by
Mateusz Lewczuk
B.Sc., University of Victoria, 2003 M.Sc., University of Victoria, 2007
A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
DOCTOR OF PHILOSOPHY
in the Department of Physics
c
Mateusz Lewczuk, 2012 University of Victoria
All rights reserved. This dissertation may not be reproduced in whole or in part, by photocopying or other means, without the permission of the author.
Study of high-multiplicity 3-prong τ decays at BaBar by Mateusz Lewczuk B.Sc., University of Victoria, 2003 M.Sc., University of Victoria, 2007 Supervisory Committee Dr. R. J. Sobie, Supervisor
(Department of Physics and Astronomy)
Dr. R. Kowalewski, Departmental Member (Department of Physics and Astronomy)
Dr. M. Lefebvre, Departmental Member (Department of Physics and Astronomy)
Dr. D. Harrington, Outside Member (Department of Chemistry)
Supervisory Committee
Dr. R. J. Sobie, Supervisor
(Department of Physics and Astronomy)
Dr. R. Kowalewski, Departmental Member (Department of Physics and Astronomy)
Dr. M. Lefebvre, Departmental Member (Department of Physics and Astronomy)
Dr. D. Harrington, Outside Member (Department of Chemistry)
ABSTRACT
This work presents measurements of the branching fractions for τ decays to 3-prong final states using a data set of 430 million τ lepton pairs, corresponding to an in-tegrated luminosity of 468 fb−1, collected with the BaBar detector at the PEP-II asymmetric energy e+e− storage rings. The τ− → (3π)−ην
τ, τ− → π−2π0ωντ and
τ−→ f
1(1285)π−ντ branching fractions are presented as well as a measurement of the
non-resonant component of the τ− → (3π)−3π0ν
τ decay. In addition this work sets
a new limit on the branching fraction of the isospin-forbidden, second-class current decay τ−
→ π−η′(958)ν τ.
Contents
Supervisory Committee ii
Abstract iii
Table of Contents iv
List of Tables vii
List of Figures viii
Acknowledgements x
Dedication xi
1 Introduction 1
2 Theory 3
2.1 Standard Model Overview . . . 3
2.2 The τ Lepton . . . 5
2.3 Probability of Decay . . . 7
2.3.1 Decay Width . . . 7
2.3.2 Decay rate for τ Semi-Leptonic Decays . . . 8
2.3.3 The Branching Fraction . . . 9
2.4 Hadronic τ Decays . . . 9
2.4.1 Isospin, Charge Conjugation and G-Parity . . . 10
2.4.2 Second Class Currents . . . 13
2.5 Existing Experimental Measurements . . . 14
2.5.1 β Decays . . . 14
3 The BaBar Detector 17
3.1 The SLAC Accelerator Complex . . . 17
3.2 The BaBar Detector . . . 18
3.3 Tracking Components . . . 20
3.4 Electromagnetic Calorimeter . . . 23
3.5 DIRC Particle Identification . . . 24
3.6 Superconducting Coil and IFR . . . 25
3.7 The BaBar Trigger . . . 28
4 Selection 29 4.1 Data/MC Samples . . . 29
4.2 Tau preselection . . . 30
4.3 Event Selection . . . 32
4.4 Tag hemisphere requirements . . . 33
4.5 Signal hemisphere requirements . . . 36
4.5.1 General Signal Selection . . . 36
4.5.2 Neutral Selection . . . 39
5 Analysis Techniques 40 5.1 Counting Events . . . 40
5.2 Systematic Corrections and Errors . . . 42
5.2.1 Tracking Efficiency . . . 42 5.2.2 Particle Identification . . . 43 5.2.3 Number of τ pairs (Nτ τ) . . . 43 6 Results 45 6.1 τ− → π−π−π+ην τ via η → γγ . . . 46 6.2 τ− → π−f 1ντ via f1→ π−π+η and η → γγ . . . 50 6.3 τ− → π−π−π+ην τ via η → 3π0 . . . 53 6.4 τ−→ π−f 1ντ via f1→ π−π+η and η → 3π0 . . . 56 6.5 τ−→ π−2π0ην τ via η → π−π+π0 . . . 59 6.6 τ−→ π−2π0ων τ via ω → π−π+π0 . . . 63
6.7 Non-Resonant and Inclusive τ−→ π−π−π+3π0ν τ . . . 67 6.8 τ−→ K−η′(958)ν τ via η′→ π−π+η and η → γγ . . . 71 6.9 τ−→ π−η′(958)π0ν τ via η′→ π−π+η and η → γγ . . . 73 6.10 τ− → π−η′(958)ν τ via η′→ π−π+η and η → γγ . . . 76
