2000 ± 0.0053
s1g = 0.04701 ± 0.00039

500

sig1 = 3282 ± 78
sig2 = 13135 ± 122

800

51

sigmaL = 0.1672 ± 0.0029

400

sigmaR = 0.00 ± 0.60
600

300

400

200

200

100

0
-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15
0.2
∆ E (GeV)

0-0.2mean = 0.027 ± 0.024
mg = 0.015 ± 0.011
s1g = 0.046 ± 0.013
sig1 = 16975 ± 2710
sig2 = 4078 ± 2707
sigmaL = 0.084 ± 0.014
sigmaR = 0.1270 ± 0.0087
-0.15

-0.1

-0.05

0

0.05

0.1

0.15
0.2
∆ E (GeV)

Figure 4.6: ∆E distributions for B ± → χc1 K ± and B ± → ψ ′ (6→ J/ψη)K ±background with fitted by Bifurcated Gaussian. For B 0 → χc1 KS0 and B 0 →ψ ′ (6→ J/ψη)KS0 backgrounds, same procedure is applied.

Chapter 5
Results and discussions
5.1

B decay signal extraction

Using the signal and backgrounds probability density functions (PDFs) described in the previous chapters, the B decay signal is extracted by an unbinned maximum likelihood fit to ∆E distribution. The fit program wastested by the pseudo-experiments using either GEANT based simulation sample or a parameterized MC (called Toy MC) sample and no significant bias
was found. Fifure 5.1 the fit to the ∆E distribution for B ± → J/ψηK ±and B 0 → J/ψηKS0 decay modes in the range of [-0.2, 0.2] GeV. We observe428±37 events for B ± → J/ψηK ± decay andq80±14 for B 0 → J/ψηKS0
decay. The statistical significance is defined as −2lnLo /Lmax , where Lmax
and Lo are the likelihood values when maximized by allowing the signal yieldvary and in the case to set to zero, respectively. We find B ± → J/ψηK ±shows 17.9σ and B 0 → J/ψηKS0 exhibits 7.1 σ statistical significance.

5.2

Resolving intermediate states by MJ/ψη distribution

Since we find the B ± → J/ψηK signal yield has enough statistics, the invariant mass of J/ψη system, MJ/ψη , is used to resolve the intermediate statesin this three-body decay. As discussed in Chapter 4, the ∆E window, -0.035
GeV < ∆E < +0.030 GeV is chosen as the optimum. Inside this ∆E window, 403 ± 35 events of B ± → J/ψηK ± signal is contained. The MJ/ψη
53

54

Events / (10MeV)

Events / (10MeV)

CHAPTER 5. RESULTS AND DISCUSSIONS
240
220
200
180

50

40

160
30

140
120
100

20

80
60
10

40
20
0
-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15
0.2
∆ E (GeV)

0
-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15
0.2
∆ E (GeV)

Figure 5.1: ∆E distribution of B ± → J/ψηK ± and B 0 → J/ψηKS0 candidate
in 5.27 GeV/c2 < Mbc < 5.29 GeV/c2 . Left is charged mode, and right isneutral mode. Dash line with red is signal’s PDF, dot-dash line with cyan
is B → ψ ′ (6→ J/ψη)K’s PDF, dot-dot-dash line with green is B → χc1 K’s
PDF and dot line with pink is other backgrounds.

