Search for the Hc Charmonium State in the Babar Experiment

Universita` degli Studi di Genova Facolt`adi Scienze Matematiche, Fisiche e Naturali

Tesi di Dottorato di Ricerca in Fisica XVII Ciclo

Search for the hc charmonium state in the BaBar experiment

Candidato: Relatore: Riccardo Capra Dott. Maurizio Lo Vetere Universit`adegli Studi di Genova Relatore Esterno: Prof. Livio Lanceri Universit`adegli Studi di Trieste

Anno accademico 2004/2005

Contents

Introduction 5

1 Charmonium physics overview 7 1.1 The discovery of Charm ...... 8 1.2 The c¯csystem ...... 9 1.3 Potential models ...... 11 1 1.3.1 The 1 P1 state ...... 14 1.4 Charmonium production at BaBar ...... 15 1.4.1 Continuum charmonium production ...... 15 1.4.2 Initial state radiation ...... 15 1.4.3 γγ fusion ...... 16 1.4.4 B meson decays ...... 17 1.4.4.1 Spectator decays ...... 17 1.4.4.2 Factorisation ...... 19 1.4.4.3 Charmed meson rescattering eﬀects in B → c¯cK decays . . . . 20 1.5 Charmonium decays ...... 21 1.5.1 Electromagnetic decays ...... 22 1.5.2 Radiative transitions ...... 22 1.5.3 Strong decays ...... 24

2 The BaBar experiment 25 2.1 The PEP–II B–Factory ...... 25 2.2 The BaBar detector ...... 28 2.2.1 The silicon vertex tracker ...... 30 2.2.2 The drift chamber ...... 31 2.2.3 The Cherenkov detector ...... 33 2.2.4 The electromagnetic calorimeter ...... 34 2.2.5 The solenoid magnet ...... 35 2.2.6 The muon and neutral hadrons detector ...... 37 2.2.6.1 Resistive plate chambers ...... 37 2.2.6.2 IFR eﬃciency history ...... 38 2.2.6.3 Limited streamer tubes ...... 39 2.3 Trigger and data acquisition ...... 39 2.3.1 Trigger ...... 40 2.3.2 Data acquisition ...... 40

1 2 CONTENTS

3 BaBar analysis tools 43 3.1 Monte Carlo simulation ...... 43 3.2 Measurement of number of BB¯ events ...... 44 3.3 Measurement of total integrated luminosity ...... 44 3.4 Central analysis ...... 45 3.4.1 Tracking ...... 45 3.4.2 Charged particles identification ...... 47 3.4.2.1 e± identification ...... 47 3.4.2.2 µ± identification ...... 47 3.4.2.3 Hadrons identification ...... 48 3.4.3 EMC clusters reconstruction ...... 48 3.4.4 Photons reconstruction ...... 49 3.4.5 Decay chains and vertexes ...... 49 0 3.4.5.1 KS reconstruction ...... 50 3.4.5.2 π0 identification ...... 50

± ± 4 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ 51 4.1 Data sample ...... 52 4.2 Semi–exclusive algorithm ...... 53 4.3 Events preselection ...... 57 4.4 Best B selection ...... 57 4.5 Background types ...... 58 4.6 Analysis approach ...... 59 4.7 Kinematics variables used in the selection ...... 59 4.7.1 Plots notation ...... 59 4.7.2 Continuum background rejection: the fisher discriminant . . . . . 60 4.7.3 Veto variables ...... 64 4.7.4 Particle identification variables ...... 68 4.7.5 Vertex fit variables ...... 68 4.7.6 Kinematics variables ...... 68

5 Cuts optimisation 71 5.1 Optimisation procedure ...... 71 5.1.1 Choice of the cuts on the not optimised variables ...... 72 5.2 Optimisation results ...... 73 ± ± 5.2.1 B → χc 1 K with χc 1 → J/ψ γ ...... 74 5.2.1.1 J/ψ → π+ π− π+ π− ...... 74 5.2.1.2 J/ψ → π+ π− π0 ...... 74 5.2.1.3 J/ψ → π+ π− K+ K− ...... 75 5.2.1.4 J/ψ → π+ π− p¯p...... 75 ± ∓ 0 5.2.1.5 J/ψ → π K KS ...... 80 5.2.1.6 J/ψ → K+ K− π0 ...... 80 ± ± 5.2.2 B → hc K with hc → ηc γ ...... 81 + − + − 5.2.2.1 ηc → π π π π ...... 81 + − + − 5.2.2.2 ηc → π π K K ...... 81 ± ∓ 0 5.2.2.3 ηc → π K KS ...... 82 + − 0 5.2.2.4 ηc → K K π ...... 82 + − + − 5.2.2.5 ηc → K K K K ...... 83 5.2.3 Conclusions ...... 83 CONTENTS 3

6 Final results 85 6.1 Unbinned maximum likelihood ﬁt ...... 85 6.1.1 Fit quality ...... 86 6.1.2 Measure precision and conﬁdence levels ...... 86 6.1.3 The CLs algorithm ...... 88 ± ± 6.2 B → χc 1 K with χc 1 → J/ψ γ results ...... 89

6.2.1 Bidimensional ﬁt in mES–mχc 1 ...... 89 6.2.2 Cross-checks ...... 91 6.2.3 Upper limit evaluation ...... 92 ± ± 6.3 B → hc K with hc → ηc γ results ...... 93

6.3.1 Bidimensional ﬁt in mES–mhc ...... 93 6.3.2 Cross-checks ...... 96 6.3.3 Upper limit evaluation ...... 96

Conclusions 97

A Optimisation plots 99 ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ ...... 99 A.1.1 J/ψ → π+ π− π0 ...... 99 A.1.2 J/ψ → π+ π− π+ π− ...... 104 A.1.3 J/ψ → π+ π− K+ K− ...... 108 A.1.4 J/ψ → π+ π− p¯p...... 112 ± ∓ 0 A.1.5 J/ψ → π K KS ...... 112 A.1.6 J/ψ → K+ K− π0 ...... 117 ± ± A.2 B → hc K with hc → ηc γ ...... 122 + − + − A.2.1 ηc → π π π π ...... 122 + − + − A.2.2 ηc → π π K K ...... 126 ± ∓ 0 A.2.3 ηc → π K KS ...... 130 + − 0 A.2.4 ηc → K K π ...... 135 + − + − A.2.5 ηc → K K K K ...... 140

Acknowledgments 145

Bibliography 147 4 CONTENTS Introduction

he Standard Model is a quantum field theory whose aim is to explain three of the fundamental forces of nature: electromagnetic, weak nuclear, and strong nuclear. 25 T particles are grouped within the Standard Model: 12 fermions, and 13 bosons. The fermion sector of the Standard Model consists of quarks and leptons. The physical interactions between them are governed through the exchange of the bosons. The charmonium is a bound system of a charm and an anti-charm quark. The study of its spectrum production, and decay properties provide essential information for the understanding of the strong force, described within the framework of the Standard Model by the quantum chromodynamics theory. The first experiments studying the charmonium used e+e− annihilations that allowed directly accessing only states with J PC = 1−−. Later, p¯pcollisions were used with the possibility to directly access a broader range of charmonium states. Due to the high backgrounds, however, this technique allows easily studying only charmonium decays with a clear signature, mainly electromagnetic decays. Recently, a new opportunity to collect and analyse large samples of charmonium states has been offered by the B–Factories: experiments like BaBar, Belle, and CLEO that study e+e− annihilations at the Υ(4S) mass energy. In these experiments, charmonium states are copiously produced not only in decays of B mesons, but also from a variety of other processes, such as inclusive production in continuum e+e− interactions, formation in e+e− after photon radiation from the initial state, or γγ fusion with two quasi-real photons. 1 This dissertation concerns a search for the 1 P1 charmonium state (hc). The properties of this state are of particular interest for the test of several phenomenological models describing charmonium spectrum and decay. This state has been observed in recent p¯pand B–Factory experiments[22][23][24], but these observations need further confirmation. Moreover a precise measure of the mass of this state is essential to put stringent constraints on the effective potential models, and still missing. Using a non-relativistic framework, indeed the expected value for the hc mass is fixed to the centre of gravity of the three χc J masses. The work presented in this document describes the analysis I have performed using data recorded by the BaBar experiment in the last 5 years, corresponding to a total integrated luminosity of about 210 fb−1 taken at the energy of the Υ(4S) mass. ± ± My analysis consists in the search of the hc charmonium state in the process B →hcK ± ± with hc→ηcγ and ηc→hadrons. As control sample, the process B →χc 1K with χc 1→J/ψγ

5 6 Introduction and J/ψ→hadrons has been analysed too. The choice of this channel is due to the fact that [1] ± ηc hadronic decays are well known and that the study of production in B decays allows setting several kinematics constraints that sensibly cut down the backgrounds. Furthermore [42][43] the hc radiative decay is expected to occur with a large rate (50%), thus not disfavouring this decay in comparison with direct hadronic decays.

During my doctoral studies, I have actively participated in the BaBar Collaboration, not only developing this analysis, but also working on the detector. Besides having taken part to data acquisition shifts, I have been responsible of the BaBar muon sub-detector, and I have worked on this sub-detector upgrade.

In the ﬁrst Chapter, after a brief introduction, I give an overview of the charmonium physics, and of the potential models developed to reproduce its mass spectrum. The chapter ends with the description of various typologies of charmonium production and decay, focusing the attention on what is relevant for my analysis. Chapter 2 shows in detail the PEP–II machine, the BaBar experiment, its sub-detectors, and the DAQ chain. Chapter 3 is dedicated to the standard tools used by all BaBar analyses: Monte Carlo techniques, luminosity and BB¯ measurement, charged and neutral particles reconstruction and identiﬁcation. In Chapter 4 I delineate the reconstruction algorithm used in my analysis, the criterion used to choose the best B candidate when more than one are available, and all the cut-based criteria considered in the signal extraction from the backgrounds. The outline of the optimisation algorithm used to improve the background rejection is presented in Chapter 5. In this chapter the optimisation results and the signal and background estimations for the hc “blinded” sample are also shown. Plots relative to the tables presented in this chapter are collected in Appendix A. The last chapter delineates the techniques used to set upper limits on the branching ± ± + − ± ± ratio for the decays B →χc 1K with χc 1→J/ψγ, and J/ψ→π π p¯p;and B →hcK with ± ∓ 0 hc→ηcγ, and ηc→π K KS. Chapter 1 Charmonium physics overview

article physics is the study of the fundamental particles interaction. The theory describing our knowledge of particle physics is called Standard Model. Arising from P Gell-Mann’s “Eight-Fold Way”[6], the Standard Model provides a basis for describing all phenomena except those where gravity is involved. In the model, there are 12 particles organized into three family of increasing mass. Each family consists of two quarks and two leptons. Each particle has an accompanying anti- particle with the same mass but opposite quantum numbers. In the model the particles interact via three forces: electromagnetic, weak and strong. The electromagnetic force occurs between any two charged particles, mediated by the photon, and aﬀects both quarks and charged leptons. The weak force occurs between all particles in the Standard Model and it is responsible for nuclear decay. Neutrinos interact only via the weak force. The mediators of ± the weak force are W and Z0. The strong force occurs between the quarks only and is the force that holds the nucleus together. The strong force is mediated by gluons. The properties of these particles are summarized in Fig- ure 1.1.

The electromagnetic and weak forces are Figure 1.1: Fundamental particles of the Stan- well understood. It has been demonstrated, dard Model indeed, that they are two manifestations of the same force, called electro-weak force[7][8][9]. The strong force, however, is much more complicated. The constant that dictates the strength of this interaction is not constant at all; it actually increases with the distance (and inversely with energy) between two quarks. This leads to a phenomena known as conﬁnement and explains why quarks are found only in composite systems, such as protons and neutrons

7 8 Charmonium physics overview and not as free particles. At very high energies (short distances), the coupling goes to zero leading to asymptotic freedom. This dissertation focuses on the charmonium system, the bound state of a charm and anti-charm quark, which is an excellent laboratory to study the nature of the strong force. However, even if is not explicitly referred, most of the arguments presented in this chapter apply as well to the bound state of a beauty and anti-beauty quark (bottomonium).

1.1 The discovery of Charm

Late in 1974 a group led by Burton Richter at SLAC noticed an enhancement in the e+–e− cross-section in a very narrow energy region near the centre of mass energy of 3.1 GeV[10] and another at 3.7 GeV[11] (Figures 1.2 and 1.3). At the same time, Samuel Ting and his group at Brookhaven measured a similar enhancement (Figure 1.4), colliding protons on a beryllium target and looking for e+e− final states with an invariant mass of 3.1 GeV[12]. In what later would be called the November Revolu- tion, these two groups submitted their findings together in November 1974 and the particle at 3.1 GeV was named J/ψ. The width of these resonances was about 1000 times less than other known resonances in this energy region. Current models of the time were not sufficient to describe the narrowness of these resonances, which correspond to unusually long lifetimes. Earlier, in 1970, Glashow, Iliopoulos and Maiani[13] had proposed an additional quark to go along with the up, down and strange quarks known at the time. This additional quark was a way of explaining strange phenomena in the neutral kaon decays: it had been ob- + + served that the decay rate for K →µ νµ (a strangeness changing charged current weak decay) was many orders of 0 + − magnitude larger than the rate KL→µ µ (a strangeness changing neutral current weak decay). [14] According to Cabibbo theory , the coupling of the Z0 to the quark was:

¯ 2 2 ¯ JZ0 = u¯u − dd cos ϑc − s¯ssin ϑc − sd + ¯sd sin ϑc cos ϑc (1.1) while the charged current coupling was given by:

Figure 1.2: Cross-sections show- J + = ud¯ cos ϑ + u¯ssin ϑ (1.2) ing the ψ[10] signal at SLAC: the W c c hadronic (a), e+e− (b) and µ+µ− (c) cross-sections respectively. In both of these expressions the last term is the strangeness changing term. The magnitudes of the two terms are comparable and a large diﬀerence in the charged and neutral currents rates would not be expected. 1.2 The c¯c system 9

Glashow, Iliopoulos and Maiani[13] proposed the existence of a fourth, up-like, quark. In that way there were two doublets of quarks (u, d) and (c, s). As in Cabibbo theory, the d and s quark eigenstates for the weak interaction are mixtures of the mass eigenstates:

0 d = d cos ϑc + s sin ϑc (1.3) 0 s = s cos ϑc − d sin ϑc (1.4)

thus, the charged current is unchanged, but the neutral one becomes

¯ 2 JZ0 = u¯u+ c¯c − dd + s¯s cos ϑc ¯ 2 ¯ ¯ − s¯s+ dd sin ϑc − sd + ¯sd − sd − ¯sd sin ϑc cos ϑc = u¯u+ c¯c − dd¯ − s¯s (1.5)

The introduction of the fourth quark produces an additional term in the neutral current that cancels with the strangeness changing term. This new quark was called charm Figure 1.3: Cross-sections showing the ψ0[11] hadronic because it “charms away” the neutral current contribution. cross-section observed at In reality, the cancellation is not complete because there is a SLAC. diﬀerence between the masses of the up and charm quarks. While this procedure, known as the GIM mechanism, nicely described why the rate for strangeness changing neutral currents was so low, it came at a high cost: the introduction of a new, undetected particle of an unknown mass. The GIM mechanism remained a rather curious result and the proposed charm quark was not accepted until the discoveries at SLAC and Brookhaven, where it was quickly realized that the narrow resonances could only be explained by identifying the resonances as a bound state of charm and anti-charm quarks[15]. Later, as the c¯csystem was better understood, it was named charmonium in analogy to the e+e− bound state, positronium, which showed a similar spectrum of states.

Figure 1.4: The e+e− invariant mass revealing the J signal at Brookhaven[12]

1.2 The c¯c system

The long lifetime of the J/ψ is due to two factors. The strong decay to charmed mesons is kinematically prohibited: the mass of the lightest charmed meson, the D0, is more than half the mass of the J/ψ. In addition, the annihilation of the charm quarks to two or three hard gluons is suppressed due to the small coupling to high-energy gluons. This eﬀect is known as Okubo-Zweig-Iizuka (OZI) suppression rule[16]. 10 Charmonium physics overview

ψ (2S)

η γ χ c(2S) c2(1P) γ∗ γ χ h (1P) c1(1P) c hadrons χ hadrons c0(1P) hadrons π0 hadrons γ hadrons γ 0 γ η,π γ ππ

J/ψ (1S) γ ηc(1S)

hadrons hadrons γ∗ radiative

JPC = 0−+ 1−− 0++ 1++ 1+− 2++

Figure 1.5: The charmonium spectrum below the open charm threshold. Unconfirmed transitions are represented by dashed lines.

Therefore, since the OZI suppressed decay is the only one allowed, the lifetime is quite long. Above the threshold of 3.729 GeV, the decay to charmed mesons is possible, so charmonium states are much more short lived. Like hydrogen and positronium, charmonium has a spectrum of radial and orbital states. The J/ψ and ψ0 are two lowest lying states with J PC = 1−−. The charmonium states below the open charm threshold are shown in Figure 1.5 and properties are summarised in Table 1.1. Charmonium states were produced and studied through the reaction e+e−→(c¯c)[10][17][18] in which the charmonium state is generated by a virtual photon and so only states with J PC = 1−− can be produced. More recently, another class of experiments[19][20][21] has made all states in the spectrum directly accessible through formation in p¯pannihilation. The high accuracy in the knowledge of beam parameters has allowed the precise measurement of resonance shape parameters. 1 1 All of the states except the 1 P1 (hc), the 2 S0 (ηc(2S)), and ψ (3836) (above the open- charm threshold) have been confirmed and well measured. Only few observation of the hc has been reported[22][23][24], but it still lacks confirmation, while, after the first claim of an

2S+1 G PC State n LJ Mass Width I (J ) 1 +2.7 + −+ ηc 1 S0 (2979.6 ± 1.2) MeV 17.3−2.5 MeV 0 (0 ) 3 − −− J/ψ 1 S1 (3096.916 ± 0.011) MeV (91.0 ± 3.2) KeV 0 (1 ) 3 + ++ χc 0 1 P0 (3415.19 ± 0.34) MeV (10.1 ± 0.8) MeV 0 (0 ) 3 + ++ χc 1 1 P1 (3510.59 ± 0.10) MeV (0.91 ± 0.13) MeV 0 (1 ) ? 1 − +− hc 1 P1 (3526.21 ± 0.25) MeV < 1.1 MeV (90%CL) 0 (1 ) 3 + ++ χc 2 1 P2 (3556.26 ± 0.11) MeV (2.11 ± 0.16) MeV 0 (2 ) ? 1 + −+ ηc(2S) 2 S0 (3654 ± 6 ± 8) MeV — 0 (0 ) 3 − −− ψ(2S) 2 S1 (3686.093 ± 0.034) MeV (281 ± 17) KeV 0 (1 )

Table 1.1: Masses, widths, and assigned quantum numbers for the charmonium states below the [1] open charm threshold . The states marked with the ? symbol need confirmation (hc and ηc(2S)). 1.3 Potential models 11

[25] ηc(2S) candidate by the Crystal Ball Collaboration , only very recently Belle, CLEO and BaBar have reported its observation[26][27][29][30]. Charmonium has proved a remarkable laboratory for the study of quantum chromodynamics (QCD). The study of its spectrum provides fundamental information about the inter-quark potential. The decays of charmonium states are a source of information about the value of the strong coupling constant. The production rate in various high-energy processes can give valuable insight into the heavy quark–anti-quark interactions as well as into the elementary processes leading to the production of the (c¯c)pair. Furthermore, these mesons are produced in several reactions of great importance for the study of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and of CP violation. The following sections deal with these points in more detail.