6.11 τ− → π−η′(958)ν τ via η′→ π−π+η and η → 3π0 . . . 80 7 Summary 83 Bibliography 85 A Appendix 88 A.1 Particle Identification Selectors . . . 88
A.2 Track Identification . . . 88
A.3 Electron and Muon Selectors . . . 88
A.4 Conversion Finder . . . 89
A.5 Neutral Cluster Identification . . . 89
List of Tables
Table 2.1 Leptons (spin 1/2) . . . 4
Table 2.2 Quarks (spin 1/2). . . 4
Table 2.3 Bosons (spin 1). . . 4
Table 3.1 Production cross-sections at the Υ(4S) resonance . . . 18
Table 4.1 List of Monte Carlo samples used in this work. . . 30
Table 5.1 PID corrections and errors. . . 43
Table 6.1 List of measured modes and the relevant reconstructed mass spec-tra which are used to determine branching fractions. . . 45
Table 6.2 τ− → π−π−π+ην τ via η → γγ Systematic Errors. . . 49
Table 6.3 τ− → π−π−π+ην τ via f1→ π−π+η and η → γγ Systematic Errors. 51 Table 6.4 τ− → π−π−π+ην τ via η → 3π0 Systematic Errors. . . 55
Table 6.5 τ− → π−f 1ντ via f1→ π−π+η and η → 3π0 Systematic Errors. . 58
Table 6.6 τ−→ π−2π0ην τ via η → π−π+π0 Systematic Errors. . . 62
Table 6.7 τ−→ π−2π0ην τ via η → π−π+π0 Systematic Errors. . . 64
Table 6.8 Number of events in τ−→ π−π−π+3π0ν τ samples. . . 68
Table 6.9 Summary of the resonant and non-resonant branching fractions for τ−→ π−π−π+3π0ν τ decays. . . 69
Table 6.10Systematic errors on the inclusive τ− → π−π−π+3π0ν τ branching fraction. . . 69
Table 6.11τ− → π−η′(958)ν τ via η′→ π−π+η via η → γγ Systematic Errors. 77 Table 6.12τ−→ π−π−π+ην τ via η → 3π0 Systematic Errors. . . 81
List of Figures
Figure 2.1 Feynman diagram for Hadronic τ decay. . . 6
Figure 2.2 Pseudoscalar Octet. . . 11
Figure 2.3 Feynman diagrams for τ− → π−π0ν τ and τ−→ ηπ−ντ . . . 12
Figure 3.1 SLAC linear accelerator and PEP-II . . . 17
Figure 3.2 Cross-section view of the BaBar detector . . . 19
Figure 3.3 The silicon vertex tracker. . . 21
Figure 3.4 Side view of the drift chamber. . . 21
Figure 3.5 dE/dx v.s momentum plot for the DCH . . . 22
Figure 3.6 A cross section view of the electromagnetic calorimeter . . . 24
Figure 3.7 A schematic of the DIRC detector system . . . 25
Figure 3.8 The angle of the Cherenkov radiation as a function of lab mo-mentum of charged tracks . . . 26
Figure 3.9 µ efficiency and π misidentification probability . . . 27
Figure 4.1 Typical three charged track event at BaBar. . . 31
Figure 4.2 Thrust after selectrion criteria . . . 32
Figure 4.3 Plots of tag variables, centre mass momentum, number of neu-trals, and neutral energy. . . 34
Figure 4.4 Plots of tag variables, centre mass momentum, number of neu-trals, and neutral energy. . . 35
Figure 4.5 Plot of the 3π3π0 mass. . . . 37
Figure 4.6 Plot of the 3πηγγ mass. . . 38
Figure 6.1 Invariant mass the γγ system . . . 48
Figure 6.2 The π+π−η invariant mass in the region of the f 1 meson (η → γγ) 52 Figure 6.3 The invariant mass the 3π0 system. . . . 54
Figure 6.4 The π+π−η invariant mass in the f 1 region (η → 3π0) . . . 57
Figure 6.5 The invariant mass the π+ π− π0 system in the η meson region
for data and signal MC. . . 60 Figure 6.6 The invariant mass the π+ π− π0 system in the η meson region
for qq and τ background. . . 61 Figure 6.7 The invariant mass the π+ π− π0 system in the region of the ω
meson for data and signal MC . . . 65 Figure 6.8 The invariant mass the π+ π− π0 system in the region of the ω
meson for qq and τ background. . . 66 Figure 6.9 Plot of the π− π− π+ 3π0 invariant mass in τ−
→ π−π−π+3π0ν τ