distribution for the candidates selected by applying the ∆E window requirement is shown in Figure 5.2. At 3686 MeV/c2 , the ψ ′ → J/ψη contribution isclearly seen. However, there is no other significant peak. The signal yield of
B ± → ψ ′ K ± and ψ ′ → J/ψη decay chain process is found to be 46 ± 8 eventsand this process is denoted as B ± → (ψ ′ → J/ψη)K ± hereafter. The MJ/ψη
distribution for ψ ′ → J/ψη signal is expressed by a double Gaussian andother contribution is described by a threshold function. By subtracting thiscontribution from the total B ± → J/ψηK ± signal, the signal yield excluding
B ± → (ψ ′ → J/ψη)K ± is found to be 357 ± 38 events. Since this contribution shows a phase space like distribution, we use B ± → J/ψηK ± (PHSP) to
denote it. Based on the MC determined efficiencies described in chapter 3,
taking the correction factors of charged particle identification, the detection
efficiency, ǫ, is estimated to be 8.7%, 8.0% and 7.5% for B ± → J/ψηK ±PHSP, B ± → ψ ′ (→ J/ψη)K ± and B 0 → J/ψηKS0 , respectively. Table 5.1
summarizes these results and we get total three-body branching fractions forcharged and neutral B mesons;
B(B ± → J/ψηK ± ) = (1.3 ± 0.1(stat.) ± 0.1(syst.)) × 10−4
B(B 0 → J/ψηKS0 ) = (4.3 ± 0.7(stat.) ± 0.4(syst.)) × 10−5

(5.1)
(5.2)

where, systematic error estimation is described in the following subsection.

Events / ( 0.015 )5.3. CORRECTION AND SYSTEMATIC UNCERTAINTIES

55

120

100

80

60

40

20

3.8

4

4.2

4.4

Events / ( 0.005 )Events / ( 0.004 )

0
3.6

35
30

14
12

25

10

20

8

15

6

10

4

5

2

0

3.64

3.66

3.68

3.7

3.72

3.74
3.76
MJ/ψ η (GeV)

4.6
4.8
MJ/ ψ η (GeV/c2)

0

3.8

3.85

3.9

3.95

4

4.05
MJ/ψ η

Figure 5.2: The J/ψη mass (MJ/ψη ) distribution forB ± → J/ψηK ± candidates. All kinematically allowed region (upper), and ψ ′ (lower, left) andX(3872) (lower, right) regions are shown.

5.3

Correction and systematic uncertainties

This section explains the estimation of the correction for possible difference
between data and MC and systematic uncertainties.

5.3.1

Tracking efficiency systematic

To estimate tracking efficiency systematic the decay chain of D ∗+ → π + D 0 ,
D 0 → π + π − KS0 and KS0 → π + π − is reconstructed. The KS0 is required todecay inside the first SVD layer and one pion from KS0 is allowed not to be
explicity detected. We call it the particly reconstructed sample. The D ∗+signal yield in the case of both KS0 daughter pions are detected is compared tothe partially reconstructed sample and the difference between data and MC
gives the conection and systematic uncertainty. This correction is (−0.13 ±56

CHAPTER 5. RESULTS AND DISCUSSIONS

Table 5.1: Summary of branching fractions. Only statistical error is quoted.
Decay
ǫ(%)
Yield
Branching fraction±±
B → J/ψηK (Total)
8.7
403±35(1.3±0.1)×10−4
B ± → ψ ′ (→ J/ψη)K ±8.0
46±8(0.2±0.03)×10−4±±
B → J/ψηK (PHSP)
8.7
357±38(1.1±0.1)×10−4
B 0 → J/ψηKS0
7.5
80±14
(4.3±0.7)×10−5
0.30 ± 0.10)% per track.

5.3.2

Correction and systematic uncertainty of K ID

The decay chain of D ∗+ → π + D 0 , D 0 → K − π + and its charge conjugate
reaction are used to calibrate charged identification efficiency. In this decay
chain, D meson daughter K and π always have opposite and same charge signwith respect to the slow π from D ∗ . The number of kaon tracks satisfying
the identification requirement are compared between data and MC. K ID
correction and uncertainty are found to be 1.0064±0.0138/track.

5.3.3

Correction and systematic uncertainty of µ ID

The lepton pair production in two photon collisions, e+ e− → e+ e− µ+ µ− isuseful to caribrate µ-on identification efficiency. Because of the singularity
in the QED, either e+ or e− is likely to escape from detection by going alongwith beampipe, while µ-ons can have enough transverse momentum to be
detected. The events in the case where only one µ-on track is explicitly
identified is called ”Single tag”, on the other hand ”Double tag” denotes theevents where both µ-ons are positively identified. The ratio between ”Single
tag” and ”Double tag” events are compared between data and MC. Sameprocedure is repeated to an inclusive J/ψ → µµ sample for validation. As aresult, µ ID efficiency correction and uncertainty are found to be 0.937±0.037
for the case both J/ψ daughters are required to be identified.