1.3 Potential models

Even though the charmonium mass spectrum is qualitatively similar to the positronium spectrum, the non-perturbative features of QCD prevent the possibility of describing it on the basis of the fundamental theory of the interaction. For this reason the natural approach to the charmonium spectroscopy is to build an effective potential model describing the observed mass spectrum. This approximation allow to integrate out many fundamental effects like gluon emission or light quark pairs and to deal with an effective potential which is the result of the (c¯c)direct interaction as well as the energy of the gluon field. This potential should nevertheless reproduce the two main features of the bound quark states in the two limits of small and large distance: asymptotic freedom and confinement. The (c¯c)system can be described with a Schröedinger equation:

H Φ(x) = E Ψ(x) (1.6) where the Hamiltonian is 0 H = H0 + H (1.7) and H0 can be expressed by a free particle Hamiltonian plus a non-relativistic potential V (r)

p2 H0 = 2mc + + V (r) (1.8) 2mc 0 where mc is the charm quark mass and p its momentum. H includes the spin and orbital dependent part of the strong interaction, explaining the charmonium ﬁne structure. V(r) can be built thinking at the properties of the strong interaction in the limit of small and large distances. At small distance the potential between the quarks is coulomb-like

4 α (r) V (r) ∼ − s (1.9) 3 r where r is the distance between the quarks and αs is the running strong coupling constant. The value of the running coupling constant αs decreases as 1/ ln r at short distances as a result of the asymptotic freedom of the strong interaction. 12 Charmonium physics overview

At large distance the conﬁnement term is dominating. It can be written in the form

V (r) ∼ kr (1.10) where k is called string constant. The energy of a (c¯c)system increases with the distance, so the absence of free quarks in nature is explained by this conﬁnement term. Putting together these two behaviours, the Cornell potential[31][32] is obtained

4 α (r) V (r) = − s + kr (1.11) 3 r 4 α V = − s + kr 3 r Figure 1.6 shows the functional behaviour of

) the potential. Due to the fact that the potential V e

G has spherical symmetry, the charmonium wave (

V function can be expressed as: 4 α V = − s m 3 r Ψ(r, ϑ, φ) = Rn, l (r) Yl (ϑ, φ) (1.12)

αs = 0.3 k = 1 GeV/fm However potential is not enough accurate to reproduce the mass diﬀerence for charmonium states in the same orbital angular momentum. r (fm) To explain the charmonium ﬁne structure one Figure 1.6: The behaviour of the Cornell po- needs additional interaction terms depending on [33] tential S and L :

0 H = VLS + VSS + VT (1.13)

Where the various terms have the following meaning: · Spin-orbit: this term splits the states with the same orbital angular momentum depending on the L~ · S~ expectation value (ﬁne structure): L~ · S~ dVV dVS VLS = 2 3 − (1.14) 2mc r dr dr

· Sin-spin this term describe the effect of the interaction between the spin of the quarks. It is responsible of the splitting between the spin singlet and triplet (hyperfine structure): 2 S~1 · S~2 2 VSS = 2 ∇ VV (r) (1.15) 3mc · Tensor the tensor potential, in analogy with electrodynamics, contains the tensor effects of the vector potential:

2 2 S~ · rˆ − s /3 2 dVV d VV VT = 2 − r 2 (1.16) 2mc r dr dr where S~ = S~1 + S~2, while VV and VS denote respectively the vectorial and scalar part into which the Cornell potential can be divided. More in detail, the coulomb part of the Cornell 1.3 Potential models 13

mState − mJ/ψ State PDG[1] MB(1983)[34] GRS(1989)[35] GJRS(1994)[36] ηc −117 MeV −113 MeV −115.8 MeV −109.0 MeV χc 0 318.3 MeV 285 MeV 315.3 MeV 318.6 MeV χc 1 413.7 MeV 391 MeV 410.1 MeV 414.4 MeV hc 429.3 MeV 428 MeV 456.6 MeV 459.1 MeV χc 2 459.3 MeV 405 MeV 421.6 MeV 429.4 MeV ηc(2S) 557 MeV 490 MeV 522.2 MeV 525.4 MeV ψ(2S) 589.17 MeV 560 MeV 592.8 MeV 588.9 MeV

Table 1.2: Charmonium mass states splitting (with respect to J/ψ). Theoretical predictions obtained with potential models and compared with experimental values

potential corresponds to one gluon exchange and contributes only to the vector part VV of the potential; the scalar part VS is due to the linear confining potential. The linear confining term could in principle contribute both to VS and VV , but the fit of the χc J masses suggests [34] that the VV contribution is small . There are other suggestions for the function of the binding potential V (r), but they are essentially coincident with the values from (1.11) in the region from 0.1 fm to 1.0 fm (the dimension scale of the (c¯c) system) and lead to similar results. The theory cannot predict the coefficients weighting the different contributions from the various terms of the potential (1.6). In addition, all theoretical energy levels can be corrected to take into account relativistic effects. All those contributions need to be compared with experimental data of charmonium spectroscopy to evaluate the relative weight. Table 1.2 shows the comparison between predictions and experimental values for the mass splitting with respect to the J/ψ. Another possibility to predict the charmonium mass spectrum is to compute it with lattice QCD, which is essentially QCD applied to a discrete four-dimensional space. The field theory fundamental principles and path integral can be used to calculate, with a computer, the properties of the strong interaction. To compute the heavy quarkonia spectrum, the NRQCD can be applied to the lattice

mState − mJ/ψ State PDG[1] Chen(2001)[38] Okamoto et al.(2002)[39] ηc 2979.6 MeV 3012 MeV 3003 MeV J/ψ 3096.916 MeV 3090 MeV 3088 MeV χc 0 3415.19 MeV 3465 MeV 3442 MeV χc 1 3510.59 MeV 3519 MeV 3517 MeV hc 3526.21 MeV — 3549 MeV χc 2 3556.26 MeV 3517 MeV 3519 MeV ηc(2S) 3654 MeV 3700 MeV 3806 MeV ψ(2S) 3686.093 MeV 3750 MeV 3849 MeV

Table 1.3: Recent results for the charmonium states masses from lattice NRQCD computation. 14 Charmonium physics overview calculation. The bottomonium spectrum is well reproduced, even if it is not possible to compare the mass value for the ηb state, which is not observed. The charmonium system, on the other side, is more relativistic and not so well described by the NRQCD; anyway the observation of the ground state ηc allows the determination of mc directly from the [37] mηc measurement . Table 1.3 summarise some lattice QCD results for the masses of the charmonium states. These results are less precise than the ones obtained with the non- relativistic potential model and have low predictive power for not observed states, but the advantage of this approach is that all the mass values come directly from the application of NRQCD just setting the scale for 1P − 1S or 2S − 1S and it is not needed to ﬁt the whole spectrum.

1 1.3.1 The 1 P1 state

The conﬁrmation of the resonance hc and the measurement of its parameters are fundamental to understand the nature of strong interactions. Using the potential model discussed in the previous paragraph, under some hypothesis it can be aﬃrmed that the responsible of the levels separation in P wave (for example the three 3 χc J states with quantum numbers 1 PJ ) are only the spin-orbit and tensor terms. 1 Thus the hc state, which has quantum numbers 1 P1, is expected to be unperturbed and its mass to be the one of the centre of gravity of the three χc J states: P J (2J + 1) mχc J mhc = P (1.17) J 2J + 1

A precise measurement of the hc mass and its diﬀerence from the centre of gravity of 3 the three 1 PJ states would give an estimation for the deviation of the vector part of the quark–anti-quark interaction from pure one gluon exchange. [22][23][24] hc has been observed in recent p¯pand B–Factory experiments , but these observations need further conﬁrmation. E760 experiment has set an upper limit on the state width of 1.1 MeV, 90%CL. Theoretical calculations suggest that this state should decay into hadrons and radiatively [40][42] into ηcγ with comparable rates . Further details are given in next paragraphs.

q ¯c ¯c

¯q γ? c γ? ? γ c ¡ c ¢ g £ ¯c g g Figure 1.7: Example of continuum production diagrams: e+e−→(cc¯) qq¯ (left), e+e−→(cc¯) gg (centre), and e+e−→(cc¯) g (right) 1.4 Charmonium production at BaBar 15 1.4 Charmonium production at BaBar

B–Factories, like BaBar, are also abundant sources of charmonium states. The main methods of production include: · Continuum e+e− interactions · Initial state radiation · γγ fusion · B meson decays A part from these methods, a charmonium state can be also produced from the decay of a heavier charmonium state. Next sections give more detail on these processes.

1.4.1 Continuum charmonium production √ At s ∼ 10.6 GeV, the dominant processes in the continuum charmonium production are (Figure 1.7): · e+e−→(c¯c) q¯q · e+e−→(c¯c) gg · e+e−→(c¯c) g

Measured[44][45] cross-sections for e+e−→J/ψ X and e+e−→ψ(2S) are about 1 pb, while [45] upper limits exist for the χc 1 and the χc 2 of 0.35 and 0.66 pb respectively. For phase space availability reasons, e+e−→(c¯c) (c¯c)process should be suppressed respect to e+e−→(c¯c) gg. In particular, in non-relativistic calculations, one can derive

σ e+e−→(c¯c) gg > σ e+e−→(c¯c) (c¯c) (1.18)

However recent measurements have surprisingly shown that[28]

+ − + − +0.15 σ e e →J/ψ (c¯c) /σ e e →J/ψ X = 0.59−0.13 ± 0.12 (1.19) which implies the dominant contribution to e+e−→(c¯c) X process is the charm fragmentation. This represents a puzzling question in the understanding of charmonium production.

1.4.2 Initial state radiation

The radiative process e+e−→hadron γ, where initial electrons or positrons radiate the photon, allows the production of 1−− charmonium states. This mechanism is called initial state radiation (Figure. 1.8). 16 Charmonium physics overview

The Born cross-section for ISR production of a vector resonance V , after integration over the photon emission angle, is given by: dσ (s, x) V = W (s, x) σ (s (1 − x)) (1.20) dx 0

√3k where x = s and k is the photon momentum. The function W (s, x) describes the probability of photon emission: √ 2α s W (s, x) = 2 ln 1 − x + x2/2 (1.21) πx me − 1

e+ µ− with α is the ﬁne structure constant and me is the electron mass.

σ0 (s) is the cross-section for hadronic production + − (c¯c) µ+ in e e annihilations and is given by the standard Breit-Wigner formula: m2 Γ2 ¡ 12πBee (c¯c) (c¯c) σ0 (s) = · (1.22) − γ 2 2 e m(c¯c) 2 2 2 s − m(c¯c) + m(c¯c)Γ(c¯c) Figure 1.8: An example diagram for the ISR production of a charmonium where m and Γ are the vector resonance mass state with JPC = 1−−. (c¯c) (c¯c) and width and Bee is the branching fraction for the process (c¯c)→e+e−. In the case of a narrow resonance, 2 one can integrate over x replacing the Breit-Wigner term with a δ s − m(c¯c) , thus obtaining

2 12π BeeΓ(c¯c) σ(c¯c) (s) = W s, x(c¯c) (1.23) m(c¯c)s 2 where x(c¯c) = 1 − m(c¯c)/s. At the Υ(4S) energy, the cross-sections for J/ψ and ψ(2S) production via ISR are about 34 and 13 pb, respectively.

1.4.3 γγ fusion Charmonium can be produced through the reaction e+e−→e+e−γ?γ?→e+e−(c¯c). The diagram of the process is shown in Figure 1.9. Due to the conservation of charge parity, only states with positive C-parity can be accessed in this process.

e− e− ¡ (c¯c) e+ e+ Figure 1.9: Diagram of the charmonium production from two photons interaction. 1.4 Charmonium production at BaBar 17

1.4.4 B meson decays

B meson decays are an abundant source of charmonium states. The B branching fraction into charmonium states are summarised in Table 1.4. They add up to about 2% of the total B meson decay width. Due to the relevance of charmonium production mechanism for this dissertation, further details are given in next sub-paragraphs.

Mode Branching fraction −3 B → ηc X < 9·10 (90%CL) B → J/ψ X (7.8 ± 0.4) ·10−3 −3 B → χc 1 X (3.34 ± 0.28) ·10 −3 B → χc 2 X (1.65 ± 0.31) ·10 B → ψ(2S) X (3.07 ± 0.21) ·10−3

Table 1.4: Measured inclusive production rates for charmonium states[1].

1.4.4.1 Spectator decays

Most of the B meson decays can be described by spectator diagrams (Figure 1.10). The name spectator comes from the feature that the quark bound to the b plays no role in the decay process. The basic interaction Hamiltonian is

GF ? ¯ ? HWeak = √ Vcb V du + V (¯sc) (¯cb) (1.24) 2 ud cs ¯ where Vcb, Vud, and Vcs are the CKM matrix elements and the terms du , (¯sc),and (¯cb) represent the interaction at each vertex. Here ¯qrepresent the creation of a quark or the annihilation of an anti-quark. Finally GF is the Fermi constant, which includes the coupling constant factor from the two vertices, and the eﬀect of the massive W propagator. Since I am only interested in charmonium states, I drop the du¯ term

GF ? HWeak = √ VcbV (¯sc) (¯cb) (1.25) 2 cs

Note that everything that is described here also applies if every particle is replaced by its corresponding anti-particle and vice versa. Figure 1.10 summarises the possible diagrams: left one is called external spectator diagram, while the right one is called internal spectator diagram. They only diﬀer for the two quark that are paired together. It must be observed that in the external spectator diagram the colour requirement is automatically satisﬁed, since the W does not carry colour charge and the c preserves the colour of the b. On the other hand for the internal spectator diagram there are nine colour pairs possible when the W decays, three of which have matching colour. Thus one would 18 Charmonium physics overview

d,¯s¯ b¯ ¯c u, c u, c W+ W+ b¯¡¯c ¢d,¯s¯ d, u d, u

Figure 1.10: Possible diagrams for the hadronic decay of a B meson naively expect that the matrix element for the internal spectator decay would be one third of that for the external one. Therefore the decay rate for the B meson to a charmonium state would be one ninth of that expected without accounting for colour[46][47]. While the spectator mechanism provides a simple model of B meson decay, it is not the whole picture. Virtual gluon interactions can take place between quarks, leading to an eﬀective neutral current. The transformation of a b into a s is not allowed by the Standard Model. However, virtual gluons can rearrange the ﬁnal state quarks, swapping the c created when the b decays with the s created from the W− decay (Figure 1.11). The gluon interactions lead to an additional term in the interaction Hamiltonian with quark pairings (¯cc) and (¯sb):

GF ? HEﬀective = √ VcbV (c1 (µ) (¯sc) (¯cb)+ c2 (µ) (¯cc) (¯sb)) (1.26) 2 cs

[49] The Wilson coeﬃcients c1 (µ) and c2 (µ) account for the gluon interactions . They can in principle be calculated from QCD:

c± (µ) = c1 (µ) ± c2 (µ) (1.27) −6γ± 33−2n αs (s) f c± (µ) = (1.28) αs (mW) where γ+ = 1, γ− = −2 and nf is the number of ﬂavours that have a mass near or below the mass of the decaying quark (5, for B meson decay).

The term αs needs to be evaluated at the proper energy value. Typically mb is the value chosen for µ. To ﬁnd the total decay rate of B mesons to charmonium one needs to combine the internal spectator diagram with the eﬀective neutral current diagram. Theoretically one can extract

b¯ ¯c ¯c c c W+

b¯ ¯s ¡¯s ¢ d, u d, u

Figure 1.11: Two diagrams leading to the charmonium production from B decay: an internal spectator diagram (left) and an effective neutral current diagram (right). 1.4 Charmonium production at BaBar 19 the contribution to charmonium from (1.25) by performing a Fierz transformation: 1 1 (¯cb)(¯sc) −→ (¯cb)(¯sc) + (¯sλ b) ¯cλic (1.29) 3 2 i where λi are the SU (3) colour matrices[48]. The relevant part of the Hamiltonian is then GF ? 1 1 i HEﬀective = √ VcbV c1 (µ) + c2 (µ) (¯cc) (¯sb) + c1 (µ) (¯sλib) ¯cλ c (1.30) 2 cs 3 2

The first part of Equation (1.30) transforms as a colour singlet with the 1/3 reflecting the colour suppression. The second part transforms as a colour octet. Kühm et al.[48] argue that the latter term cannot contribute to the formation of charmonium since a meson must be in a colour-singlet state. In this case, B meson decay into hc, χc 0, and χc 2 states are forbidden by conservation rules. Their predicted production ratios for B→(c¯c) X are 0.57 : 1 : 0.27 : 0.31 for ηc : J/ψ : χc 1 : ψ(2S). Recently Bodwin et al.[49] have stated that charmonium can also be formed in the decay of a B meson to the c¯ccolour octet in a S-wave state. The c¯ccolour octet can then radiate a soft gluon to form a colour singlet P -wave state. In that way they find a ratio of 1.3 : 0.3 : 1 : 1.3 for hc : χc 0 : χc 1 : χc 2.

1.4.4.2 Factorisation

The two non-charm quarks in both the internal spectator (charged current) and effective neutral current diagrams form one or more mesons in a process called hadronization. If the momenta of the two quarks are well matched they can form a single meson, but if their momenta are significantly different they separate and pop quark–anti-quark pairs out of the vacuum to form multiple mesons. When only one meson is formed from the non-charm quarks, it is possible to separate the Hamiltonian into two parts, one part describing the formation of the charmonium state, and the other one describing the formation of a meson from the non-charm quarks. This “factorisation” works extremely well in semi-leptonic decays, where the W decays into a lepton and anti-neutrino. Leptons have no colour, so that they do not interact with the c or spectator quarks. The factorisation can be extended to diagrams where the W decays into quark anti-quark pairs. The assumption here is that once the quarks from the W are formed they move away from the interaction region quickly enough that gluon interactions with the remaining quarks are negligible. One is even temped to apply factorisation to effective neutral currents, despite the requirement that there must be some gluon interactions. Bauer, Stech and Wirbel (BSW)[50] modify Equation (1.26) to

GF ? HEﬀective = √ VcbV (a1 (¯sc) (¯cb) + a2 (¯cc) (¯sb)) (1.31) 2 cs

where a1 ' c1 + ξc2 and a2 ' c2 + ξc1, ξ is a colour factor which is normally equal [50] to 1/Nc (Nc is the number of colours, Nc = 3 in QCD) . Note that a2 coeﬃcient with ξ = 1/3 matches the term in Equation (1.30). The coeﬃcients a1 and a2 are determined from experiment. 20 Charmonium physics overview

Decay Branching fraction − − 2 B →J/ψK 1.819% a2 − ? − 2 B →J/ψK 2.932% a2 ¯ 0 ¯ 0 2 B →J/ψK 1.817% a2 ¯ 0 ¯ ? 0 2 B →J/ψK 2.927% a2 − − 2 B →ψ(2S)K 1.068% a2 − ? − 2 B →ψ(2S)K 1.971% a2 ¯ 0 ¯ 0 2 B →ψ(2S)K 1.065% a2 ¯ 0 ¯ ? 0 2 B →ψ(2S)K 1.965% a2

Table 1.5: The predictions of BSW model as updated by Neubert et al. for the exclusive branching (?) (?) 2[50] fractions B→J/ψK and B→ψ(2S)K in terms of the constant a2

In this scheme all B meson decays into two mesons can be divided into three groups. The first group consists of decays where the charged current directly produces a meson. The second group consists of decays where the effective neutral current produces a meson. In the third group are decays in which both the charged and effective neutral currents produce a meson. In this third category falls for example B−→D0π−. Decays to charmonium states instead are all in the second group. For this reason measurements of decays to J/ψ provide the best measurement of a2. The predictions of the relative charmonium branching fractions using Equation (1.31) are summarised in Table 1.5. Comparison of these predicted relative rates with experiments provides an important test for the BSW model.

1.4.4.3 Charmed meson rescattering effects in B → c¯cK decays

In paragraph 1.4.4.1 it has been shown that B meson decays into hc, χc 0, and χc 2 states are allowed only considering colour-octet mechanisms. Another alternative way to obtain this ± 0 ± ± result is make calculations considering the rescattering process B →X¯ucY¯cs →K (c¯c). X and Y denote open-charm (D) mesons produced by weak B transitions, which then rescatter to the ﬁnal state K±(c¯c), where (c¯c)represent one of the charmonium states. (?) 0 (?) ± The lowest lying X and Y states are the D and Ds mesons. A typical diagram is shown in Figure 1.12: for the analysis of these diagrams, one needs the weak vertices

(c¯c) K− D(?) 0 D(?) 0

− (?) 0 − (?) + B D B Ds (?) − (?) − ¡Ds ¢Ds K− (c¯c)

Figure 1.12: Example of rescattering diagrams contributing to a two-body B-decay into charmonium B±→(cc¯)K±. 1.5 Charmonium decays 21

(?) 0 (?) ± B→D Ds and two strong vertices, which describe the coupling of a pair of charmed mesons to a kaon and to a charmonium state, respectively. This process basically corresponds to a rearrangement of the quarks in the final state and it is known as final state interaction. Such effect can be extremely relevant, as it can change the decay amplitudes and even the dependence on the CKM matrix elements (in Paragraph 1.4.4.1. This last dependence change is the one shown in Equation (1.26). Using this method P. Colangelo et al. have predicted[40] a range of possible values for the ± ± ± ± −4 branching ratio of B →hcK : BR B →hcK = (2–12) ·10 . Results of my analysis are compared against this predicted range.

1.5 Charmonium decays

Since the discovery of the J/ψ, a really surprising feature of such a massive resonance was its narrowness. The measurement of the width of a resonance is very important because it gives information about the lifetime of the particle, which is related to the kind of interaction causing the decay and to the number of accessible channels. Also the partial width, related to the specific decay channel of the resonance plays an important role in the understanding of the physics mechanism of the particle decay. The J/ψ has a very large mass and small decay width, if compared with the mesons made containing light quark (u, d, and s). The small width can be explained observing that its decay can occur only violating the OZI rule[16]. While the c¯cstates above the open charm threshold can quickly decay into DD¯ pairs, which are OZI favourite, the situation for the states with mass below 3.729 GeV is different. Anyway the OZI rule cannot explain the +2.7 [1] [1] differences between ηc (17.3−2.5 MeV ) and J/ψ ((91.0 ± 3.2) KeV ) width. In QCD this is explained by observing that the two states decay via annihilation in two gluons (ηc) and three gluons (J/ψ), which are respectively favoured and suppressed. Charmonium decay modes can be classified into electromagnetic, radiative and hadronic. Table 1.6 shows the approximate decay ratio in each one of these three categories. More details of these processes are given in next paragraphs.

State ΓEm/ΓTot ΓRad/ΓTot ΓHadr/ΓTot −4 ηc O 10 0 ∼ 100% J/ψ ∼ 10% ∼ 5% ∼ 85% −4 χc 0 O 10 ∼ 1% ∼ 99% χc 1 0 ∼ 30% ∼ 70% hc (Theoretical) 0 ∼ 50% ∼ 50% −4 χc 2 O 10 ∼ 20% ∼ 80% ψ(2S) ∼ 2% ∼ 25% ∼ 73%

Table 1.6: Approximate ratio of the electromagnetic, radiative and hadronic decay widths to the [1] [42] total width . hc values are the theoretical ones . 22 Charmonium physics overview

¯c e− ¯c γ γ ¡ ¢γ c e+ c Figure 1.13: Charmonium electromagnetic decay at the leading order in α.

1.5.1 Electromagnetic decays

The widths for the electromagnetic processes, such as radiative transitions or lepton pair decay, can be calculated with good approximation with QED. When hadrons are present in the ﬁnal state the process should be described using QCD but, because of its non-perturbative nature, all the calculations of strong processes have always a high theoretical uncertainty. At the leading order approximation in α (where α is the ﬁne structure constant) the annihilation of a c¯cpair can occur into a lepton pair via a virtual photon for the 1−− states or in γγ for the states with C = +1, as shown in Figure1.13:

2 −− + − + − 2 2 |Ψ (0)| αs Γ 1 →e e , µ µ = 16πα ec 2 1 − 16 (1.32) 4mc 3π 2 2 4 |Ψ (0)| αs Γ(ηc, ηc(2S)→γγ) = 12πα ec 2 1 − 3.4 (1.33) mc π 2 2 4 |R (0)| αs Γ(χc 0→γγ) = 27α ec 4 1 + 0.2 (1.34) mc π 2 36 2 4 |R (0)| αs Γ(χc 2→γγ) = α ec 4 1 − 16 (1.35) 5 mc 3π where ec = +2/3 (the quark charge in electron charge unit), mc is the charm mass, Ψ is the wave function deﬁned in Equation (1.12), and R is its radial part. It must be noted that the [41] 1 Yang theorem forbid this process for the χc 1 and, in general, for the J = 1 states . The annihilation into three photons (for C = −1 states) is at the next to the leading order approximation in α. This decay channel is not observed experimentally for any c¯cstate because of the small branching ratio.

1.5.2 Radiative transitions

The radiative transitions, as in atoms, occur from an exited to a lower mass c¯cstate with the emission of a photon. They are subdivided in electric dipole transitions (E1), obeying to the selection rules ∆L = ±1, ∆S = 0 and magnetic dipole transitions (M1), with the selection

1The Yang theorem states that particles with J = 1 cannot decay into two massless 1−− particles such as photons and gluons. 1.5 Charmonium decays 23 rules ∆L = 0, ∆S = ±1. The transition widths between S and P waves can be calculated using the expressions:

4 2Jf + 1 2 3 2 Γ(S→P γ) = ec αk |Eif | (1.36) 9 2Ji + 1 4 Γ(P →S γ) = e2αk3|E |2 (1.37) 9 c if (1.38) where k is the photon momentum in the decaying particle frame, and |Eif | is the dipole transition matrix element M 2 − M 2 k = i f (1.39) 2Mi Z +∞ 3 |Eif | = Ri (r) Rf (r) r dr (1.40) 0

Apart from the hc→ηcγ decay, all the radiative transition widths between charmonium states below the open charm threshold are measured (Table 1.7). Due to the fact that in (1.40) R depends on n and L quantum numbers only, it is possible to predict the partial width of hc→ηcγ decay using the measured values of |Eif | of [42] Γ(χc J →J/ψγ). For example obtains:

Γ (hc→ηcγ) = (520 ± 90) KeV (1.41)

The only magnetic dipole transition between charmonium states experimentally observed are J/ψ, ψ(2S)→ηcγ and the decay width is

3 4 2 k k 2 Γ n S0→ηcγ = ec α q |Iif | (1.42) 3 mc 1 + k/ m2 + k2 ηc where ! Z ~k · ~x |I | = Ψ? (~x)Ψ (~x) cos d~x (1.43) if f i 2

Transition Kind Partial width J/ψ→ηcγ M1 (1.2 ± 0.4) KeV χc 0→J/ψγ E1 (0.12 ± 0.02) MeV χc 1→J/ψγ E1 (0.29 ± 0.05) MeV hc→ηcγ E1 — χc 2→J/ψγ E1 (0.43 ± 0.05) MeV ψ(2S)→ηcγ M1 (0.79 ± 0.05) KeV ψ(2S)→χc 0γ E1 (24 ± 2) MeV ψ(2S)→χc 1γ E1 (24 ± 3) MeV ψ(2S)→χc 2γ E1 (18 ± 2) MeV

Table 1.7: Partial width for charmonium radiative transitions[1] 24 Charmonium physics overview

¯c

¡ c¯c¢ c¯c c Figure 1.14: Charmonium strong decay into hadrons (left) and strong radiative decay (right)

1.5.3 Strong decays

The strong decay can be treated by applying the same conservation laws used for the electromagnetic decays. The diﬀerences, from a qualitative point of view, are: · Gluons have colour charge: they are SU (3) colour octet states. Since all observable particles are colour singlets, the annihilation of the c¯cpair is forced by the colour conservation to proceed through at least 2 gluons · Gluons and quarks do not exist as free states in nature: they can only exist in colour singlet combinations. Thus gluonic decay is always followed by hadronization of the ﬁnal state

· Given the high value of αs, especially for low momentum transfer, QCD cannot always be treated as a perturbative theory

Two main kinds of strong decay processes can occur. The ﬁrst, related to the complete annihilation of the heavy q¯q(for example ηc→φφ), has the emission of high momentum gluon and can be treated in a perturbative way. The second one is the hadronic deexcitation of charmonium (for example ψ(2S)→J/ψππ), accompanied by the emission of two or more soft gluons and followed by their hadronization. The low momentum carried by the gluons does not allow a perturbative treatment of the reaction. The two categories are shown in Figure 1.14. Chapter 2

The BaBar experiment

he data used in the analysis subject of this thesis were collected by the BaBar detector, which records e+–e− collision inside the PEP–II storage ring at the Stanford Linear T Accelerator Center (SLAC). BaBar is a high-energy physics experiment involving a collaboration of nearly 600 physicists. The first aim of the BaBar experiment is the precision study of CP violation in the B meson system. As the branching fractions of B decays interesting for this kind of studies are extremely small (below 10−4 [1]), the detector and accelerator design are optimised to maximize the B production (this is the reason why PEP–II is also called a B–Factory). Workshops taken place at the end of the 80’s[51][52] demonstrated that an excellent environment to study the CP violation in the B meson system was an e+–e− collider working at the Υ(4S) centre of mass energy1. At this energy indeed the e+e−→bb¯ cross-section is enhanced by a factor 4 compared with near bb¯ continuum and backgrounds can be reduced using constraints on the Υ(4S) kinematics: the B mass, the Υ(4S) mass and the fact that the B–B¯ are produced in a coherent l = 1 state. Finally, using beams at different energies, the centre of mass frame does not match the laboratory frame and the difference in time between the decay of the two B mesons can be measured directly from the spatial separation between the decay vertices, thus allowing the carrying out of time-dependent measurements, necessary for CP violation studies. In this chapter I examine the PEP–II and BaBar basics, focusing on the requirements they satisfy and the performances achieved.

2.1 The PEP–II B–Factory PEP–II is an asymmetric e+–e− double ring collider with a diameter of 2200 meters (Fig- ure 2.1). The beams are fed by the SLAC 2-miles linear accelerator. Its original design luminosity of 3·1033 cm−2 s−1 was achieved in July 2001. At the end of the fourth period of run (Run 4)

1Even if with higher backgrounds hadronic accelerators could also access this kind of physics studies with enough statistics.

25 26 The BaBar experiment

Figure 2.1: PEP–II schematic drawing. the peak luminosity was nearly 8·1033 cm−2 s−1. Since 1999, it has delivered an integrated luminosity of 253.55 fb−1: 90.7% were delivered at the Υ(4S) energy and the difference ∼ 40 MeV below. The BaBar recording efficiency has been 91.5% Off Υ(4S) peak data are mainly taken to characterize the e+e−→(u¯u), dd¯, (s¯s), (c¯c) background events and for the BB¯ measurement (Paragraph 3.2). Figure 2.2 shows the integrated Luminosity history of the BaBar experiment since the beginning in 1999.

240 A A R 220 B B

200 PEP-II Delivered 253.55/fb

) 180 BABAR Recorded 244.06/fb -1 BABAR off-peak 22.68/fb 160

140

120

100

Integrated Luminosity (fb 80

0 Nov 1Jan 1Mar 1May 1Jul 1 Sep 1Nov 1Jan 1Mar 1May 1Jul 1 Sep 1Nov 1Jan 1Mar 1May Jul1 1 Sep 1Nov 1Jan 1Mar 1May 1Jul 1 Sep 1Nov 1Jan 1Mar 1May Jul1 1

1999 2000 2001 2002 2003 2004

Figure 2.2: Integrated luminosity (left) and daily luminosity (right) for Run 1-4 (October 1999 – June 2004). 2.1 The PEP–II B–Factory 27

e− beam energy: 9.0 GeV e+ beam energy: 3.1 GeV Centre of mass energy: 10.5 GeV βγ boost: 0.56

Table 2.1: PEP–II machine parameters[3]

Other parameters of the PEP–II machine are listed in Table 2.1: The high luminosity of PEP–II is achieved through high beam currents and strong focusing. To obtain so high performances, part of the accelerator optics is inside the detector volume. Figure 2.3 shows the magnets around the interaction point region.

The magnetic quadrupole (Q1) focuses the beams while the magnetic dipole (B1) separates the beams. Both of them are inside the 1.5 Tesla detector magnetic field. Conventional iron magnets cannot operate in this environment. Due to the limited space available, B1 cannot be a superconducting magnet. For this reason the only possible solution left for Q1 and B1 is a permanent magnet. The bending near the interaction point required to separate the beams generates a large synchrotron radiation flux that is not present in more conventional e+–e− colliders. This radiation flux not only is a strong source of backgrounds but could also damage the BaBar sub-detectors. For this reason the design strategy of the machine elements near the detector was to choose the placement and apertures of these elements in such a way as to ensure that most of the synchrotron radiation power produced close to the collision point is absorbed on downstream surfaces far from the detector.

The two Q1 magnets, the two B1 magnets, the beam pipe section around the interaction point, the synchrotron radiation shielding and the vertex detector are assembled into a single rigid support barrel. This allows a better alignment between these various components, while the multiple scattering due to the ∼ 0.005 X0 of material has a negligible eﬀect on the

Vertex

¢ ¢ Carbon-fiber detector

support tube

£ £ £ £ £ £ £ £ £ Distributed 0.5% Xo B1 trim Q1

B1 dipole ion pump

¡¡ ¡¡ ¡¡ ¡ £ £ £ £ £ £ £ £ £ £ ¢ ¢

£¤ £ £ £ £ £ £ £ £ £

¡ ¡ ¡ ¢ ¡ ¤ ¢

Q1 trim Magnet support 2.5 cm radius Be 43 cm OD beam pipe (cooled) Inboard and outboard LEB masks Z5-6 3:48 (water cooled) 7379A144

Figure 2.3: Support barrel for the interaction point components inside the detector: B1 is 21 cm [2] from the interaction point, while Q1 is 90 cm from the interaction point . 28 The BaBar experiment

Run 1 October 1999 20.5 fb−1 (on) + 2.6 fb−1 (off). October 2000 Shutdown Run 2 February 2001 61.5 fb−1 (on) + 7.1 fb−1 (off). June 2002 Shutdown Run 3 December 2002 31.4 fb−1 (on) + 2.4 fb−1 (off). June 2003 Shutdown Forward end-cap RPC were replaced with new ones Run 4 September 2003 99.8 fb−1 (on) + 9.9 fb−1 (off). July 2004 In December 2003 e+ beam started operating in trickle injection mode and several tests has been performed to operate both beams in trickle injection mode. Shutdown IFR had two of the six RPCs sextants replaced by LSTs Run 5 — Start up planned for middle March

Table 2.2: Run 1–5 periods and shutdowns. resolution of the charged tracks. PEP–II typically operated on a 40 minutes fill cycle with a refill time of about 5 minutes for both beams. Since the fall of 2003 tests have been performed to evaluate if the detector could operate in a different mode, called trickle injection, in which the beams are continuously refilled. Since December 2003, BaBar has taken data with the e+ beam in trickle injection mode. In this configuration fill cycles for the e− beam lasted 2 hours. The data recorded by BaBar have been divided in 4 periods called Run 1, Run2, Run3 and Run 4. These periods were separated by long maintenance shutdowns, in which the detector and the collider were upgraded. Data taking and shutdown periods are summarized in Table 2.2.

2.2 The BaBar detector The primary physics goal of the BaBar experiment is the systematic study of CP-violating asymmetries in the decay of B mesons system. Secondary goals are precision measurements of decays of bottom and charm mesons and of τ leptons, and searches for rare processes that become accessible with the high luminosity of the PEP–II B–Factory. The design of the detector was optimised for CP-violation measurements, but it is also well suited for these other physics topics. The very small branching ratios of B mesons to CP eigenstates and the need for full reconstruction of ﬁnal states with 2 or more charged tracks and often several π0s, plus the need to tag the second neutral B, place stringent requirements on the detector: · Large and uniform acceptance down to small polar angles in the centre-of-mass system 2.2 The BaBar detector 29

JKZKIZUX) 2

.3897:2*39*) 9IGRK S /6 +1:=7*9:73 .+7 ('('8)UUXJOTGZK9_YZKS '&77*1 _ 8:5*7(43):(9.3, ^ (4.1

*1*(9742&,3*9.( ` (&147.2*9*7 (7>4,*3.( *2( (-.23*>

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.+7 *3)(&5 (-*7*304;

)*9*(947 +47<&7) ).7( *3)51:,

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,2558

Figure 2.4: Longitudinal view of the BaBar detector[3].

· Very good vertex resolution · Excellent reconstruction eﬃciency for charged particles down to 60 GeV and for photons down to 20 GeV · Good discrimination power between e±, µ±, π±,K± and p over a wide range of momenta · Neutral hadrons identiﬁcation capabilities

The schematic layout of the detector is shown in Figures 2.4 and 2.5. The boost originated by the asymmetric beams together with the requirement of uniform acceptance in the centre of mass energy lead to an asymmetric detector. The majors sub-systems are: a micro-strip silicon detector (SVT) that provides reconstruction of the primary and secondary decay vertices and, together with the drift chamber (DCH), measures charged tracks momentum; a detector of internally reflected Cherenkov light (DIRC) that allows discriminating between K± and π± over a wide range of energies; an electromagnetic calorimeter (EMC) that allows identifying photons and electrons. These four detectors are inside a 1.5 Tesla magnetic field supplied by a superconducting solenoid. The yoke for the flux return of the magnetic field (IFR) is highly segmented and instrumented with resistive place chambers (RPC) and limited streamer tubes (LST). Each sub-detector is described in detail in the next sections. 30 The BaBar experiment

Figure 2.5: Three-dimensional view of the BaBar detector.

2.2.1 The silicon vertex tracker

The main purpose of the BaBar silicon vertex detector is the reconstruction of the decay vertices of the two B mesons with enough precision for the CP asymmetry measurements. To avoid significant impact of the resolution on these kinds of measurements, the mean vertex resolution along the z-axis for a fully reconstructed B decay must be better than ∼ 80 µm[2]. More over the SVT is the only detector which measures tracks with transverse momentum less than ∼ 100 MeV/c. This feature is fundamental for the identification of slow pions from D? meson decays. The SVT uses double-sided silicon strip sensors mounted on a carbon fibre frame. It is subdivided in 5 layers with a radial distance from the beam axis ranging from 32 mm to 144 mm. It covers a polar angle from 20.1◦ to 150.2◦ and it is designed to maximize the coverage in the forward direction. The 3 internal layers are straight, while the 2 external ones are arch shaped. This design (Figure 2.7) was chosen to minimize the amount of material traversed by particles and the amount of silicon required to cover the solid angle. Figure 2.6: Schematic view of the SVT. (transverse section) 2.2 The BaBar detector 31

Figure 2.7: Schematic view of the SVT. (longitudinal section)

The internal layers have 6 modules in the azimuthal direction (φLab) and are tilted in φLab by 5◦, allowing an overlap region between adjacent modules (Figure 2.6). The outer modules cannot be tilted, because of the arch geometry. To avoid gaps and to have a suit- 16 0 able overlap in the φLab coordinate, these layers are divided into two sub-layers and placed at slightly dif- 15 0 ferent radii. 14 0 13 0 [3] The intrinsic resolution of the SVT is 10÷15 µm 12 -57 for the internal layers and ∼ 40 µm for the external 11 -55 ones. The average vertex resolution of a fully recon- 10 -54 [53] structed B is 70 µm . 9 -52

The SVT overall eﬃciency is 97%. It is calculated 8 50 as the ratio between the number of associated hits and 7 48 the number of tracks crossing the active area of each 6 47 section, excluding 9 out of 208 defective read-out sec- 5 45 tions. 4 0 Finally the time-over-threshold value reported by 3 0 the SVT sensors allows obtaining the pulse height of 2 0 the signal and hence the ionisation dE/dx in the SVT 1 0 sensor. This allows achieving a separation of at least Layer Stereo 2σ between kaons and pions up to 500 MeV/c and be- 4 cm tween kaons and protons beyond 1 GeV/c. Sense Field Guard Clearing

1-2001 8583A14

2.2.2 The drift chamber Figure 2.8: Layout of the first 16 layers of the DCH. Sensible wires are drawn with the + symbol, while field The drift chamber is the primary tracking device wires are drawn with the ◦ symbol. for charged tracks with a transverse momentum above Wires used to screen the internal ∼ 100 MeV/c. field from the external environment are drawn with the • and × symbols. 32 The BaBar experiment

It is a 2.80 m long cylinder made up of 7104 hexagonal cells arranged in 40 concentric layers. The dimension of each cell is approximately 12 cm in the radial direction and 18 cm in the azimuthal one. The layout of the first 16 layers is shown in Figure 2.8. The DCH covers the angular region ◦ ◦ 17.2 < ϑLab < 152.6 . The chamber is built with materials that minimize the Sense Guard 1-2001 radiation lengths a particle has to cross before reaching the Field 8583A16 electromagnetic calorimeter (its length is ∼ 0.04 X0). The Figure 2.9: Layer 3 and 4 cells gas used in the chamber is a mixture of helium (80%) and isochrones spaced by 100 ns. isobutane (20%), which gives a reasonable drift time, a good dE spatial, dx and transverse momentum resolution. Sense wires are tungsten-rhenium gold-plated wires with a diameter of 20 µm, while field wires 0.4 are aluminium gold-plated wires with a diameter of 120 µm. The nominal voltage is +1960 V for sense wires, while field wires are grounded. The 0.3 gain of the avalanche effect with this voltage is about 5·104. 0.2

The spatial resolution of each cell is 140 µm Resolution (mm) (Figure 2.10); on the average, while the spatial 0.1 resolution on the transverse momentum is shown in Figure 2.11. Finally the resolution on the en- 0 –10 –5 0 5 10 dE 1-2001 ergy loss ( dx ) is 7.5% (Figure 2.13). 8583A19 Distance from Wire (mm) The precision on the energy loss allows dis- cerning between K± and π± with more than 3σ Figure 2.10: DCH Position resolution as a function of the distance from the sensible up to 700 MeV/c (Figure 2.12). wire[3].

2.0 (%) t )/p t

(p 1.0 σ

0 0 4 8 1-2001 8583A23 Transverse momentum (GeV/c)

Figure 2.11: DCH momentum resolution. It is evaluated using cosmic muons[3]. The line resulting from the fit is σ pT =(0.13 ± 0.01) % pT +(0.45 ± 0.03) %. pT GeV/c 2.2 The BaBar detector 33

dE/dx vs momentum

10 4 d p BABAR K

10 3 π e

80% truncated mean (arbitrary units) µ

-1 10 1 10 Track momentum (GeV/c)

dE [3] Figure 2.12: Measurement of dx in the DCH as a function of the track momenta .

2.2.3 The Cherenkov detector

The main task of the detector of internally reflected Cherenkov light (DIRC) is to discern between K± and π± up to 4.5 GeV/c. A good separation between these particle types is needed not only for CP studies where the tagging of the B flavour is obtained counting the number of charged kaons in the B decay, but also for the study of the rare two body decays B0→π+π− and B0→π±K∓. The DIRC is novel type of ring-imaging Cherenkov device[54][55], based on the principle that the magnitudes of angles are maintained upon reflections on a flat surface. Figure 2.14 300 shows the schematics of the device. The ra- 200 diator material is quartz shaped into 144 bars ks ac r T arranged around the drift chamber. These bars works both as radiator and as 100 light pipes. Once photons arrive at the instru- 0 mented end, most of them emerge into expan- -0.4 0 0.4 1-2001 sion region filled with purified water (water and 8583A21 (dE/dxmeas.– dE/dxexp.) / dE/dxexp. quartz have almost the same index of refrac- tion). This region is outside the magnetic field Figure 2.13: dE resolution, using the control in the backward end (to avoid instrumenting dx sample e+e−→e+e−[3]. The Gaussian distribu- both ends of the bar with photon detectors, a tion has a standard deviation of 7.5%. mirror is placed at the forward end) and it is instrumented with an array of densely packed photomultiplier tubes. Figure 2.15 shows an event detected by the DIRC.

The DIRC has a thickness of ∼ 0.22 X0 for a perpendicular particle and a width in the radial direction of only 80 mm (important to reduce the volume and then the costs of the electromagnetic calorimeter). The DIRC allows discriminating between K± and π± of more than 4σ in the momentum range 700 MeV/c–4.5 GeV/c. Below this range the discrimination between these particles is 34 The BaBar experiment

Figure 2.14: DIRC schematics.

dE mainly based on the dx DCH measurement. Figure 2.16 shows the background reduction that is obtained using DIRC information on the K±π∓ spectrum around the D0 invariant mass.

2.2.4 The electromagnetic calorimeter

The electromagnetic calorimeter is projected to detect electromagnetic showers with an excellent energy and angular resolution in the energy range 20 MeV < E < 9 GeV. This allows reconstructing with a good efficiency both B decays with one or more π0 and η02and QED processes like e+e−→e+e− (γ) and e+e−→γγ that are essential for the luminosity measurement (Paragraph 3.3) and the detector calibration. Moreover the electromagnetic calorimeter is the main electron detection device. It is essential in all the processes with electrons in the final states. In particular it contributes at the reconstruction of vectorial mesons like J/ψ and ψ(2S) and at the identification of the B flavour in semi-leptonic decays. Figure 2.18 shows the structure of the electromagnetic calorimeter. It is made up of 6580 CsI (Tl) trapezoidal crystals (Figure 2.17) arranged into a cylindrical structure in the barrel and a conical structure in the forward end-cap. Crystals have a radiation length of 1.85 cm and Molière radius of 3.8 cm. Due to the high magnetic field (1.5 Tesla) the scintillation photons are detected with p– Figure 2.15: Event display of the Cherenkov rings generated by two i–n diodes. muons e+e−→µ+µ−[3]. The calorimeter has an internal radius of 90 cm and an ◦ ◦ external one of 136 cm and covers the polar region 15.8 < ϑLab < 141.8 . As showers cannot be detected completely on the edges, the angular fiducial region is slightly smaller. Crystals thickness spreads from 16.0 X0 up to 17.5 X0 and are supported by an external structure to minimize the probability of pre-showering. 2.2 The BaBar detector 35

Without DIRC x 10 2 1500 2

1000

entries per 5 MeV/c With DIRC 500

0 1.75 1.8 1.85 1.9 1.95 Kπ mass (GeV/c2)

Figure 2.16: Invariant mass spectrum K+K− with and without applying the DIRC information. The peak shown is at the D0 mass[3].

The energy resolution (Figure 2.19) is empirically described with the function:

v σ u a2 E = u + b2 (2.1) E tq E GeV where the ﬁt parameters of Figure 2.19 have values[3] a =3.87 ± 0.07 mrad and b =0.00 ± 0.04 mrad. The angular resolution is 12 mrad at low energies and 3 mrad at higher energies. Figure 2.19 shows experimental results empirically described with the function: a σϑ = + b (2.2) q E GeV where the ﬁt parameters of Figure 2.19 have values[3] a =3.87 ± 0.07 mrad and b =0.00 ± 0.04 mrad. Figure 2.17: EMC crystal schematic view.