5.3.4

Electron ID correction and systematic uncertainty

In order to check electron ID systematic, we use an inclusive J/ψ → e+ e− (γ)
sample. We define two cases for J/ψ reconstruction :5.3. CORRECTION AND SYSTEMATIC UNCERTAINTIES

57

1. Single tag : when one electron has Le > 0.9 while other has no condition
applied for the identification.
2. Double tag : when one electron has Le > 0.9 and other has Le > 0.01.
Similaly to µID case, the ratio between single-tag yield and double tag yieldis compared between data and MC. As a result, we estimate electron ID
correction and uncertainty as 0.9516±0.0082 for the case both J/ψ daughters
are required to be identified.

5.3.5

η detection systematic uncertainty

For η → γγ decay’s systematic, the ratio of the signal yields for η → γγ andη → π 0 π 0 π 0 are compared between data and MC. As a result, we assign 4.0%
as the uncertainty.

5.3.6

Correction and systematic uncertainty of KS0 π + π −detection

In order to estimate KS0 → π + π − samples. One is selected by ”loose” and theother is ”tight”. The ”loose” sample is collection of the oppositely charged
pion pairs without any special requirement on each track with very wide invariant mass window from 350 MeV/c2 up to 650 MeV/c2 . Among thesepion pairs, the proper KS0 → π + π − selection criteria are applied to have the”tight” sample.
The ratio between the signal yield in ”tight” sample and ”loose” sample’s
number of events is compared between data and MC. As a result, the correction factor for efficiency of KS0 → π + π − detection as well as its uncertainty
are obtained to be 0.9879±0.0073.

5.3.7

Signal MC statistics

Our detection efficiency estimation is based on the signal MC samples with
0.5 Million events. Statistical error of these samples result in 0.5% for B
decay branching fractions.

58

5.3.8

CHAPTER 5. RESULTS AND DISCUSSIONS

Number of B meson pairs

This systematic is due to the uncertainty on the number of B meson pairs,
NBB̄ , for experimented data. It is obtained to be (771.58±10.6)×106 which
gives a systematic uncertainty of 1.4%.

5.3.9

Branching fraction uncertainties

We are using secondary branching fractions such as J/ψ → e+ e− or µµ,η → γγ and KS0 → π + π − . Uncertainty of these secondary branching fractions
are taken into account as summarized in Table 5.2.
Decay mode
J/ψ → e+ e−
J/ψ → µ+ µ−+ −J/ψ → ℓ ℓ (Combining above two)η → γγBranting ratio Uncertainty (%)
0.0594±0.0006
1.01
0.0593±0.0006
1.01
0.1187±0.0008
0.7
0.39±0.0020
0.51

Table 5.2: Summary of secondary branching fractions and uncertainties.

5.3.10

PDF systematic uncertainties

We extract signal yield by performing a fit to data. Our signal yield depends
upon the parameter fixed in the fit. We may have uncertainty from themodeling of the different components for the distribution (PDF). For thispurpose we repeat fits by varying the fixed parameters of the PDF by ±1σ
to see the variation of results. From this procedure, we estimate the PDF
uncertainty for B ± → J/ψηK ± , B ± → ψ ′ (→ J/ψη)K ± and B 0 → J/ψηKS0
as 7.3%, 3.9% and 8.4%, respectively.

5.3.11

Summary of systematic uncertainties

The systematic uncertainty estimated by the procedures described above issummarized in the Table 5.3.