2.2.5 The solenoid magnet

The BaBar magnet system is made up of a superconducting solenoid, a steel ﬂux return (which is instrumented with RPC and LST) and a ﬁeld-compensating coil.

2π0 decays in two photons with a branching ratio of 98.792 ± 0.032%[1], while η0 decays almost exclusively into photons and π0. 36 The BaBar experiment

Figure 2.18: EMC crystals layout.

The superconducting solenoid produces a central magnetic field of 1.5 Tesla. The field uniformity is ±2% within the tracking volume (r < 80 cm, −1.17 m < z < 1.91 m). The superconducting windings consist of 20 Rutherford NbTi (Cu) wires, which are embedded in a pure aluminium matrix, using a coextrusion process. The windings are cooled to an operating temperature of 4.5 K by liquid helium. They are directly wound inside an aluminium support cylinder and impregnated with epoxy. To meet the requirements for field uniformity the current density has to be higher at ends than in the central region. Therefore there are two different winding types: thinner windings at the ends (3.4 mm) and thicker ones in the central region (6.2 mm). In total there are 210 turns in each of the end region and 315 turns in the central region. The superconducting solenoid is surrounded by a cryostat consisting of a tubular vacuum vessel containing the cold mass and the thermal shielding held at 80 K.

0.07 π0 → γγ 14 η → γγ π0 → γγ (E) / E

0.06 ) (mrad) 12 σ Bhabhas θ η → γγ χc → J/ψ γ ( 0.05 σ 10 MonteCarlo MonteCarlo 0.04 8

0.03 6

0.02 4

0.01 2

0 -1 0 10 1 0 0.5 1 1.5 2 2.5 3 Photon Energy (GeV) Photon Energy (GeV)

Figure 2.19: The energy resolution (left) and angular resolution[3] (right) of EMC, measured using photons and electrons from various processes. The solid curve is the fit of function (2.1)[3] and function (2.2) respectively. The shaded area in the left plot denotes the RMS error of the fit. 2.2 The BaBar detector 37

2.2.6 The muon and neutral hadrons detector

A novel characteristic of BaBar with respect to other high-energy physics experiments is the fine segmentation and instrumentation of the steel flux return of the magnetic field (IFR). The iron is segmented into 19 layers in the barrel, 18 layers in the forward and backward doors layers. The thickness of the internal layers is 2 cm spaced by 3.2 cm and reaches in the external ones 10 cm of thickness separated by 3.5 cm. Finally there are two more layers between the magnet and the calorimeter with a cylindrical shape. IFR has been instrumented with RPC[56] (resistive plate chambers), LST[57] (limited streamer tubes) and with passive elements (brass). The schematic layout is shown in Figure 2.20 0 The main task of IFR is the muon and KLdetection with high efficiency in a wide momenta range. identification is important to tag the flavour of B that decay semi-leptonically and for 0 the reconstruction of vectorial mesons like J/ψ and ψ(2S), while KL identification is essential to completely reconstruct decays of B in some CP eigenstates. For this reasons, the µ± must 0 be detected in a wide solid angle with a good noise rejection, while KL must be detected with a good angular resolution.

2.2.6.1 Resistive plate chambers

RPC are chambers constituted by two 2 mm thick bakelite sheets separated by 2 mm gap, kept uniform by means of spacers. External surfaces are coated with graphite: one of them is connected to high voltage (around 7.6 kV) and the other one to ground. The graphite is covered with a thin mylar ﬁlm. Then foam spaces the aluminium strips, which pick up signals induced by the discharges. Aluminium strips are oriented in orthogonal direction on the two sides, so to give a two dimensional information. Internal surfaces of the bakelite are treated with linseed oil to improve their smoothness and their ultraviolet absorption. The gap is

3200 342 RPC FW Modules 920 3200 19 Layers

18 Layers BW 12501940

432 RPC Modules

1-2001 8583A3

Figure 2.20: Overview of the IFR: the barrel region (left) and the forward and backward end- doors are shown. Dimensions are in mm 38 The BaBar experiment

filled with a non-flammable gas mixture of argon (∼ 60%), freon 134a (∼ 35%) and isobutane (∼ 5%). Figure 2.21 shows RPC structure. RPC were chosen for several advantages: they are simple low cost object, which can be easily shaped. These properties allow cover- ing a sensible surface of ∼ 2000 m2 at reasonable costs and minimizing the dead space. Furthermore they have fast signal response and a good resolution. However during these 5 years of BaBar data taking, RPC had a sensible loss of performances. Due to this deterioration, IFR has sustained relevant upgrades in these last years. During summer 2003, forward end- cap RPCs were replaced with new ones, single and double-layered and with brass ab- sorbers. During summer 2004, 2 of the 6 sex- Figure 2.21: Cross-section of a RPC. tants of the barrel have been replaced with LST tubes and the complete upgrade of the barrel with LST is scheduled for the next years. Current IFR configuration uses 228 RPC modules in the barrel region, 216 modules in the backward region, 180 new generation modules in the forward region and finally 32 modules in the cylindrical layers.

2.2.6.2 IFR efficiency history

IFR efficiency is monitored analysing both collision and cosmic rays data. After the instal- lation, all the RPCs were tested and resulted good: the chambers showed typically less than 10 µ A m−2 dark current and > 95% efficiency. During the first summer of operation, in 1999, an unexpected temperature rise occurred and more than 37◦ C were reached in the iron slots; in this period many chambers showed a dramatic increase in the dark currents and efficiency loss. A cooling system was installed, which stopped the rapid drop in efficiency,

Average efficiency Average efficiency Average efficiency of chambers with efficiency > 10% Average efficiency of chambers with efficiency > 10% Percentage of chambers with efficiency < 10% Percentage of chambers with efficiency < 10%

Figure 2.22: RPC efficiency history for Run 1–4 for barrel (left), backward end-cap (centre) and the new forward end-cap (right). These efficiencies are obtained using collision data and only for the forward cosmic rays data too. The machine backgrounds cause a reduction of efficiency due to dead time (forward end-cap plot). 2.3 Trigger and data acquisition 39 but, since then, efficiency has continued to decrease for some chambers, although at a slower pace (Figure 2.22). Several studies has been developed to understand the original causes of this efficiency decrease and to try to recover the efficiency loss. Some chambers have been monitored for week, working at temperatures higher than 36◦ C in a test-end. There has been studies on the gas mixture an on the chemical composition of the output mixture. The gas flow and the polarity of the chambers have been reversed and a small percentage of water has been added to the gas mixture in order to humidify the bakelite.

2.2.6.3 Limited streamer tubes LSTs are made up of a plastic (PVC) extruded profile containing 8 cells with a section of 9 × 9 mm2 . The profile is coated with a layer of graphite, having a typical surface resistivity of ∼ MΩ m−2. A silver plated wire 100µ m in diameter is located at the centre of the cell and kept in place with special spacers. Profiles are inserted into plastic tubes of matching dimensions and hermetically sealed for gas containment. Figure 2.23 shows a schematic view of an LST tube. LSTs operates with a non-flamable gas mixture of CO2 (89%), Isobutane(8%), and Argon(3%). Out- side the plastic tube, there are 35 mm-wide strips orthogonal to the wires, which allow obtaining a bidimensional position of the discharge. First LSTs have been installed in the two hori- zontal sextant of the IFR during 2004 summer shutdown: 13 gaps were instrumented and 6 were filled Figure 2.23: Schematic layout of a LST tube. with bass.

2.3 Trigger and data acquisition The BaBar trigger system is required to select BB¯ events and other events of interest with a high, stable, and well-understood eﬃciency of over 99% for all BB¯ events and at least 95% for continuum events, while rejecting background events and keeping the total event rate low (below 120 Hz at design luminosity). The rates of beam-induced background are typically about 20 kHz each for one or more tracks in the DCH with pT > 129 MeV/c or at least one EMC cluster with E > 100 MeV at a luminosity of 3·1033 cm−2 s−1, a few orders higher than the production rates of interested events as shown in Table 2.5. The BaBar trigger system must be robust and ﬂexible in order to function even under extreme background situations. It must also be able to operate in an environment with dead and noisy electronics channels, and it should contribute no more than 1% to dead time. 40 The BaBar experiment

2.3.1 Trigger

The trigger system is implemented as a two-level hierarchy, the level 1 (L1), which executes in hardware and level 3 (L3), which executes in software after the event assembly. It is designed to accommodate up to ten times the initially projected PEP–II background rates at design luminosity and to degrade slowly for backgrounds above that level. Provision is made for an intermediate trigger (level 2) should severe conditions require additional sophistication. The Level 1 trigger consists of three hardware processors: a drift chamber trigger (DCT), for charged tracks in the DCH, an electromagnetic trigger (EMT), for showers in the EMC, and an instrumented flux return trigger (IFT), for tracks in IFR. Each of the three L1 trigger processors generates trigger primitives, summary data on the position and energy of particles, which are sent to the global trigger (GLT) every 134 ns. The GLT processes all trigger primitives and then delivers them to the fast control and timing system (FCTS). If the trigger primitives satisfy trigger criteria, a L1 Accept is issued. The DCT and EMT both satisfy all trigger requirements independently with high efficiency over 99% for BB¯ events, and thereby provide a high degree of redundancy, which enables the measurement of trigger efficiency, and gives a combined efficiency of ∼ 99.9% for selecting BB¯ events. The L3 trigger system receives the output from L1, performs a second stage rate reduction for the main physics sources, and identifies and flags the special categories of events needed for luminosity determination, diagnostic, and calibration purposes. At design luminosity, the L3 physics event acceptance rate is about 100 Hz, while 30 Hz contain the other special event categories. The L3 trigger is a software based system, complying with the same software conventions and standards used in all other BaBar software, thereby simplifying its design, testing, and maintenance. The L3 trigger system has full access the complete event data, including the output of the L1 trigger, for making its event selection. To provide optimal flexibility under different run conditions, L3 is designed according to a general logic model that can be con- figured to support an unlimited variety of event selection mechanisms. Event classification in L3 is based on several key event parameters, such as L3 DCH tracks, constructed by L3 fast track finding and track fitting, L3 EMC clusters, formed by L3 EMC-based trigger using an optimised look-up-table technique. The L3 system runs within the online event-processing (OEP) framework. Events passing L3 are recorded and passed to the online prompt reconstruction (OPR) system for full reconstruction.

2.3.2 Data acquisition

The BaBar online computing system consists of the DAQ system, detector and DAQ control and monitoring systems, data quality control and online calibration systems. The major sub- systems include: online dataﬂow (ODF), which is responsible for communication with and control of the front-end electronic (FEE), and the acquisition of event data from them; online event-processing (OEP), which is responsible for processing of complete events, including L3 triggering, data quality monitoring, and ﬁnal stages of calibrations; logging manager (LM), which is responsible for receiving events from OEP and writing them to disk as input to the online prompt reconstruction (OPR) processing; online detector control (ODC), which 2.3 Trigger and data acquisition 41 78

raw processed digital analog digital event signals signals data Event Bldg BABAR FrontEnd VME Dataflow Intermediate L3 Trigger detector Electronics Crates Event Store Monitoring trigger L1 Accept, clocks data and trigger data 24 L1 Trigger Fast Control Processor trigger and Timing lines

BABAR Figure 2.24: SchematicFig layouture 2.29 of: Sc thehem BaBaratic di DAQagram system.of the DAQ system.

is responsiblethe Data forﬂow thecrat controles. The R andOMs monitoringare based on ofsing environmentalle-board comput conditionsers that run t ofhe theVx- detector systems; online run control (ORC), which ties together all the other components, and is Works [66] realtime operating system and detector speciﬁc software. ODF builds the responsible for sequencing their operations, and providing a graphical user interface (GUI) for operatorcompl control.ete event data and then pass them from the ROMs to a farm of 32 Unix worksta-

ThetBaBarions, whDAQich run systemthe OE wasP soft designedware inclu todin supportg L3 filter aning. L1Ev triggerents pass rateing t ofhe upL3 t torigg 2e kHz,r with an average event size of ∼ 32 kB and an L3 output rate of up to 120 Hz. It must contribute no morear thane sent ato time-averagedthe LM, which 3%com deadbines timeall the duringevents normalfrom 32 O DAQ.EP nodes and write to a Thes componentsingle file for ea ofch therun.BaBarThis fiDAQle is th systemen proce aressed shownfor full schematicallyevent reconstruc intion Figureby the 2.24. All BaBar sub-detectors share common electronics architecture. Raw analog signals from detectors areO processed,PR, which s digitised,elects phys andics ev bufferedents and incoll theects FEEs.monitor Uponing dat thea for L1qu Acceptality con signal,trol, and under the controlfi ofna ODF,lly writ rawe the dataoutpu fromt into thean o FEEsbject or ofien eachted ev sub-detectorent store. are passed via optical fibres to the VME based readout modules (ROMs) in the dataflow crates. The ROMs are based on single-boardThe computersOPR also pe thatrform runs one theimp Vx-Worksortant task o real-timef rolling ca operatinglibrations, w systemhere cali andbra- detector specifict software.ion constan ODFts gene buildsrated d theuring completeevent reco eventnstruct dataion fo andr one thenrun, a passre th themen used fromdurin theg ROMs to a farm of 32 Unix workstations, which run the OEP software including L3 filtering. Events passingt thehe r L3econ triggerstructio aren of sentevent tos in thethe LM,next whichrun by combinesOPR. The allse c theonsta eventsnts are fromstore 32d in OEPa nodes and write to a single file for each run. This file is then processed for full event reconstruction by the OPR,conditio whichn datab selectsase for u physicsse when eventsreading andthe p collectsrocessed e monitoringvents from th datae even fort sto qualityre. control, and finally write the output into an object oriented event store. The OPR also performs the important task of running calibrations: calibration constants generated during the event reconstruction of one run, are used by OPR during the next one. These constants are also stored in a database and retrieved when processed events are read from the event store. 42 The BaBar experiment Chapter 3

BaBar analysis tools

he BaBar software environment includes online and offline systems. The online system is responsible for real-time control of the detector, monitoring, calibration, and data ac- T quisition as summarized in the previous chapter (Paragraph 2.3.2). The offline system consists of tools for simulation, reconstruction, data quality control and physics analysis. Both online and offline systems are based on object-oriented design and use C++ as their primary programming language. Codes are divided into modules, each of which performs a particular task, such that they can be reused for many purposes and across the two systems. The offline tools share the same object-oriented architecture in the BaBar application framework, which is a flexible, general-purpose structure to enforce certain well-designed standards of code behaviour, using the TCL language as the user interface. The framework is implemented as a class library, which defines the interface of all user classes and the interactions between them.

3.1 Monte Carlo simulation

BaBar largely employs simulations based techniques both for the detector development and for analysis studies like analysis strategy optimisation, determination of the selection efficiencies, modelling of fit variables, background studies and analysis validation. Monte Carlo simulation in BaBar uses the Jetset[58] package for the generation of inclusive B meson decays and continuum events and EvtGen[59] package for the generation of B mesons to exclusive final states. Secondly the full BaBar detector simulation is performed using the Geant 4 Simulation Toolkit[60][61][62], which allows modelling of the geometry of the detector in great detail and simulates the passage of the particle through it. The final output of the simulation contains the signals into the detector and the associated information about the simulated particle that generated them. Signals then are digitised in the same format of real data and undergo the same reconstruction steps. However the associated information allow verifying if the particles that generated the signals match the reconstructed ones. Machine backgrounds are included in the simulation inserting events recorded during data taking with random triggers.

43 44 BaBar analysis tools

Only in 2004, 1.5·109 generic and exclusive events were generated. These events are generated using all the diﬀerent detector conditions of Run 1–4 (due either to geometry or to eﬃciency changes) and with the right luminosity proportion.

3.2 Measurement of number of BB¯ events

Branching fraction measurements require knowledge of the total number of B mesons in the dataset. BaBar determines this quantity by attributing the increase in the rate of hadronic events from the oﬀ- to the on-resonance data to the Υ(4S) decays. The number of BB¯ events may then be measured using

N on ! 1 on µ+µ− oﬀ NBB¯ = NH − oﬀ · κ · NH (3.1) εBB¯ Nµ+µ− where

on oﬀ · NH is the number of events satisfying a hadronic selection in each data sample. on oﬀ · Nµ+µ− is the number of events satisfying a muon selection in each data sample.

on off · Nµ+µ− /Nµ+µ− is the ratio between the two datasets luminosities (neglecting efficiencies differences). ¯ · εBB¯ is the efficiency of the hadronic selection on BB events. It is evaluated on Monte Carlo and particular attention has been made to confirm that all the significant variables distributions are well reproduced by data. · κ accounts continuum cross-section, continuum efficiency, µ+µ− cross-section and µ+µ− efficiency differences at the two different energies (it is κ ∼ 1).

This relation assumes that BR Υ(4S)→BB¯ = 1, which is a reasonable approximation[1]. The number of BB¯ events used in this analysis is (231.7 ± 1.5) ·106.

3.3 Measurement of total integrated luminosity

The usual method for determining the luminosity in e+–e− colliders is through the relationship L=N/σ (Vis), where N is the number of events observed for a reference reaction and σ (Vis) = ε · σ (Th) is the visible cross-section for this reaction. σ (Th) is the theoretically expected cross-section and ε is the eﬃciency for identifying these events in the experiment. ε is calculated using full detector simulation. The requirements for such a method are evident: · The reactions used must have high and well-known theoretical cross-section · The simulation of the detector must be exact and easy to validate using real data 3.4 Central analysis 45

The redundancy oﬀered by the use of multiple such reactions can be a powerful tool in minimizing systematic errors. In BaBar luminosity is measured through the rates of e+e−→e+e− (γ) and e+e−→µ+µ− (γ) events. e+e−→γγ events are only considered as a crosscheck, but are not used in the luminosity measurement. The total integrated luminosity used in this analysis is 210.487 fb−1.

3.4 Central analysis

The tracks and neutral clusters reconstruction and the particle identiﬁcation in BaBar are performed with common analysis techniques shortly after data is collected. The next chapter summarizes the algorithms used for this part of analysis and the performances obtained.

3.4.1 Tracking

Complete reconstruction of B decays (in addition to other major BaBar analysis techniques, such as tagging) requires precise and efficient charged particle tracking. To satisfy these stringent particle tracking requirements, BaBar combine tracks information from SVT and DCH. Track reconstruction begins in the DCH using tracks found by the L3 trigger algorithm as a starting point. A Kalman fitting algorithm is carried out on the hits associated with these tracks taking into account the material and small variations in the magnetic field. Additional drift chamber hits, which are found to be consistent with the tracks, are added in. Two more track finders are then run over the remaining drift chamber hits. These look for tracks which do not span the whole chamber, or which do not originate from the interaction point. All the tracks found in the drift chamber are extrapolated into the SVT (again taking into account the material and variation in the field) and any SVT hit, which is consistent with the tracks, is added in. Finally a stand-alone SVT track finder is run on the remaining SVT hits to and low momentum tracks, which do not reach the drift chamber.

During each tracks ﬁt iteration the estimation of the collision time t0 is reﬁned. The reconstruction of t0 is necessary both for rejecting out-of-time hits within the SVT and to 49

800 a) b) c) d) s k c

a 400 r T

0 –0.2 0 0.2 –0.2 0 0.2 –4 0 4 –4 0 4 1-2001 -3 8583A29 ∆d0 (mm) ∆z0 (mm) ∆Φ0 (mrad) ∆tanλ (10 )

Figure 43. Measurements of the diﬀerences between the ﬁtted track parameters of the two halves of Figure 3.1:cosmdi0c,rza0y,mφu0onands, wittanh tr (aλn)svresolutions.erse momenta above 3 GeVc, a) ∆d0, b) ∆z0, c) ∆φ0, and d) ∆ tan λ.

are symmetric; the non-Gaussian tails are small. σ The distributions for the diﬀerences in z0 and 0.4 z0 tan λ show a clear oﬀset, attributed to residual σd0 problems with the internal alignment of the SVT. Based on the full width at half maximum of these 0.3 distributions the resolutions for single tracks can )

be parametized as m 0.2 m (

σd0 = 23µm σφ0 = 043 mrad σ −3 σz0 = 29µm σ λ = 053 10 tan · 0.1

The dependence of the resolution in d0 and z0 on the transverse momentum pt is presented in 0 Figure 44. The measurement is based on tracks 0 1 2 3 1-2001 in multi-hadron events. The resolution is deter- 8583A28 Transverse Momentum (GeV/c) mined from the width of the distribution of the Figure 44. Resolution in the parameters d0 and difference between the measured parameters, d0 z0 for tracks in multi-hadron events as a function and z0, and the coordinates of the vertex reconstructed from the remaining tracks in the event. of the transverse momentum. The data are cor- These distributions peak at zero, but have a tail rected for the effects of particle decays and ver- for positive values due to the effect of particle de- texing errors. cays. Consequently, only the negative part of the distributions reflects the measurement error and Figure 45 shows the estimated error in the mea- is used to extract the resolution. Event shape surement of the difference along the z-axis be- cuts and a cut on the χ2 of the vertex fit are ap- tween the vertices of the two neutral B mesons, plied to reduce the effect of weak decays on this one of them is fully reconstructed, the other measurement. The contribution from the vertex serves as a flavor tag. The rms width of 190 µm errors are removed from the measured resolutions is dominated by the reconstruction of the tagging in quadrature. The d0 and z0 resolutions so mea- B vertex, the rms resolution for the fully recon- sured are about 25 µm and 40 µm respectively at structed B meson is 70 µm. The data meet the pt = 3 GeVc. These values agree well with ex- design expectation [2]. pectations, and are also in reasonable agreement While the position and angle measurements with the results obtained from cosmic rays. near the IP are dominated by the SVT measure- 49

800 a) b) c) d) s k c

a 400 r T

0 –0.2 0 0.2 –0.2 0 0.2 –4 0 4 –4 0 4 1-2001 -3 8583A29 ∆d0 (mm) ∆z0 (mm) ∆Φ0 (mrad) ∆tanλ (10 ) 46 BaBar analysis tools Figure 43. Measurements of the differences between the fitted track parameters of the two halves of cohavesmic era majory muon precisions, with tra onnsve therse m trackomen hitsta ab inove the3 G DCH,eVc, a since) ∆d0, theb) ∆ positionz0, c) ∆φ of0, theand hitd) ∆ withintan λ. a given cell is related to the drift time. Charged tracks are finally parameterised with ar5e variablessymmetric and; the theirnon-G erroraussi matrix.an tails are small. σ The distributions for the differences in z0 and 0.4 z0 σ tan λ•shdo0wdefineda clear asoff theset, distanceattributed ofto theres trackidual to the d0 problemzs-axiswith t athe theinte trackrnal ali pointgnmen oft o closestf the SV approachT. Based oton th thee fuzll-axiswidth at half maximum of these 0.3 distributions the resolutions for single tracks can )

be pa•razm0etdeﬁnedized as as the distance of the track point m 0.2 m (

of closest approach from the origin along the σd0 = 23µm σφ0 = 043 mrad σ z-axis −3 σz0 = 29µm σ λ = 053 10 tan · 0.1 • φ defined as the azimuthal angle of the track The de0pendence of the resolution in d and z at the track point of closest approach0 0 on the transverse momentum pt is presented in 0 Figure 44. The measurement is based on tracks 0 1 2 3 • λ defined as the dip angle with respect to the 1-2001 in multi-hadron events. The resolution is deter- 8583A28 Transverse Momentum (GeV/c) mined ftransverserom the wid planeth of the distribution of the Figure 44. Resolution in the parameters d0 and difference between the measured parameters, d0 Figure 3.2: d0, z0 resolutions as a function z0 for tracks in multi-hadron events as a function and z•0,ωandefinedd the coo asrd theinate tracks of th curvature.e vertex reco Itn- is pro- of pT. structedportionalfrom the torema1ining tracks in the event. of the transverse momentum. The data are cor- pT These distributions peak at zero, but have a tail rected for the effects of particle decays and ver- for positive values due to the effect of particle de- texing errors. cays.TheCons performancesequently, only th ofe n theegati trackingve part of systemthe are monitored using collision dilepton and dhadronicistributions events,reflects asthe wellmeas asure cosmicsment erro rayr and data. TheFigu resolutionsre 45 shows t ofhe des0t,imza0t,edφ0errandor in tanthe m (λe)a- isareuse dominatedd to extract byth thee res SVT.olution. Event shape surement of the difference along the z-axis be- 2 tween the vertices of the two neutral B mesons, 50 cuts and a cut on the χ of the vertex fit are applied to reduce the effect of weak decays on this Figureone of 3.1the showsm is f theully resolutionreconstruct oned, thesethe o pa-ther measurement. The contribution from the vertex rametersserves obtainedas a flavor usingtag. T cosmicshe rms w raysidth o travers-f 190 µm errors are removed from the measured resolutions ing theis do detectorminated andby th fittinge recon thestruc uppertion of andthe t loweragging in quadrature. The d0 and z0 resolutions so mea- halvesB v ofert eachex, th tracke rms asres aolu separatetion for t track.he fully Onlyrecon- 400 sured are2a.0bout 25 µm and 40 µm respectively at tracksstru abovected B 3 GeVmeson areis 7 considered0 µm. The d andata furthermeet the pt = 3 GeVc. These values agree well with ex- design expectation [2]. ) cuts are applied on d0, z0 and λ in order to % m pectations, and are also in reasonable agreement While the position and angle measurements (

µ consider only tracks passing near the interac-

8 near the IP are dominated by the SVT measure- p with the results obtained from cosmic rays. / /

) tion point. The resolutions found are: σ = s z

t 0 t p n

200 ( 1.0 e 29 µm, σd = 23 µm, σφ = 0.43 mrad, σ = σ 0 0 tan(λ) v

E 0.53·10−3.

The dependence of the d0 and z0 resolution 0 on the transverse momentum pT is shown in Fig- 0 ure 3.2. 0 4 8 0 0.2 0.4 1-2001 2-2001 8583A23 Transverse Momentum (GeV/c) 8583A37 σ∆z (mm) The pT resolution and the overall tracking ef- Figure 46. Resolution in the transverse mo- ﬁciency are dominated by the DCH. The trans- Figure 45. Distribution of the error on the dif- mFigureentum 3.3:p dpeTteresolutionrmined from asco asm functionic ray mu ofons verse momentum resolution shown in Figure 3.3 ference ∆z between the B meson vertices for a t tprTa.versing the DCH and SVT. sample of events in which one B0 is fully recon- is well represented by a linear function structed. σpT = (0.13 ± 0.01) % · pT + (0.45 ± 0.03) % (3.2) pT ments, the DCH contributes primarily to the pt measurement. Figure 46 shows the resolution in where the transverse momentum pT is measured in GeV/c. Finally Figure 3.4 shows the the transverse momentum derived from cosmic overall20 tracking00 eﬃciency. muons. The data are well represented by a linear function, 2 c / V e

σpt pt = (013 001)% pt + (045 003)% M 4

· /

s 1000 e i r where the transverse momentum pt is measured t n in GeVc. These values for the resolution param- E eters are very close to the initial estimates and can be reproduced by Monte Carlo simulations. More sophisticated treatment of the DCH time- 0 to-distance relations and overall resolution func- 3.0 3.1 3.2 2-2001 + − 2 tion are presently under study. 8583A35 Mass M(µ µ ) (GeV/c ) Figure 47 shows the mass resolution for Jψ + − Figure 47. Reconstruction of the decay Jψ mesons reconstructed in the µ µ final state, µ+µ− in selected BB events. → averaged over all data currently available. The reconstructed peak is centered 0.05% below the expected value, this difference is attributed to 7.4. Summary the remaining inaccuracies in the SVT and DCH The two tracking devices, the SVT and DCH, alignment and in the magnetic field parameteriza- have been performing close to design expectations tion. The observed mass resolution differs by 15% from the start of operations. Studies of track res- for data recorded at the two DCH HV settings, olution at lower momenta and as a function of it is 130 03 MeVc2 and 114 03 MeVc2 at polar and azimuthal angles are still under way. 1900 V and 1960 V, respectively. Likewise, the position and angular resolution at 3.4 Central analysis 47

3.4.2 Charged particles identification Only five types of charged tracks are sufficiently long-lived to leave a track in the BaBar detector: electrons, muons, pions, kaons and protons. All other charged particles decay before reaching the first SVT layer. 48 Due to the dominant numbers of pions in multi- hadron events, for the general reconstruction, all c 8000 a) majority of these low momentum pions the mo- /

V Data

tracks are assumed to be a pion in the initial track- e Simulation mentum resolution is limited by multiple scat- M ing ﬁts and pion mass is used in deﬁning the mo- tering, but the production angle can be deter- 0 1 / 4000 mined from the signals in innermost layers of

mentum of the track. Studies have been done to s k

c the SVT. Figure 41 shows the mass difference show that this assumption has a negligible effect a r − − except in low momentum particles and it is easy T ∆M = M(K π+π+) M(K π+), for the to- 0 − to correct for a different particle hypothesis in the b) tal sample and the subsample of events in which the slow pion has been reconstructed in both the later analysis if another choice is needed. y 0.8 c

n SVT and the DCH. The difference in these two e i c has developed specialized non-mutually i BaBar f distributions demonstrates the contribution from f 0.4 exclusive algorithms to identify charged particles. E SVT standalone tracking, both in terms of the More details are given in the next paragraphs. gain of signal events and of resolution. The gain 0.0 in efficiency is mostly at very low momenta, and When particle ID is used to identify a track, the 0.0 0.1 0.2 0.3 0.4 1-2001 corresponding mass hypothesis is assigned. 8583A27 Transverse Momentum (GeV/c) the resolution is impacted by multiple scattering and limited track length of the slow pions. To Figure 3.4: Track efficiency as a function Figure 42. Monte Carlo studies of low momentum derive an estimate of the tracking efficiency for of pT. tracks in the SVT: a) comparison of data (contri- these low momentum tracks, a detailed Monte 3.4.2.1 e± identification butions from combinatoric background and non- Carlo simulation was performed. Specifically, the BB events have been subtracted) with simulation pion spectrum was derived from simulation of the The main properties used for electron identificationof comesthe tra fromnsvers EMC:e momentum spectrum of pions inclusive D∗ production in BB events, and the ∗+ 0 + from D D π in BB events, and b) effi- Monte Carlo events were selected in the same way · E/p ratio (near 1 for electrons), where E iscie thency depositedfor sl→ow pio energyn detect andion dperisive thed fr trackom simu- momentum as the data. A comparison of the detected slow lated events. pion spectrum with the Monte Carlo prediction is · Shower energy presented in Figure 42. Based on this very good The absolute DCH tracking efficiency is deter- agreement, the detection efficiency has been de- · Shower lateral momentum (LAT ), defined as:mined as the ratio of the number of reconstructed rived from the Monte Carlo simulation. The SVT DCH tracks to the number of tracks detected N significantly extends the capability of the charged Pin thEe rS2VT, with the requirement that they fall LAT = i=3 i i (3.3) particle detection down to transverse momenta of PN 2within the acce2ptance of the DCH. Such stud- Eir + (E1 + E2) r 50 MeVc. i=3 iies have been p0erformed for different samples of ∼ where N is the number of EMC crystals associatedmulti-hadr withon ev theents track,. FiguErei is40 theshow energys the re- 7.3. Track Parameter Resolutions deposited in the i-th crystal (with E1 > ···sult>of EoNne), surichisst theudy distancefor the tw ofo thevoltai-thge set- The resolution in the five track parameters is − − crystal from the shower centre and r0 is theting averages. The m distanceeasuremen betweent errors a twore do crystalsminated by monitored in OPR using e+e and µ+µ pair (approximately 5 cm for the BaBar calorimeter.the uncertainty in the correction for fake tracks events. It is further investigated offline for tracks in the SVT. At the design voltage of 1960 V, in multi-hadron events and cosmic ray muons. LAT usually is small for electrons as they depositthe effi mostciency ofav theirerage energys 98 1 in% twoper ortra threeck above Cosmic rays that are recorded during normal crystals 200 MeVc and polar angle θ > 500 mrad. The data-taking offer a simple way of studying the data recorded at 1900 V show a reduction in effi- track parameter resolution. The upper and lower Other quantities used are the DCH dE/dx measure,ciency theby a numberbout 5% offo crystalsr tracks inat theclos shower,e to normal halves of the cosmic ray tracks traversing the the Cherenkov angle and the number of Cherenkovinc photonsidence, i produced.ndicating that the cells are not fully DCH and the SVT are fit as two separate tracks, efficient at this voltage. and the resolution is derived from the difference of The standalone SVT tracking algorithms have the measured parameters for the two track halves. 3.4.2.2 µ± identification a high efficiency for tracks with low transverse To assure that the tracks pass close to the beam momentum. This feature is important for the de- interaction point, cuts are applied on the d , z , ∗ 0 0 Muon identification mainly relies on information fromtection IFRof D andd EMC.ecays. ATo muonstudy isth expectedis efficiency, and tan λ. The results of this comparison for the ∗+ 0 + to deposit a minimum energy in the EMC and passdec troughays D severalD layersπ a ofre steelselec inted theby fluxrecon- coordinates of the point of closest approach and → ¯ ∗+ return. Several variables are used for muon identification,structing including:events of the type B D X fol- the angles are shown in Figure 43 for tracks with lowed by D∗+ D0π+ K−π→+π+. For the → → momenta above pt of 3 GeVc. The distributions 48 BaBar analysis tools

· The energy deposit in the EMC · The number of IFR layer in the cluster

· The number of interaction lengths traversed by a track through the whole BaBar detector, considering the last IFR layer hit · The difference between the measured and the expected number of interaction lengths transversed · The average number of strips hit per layer and the corresponding standard deviation · The IFR hits continuity, defined as the fraction of IFR layers hit out of the total number of layers from the first hit layer to the last one. · The χ2 per degree of freedom of two fits: the IFR hit strips in the cluster with respect to the cluster extrapolation and the two-dimensional polynomial fit of IFR cluster.

3.4.2.3 Hadrons identification

The selection of charged hadrons mainly uses DCH and SVT dE/dx measure, the Cherenkov angle and the number of Cherenkov photons produced in the DIRC. The dE/dx distribution follows the Bethe-Block formula according to the particle hypothesis and the momentum. The number of Cherenkov photons produced in the quartz by a given particle follows a Poissonian distribution with a central value depending on the particle type and charge, the momentum and the polar angle and the position of the hit quartz bar. Finally the Cherenkov angle is a function of the momentum and particle type. These variables are the input for either likelihood-based or neural network-based particle type selectors. For each particle type there are several selectors available that differs for the selection and misidentification efficiencies. Selectors used for this analysis are summarised in Table 4.5.

3.4.3 EMC clusters reconstruction

Crystals with signal in the EMC are clustered together using a three-step algorithm. In the ﬁrst step, the algorithm searches crystals that have detected energy greater than 10 MeV and then all the neighbours of this crystal are examined and kept as part of the cluster if they have energy greater than 1 MeV. Similarly the neighbours of all the crystals in the cluster are examined and added into the cluster if they pass the 1 MeV threshold, and this is iterated until all the crystals outside the cluster fail the energy threshold cut. The second step consists in a bump ﬁnding algorithm, which tries to split the cluster into bumps, which have local maxima in energy. These bumps could be formed if two photons hit the calorimeter close together and their calorimeter showers overlap. Finally there is a track-cluster and track-bump matching algorithm, which calculates if the cluster/bump is associated to a charged track. If the matching is greater than a threshold the bump/cluster is assumed to have originated from the charged particle producing the track, and is associated with that track in further reconstruction and analysis. 3.4 Central analysis 49

Bumps without a track associated are considered generated by neutral particles. As only photons are relevant for this analysis, this chapter does not treat the other neutral particles.

3.4.4 Photons reconstruction Bumps identiﬁed as photons are required to have:

· A minimum energy: ELab > 30 MeV 0 · LAT < 0.80: indeed backgrounds due to hadronic interactions, either by KL or neutrons can be fought by applying requests on the shape of the calorimeter cluster: photons, like electrons, have small LAT values

As initial approximation, momenta and angles consistent with photons originating from the axis origin are assigned to cluster that pass the previous cuts. Then, when it is possible, photons momentum direction is reﬁned using the vertex of the particle emitting it.

3.4.5 Decay chains and vertexes BaBar analyses typically require the reconstruction of at least one entire B meson decay chain. Signal-to-background ratios, mass and momentum resolutions can be improved by applying geometric and kinematics constraints deriving from the physics properties of decay. Types of constraints include, for instance, the identification of the decay vertices and the application of mass or energy constraints. Designed vertexing algorithms allow dealing with complex decay chains in a simple way: composite particles are built from the original particles and are subsequently used in their place in fits and analyses. Kinematics fits are generally based on the least squares method combined with Lagrangian multipliers to impose the constraints. Vertex reconstruction algorithms instead minimize the sum of the squares of the tracks distances of closest approach. The curvature of the tracks and the non-linearity of the fits imply an iterative procedure. 0 This is of relevance especially in the presence of long-living particles, such as KSs. In other cases, a single iteration give accurate enough vertex constraints. The size of the interaction point is about 120 µm in x and 9 mm in z: many applications benefit from a more accurate estimate of the primary vertex. This is the case, in particular, of neutral particles, such as photons or π0s, where the decay origin is used to measure the direction of the particle. The primary vertex is estimated on an event-by-event basis from a vertex fit which uses charged tracks having |d0| < 1 mm and |z0| < 3 mm with respect to the beam spot position determined in the previous run with two-prong events. Tracks must also have pT > 100 MeV/c, p < 10 GeV/c and at least 20 DCH hits. Tracks with a high χ2 contribution to the vertex fit are removed until an overall χ2 probability is better than 1%. In this way, a typical resolution of about 70 µm both in x and in z is obtained for the primary vertex. 27

Pi0 Mass : pi0VeryLoose Cuts Pi0 Momentum : pi0VeryLoose Cuts

16000 10000

14000 8000 12000

10000 6000

8000 4000 6000

4000 2000 2000

0 0 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 50 Pi0 Mass (GeV) BaBar analysis tools Efficiency: pi0VeryLoose Relative Efficiency: pi0VeryLoose 1.1 1.2

1.05 1.15

1 1.1

0.95 1.05

0.9 1

0.85 0.95

0.8 0.9

0.75 0.85

0.7 0.8 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Pi0 Momentum (GeV) Pi0 Momentum (GeV) Figure 3.5: π0 efficiency Figure 23: For pi0V eryLoose list, data (black) and MC (blue): a. π0 mass; b. π0 momentum; 0 0 c.0 π yield after pi0V eryLoose / π yield before pi0V eryLoose selection; d. Relative eﬃciencies, 3.4.5.1 KS reconstruction data/MC. 0 + − In my analysis, neutral kaons are reconstructed only through decay KS→π π (branching fraction of 68.95%[1]). The selector used combines two opposite charged tracks from the tracks 0 list and applies on the KS candidatePi0 Mass : pi0DefaultMass the following Cuts criteria: Pi0 Momentum : pi0DefaultMass Cuts

16000 9000 · 300 GeV < mπ+π− < 700 GeV 14000 8000 7000 · Tracks are ﬁtted with12000 a geometric constraint 6000 100000 [1] · mπ+π− of the ﬁtted KS candidate must be within ±7 MeV from the5000 PDG value 8000 4000 6000 3000 4000 2000 3.4.5.2 π0 identification 2000 1000

0 0 0 0 0.05 0.1 0.15 0.2 0.25 0 [1] 1 2 3 4 5 6 π is reconstructed only into γγ decays (the branching ratioPi0 Mass is (GeV) 98.792 ± 0.032% ). Apart from the photon criteria described in the previous section, the following additional conditions Efficiency: pi0DefaultMass Relative Efficiency: pi0DefaultMass must be satisﬁed: 1.1 1.2

1.05 1.15 · Eπ0 > 200 MeV 1 1.1 · 115 MeV < mπ0 < 150 MeV 0.95 1.05

0.9 1 Finally a mass constraint is applied. Momenta and angles are calculated as if the photons were originated from the primary0.85 vertex. 0.95 0.8 0.9 The selection eﬃciency with these criteria is shown in Figure 3.5. 0.75 0.85

0.7 0.8 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Pi0 Momentum (GeV) Pi0 Momentum (GeV)

Figure 24: For pi0DefaultMass list, data (black) and MC (blue): a. π0 mass; b. π0 momentum; c. π0 yield after pi0DefaultMass / π0 yield before pi0DefaultMass selection; d. Relative eﬃciencies, data/MC. Chapter 4 Reconstruction of the ± ± process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

± ± his analysis searches for the production of hc state in the decay B →hcK with hc→ηcγ and ηc→hadrons. Compared to the direct hadronic decay of hc this method has some T advantages:

· The ηc hadronic decays are well-known

· The ηc mass and the γ direction can be used to reject backgrounds

and the expected branching ratio around 50% for the radiative decay hc→ηcγ mitigates the ± ± disadvantage of having one more decay. Finally, the B →hcK branching ratio is expected ± ± to be almost the same as for B →χc 0K . Due to the high backgrounds, no efforts have been spent yet for an analogous analysis for B0 mesons, even if the analysis tools are available. ± ± This analysis has been performed blind. The decay channel B →χc 1K with χc 1→J/ψγ, and J/ψ→hadrons was used as unblind control sample. The blind analysis is a technique used to hide the signal region of the data sample until the analysis has been optimised and all the problems have been fixed. A false signal could be enhanced if the selection criteria are made to do so intentionally. By not looking at the signal region, this blind procedure reduces the risk of any such bias introduced while tuning the analysis parameters. The signal region is unblinded only at the end, when the analysis has been finalized. The number of expected events, assuming 100% of efficiency, for Run 1–4 luminosity (210.487 fb−1) is shown in Table 4.2.

51 ± ± 52 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

` ± ±´ −4 BR B →hcK (2.7 ± 0.7) ·10 theoretical, from BaBar ` ± ±´[64] BR B →χc 0K BR (hc→ηcγ) 50% theoretical ` + + − −´ BR ηc→π π π π (1.20 ± 0.030) % ` + − + −´ BR ηc→π π K K (1.5 ± 0.6) % ` ± ∓ 0 ´ 0 + − BR ηc→π K KS (1.31 ± 0.37) % with KS→π π ` + − ´ BR ηc→π π p¯p < 1.2% 90% C.L. ` + + − −´ + − BR ηc→K K K K (0.35 ± 0.10) % including φ→K K decays ` + + 0´ 0 BR ηc→K K π (0.94 ± 0.26) % with π →γγ ` ± ±´ −4 BR B →χc 1K (6.8 ± 1.2) ·10 BR (χc 1→J/ψγ) (31.6 ± 3.3) % BR `J/ψ→π+π+π−π−´ (0.40 ± 0.10) % BR `J/ψ→π+π+π0´ (1.50 ± 0.20) % BR `J/ψ→π+π−K+K−´ (0.72 ± 0.23) % ` ± ∓ 0 ´ −3 0 + − BR J/ψ→π K KS (1.40 ± 0.22) ·10 with KS→π π BR `J/ψ→π+π−p¯p´ (0.60 ± 0.05) % BR `J/ψ→K+K+K−K−´ (1.68 ± 0.35) ·10−3 including φ→K+K− decays BR `J/ψ→K+K+π0´ (1.00 ± 0.16) ·10−3 with π0→γγ

Table 4.1: Decay rates relevant for this analysis. If it is not differently stated, the branching ratios are taken from PDG 2004[1].