5.4. UPPER LIMIT FOR RESONANCE IN J/ψη FINAL STATE

Tracking
K ID
Lepton ID
η → γγ detection
KS0 → π + π −Signal MC state
Secondary Br.
PDF uncertainty

B ± → J/ψηK ±
0.9
1.4
2.4
4.0
N/A
0.5
0.7
7.3
8.9%

B ± → ψ ′ (→ J/ψη)K ±
0.9
1.4
2.4
4.0
N/A
0.5
0.7
3.9
6.4%

59

B 0 → J/ψηKS0
1.3
N/A
2.4
4.0
0.7
0.5
0.7
8.4
9.8%

Table 5.3: Summary of systematic uncertainty of branching fraction. Here,
lepton ID is 3.9% for µ, 0.4% for e and averaged effect is quoted in the Table.

5.4

Upper limit for resonance in J/ψη final
state

Based on the fact that we found no significant peak in MJ/ψη distribution except for the well known state ψ ′ , we calculate the upper limit on the productof branching fraction at 90% confidence level using a frequentist approach.
We provide upper limits for X(3872), ψ(3770) and narrow resonance (hypothesis at 4020 MeV/c2 , 4220 MeV/c2 , 4420 MeV/c2 and 4620 MeV/c2 ).

5.4.1

X(3872)

We fit data at X(3872) as shown in Fig5.3. The signal PDF is determined by
the signal MC with setting width to be zero. We get signal yeild to be 2.3±5.2
events. Therefore we get Br(B ± → X(3872)K ± )Br(X(3872) → J/ψη) <3.8 × 10−6.

5.4.2

Narrow resonances at other mass points

We repeat same procedure for narrow resonance at other mass points. The
narrow resonances visited mass points are 4020 MeV/c2 , 4020 MeV/c2 , 4220
MeV/c2 , 4420 MeV/c2 and 4620 MeV/c2 . The upper limit at 90% C.L. isestimated same approach as X(3872) case. Table 5.4 and Figure 5.4 show

60

Events / ( 0.005 )CHAPTER 5. RESULTS AND DISCUSSIONS

bkg = 289 ± 18
sig = 2.3 ± 5.2

14slope1 = 0.032 ± 0.099

12
10
8
6
4
2
0

3.8

3.85

3.9

3.95

4

4.05
MJ/ ψ ηFigure 5.3: Fit result of MJ/ψη distribution at X(3872) region.

summary of upper limit.
Resonance
X(3872)X(4070)X(4270)X(4470)X(4670)Efficiency(%)
8.12
9.75
9.79
9.43
8.4

Yield(90% C.L.)
10.6
10.5
9.2
17.25
7.0

Br(×10−6 )
3.8
3.1
2.7
5.3
2.4

Table 5.4: Summary of the obtained upper limits for the product of branchig
fractions.

5.4. UPPER LIMIT FOR RESONANCE IN J/ψη FINAL STATE

61

U.L. of Br(B±→ X( → J/ ψ η)K±)

-6

10

×10

9
8
7
6
5
4
3
2
1
0
3800

3900

4000

4100

4200

4300

4400

4500

4600
4700
MJ/ ψ η[GeV/c2]

Figure 5.4: U.L. (@ 90% C.L.) on the B(B ± → XK ± ) · B(X → J/ψη)
estimated at different masses using narrow width hypothesis.

Chapter 6
Summary
We observed B ± → J/ψηK ± signal yield as 428 ± 37 events from Belledata corresponding to 772 B B̄ pair. In this B decay sample, the fit to
MJ/ψη distribution tells that ψ ′ → J/ψη signal yield is 44.3 ± 8.1 events.
Otherwise, the B decay signal event show phase space like distribution thus
we do not have any signiture of a narrow resonance in J/ψη final state.
As a consequence, we get B(B ± → X(3872)K ±) · B(X(3872) → J/ψη) <3.8×10−6 .
We reconstructed B 0 → J/ψηKS0 and its signal yield is obtained to be 80±14
events. As a result, we present
B(B ± → J/ψηK ± )=(1.3 ± 0.1(stat) ± 0.1(syst)) × 10−4
B(B 0 → J/ψηKS0 )=(4.3 ± 0.7(stat) ± 0.4(syst)) × 10−5 .

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