4.1 Data sample The data sample used for my analysis consists of the data collected by BaBar since October 1999 up to June 2004. This corresponds to a total luminosity of 210.487 fb−1 taken at the Υ(4S) mass and 21.587 fb−1 taken 40 MeV below the resonance peak. In addition to real data events, the analysis uses Monte Carlo generated events are used to simulate expected signal and generic backgrounds events. Selection criteria are tuned on the simulated data considering the rejection power of the backgrounds and the ﬁnal selection eﬃciency. Generic Monte Carlo events are used to simulate the backgrounds (the equivalent luminosities are summarized in Table 4.3). Paragraph 3.1 gives a detailed description of the tools used to generate Monte Carlo events. Monte Carlo signal consists of about 20.000 events for each channel of interest. The exact number of events available for each channel is summarized in Table 4.4. When the angular

Expected events with ε = 100% ηc J/ψ π+π+π−π− 358 190 π+π+π0 — 712 π+π−K+K− 448 342 ± ∓ 0 π K KS 391 66 π+π−p¯p < 358 285 K+K+K−K− 104 80 K+K+π0 280 47

Table 4.2: Expected events for 210.487 fb−1 using branching ratios from Table 4.1 4.2 Semi–exclusive algorithm 53

On–peak data 210.487 fb−1 Oﬀ–peak data 21.587 fb−1 B±B∓ generic Monte Carlo 1166 fb−1 B0B¯ 0 generic Monte Carlo 1120 fb−1 uu¯, dd¯ and ss¯ generic Monte Carlo 179 fb−1 cc¯ generic Monte Carlo 164 fb−1

Table 4.3: Data and Monte Carlo luminosities. distributions of the decays were not available, phase-space-only distributions were assumed. Monte Carlo B candidates are properly weighted in order to reproduce the data luminosity. The overall correction factor can be written in the following way:

n TracksY w = wLuminosity × wi (4.1) i = 1

where wLuminosity is the rescaling factor to adapt all Monte Carlo datasets to the data luminosity (LData/LMontecarlo category). For generic Monte Carlo Signal events ηc J/ψ + + − − categories the luminosity is NMontecarlo category/ π π π π 18789 20747 + + 0 /σMontecarlo category, while for the signal categories it π π π 21819 + − + − is NSignal/(2×σB+B− ×Branching ratio). The branch- π π K K 19631 21874 ± ∓ 0 ing ratios are the ones reported in Table 4.1. π K KS 19887 22501 π+π−p¯p 22652 w is the correction factor due to the discrepan- i K+K+K−K− 20604 cies between data and Monte Carlo on the track re- K+K+π0 20520 22952 construction eﬃciency εi, Data/εi, MC. The correction factor is a function of the direction and momentum of the track. An example of correction factor distribution Table 4.4: Events used to simulate the signal (private SP6 production). is shown in Figure 4.1.

4.2 Semi–exclusive algorithm A generic reconstruction technique, named semi-exclusive, has been developed in order to account the large number of hadronic final states of (c¯c)L. The algorithm uses three lists of particles as input: a list of charged hadron candidates (π±s, K±s, and protons), a list of neutral hadron candidates (π0s and K0s) and a list containing seeds particles. Seeds are fictitious particle candidates and are the combination of a photon candidate with a charged kaon candidate. The photon is the candidate for the ra- ± ± diative decay (c¯c)H→(c¯c)Lγ and the kaon is the candidate of the decay B →(c¯c)HK . Each seed carries information about the photon and kaon that generated it and has a momentum that is the sum of the two candidates momenta. Selection criteria of particles candidates are reported in Table 4.5. Seeds are required to have a kinematics compatible with the decay of B± in a charmonium state. More in detail if X±→γK± is one of these fictitious particles, it must exists a ± ± 54 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

QnTracks Figure 4.1: Typical i = 1 wi correction factor distribution.

charmonium state (c¯c)L chosen between J/ψ and ηc and a charmonium state (c¯c)H chosen between ψ(2S), hc, χc 0, χc 1, χc 2 and ηc(2S) such as

± ± ν B →(c¯c)HK < 2

|ν ((c¯c)H→(c¯c)Lγ)| < 3 (4.2) ± ± ν B →(c¯c)LX < 3 where γ(E(cms) − m ) + E ν (1→2 3) = 2 1 3 (4.3) (cms) γ β p2

p 2 (cms) (cms) with γ = E1/m1, β = 1 − 1/γ and E2 and p2 obtained from kinematics con- strains using the three masses. ν is expected to lie between -1 and 1, neglecting the detector resolution. ν computation does not require knowing the energy or momentum of particle 2. ± ± ± The masses used are the nominal masses for B ,K , (c¯c)H and (c¯c)L, while the X mass ± ± is computed from K and γ momenta. B energy is half of the beams energy and (c¯c)H energy is computed as EB± − EK± . Instead charged hadrons are combined into pairs (V 0) and groups of four tracks with total 0 0 0 ± charge 0 (W ). Possible overlaps of V with KS candidates are removed. B candidates are generated using a seed candidate that have passed the ν conditions and then adding V 0s W 0s and neutral hadrons with the following criteria:

· If the intermediate candidate has −200 MeV < ∆E < 65 MeV and mES > 5.18 GeV then it is kept as B± candidate and can be also used as seed in further iterations. 4.2 Semi–exclusive algorithm 55

Hadronic π± Charged tracks with: ± Seed K · Momentum < 10 GeV Charged tracks with a likelihood based selector for kaons · d0 < 1.5 cm

· −10 cm < z0 < 10 cm Seed photon and not identiﬁed as e±, µ±, π± Photon candidates with and K± · E > 30 MeV Hadronic π0 · LAT < 0.8 Details given in Para- graph 3.4.5.2 Seed ± Combination of a K± and a pho- Hadronic K ton with Charged tracks with a neural network based selector for kaons · Cuts on ν variables (see

Equation (4.2)) 0 Hadronic KS · Momentum that is the ± Details given in Para- sum of the photon and K graph 3.4.5.1 momenta

Hadronic proton Charged tracks with a likelihood based selector for protons

Table 4.5: Particle selection criteria.

· If the intermediate candidate has ∆E > 65 MeV and mES > 5.18 GeV then it is kept as B± candidate, but no further iterations as seed candidate are possible as adding another particle would cause to have ∆E > 65 MeV + mπ0 ∼ 200 MeV.

· If the intermediate candidate has ∆E > 65 MeV and mES < 5.18 GeV then it cannot be used either as seed or as B± candidate. · In the other cases the candidate is considered as seed but not as B± candidate. See Figure 4.2 for further details.

The variables used in the algorithm are:

s 2 (s/2 + ~p0 · ~p) mES = 2 − |~p| (4.4) E0 √ s ∆E = E? − (4.5) 2 ± ± 56 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

∆ E Rejected B candidate 200 MeV candidates only 65 MeV 0 MeV B candidate −200 MeV Seed only and seed

5.18 GeV M ES

Figure 4.2: Zones that defines if intermediate candidates are seeds or B± candidates.

where (E,~p) is the B candidate momentum, (E0, ~p0) is the Υ(4S) momentum as s is the squared centre of mass energy. Finally the superscript ? is used to distinguish the variables evaluated in the centre of mass frame from the ones evaluated in the laboratory frame. B candidates with hadronic decays diﬀerent from the ones interesting for my analysis purposes are discarded. Once obtained the list of possible B± candidates, the decay tree is completely rearranged.

First of all the hadrons (that makes (c¯c)L candidate) are constrained with a geometric ﬁt, requiring that all tracks pass from a common point. Then the photon is added to the (c¯c)L ± requiring again a geometric constraint. Finally the K is added to the (c¯c)H and again the geometric constraint is applied to the rebuilt B± candidate. In the B±→h K± analysis the B mesons must have 2.922 GeV < m < 3.038 GeV, c (c¯c)L while in the B±→χ K± analysis the B mesons must have 3.038 GeV < m < 3.154 GeV. c 1 (c¯c)L

4.3 Events preselection

Eﬃciencies ηc J/ψ π+π+π−π− 19.5 ± 0.3% 22.6 ± 0.3% π+π+π0 — 17.5 ± 0.3% π+π−K+K− 11.3 ± 0.2% 13.7 ± 0.2% ± ∓ 0 π K KS 15.3 ± 0.3% 18.1 ± 0.3% π+π−p¯p — 13.5 ± 0.2% K+K+K−K− 5.7 ± 0.2% — K+K+π0 9.3 ± 0.2% 11.2 ± 0.2%

Table 4.6: Efficiency of the semi-exclusive reconstruction with BCMultiHadron and best B criteria on Monte Carlo signal. 4.4 Best B selection 57

BCMultiHadron

· At least 3 charged tracks with 23.5◦ < ◦ ϑLab < 145.5

· R2, deﬁned in Equation (4.9) must be < 0.5

· ETot > 4.5 GeV · Primary vertex with z < 6 mm · Primary vertex with r < 0.5 mm

Table 4.7: BCMultiHadron selection criteria.

In order to avoid processing all the events recorded by BaBar, the semi-exclusive algorithm is applied only on a subset of events called BCMultiHadron. This subset is about 23% of the data recorded by BaBar and has about 98% of eﬃciency on the signal. A summary of the cuts applied in the BCMultiHadron selection is shown in Table 4.7 The overall eﬃciency of the semi-exclusive algorithm and BCMultiHadron condition is shown in Table 4.6 for each channel of interest.

4.4 Best B selection

BaBar analyses are divided into several steps. Each step takes as input a collection of events and tightens the signal selection criteria. The first step is the BCMultiHadron condition followed by the semi-exclusive reconstruction algorithm. After these steps the analysis can be run with standard physics analysis packages like root and paw. However processing time is still J/ψ Channel ηSignal ηBackground too long. The third selection criteria consist in π+π+π−π− 90.1% 76.5% the choice of the best B candidate. This means π+π+π0 93.6% 87.4% that for each event that has more than one π+π−K+K− 88.2% 81.4% ± ∓ 0 B candidate obtained with the semi-exclusive π K KS 92.5% 87.4% algorithm, only one of them is kept, while the π+π−p¯p 87.7% 85.4% other candidates are discarded. The criterion used to choose the best B can- Table 4.8: η variable defined in Equation (4.6). The table reppresents the efficiency loss on didate is based on ∆E variable: the candidate Monte Carlo signal and backgrounds due to kept is the one with the smaller |∆E|. the application of the best B criterion before ± ± a standard set of cuts for B → χc 1 K with Usually the best B selection is performed χc 1 → J/ψ γ hadronic channels as last step of the cut based selection, before performing the final fit. However for this analysis it was decided to perform the best B at the beginning to sensibly reduce the huge computing time. ± ± 58 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

Table 4.8 summarizes the eﬃciency loss. The variable reported is the ratio between the number of events passing the selection applying as ﬁrst step the best B selection and then a generic cut based selection and the number of events passing the selection the previous two steps are swapped: N (Best B + Cuts) η = (4.6) N (Cuts + Best B)

η variable is calculated on Monte Carlo signal and Monte Carlo backgrounds for all the interesting J/ψ decays applying a generic standard cut selection, but the one obtained from next chapter optimisation.

4.5 Background types

Backgrounds surviving the previous selection steps can be roughly subdivided into the following categories. · Continuum (e+e−→(q¯q)) events. They are expected to have diﬀerent shape from the signal in the ∆E, m and m distributions. Moreover light quark events are ES (c¯c)L, H expected to have a two-jets topology, while BB¯ events have a mainly spherical shape, due to the fact that B mesons have low momenta.

· Peaking background, which behaves similar to the signal in the ∆E–mES region, but differently in the m distributions. This background is mainly due to B decays in (c¯c)L, H which the final states are the same of the signal. · Combinatorial events, which comes from signal events where the chosen B candidate has a wrong combination of final states.

The number of events surviving the semi-exclusive reconstruction and the BCMultiHadron condition evaluated on Monte Carlo events are listed in Table 4.9. In this analysis the techniques used to reduce these kind of background are mainly statistical methods and at the end the residual contamination is evaluated with a ﬁt.

Eﬃciencies ηc J/ψ π+π+π−π− 4401937 4593816 π+π+π0 — 4449562 π+π−K+K− 1416887 1540457 ± ∓ 0 π K KS 522305 545798 π+π−p¯p — 1043753 K+K+K−K− 15421 — K+K+π0 458648 458648

Table 4.9: Monte Carlo background events surviving the semi-exclusive reconstruction with BCMultiHadron and best B criteria. 4.6 Analysis approach 59 4.6 Analysis approach The strategy used for my analysis is the following: 1. Events passing the BCMultiHadron condition are considered 2. The semi-exclusive algorithm is applied 3. Best B is chosen on best ∆E basis 4. Kinematics variables cuts are optimised semi-automatically with an iterative process. m and m are not considered in the optimisation process and are treated with a ES (c¯c)H loose cut 5. Cuts are applied following the optimisation results 6. The residual background is studied on the Monte Carlo events 7. A bidimensional unbinned maximum likelihood ﬁt is performed in the m –m ES (c¯c)H plane. Due to the high backgrounds and to the low number of signal events expected, for simplicity, the analysis on the control sample (χc 1) has been performed unblind. Experience and tools developed have been used for a similar blind analysis of the hc state.

4.7 Kinematics variables used in the selection

4.7.1 Plots notation Plots presented in the following paregraphs (for example, Figure 4.6) share the same colour scheme. Backgrounds (u¯u,dd¯ and s¯s;c¯c;B±B∓;B0B¯ 0; combinatorial) are represented with piled up solid histograms with diﬀerent violet shades. Signal is piled up with solid cyan, but if it is negligible compared with backgrounds it is rescaled and is plotted overlapped to the backgrounds. Finally data events are represented with black stars overlapped to the other categories. On the right of each plot there is a short summary of statistical quantities related to each category (mean, standard deviation, number of events below and over the histogram window, number of events in the histogram window and total number of events). . The graph on the bottom shows for each histogram bin the following quantity:

PNMonte Carlo NData − i=1 wi q (4.7) PNMonte Carlo 2 NData + i=1 wi where the sum runs on all the Monte Carlo events (signal and background) and wi is the weight of each event. That graph shows the discrepancy between Data and Monte Carlo measured in number of standard deviations for each bin. ± ± 60 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

4.7.2 Continuum background rejection: the fisher discriminant

The idea to reduce continuum backgrounds is the different topology that B meson decays (spherical) have from the light quark decays (two jets topology) in the centre of mass frame. There are several variables that could be used for this purpose and obviously there is a correlation between all of them (Figure 5.2) The variable with the highest discrimination power is chosen using the Fisher method. P i i The Fisher variable (F 0 is a non-homogeneous linear combination F = i α v + β of the following vi variables: · Polar angle of the B candidate in the Υ(4S) rest frame. As the Υ(4S)→BB¯ is devay 2 with angular momentum L = 1, the B angular distribution is sin ϑB for the signal. · Cosine of the angle between the reconstructed B candidate and the event thrust in the Υ(4S) rest frame. The event thrust is defined as the direction Tˆ that maximizes the variable T defined as:

P ˆ i T · pî T = P (4.8) i |pî| where index i runs only on the reconstructed charged tracks. Due to the fact that B mesons have spherical shape, the average value of T is 0.5 and no particular direction Tˆ is preferred. For this reason, signal distribution is flat. On the other hand backgrounds events have a defined direction (T ∼ 1) and tracks used to reconstruct the B candidate lie on this direction. For this reason, the variable has a distribution peaked at 1. · Cosine of the thrust polar angle.

Figure 4.3: Typical distributions of a variable used in the Fisher: the polar angle of the B candidate. It is shown with the only BCMultiHadron condition set. 4.7 Kinematics variables used in the selection 61

Figure 4.4: Typical distributions of the variables used in the Fisher: the cosine of the angle between the reconstructed B candidate and the event thrust (top), the cosine of the thrust polar angle (bottom). These variables are shown with the only BCMultiHadron condition set. ± ± 62 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

Figure 4.5: Typical distributions of the variables used in the Fisher: the second order Fox Wolfram momentum normalized (top) and the magnitude of the event thrust (bottom). These variables are shown with the only BCMultiHadron condition set. This condition has a cut on R2 computed with charged tracks only (see Table 4.7) that affects the variables distribution. 4.7 Kinematics variables used in the selection 63

· Second order Fox Wolfram momentum normalized and computed with both charged and neutral tracks. It is deﬁned as

P 2 i j |~pi||~pj| 3 cos ϑi j − 1 R2 = P (4.9) 2 i j |~pi||~pj|

R2 spreads from 0 (spherical events) to 1 (two-jets events). · Magnitude of the event thrust T computed with both charged tracks and neutral clusters.

Figures 4.3, 4.4 and 4.5 show the typical distributions of each one of these variables. The Fisher combination maximizes the separation of Monte Carlo signal and background (B±B∓,B0B¯ 0, u¯u, dd,¯ s¯sand c¯cgeneric) distributions:

2 F¯ − F¯ S B (4.10) σ2 + σ2 FS FB

This constraint leaves some degrees of freedom: if F is a solution, then aF +b is a solution too. These degrees of freedom are constrained requiring F¯S = 1 and F¯B = −1. i i 2 i j 2 i j Indicating withx ¯S,x ¯B the variables mean and with σS , σB the covariance matrixes

Figure 4.6: Typical Fisher distribution. ± ± 64 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ respectively on signal and backgrounds distributions, it follows that

i i 2γ α = (4.11) P j j j j γ x¯S − x¯B X i i β = 1 − α x¯S (4.12) i with i j i X j j 2 2 −1 γ = x¯S − x¯B σS + σB (4.13) j

A typical distribution of the Fisher variable is presented in Figure 4.6.

4.7.3 Veto variables

B decays that have final states similar to the signal ones but that have larger branching fractions can be especially dangerous. As a real B is reconstructed, the background peaks in the ∆E–m distribution (peaking background) and even if the distribution in m is ES (c¯c)L, H different, the signal could be contaminated due to the larger decay rate. For this reason, B candidates that have final states in common with other particles are explicitly rejected. · If the photon of the radiative decay combined with any other photon has the π0 mass, the B candidate is reject · If the K± either of the B decay or of the hadronic decay combined with a π∓ has the D0 mass, the B candidate is reject · If the K± of the B decay with another K∓ has the φ mass, the B candidate is reject, but if the two kaons are both from the hadronic decay the B± candidate is kept. · If the π± of the hadronic decay combined with a K∓ has the D0 mass, the B candidate is reject

Photons K± Photon candidates with Charged tracks with a likelihood · E > 30 MeV based selector for kaons · LAT < 1.1 Hadronic π0 ◦ ◦ · 23.5 < ϑLab < 138 Charged tracks not identiﬁed as e±, µ±, π± and K±

Table 4.10: Selection criteria applied to the particle outside the B decay tree used in the veto algorithm. 4.7 Kinematics variables used in the selection 65

Figure 4.7: π0 and φ veto distributions. ± ± 66 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

Figure 4.8: D0 veto distributions using a π± of the hadronic decay (top) and a K± either of the hadronic decay or of the B decay (bottom). 4.7 Kinematics variables used in the selection 67

Figure 4.9: Typical veto variable distribution.

Conditions satisfied by photons and tracks used in the combination are listed in Table 4.10. For each one of these 4 categories, histograms of the invariant mass are generated (all the possible combination are accumulated for each B candidate). Then through a fit the mean and standard deviation are obtained for each one of these 4 categories. Finally for each B candidate, the variables vi are defined: ( ) xj − x¯ i i vi = Min (4.14) σi where i runs on the four categories and j runs of all the possible combinations.

In other words vi represent the distance of the best combination of two photons or two 0 0 tracks from the π ,D or φ mass (mass that is measured on data). The cut applied on vi must reject B candidates with vi near zero. The definition of this variable is essential in order to optimise the cuts on the veto using the optimisation algorithm described in the next chapter. The fits obtained are shown in Figures 4.7 and 4.8. In light violet are accumulated events with the particle to be vetoed present once or more in the Monte Carlo decay tree, while in dark violet are accumulated the remaining events. The green box on the right shows the fit results. An example of the typical shape of the variable used in the optimisation is shown in Figure 4.9. ± ± 68 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ

4.7.4 Particle identification variables The charged hadrons of the hadronic decay have rather tight selection criteria. For this reason they are not considered in the optimisation process. The only charged track whose selection criteria could be tightened is the K± of the B decay. For charged tracks, particle identification criteria are represented with several bits that are set to 1 when a particular filter is satisfied by the track. These bits are not mutually exclusive, however fixed the particle hypothesis and the algorithm used (cut based, neural network or likelihood), the criteria can be sorted by their tightness. For K± likelihood based criteria the bits are named NotPion, VeryLoose, Loose, Tight and VeryTight. The variable used for the optimisation process is a discrete variable that is set to 6 if VeryTight bit is set, 5 if the previous bit is not set, but the Tight is instead set, and so on till 2 if the only NotPion bit is set. This bit is always set due to the fact that K±s of the B decay are selected using this criterion. 0 0 For neutral hadrons (KS and π ) the variables used for the optimisation process are the particle mass and the fit probability of the geometric constraint. Finally for the photon the variables considered in the optimisation process are the number [63] of associated EMC crystals, the lateral momentum LAT and the Zernike momentum A4, 2 defined as: E r X i i −imφi An, m = fm, n e (4.15) EMis R0 ri

This variable is a measurement of the shower shape and allows discriminating hadronic showers (more irregular) from the electromagnetic ones.

4.7.5 Vertex fit variables The geometric constraint on the decay vertices gives in output the vertex ﬁt probabilities. In ± ± the optimisation process, the probabilities on the (c¯c)L→hadrons and B →(c¯c)HK vertices are used. These variables should be equally distributed between 0 and 1 for the signal and have a peak at 0 for the background.

4.7.6 Kinematics variables

The kinematics variables used in the analysis are ∆E defined in (4.5), mES defined in (4.4), the mass of the heavy charmonium state and the mass of the light charmonium state. Of these variables, ∆E has been used for the best B selection criterion and it cannot used in a fit has both signal and backgrounds have a peak in 0. Only a cut can be applied on it and is inserted between the variables considered in the optimisation process. mES and the heavy-charmonium are used for the fit: no cuts are applied on them. Finally the light charmonium mass is optimised too. 4.7 Kinematics variables used in the selection 69

Other kinematics variables considered in the optimisation process are the ν variables, ± ± deﬁned in (4.2) and (4.3), but only ν B →(c¯c)LX is used as the other two variables need to know the heavy charmonium mass and for hc this mass is not known. Another variable used in the optimisation process is the cosine of the direction of the photon relative to the direction of the kaon in the light charmonium rest frame.

This variable has a diﬀerent distribution for J/ψ and ηc decays. The distributions can ± ± be explained in the following way. Consider the B decay into (c¯c)H and K : the total angular momentum must be conserved. This means ~l + ~j = 0. As ~l · ~p = 0 (with ~p (c¯c)H ± the K momentum), it follows that in the (c¯c)H rest frame (c¯c)H spin is orthogonal to the ~p direction or j = 0. pˆK± At the same way, considering the (c¯c) decay into (c¯c) and γ, it follows that ~j = H L (c¯c)H ~l +~j +~j and then j = j +~j . (c¯c)L γ (c¯c)H, pˆγ (c¯c)L, pˆγ γ, pˆγ ~ As jγ, pˆγ can only be ±1, and ηc has spin 0, it follows that jhc, pˆγ = ±1. 2 The quantity j = 0 j = ±1 = 1 sin2 ϑ . It follows that the dis- hc, pˆK± hc, pˆγ 2 pˆK± , pˆγ tribution of the cos ϑ is ∝ 1 − cos2 ϑ. The J/ψ case is rather more complex. The allowed combinations are:

jχc 1, pˆγ jJ/ψ, pˆγ 0 +1 0 −1 +1 0 −1 0

Using the Clebsch-Gordan coeﬃcients it can be demonstrated that all the cases have the same probability. 2 Finally j = 0 j = 0 = cos2 ϑ . It follows that the distribution of hc, pˆK± hc, pˆγ pˆK± , pˆγ the cos ϑ is ∝ 1 + cos2 ϑ. The experimental distribution of the backgrounds is almost ﬂat with a peak at cos2 ϑ near 1. ± ± 70 Reconstruction of the process B → (c¯c)H K with (c¯c)H → (c¯c)L γ Chapter 5 Cuts optimisation

uts to apply on the discriminating variables described in the previous chapter are optimised with an algorithm that maximises a function of the signal S and of the back- C ground B. √ √ Typical functions√ are S/B, S/ S + B and S/ B ratios. Usually the optimisation is maximised using S/ S + B function, that means maximise the expected signal compared to ± ± the expected data fluctuations. However√ due to the fact that B → hc K and hc → ηc γ branching fractions are unknown, the S/ B ratio is preferred. This ratio means maximize the expected signal compared with the background fluctuations and is the correct criterion if I would√ demonstrate the absence of hc signal: in that case the expected data fluctuation would be B only.

5.1 Optimisation procedure Starting from a reasonable loose cuts configuration, all the cut conditions has been examined one by one choosing√ each time (without the help of an automated algorithm) the cut threshold that maximizes S/ B and at the same time does not disadvantage the efficiency. This choice is based on graphs that show the integral of the signal, of the background and eventually of the data as a function of the cut under study when all the other cuts are applied with the current optimised values. √ On these graphs S/√ B is also plotted so it is√ possible to directly compare the loss of efficiency with the S/ B gain. On these plots S/ B errors have been propagated in order to consider during the optimisation process at least the errors due to the limited simulated events statistics.

The previous process is iterated more than once on all discriminating variables√ until a stable condition has been reached. Cuts that do not bring a significant gain on S/ B are not applied, but are still considered in the next optimisation iterations. For each iteration, the Fisher linear combination is optimised too, applying all the other cuts. In that way the Fisher rejection power is always maximized. As the analysis is finalized accumulating together all the significant hadronic decays and then applying a bidimensional fit on m –m , these two variables are not considered in (c¯c)H ES

71 72 Cuts optimisation the iterative optimisation process and a ﬁxed very loose selection cut (with ∼ 100% of signal eﬃciency) is applied to m (5.269 < m < 5.289). No selections are applied on m , ES ES (c¯c)H as the hc mass in not known. Figure 5.1 shows the mES distribution as it appears for the J/ψ → π+ π− π0 with the BCMultiHadron and best B selections only.

The next paragraphs shortly describes how the cuts on mES aﬀect the optimisation process and if it is possible to accumulate separately optimised hadronic channels without loosing the optimisation process.

5.1.1 Choice of the cuts on the not optimised variables

Figure 5.2 shows the cross-correlation between the selection variables for signal, background and data. hvivjiS − hviiS hvjiS Cross-correlationi, j = q q (5.1) hv2i − hv i2 v2 − hv i2 i S i S j S j S where S is the signal distribution and could be replaced with the background or data ones.

As it is demonstrated in Figure 5.2, mES variable is uncorrelated with any other variable used in the optimisation. It is easy to demonstrate that if two sets of variables ~x and ~y are uncorrelated, then their optimisation is completely independent.

± ± + − Figure 5.1: mES distribution for B →χc 1K with χc 1→J/ψγ and J/ψ→π π pp¯ decay before any cut applied. 5.2 Optimisation results 73

The total signal S is the integral Z Z S (~cx,~cy) = s (~x,~y) d~xd~y (5.2) Γ~cx Γ~cy where ~cx, y are the choice of cuts respectively for the sets of variables ~x and ~y, and s(~x,~y) is the signal distribution. If ~x and ~y are uncorrelated then s(~x,~y) = sx(~x)sy(~y) and then Z Z S (~cx,~cy) = sx (~x) d~x × sy (~y) d~y = Sx (~cx) × Sy (~cy) (5.3) Γ~cx Γ~cy

Then follows that S Sx Sy √ = √ × p (5.4) B Bx By

When the ~cy set of cuts is optimised

∂ S ∂ Sy √ = 0 ⇐⇒ p = 0 (5.5) ∂~cy B ∂~cy By

So whatever is the ﬁxed set of cuts ~cx, the same result is always obtained. In my analysis mES is uncorrelated with all the other selection variables and for this reason whatever is the cut chosen on mES, I obtain the same optimisation result.

5.2 Optimisation results In the next pages optimisation results are shown for all the channels under study. ± ± However only B → χc 1 K with χc 1 → J/ψ γ and J/ψ → π+ π− p ¯p plots are shown. All the analysis optimisation plots are available in Appendix .

Figure 5.2: Cross-correlation between variables considered during the optimisation process for signal (left), background (right) and data (top). The first five variables are the ones used in ± ± the Fisher linear combination. These results are relative to the B → χc 1 K with χc 1 → J/ψ γ and J/ψ → π+ π− p ¯p decay. 74 Cuts optimisation

± ± 5.2.1 B → χc 1 K with χc 1 → J/ψ γ

5.2.1.1 J/ψ → π+ π− π+ π− Variables Cuts Fisher > 0.50 Veto π0 — Veto φ — Veto D0 — ∆E > −30 MeV < 20 MeV Prob (B fit) > 0.001 mJ/ψ > 3.085 GeV < 3.105 GeV Prob (J/ψ fit) > 0.0001 Number of crystals hit by the γ ≥ 7 γ lateral momentum — γ Zernike momentum (4, 2) — γ Direction relative to K± in the J/ψ frame — |νMissing| — K± identification ≥ 4 (at least Loose) Signal (11.4 ± 0.3) Background (1086 ± 33) Data 1207 ε √ (6.3 ± 0.16) % S/ B (0.345 ± 0.011) S/B (10.5 ± 0.4) ·10−3

5.2.1.2 J/ψ → π+ π− π0 Variables Cuts Fisher > 0.60 Veto π0 > 1.5 Veto φ — Veto D0 — ∆E > −50 MeV < 20 MeV Prob (B ﬁt) > 0.001 mJ/ψ > 3.065 GeV < 3.110 GeV Prob (J/ψ ﬁt) > 0.0001

mπ0 — Prob `π0 ﬁt´ — Number of crystals hit by the γ ≥ 7 γ lateral momentum — γ Zernike momentum (4, 2) — γ Direction relative to K± in the J/ψ frame — |νMissing| — K± identiﬁcation ≥ 4 (at least Loose) Signal (20.8 ± 0.8) Background (585 ± 24) Data 641 ε √ (3.08 ± 0.11) % S/ B (0.86 ± 0.03) S/B (35 ± 2) ·10−3 5.2 Optimisation results 75

5.2.1.3 J/ψ → π+ π− K+ K−

Variables Cuts Fisher > 0.00 Veto π0 — Veto φ — Veto D0 — ∆E > −40 MeV < 20 MeV Prob (B fit) > 0.001 mJ/ψ > 3.085 GeV < 3.110 GeV Prob (J/ψ fit) > 0.0001 Number of crystals hit by the γ ≥ 7 γ lateral momentum — γ Zernike momentum (4, 2) — γ Direction relative to K± in the J/ψ frame — |νMissing| — K± identification ≥ 4 (at least Loose) Signal (14.6 ± 0.4) Background (647 ± 25) Data 524 ε √ (4.49 ± 0.14) % S/ B (0.57 ± 0.02) S/B (22.5 ± 1.1) ·10−3

5.2.1.4 J/ψ → π+ π− p ¯p Plots presented (for example, Figure 5.3) share the same colour scheme. Backgrounds (u¯u, ¯ ± ∓ 0 ¯ 0 dd and s¯s; c¯c;B B ;B√ B ; combinatorial) are represented in violet; signal is in cyan√ and data in black. The S/ B is plotted in green. The left y axis and the grid refer to the S/ B values while the axis on the right side refers to the signal efficiency. Variables Cuts Fisher > 0.60 Veto π0 — Veto φ — Veto D0 — ∆E > −40 MeV < 20 MeV Prob (B fit) > 0.0001 mJ/ψ > 3.090 GeV < 3.105 GeV Prob (J/ψ fit) > 0.0001 Number of crystals hit by the γ ≥ 6 γ lateral momentum — γ Zernike momentum (4, 2) — γ Direction relative to K± in the J/ψ frame — |νMissing| — K± identification ≥ 3 (at least VeryLoose) Signal (11.6 ± 0.4) Background (79 ± 9) Data 67 ε √ (4.27 ± 0.13) % S/ B (1.30 ± 0.08) S/B (0.15 ± 0.02) 76 Cuts optimisation

± ± + − Figure 5.3: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π p p¯ variables optimisation 5.2 Optimisation results 77

± ± + − Figure 5.4: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π p p¯ variables optimisation 78 Cuts optimisation

± ± + − Figure 5.5: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π p p¯ variables optimisation 5.2 Optimisation results 79

± ± + − Figure 5.6: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π p p¯ variables optimisation 80 Cuts optimisation

± ∓ 0 5.2.1.5 J/ψ → π K KS Variables Cuts Fisher > 0.20 Veto π0 — Veto φ — Veto D0 — ∆E > −40 MeV < 20 MeV Prob (B fit) > 0.001 mJ/ψ > 3.085 GeV < 3.110 GeV Prob (J/ψ fit) > 0.0001 m 0 — KS ` 0 ´ Prob KS fit > 0.001 0 KS time of flight — Number of crystals hit by the γ ≥ 6 γ lateral momentum — γ Zernike momentum (4, 2) — γ Direction relative to K± in the J/ψ frame — |νMissing| — K± identification ≥ 4 (at least Loose) Signal (4.43 ± 0.19) Background (172 ± 13) Data 130 ε √ (2.45 ± 0.10) % S/ B (0.34 ± 0.02) S/B (25 ± 2) ·10−3

5.2.1.6 J/ψ → K+ K− π0 Variables Cuts Fisher > 0.50 Veto π0 > 0.50 Veto φ — Veto D0 — ∆E > −55 MeV < 25 MeV Prob (B ﬁt) > 0.001 mJ/ψ > 3.070 GeV < 3.115 GeV Prob (J/ψ ﬁt) > 0.0001

mπ0 — Prob `π0 ﬁt´ — Number of crystals hit by the γ ≥ 6 γ lateral momentum — γ Zernike momentum (4, 2) — γ Direction relative to K± in the J/ψ frame — |νMissing| — K± identiﬁcation ≥ 3 (at least VeryLoose) Signal (1.53 ± 0.11) Background (165 ± 13) Data 135 ε √ (0.85 ± 0.06) % S/ B (0.119 ± 0.10) S/B (9.3 ± 1.0) ·10−3 5.2 Optimisation results 81

± ± 5.2.2 B → hc K with hc → ηc γ

+ − + − 5.2.2.1 ηc → π π π π

Variables Cuts Fisher > 0.80 Veto π0 — Veto φ — Veto D0 — ∆E > −50 MeV < 30 MeV Prob (B ﬁt) > 0.001

mηc > 2.940 GeV < 3.010 GeV Prob (ηc ﬁt) > 0.0001 Number of crystals hit by the γ ≥ 7 γ lateral momentum < 4 γ Zernike momentum (4, 2) — ± γ Direction relative to K in the ηc frame < 0.8 |νMissing| — K± identiﬁcation ≥ 4 (at least Loose) Signal (17.1 ± 0.7) Background (1104 ± 33) ε √ (4.77 ± 0.15) % S/ B (0.51 ± 0.02) S/B (15.5 ± 0.8) ·10−3

+ − + − 5.2.2.2 ηc → π π K K

Variables Cuts Fisher > 0.50 Veto π0 > 1 Veto φ — Veto D0 — ∆E > −50 MeV < 30 MeV Prob (B ﬁt) > 0.001

mηc > 2.950 GeV < 3.010 GeV Prob (ηc ﬁt) > 0.0001 Number of crystals hit by the γ ≥ 8 γ lateral momentum — γ Zernike momentum (4, 2) — ± γ Direction relative to K in the ηc frame < 0.7 |νMissing| — K± identiﬁcation ≥ 3 (at least VeryLoose) Signal (11.2 ± 0.4) Background (333 ± 18) ε √ (2.51 ± 0.11) % S/ B (0.61 ± 0.03) S/B (34 ± 2) ·10−3 82 Cuts optimisation

± ∓ 0 5.2.2.3 ηc → π K KS

Variables Cuts Fisher > 0.40 Veto π0 > 1 Veto φ — Veto D0 — ∆E > −50 MeV < 30 MeV Prob (B ﬁt) > 0.001

mηc > 2.950 GeV < 3.010 GeV Prob (ηc ﬁt) > 0.0001 Number of crystals hit by the γ ≥ 7 γ lateral momentum — γ Zernike momentum (4, 2) — ± γ Direction relative to K in the ηc frame < 0.7 |νMissing| — K± identiﬁcation ≥ 3 (at least VeryLoose) Signal (16.9 ± 0.6) Background (121 ± 11) ε √ (4.32 ± 0.14) % S/ B (1.53 ± 0.09) S/B (0.140 ± 0.13)

+ − 0 5.2.2.4 ηc → K K π

Variables Cuts Fisher > 0.50 Veto π0 > 1 Veto φ — Veto D0 — ∆E > −50 MeV < 30 MeV Prob (B ﬁt) > 0.001

mηc > 2.950 GeV < 3.010 GeV Prob (ηc ﬁt) > 0.0001 Number of crystals hit by the γ ≥ 8 γ lateral momentum — γ Zernike momentum (4, 2) — ± γ Direction relative to K in the ηc frame < 0.7 |νMissing| — K± identiﬁcation ≥ 3 (at least VeryLoose) Signal (5.9 ± 0.3) Background (87 ± 9) ε √ (2.11 ± 0.10) % S/ B (0.63 ± 0.05) S/B (68 ± 8) ·10−3 5.2 Optimisation results 83

+ − + − 5.2.2.5 ηc → K K K K

Variables Cuts Fisher > 0.0 Veto π0 — Veto φ — Veto D0 — ∆E > −60 MeV < 30 MeV Prob (B ﬁt) > 0.001

mηc > 2.950 GeV < 3.020 GeV Prob (ηc ﬁt) > 0.0001 Number of crystals hit by the γ ≥ 8 γ lateral momentum — γ Zernike momentum (4, 2) — ± γ Direction relative to K in the ηc frame < 0.8 |νMissing| — K± identiﬁcation ≥ 4 (at least Loose) Signal (2.15 ± 0.15) Background (13 ± 4) ε √ (2.10 ± 0.10) % S/ B (0.61 ± 0.09) S/B (0.17 ± 0.05)

5.2.3 Conclusions

Next paragraph presents the branching ratios measurement. Due to the high backgrounds√ of almost all the channels, I have chosen to consider only hadronic decays with S/ B of at least 1. This limits the number of anlysed channels to two:

± ± + − · B → χc 1 K with χc 1 → J/ψ γ and J/ψ → π π p ¯p

± ± ± ∓ 0 · B → hc K with hc → ηc γ and ηc → π K KS 84 Cuts optimisation Chapter 6 Final results

n this chapter, after a brief introduction on the techniques used to extract and set the signal upper limit from data, I present the results I have obtained for the two channels I of interest:

± ± + − · B → χc 1 K with χc 1 → J/ψ γ, and J/ψ → π π p ¯p

± ± ± ∓ 0 · B → hc K with hc → ηc γ, and ηc → π K KS

6.1 Unbinned maximum likelihood fit

A likelihood function L (~p; ~x) is deﬁned as the probability distribution function of an observable X~ evaluated for a measurement ~x, and treated as function of the probability distribution parameters ~p.

Suppose it has been made n measurements ~x1, . . . ~xn of an observable X~ , with probability distribution f (~x|~p) then the likelihood function is L (~p; ~x1, . . . ~xn) = f (~x1|~p) ··· f (~xn|~p). The unbinned maximum likelihood ﬁt, looks for the parameters ~p that maximize the likelihood. It is easy to demonstrate that the parameters ~p obtained with this method approximate the real parameters ~p? in the limit of high statistics. Indeed n X ln L (~p; ~x1, . . . ~xn) = ln f (~xi|~p) (6.1) i=1 and with enough statistics this can be rewritten Z ? ln L (~p; ~x1, . . . ~xn) = n ln f (~x|~p) f (~x|~p ) d~x (6.2)

Then ∂ ln L (~p; ~x , . . . ~x ) Z f (~x|~p?) ∂f (~x|~p) 1 n = n d~x (6.3) ∂~p f (~x|~p) ∂~p

85 86 Final results when ~p = ~p?

? Z ∂ ln L (~p ; ~x1, . . . ~xn) ∂ ∂1 = n f (~x|~p) d~x = n = 0 (6.4) ∂~p ~p=~p? ∂~p ~p=~p? ∂~p ~p=~p?

It could be also demonstrated that the matrix

2 ∂ ln L (~p; ~x1, . . . ~xn) (6.5) ∂pi ∂pj ~p=~p? asymptotically is deﬁnite negative. Using a notation common in several likelihood-based analyses, the plots in this chapter show the negative of the logarithm of the likelihood (NLL = − ln L) in place of the plain likelihood.

6.1.1 Fit quality

To evaluate the quality of the unbinned maximum likelihood fits, I use toy Monte Carlos. This means that if I obtained the parameters ~p from the likelihood fit on n data events, then I use these parameters as input to generate other n events randomly distributed as f (~x|~p). These fake events are fitted with the same maximum likelihood algorithm, and this procedure is iterated on other m experiments. In that way I can obtain the distribution f (NLL) for the NLL variable calculated from an unbinned maximum likelihood fit of n events distributed as f (~x|~p). This distribution can be used to calculate the probability of obtaining a worse fit of the one obtained on data.

Z +∞ Probability (worse ﬁt) = f (NLL) dNLL NLLExp Number of MC experiments with NLL > NLL = Exp (6.6) m

6.1.2 Measure precision and confidence levels

The probability of measuring ~p given ~x1, . . . ~xn (f (~p|~x1, . . . ~xn)) is called conditional probability distribution of the parameters ~p. This probability distribution must be known in order to evaluate the precision on the measurement of the parameters ~p. It can be determined applying the Bayes theorem: f (a&b) = f (a|b) f (b) = f (b|a) f (a).

f (~p) f (~x1, . . . ~xn|~p) f (~p) f (~p|~x1, . . . ~xn) = f (~x1, . . . ~xn|~p) = R (6.7) f (~x1, . . . ~xn) f (~x1, . . . ~xn|~p) f (~p) d~p 6.1 Unbinned maximum likelihood ﬁt 87

Note that f (~x1, . . . ~xn|~p) is the likelihood. Usually f (~p) is not known, and treated as a constant. This choice is rather questionable. I return later in this section on the problem.

L (~p; ~x1, . . . ~xn) f (~p|~x1, . . . ~xn) = R (6.8) L (~p; ~x1, . . . ~xn)d~p

The values of ~p that have the highest probability are the ones obtained form the maximum likelihood fit. However it is also important to estimate the confidence interval I of values of ~p whose integral probability is a prefixed number called confidence level (CL). In other words:

f (~pa|~x1, . . . ~xn) ≥ f (~pb|~x1, . . . ~xn) ∀~pa ∈ I, ~pb ∈/ I (6.9) Z f (~p|~x1, . . . ~xn) d~p = CL (6.10) I

In the same way can be also estimate the upper/lower limit on a single parameter pi:

Z +∞ Z pi, Max Z +∞ ··· ··· f (p1, . . . pi, . . . pk|~x1, . . . ~xn) dp1 ··· dpi ··· dpk = CL −∞ −∞ −∞ Z +∞ Z +∞ Z +∞ ··· ··· f (p1, . . . pi, . . . pk|~x1, . . . ~xn) dp1 ··· dpi ··· dpk = CL −∞ pi, Min −∞ (6.11)

However as I have remarked before assuming f (~p) constant is not always possible. For the branching fraction measurement this is obviously false as it is known that f (Br) = 0 for Br < 0. Moreover the point 0 is a real special point. Even if it is a set of measure zero, probably people would give anyway some probability to this point. This means that f (~p) must contain a delta function too. My analysis obtains the branching fraction upper limit using a more complex technique: I consider separately the probability distribution functions s (~x|~ps) for the signal, and b (~x|~pb) for the background. The overall distribution is

f (~x|~ps, ~pb, η) = η s (~x|~ps) + (1 − η) b (~x|~pb) (6.12) where η is the fraction of signal events. The background distribution is determined from data events, while the signal distribution is obtained from signal Monte Carlo events. The method considers the quantity

L (x , . . . x ; ~p , ~p , η) X = s+b 1 n s b (6.13) Lb (x1, . . . xn; ~pb)

This quantity has the property to increase monotonically[65][66] for increasingly signal-like (decreasingly background-like) experiments. The conﬁdence in the signal plus background hypothesis is given by the probability that X is less than or equal to the value observed in the experiment XObs. 88 Final results

CLs+b = Ps+b (X ≤ XObs) (6.14)

At the same way it could be evaluated the conﬁdence of the background-only hypothesis as CLb = Pb (X ≤ XObs) (6.15)

Finally the ratio CLs = CLs+b/CLb is considered. It could be demonstrated that in the case a single channel counting experiment 1 − CLs gives an upper limit equation similar to (6.11) R s L (s, b; n)ds 1 − CL = 0 (6.16) s R +∞ 0 L (s, b; n)ds where s and b are the expeted signal and background events, and n is the number of events observed.

6.1.3 The CLs algorithm

To set the signal upper limit, first of all the 5.2 < m < 5.3 GeV, 3.2 < m < 3.8 GeV ES (c¯c)H region is divided into 20 × 20 bins. For each bin the expected number of background events, the expected number of signal events, and the number of observed data events is computed. Background and signal expected numbers are obtained respectively from fits on data side- bands, and signal Monte Carlo. More details are given in next sections. Then the X value is calculated: it is the product of Poissonian terms. Then generating 100000 toy Monte Carlos it has been possible to calculate the probabilities CLs+b, the CLb, and finally their ratio, CLs. [65][66][1] If CLs < α, the signal hypothesis is considered excluded at 1−α of confidence level .

Changing the fraction η of signal, it is possible to ﬁnd the value of η for which CLs = α. This value of η is used to set the upper limit at 1 − α of conﬁdence level on the number of expected signal events, and on the channel branching fraction.

It is important to note that CLs is not a real upper limit. However using CLs for the upper limit evaluation, a more conservative result is obtained[1]. The relation between the number of observed signal and the branching fraction is N BR = Observed signal events (6.17) εSelectionNB± events

+ − where NObserved signal events = NObserved data events × η and, assuming BR Υ(4S)→B B = 50%, NB± events = NBBpairs¯ . In the next paragraphs, both the unbinned maximum likelihood ﬁt, and the upper limits obtained with this method are presented for two interesting channels. ± ± 6.2 B → χc 1 K with χc 1 → J/ψ γ results 89

Figure 6.1: Significance of the signal fraction parameter (left) and fit quality (right) of the ± ± + − bidimensional fit on B →χc 1K with χc 1→J/ψγ, and J/ψ→π π pp.¯

± ± 6.2 B → χc 1 K with χc 1 → J/ψ γ results

6.2.1 Bidimensional fit in mES–mχc 1 Three components are assumed to contribute to the sample: · Signal: described with a Gaussian in m and m ES (c¯c)H · Peaking background: described with a Gaussian and a second order polynomial in m (c¯c)H

· Combinatorial background: described with an Argus function in mES and a second order polynomial in m (c¯c)H

± [1] The B and χc 1 masses are fixed to the PDG values , and the widths of the peaks are obtained form signal Monte Carlo fits (Table 6.1). Combinatorial background parameters and relative peaks height are left free. Figure 6.2 shows the fitted function superimposed to data points, and Monte Carlo distributions. Figure 6.1 shows the fit quality, and significance of the signal fraction parameter. The measured signal fraction is 5 ± 3. The probability of obtaining a worse fit is 42.8 ± 1.6%. As my result is compatible with 0 within 2σ, in Paragraph 6.2.3 I calculate the upper limit branching fraction with the method described in Paragraph 6.1.3.

Parameter Value

mB± 5.2790 GeV

mχc 1 3.51059 GeV σB± 2.67 MeV

σχc 1 12 MeV

Table 6.1: Fixed parameters values 90 Final results

± ± + − ¯ Figure 6.2: mES–mχc 1 bidimensional fit of B →χc 1K with χc 1→J/ψγ, and J/ψ→π π pp. Signal is in solid light green, peaking background in solid dark green, and Argus background in dashed dark green. ± ± 6.2 B → χc 1 K with χc 1 → J/ψ γ results 91

6.2.2 Cross-checks

As cross-check, a 3σ cut is applied on mES (5.271 < mES < 5.287 GeV), and the χc 1 mass only is fitted with a first order polynomial for the background, and a Gaussian distribution for the signal. Gaussian parameters are still fixed to the ones of Table 6.1. Fit results are shown in Figure 6.3. The measured signal fraction is 6±3. The probability of obtaining a worse fit is 47.5 ± 1.6%. Finally I perform a second cross-check splitting the bidimensional distribution in slices of

30 MeV in mχc 1 and then ﬁtting each slice in mES with an Argus function plus a Gaussian peak. Gaussian parameters are still ﬁxed. The plot in Figure 6.4 shows the number of expected signal events for each slice.

± ± + − ¯ Figure 6.3: mχc 1 fit of B →χc 1K with χc 1→J/ψγ, and J/ψ→π π pp. In the top plot signal fit is in solid light green, and background fit in solid dark green. The two bottom plots are respectively the significance of the signal fraction parameter (left) and the fit quality (right). 92 Final results

± ± + − ¯ Figure 6.4: Scan in mχc 1 for B →χc 1K with χc 1→J/ψγ, and J/ψ→π π pp.

6.2.3 Upper limit evaluation

I still assume that the three components contribute to the sample: signal, peaking background, and Argus-shaped background. For the signal the central values are set from the PDG[1], while the widths are obtained from a fit on the signal Monte Carlo events alone. Backgrounds are described with an Argus function plus a peak in m , and with a second order polynomial in m . ES (c¯c)H Background peak has the average value fixed to the PDG B± mass. m and m ES (c¯c)H distributions are fitted with a bidimensional unbinned maximum likelihood fit on real data, where the signal region 5.271 < m < 5.287 GeV, 3.4 < m < 3.6 GeV has been removed. ES (c¯c)H

Using these probability distribution functions as input for the CLs algorithm described in Paragraph 6.1.3, I am able to calculate CLs in function of η (Figure 6.5). The upper limit set for this channel is 14 events at the 90% of conﬁdence level. Combining this result with then number of B± events of page 44, and the eﬃciency of

Figure 6.5: CLs distribution as a function of the number of observed events. The upper limit at 90% of confidence level is obtained looking for the number of events corresponding to a CLs of 10%. This is satisfied by the red point at N = 14. ± ± 6.3 B → hc K with hc → ηc γ results 93

± ± Figure 6.6: Fit quality (right) of the bidimensional fit on B →hcK with hc→ηcγ, and ± ∓ 0 ηc→π K KS. table at Paragraph 5.2.1.4. I obtain the following branching fraction:

± ± + − −6 BR B →χc 1K × BR (χc 1→J/ψγ) × BR J/ψ→π π p¯p < 1.5·10 90% C.L. (6.18) that is compatible with the PDG[1] value of

± ± + − −6 BR B →χc 1K × BR (χc 1→J/ψγ) × BR J/ψ→π π p¯p = (1.3 ± 0.3) ·10 (6.19)

± ± 6.3 B → hc K with hc → ηc γ results

6.3.1 Bidimensional fit in mES–mhc

I have followed the same procedure described in Paragraph 6.2.1 for the χc 1 analysis with three components: signal, peaking background, and Argus-shaped background. ± [1] [23] The B mass is fixed to PDG value , and hc mass to the E835 measured value . Widths of the peaks are fixed to the signal Monte Carlo events (Table 6.2). Combinatorial background parameters and the relative peaks height are left free. Figure 6.7 shows the fitted function superimposed to data points, and Monte Carlo distributions. The signal fraction returned by the fit is negative even if compatible with zero

Parameter Value

mB± 5.2790 GeV [23] mχc 1 3.5258 GeV σB± 2.46 MeV

σχc 1 21 MeV

Table 6.2: Fixed parameters values 94 Final results

± ± ± ∓ 0 Figure 6.7: mES–mhc bidimensional fit of B →hcK with hc→ηcγ, and ηc→π K KS. Signal is in solid light green, peaking background in solid dark green, and Argus background in dashed dark green. ± ± 6.3 B → hc K with hc → ηc γ results 95

± ± ± ∓ 0 Figure 6.8: mhc fit of B →hcK with hc→ηcγ, and ηc→π K KS. In the top plot, the signal fit is in solid light green, and background fit in solid dark green, while in the bottom one it is shown the fit quality.

± ± ± ∓ 0 Figure 6.9: Scan in mhc for B →hcK with hc→ηcγ, and ηc→π K KS. 96 Final results

(−0 ± 2 events). There is no evidence of signal. Figure 6.6 summarises the overall ﬁt quality: the probability of obtaining a worse ﬁt is 16.7 ± 1.2%.

6.3.2 Cross-checks

In analogy with χc 1 cross-checks, I have applied a cut on mES (5.271 < mES < 5.287 GeV), and I have fitted with a first order polynomial for the background, and a Gaussian distribution for the signal the hc mass only. Gaussian parameters are still fixed to the ones of Table 6.2. Fit results are shown in Figure 6.8. The measured signal fraction is negative: −1 ± 3. The probability of obtaining a worse fit is 0.1 ± 0.2%. Finally I split the bidimensional distribution

in slices of 30 MeV in mχc 1 . Then I fit each slice in mES with an Argus function plus a Gaus- sian peak. Gaussian parameters are still fixed. Figure 6.9 shows the number of expected signal events for each slice. Figure 6.10: CLs distribution as a function of the number of observed events. The upper limit at 90% of confidence level is obtained looking for the number of events corresponding to a CLs of 10%. This is satisfied by the red point at N = 4.6. 6.3.3 Upper limit evaluation I apply the same fits and procedures described in Paragraph 6.2.3. I observe less than 4.6 events at the 90% of confidence level for this channel. Figure 6.10 shows the CLs distribution. Combining this result with then number of B± events of page 44, and the efficiency of Table at page 5.2.2.3, I obtain the following branching fraction: ± ± BR B →hcK × BR (hc→ηcγ) × ± ∓ 0 0 + − −7 × BR ηc→π K KS × BR KS→π π < 4.8·10 90% C.L. (6.20)

± ∓ 0 0 + − Using the PDG value for the branching ratio BR ηc→π K KS × BR KS→π π = = (9 ± 3) ·10−3[1], I obtain the following upper limit: ± ± −5 BR B →hcK × BR (hc→ηcγ) < 8.0·10 90% C.L. (6.21) To compare this result with the one obtained by the Belle Collaboration[67], and with the one [40] predicted by P. Colangelo et al. , I assume a branching fraction of 50% for hc→ηcγ. ± ± −4 The upper limit I obtain is BR B →hcK < 1.6·10 . This result set a more stringent ± ± −4[67] upper limit of the one obtained by the Belle Collaboration BR B →hcK < 3.2·10 lies below the P. Colangelo et al. range[40] (2 – 14) ·10−4. Conclusions

he first aim of this thesis was the search of the hc charmonium state in the process ± ± B →hcK with hc→ηcγ, and ηc decaying into hadrons. The analysis has been realized T using the data collected at the BaBar experiment during 5 years of data taking. The total analysed integrated luminosity is 210.487 fb−1 and corresponds to (231.7 ± 1.5) ·106 BB¯ events. This analysis work has been performed “blind”, using as a “non-blind” control sample the ± ± decay B →χc 1K with χc 1→J/ψγ, and J/ψ decaying into hadrons. The branching fractions [1] for this chain are well known and, even if the relevant hadronic decays for ηc and J/ψ are partially different, the study of this decay has been essential to develop, test, and tune all the analysis tools. The reconstructions have been realized using an algorithm, which allows reconstructing a large number of exclusive hadronic decays. B± meson selection was primely based on a set of cuts√ on discriminating variables. The cut values have been optimised with respect to the S/ B ratio using a non-automated, graph-based optimisation algorithm. This method allowed maximising the sensitivity to observation without a significant efficiency penalization. Each hadronic decay has been optimised and studied separately. √ After the optimisation process, only hadronic decays with an S/ B of at least 1 have been considered for the branching ratio measurement:

± ± + − · B →χc 1K with χc 1→J/ψγ, and J/ψ→π π p¯p

± ± ± ∓ 0 · B →hcK with hc→ηcγ, and ηc→π K KS Then, the analyses of these channels have been finalised with an unbinned maximum likelihood fit in the m –m plane, where m is the beam constrained mass of the B candidate, and ES (c¯c)H ES m is the mass of either the χ or h state. The number of events observed is 5 ± 3 for (c¯c)H c 1 c ± ± + − ± ± B →χc 1K with χc 1→J/ψγ, and J/ψ→π π p¯p; and −0 ± 2 for B →hcK with hc→ηcγ, ± ∓ 0 and ηc→π K KS. Due to the compatibility within 2σ with zero for both results, upper limits have been [1][65][66] calculated using the CLs method . This is a conservative method to set the upper limit: it is based on several Monte Carlo generated experiments with different proportions of signal and background. Background probability distribution functions are obtained from fits [1][23] on data, while signal has χc 1 and hc masses fixed to the most recent values . With this technique I obtained

± ± + − −6 · BR B →χc 1K × BR (χc 1→J/ψγ) × BR (J/ψ→π π p¯p) < 1.5·10

± ± ± ∓ 0 0 + − −7 · BR B →hcK × BR (hc→ηcγ) × BR ηc→π K KS × BR KS→π π < 4.8·10

97 98 Conclusions

[1] ± ± The ﬁrst result is compatible with the expected value BR B →χc 1K × + − −6 BR (χc 1→J/ψγ)×BR (J/ψ→π π p¯p) = (1.3 ± 0.3) ·10 , while the second one, using known [1] ± ± −5 secondary branching fractions , gives BR B →hcK × BR (hc→ηcγ) < 8.0·10 . [40][42][67] Assuming a branching fraction of 50% for hc→ηcγ, my result implies ± ± −4 BR B →hcK < 1.6·10 . This sets a more stringent upper limit than the one reported by ± ± −4[67] [40] the Belle Collaboration BR B →hcK < 3.2·10 and lies below the predicted range (2 – 14) ·10−4. Appendix A Optimisation plots

± ± A.1 B → χc 1 K with χc 1 → J/ψ γ

A.1.1 J/ψ → π+ π− π0

± ± + − 0 Figure A.1: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π variables optimisation

99 100 Optimisation plots

± ± + − 0 Figure A.2: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 101

± ± + − 0 Figure A.3: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π variables optimisation 102 Optimisation plots

± ± + − 0 Figure A.4: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 103

± ± + − 0 Figure A.5: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π variables optimisation 104 Optimisation plots

A.1.2 J/ψ → π+ π− π+ π−

± ± + − + − Figure A.6: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π π variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 105

± ± + − + − Figure A.7: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π π variables optimisation 106 Optimisation plots

± ± + − + − Figure A.8: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π π variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 107

± ± + − + − Figure A.9: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π π π variables optimisation 108 Optimisation plots

A.1.3 J/ψ → π+ π− K+ K−

± ± + − + − Figure A.10: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π K K variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 109

± ± + − + − Figure A.11: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π K K variables optimisation 110 Optimisation plots

± ± + − + − Figure A.12: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π K K variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 111

± ± + − + − Figure A.13: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π π K K variables optimisation 112 Optimisation plots

A.1.4 J/ψ → π+ π− p ¯p

Presented in Chapter , Figures 5.3, 5.4,5.5 and 5.6.

± ∓ 0 A.1.5 J/ψ → π K KS

± ± ± ∓ 0 Figure A.14: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π K KS variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 113

± ± ± ∓ 0 Figure A.15: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π K KS variables optimisation 114 Optimisation plots

± ± ± ∓ 0 Figure A.16: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π K KS variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 115

± ± ± ∓ 0 Figure A.17: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π K KS variables optimisation 116 Optimisation plots

± ± ± ∓ 0 Figure A.18: B → χc 1 K with χc 1 → J/ψγ and J/ψ → π K KS variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 117

A.1.6 J/ψ → K+ K− π0

± ± + − 0 Figure A.19: B → χc 1 K with χc 1 → J/ψγ and J/ψ → K K π variables optimisation 118 Optimisation plots

± ± + − 0 Figure A.20: B → χc 1 K with χc 1 → J/ψγ and J/ψ → K K π variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 119

± ± + − 0 Figure A.21: B → χc 1 K with χc 1 → J/ψγ and J/ψ → K K π variables optimisation 120 Optimisation plots

± ± + − 0 Figure A.22: B → χc 1 K with χc 1 → J/ψγ and J/ψ → K K π variables optimisation ± ± A.1 B → χc 1 K with χc 1 → J/ψ γ 121

± ± + − 0 Figure A.23: B → χc 1 K with χc 1 → J/ψγ and J/ψ → K K π variables optimisation 122 Optimisation plots

± ± A.2 B → hc K with hc → ηc γ

+ − + − A.2.1 ηc → π π π π

± ± + − + − Figure A.24: B → hc K with hc → ηcγ and ηc → π π π π variables optimisation ± ± A.2 B → hc K with hc → ηc γ 123

± ± + − + − Figure A.25: B → hc K with hc → ηcγ and ηc → π π π π variables optimisation 124 Optimisation plots

± ± + − + − Figure A.26: B → hc K with hc → ηcγ and ηc → π π π π variables optimisation ± ± A.2 B → hc K with hc → ηc γ 125

± ± + − + − Figure A.27: B → hc K with hc → ηcγ and ηc → π π π π variables optimisation 126 Optimisation plots

+ − + − A.2.2 ηc → π π K K

± ± + − + − Figure A.28: B → hc K with hc → ηcγ and ηc → π π K K variables optimisation ± ± A.2 B → hc K with hc → ηc γ 127

± ± + − + − Figure A.29: B → hc K with hc → ηcγ and ηc → π π K K variables optimisation 128 Optimisation plots

± ± + − + − Figure A.30: B → hc K with hc → ηcγ and ηc → π π K K variables optimisation ± ± A.2 B → hc K with hc → ηc γ 129

± ± + − + − Figure A.31: B → hc K with hc → ηcγ and ηc → π π K K variables optimisation 130 Optimisation plots

± ∓ 0 A.2.3 ηc → π K KS

± ± ± ∓ 0 Figure A.32: B → hc K with hc → ηcγ and ηc → π K KS variables optimisation ± ± A.2 B → hc K with hc → ηc γ 131

± ± ± ∓ 0 Figure A.33: B → hc K with hc → ηcγ and ηc → π K KS variables optimisation 132 Optimisation plots

± ± ± ∓ 0 Figure A.34: B → hc K with hc → ηcγ and ηc → π K KS variables optimisation ± ± A.2 B → hc K with hc → ηc γ 133

± ± ± ∓ 0 Figure A.35: B → hc K with hc → ηcγ and ηc → π K KS variables optimisation 134 Optimisation plots

± ± ± ∓ 0 Figure A.36: B → hc K with hc → ηcγ and ηc → π K KS variables optimisation ± ± A.2 B → hc K with hc → ηc γ 135

+ − 0 A.2.4 ηc → K K π

± ± + − 0 Figure A.37: B → hc K with hc → ηcγ and ηc → K K π variables optimisation 136 Optimisation plots

± ± + − 0 Figure A.38: B → hc K with hc → ηcγ and ηc → K K π variables optimisation ± ± A.2 B → hc K with hc → ηc γ 137

± ± + − 0 Figure A.39: B → hc K with hc → ηcγ and ηc → K K π variables optimisation 138 Optimisation plots

± ± + − 0 Figure A.40: B → hc K with hc → ηcγ and ηc → K K π variables optimisation ± ± A.2 B → hc K with hc → ηc γ 139

± ± + − 0 Figure A.41: B → hc K with hc → ηcγ and ηc → K K π variables optimisation 140 Optimisation plots

+ − + − A.2.5 ηc → K K K K

± ± + − + − Figure A.42: B → hc K with hc → ηcγ and ηc → K K K K variables optimisation ± ± A.2 B → hc K with hc → ηc γ 141

± ± + − + − Figure A.43: B → hc K with hc → ηcγ and ηc → K K K K variables optimisation 142 Optimisation plots

± ± + − + − Figure A.44: B → hc K with hc → ηcγ and ηc → K K K K variables optimisation ± ± A.2 B → hc K with hc → ηc γ 143

± ± + − + − Figure A.45: B → hc K with hc → ηcγ and ηc → K K K K variables optimisation 144 Optimisation plots Acknowledgments

miei ringraziamenti vanno innanzittutto ai miei genitori ed a mio fratello Gabriele per avermi supportato in questi anni cos`ıfaticosi. Non voglio poi dimenticare le altre due I persone che da sempre sono nella mia vita, Doddo e G.B.: a voi cinque grazie veramente di cuore. In secondo luogo non posso astenermi dal ringraziare tutto il gruppo BaBar–Totem di Genova con cui credo di aver condiviso una buona fetta di questi ultimi 4 anni: in particolare il mio relatore Maurizio Lo Vetere per avermi aiutato a completare questo altrimenti difficile traguardo. E poi tutti voi altri: Marco Bozzo, Alberto Buzzo, Roberto Contri, Fabrizio Ferro, Mario Macr`ı,Saverio Minutoli, Roberta Monge, Aldo Morelli, il rinnovato papàMarco Negri, Stefano Passaggio, Claudia Patrignani, Enrico Robutti, Alberto Santroni e Giuseppe Sette. Grazie: da tutti voi ho imparato molto, e non solo di fisica. A parte va ringraziato Silvano perché,seppur per tutti e due non sia stata facile, èsempre stato un ottimo e leale compagno di laboratorio. Ci sono poi altre persone che vanno ricordate! Se mai qualcuno mi chiedesse cos’èche mi ha lasciato l’esperienza al CERN, beh non esiterei un’attimo e direi voi: Carlo, senza di te non si sarebbe mai creato ed affiatato quel simpatico gruppetto di ragazzi e ragazze della lontana estate del 2001; il mio “socio di sventure” Vitto — quanto freddo che ci siamo presi in quella maledetta counting room — ed infine il Dott. Andrea Fontana, semplicemente per la persona che è. Ho sempre ripetuto che c’èstato un bel legame di amicizia tra Totem–Athena, ma in effetti se ne èformato un secondo in questi ultimi due anni tra BaBar–Geant 4. Un ricordo va a tutte le donne ed ai rari uomini del G4PinkLadies Group: Barbs, Susi, Simona, Michela, Raffaella, Svamp, Giorgio, Coco Chanel ed il loro “President–40%–donna” nonchèmio fedele compagno di sci, Alf! (tra parentesi, OK per il 16!) Senza tutti voi questi anni non sarebbero stati cos`ıdivertenti! Un ricordo va pure ai miei compagni di casa, vecchi e nuovi, per essere sempre stati disponi- bili ed affidabili, in poche parole, per essere stati dei buon compagni di casa! Alessandro (ci mancano i tuoi vasetti di Kir!), Luigi, Rocco, Daniele ed Alexj. Non voglio poi dimenticare assolutamente la Ipertech s.r.l. per aver riempito i miei “altrimenti vuoti” week-end, per avermi fatto assaggiare ciòche realmente si fa nel mondo del lavoro e forse anche per le lunghe pause pranzo estive alla spiaggia! Ne voglio anche ringraziare i soci Marco ed Alessandro per la loro amicizia. Infine, l’ultimo pensiero èper tutte quelle persone che, a vario titolo, in questo momento, stanno dandomi una mano a progettare e costruire quello che saràun brillante futuro.

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