decays. . . 70 Figure 6.10The π+ π− η invariant mass for τ−→ K−η′(958)ν
τ decays. . . . 72
Figure 6.11The π+ π− η invariant mass for the τ−→ π−η′(958)π0ν
τ decay. 75
Figure 6.12The η′ peak for the τ− → π−η′(958)ν
τ via η′ → π−π+η and
η → γγ mode. . . 78 Figure 6.13The η′ peak in the qq enhanced sample for the τ−→ π−η′(958)ν
τ
via η′→ π−π+η and η → γγ mode. . . . 79
Figure 6.14The η′ peak for the τ− → π−η′(958)ν
τ via η′ → π−π+η and
ACKNOWLEDGEMENTS I would like to thank:
Randy and
People who, if not mentioned in the acknowledgements, would resent me.
We are scientists We do genetics We leave religion To the psychos and fanatics But we are tired We got nothing to believe in We are lost Go tell the women that we’re leaving Nick Cave
DEDICATION To everyone except for you.
Introduction
The Standard Model (SM)[1] describes and organizes the fundamental constituents of matter and the forces that mediate interactions. Although the SM successfully describes all experimental observations, the SM is predicted to break down at higher-energies and there is an intense effort to search for new physics phenomena beyond the predictions of the SM. Ongoing tests of the SM are done, for example, through accelerator-based high energy particle physics experiments. By accelerating sub-atomic particles to nearly the speed of light, and subsequently colliding them inside of a detector, it is possible to measure the properties of the particles and their inter-action, which gives insight into the underlying physics. The work presented in this thesis uses the electron-positron collider located at the SLAC National Laboratory in Palo Alto, California to produce a large sample of tau leptons. The subsequent decay of the tau leptons can be used to test the predictions of the SM.
The electrons and positrons are collided at a single point in the PEP-II storage rings. A large multi-component detector surrounds the collision point and is designed to measure the identity, momentum and energy of charged and neutral particles pro-duced in each collision. At SLAC the detector was constructed by the BaBar Col-laboration and is often referred to as the BaBar detector. The ensemble of collisions acquired by the BaBar detector can be used to study and test the predictions of the SM.
This work studies the decay of the τ lepton to rare or forbidden modes. One focus is to improve our understanding of the properties of the τ lepton as many of the rare decays modes observed in this study are poorly measured or have never been observed. Improving our knowledge of the properties of the τ is essential if the τ is to be used as a probe to test the SM. In addition, it is predicted that one might observe
certain decays of the τ lepton that are suppressed due to conservation laws based on imperfect symmetries. Of interest in this work is the isospin symmetry which predicts the equality of the strong interaction between the up and down quarks. In particular, there are classes of τ decays which have decay rates that are proportional to the sum and difference of the up and down quark masses, often referred to as first-class and second-class current decays. If isospin were an exact symmetry for all interactions, then the decay rate of second-class current decays would be zero.
There have been no observations of second-class current τ decays [2]. The focus of this work is the search for a τ lepton decay to a η′(958)π−ν
τ final state. A recent
paper [3] predicts that the rate of this decay should be less than 1.4 × 10−6. The
η′(958) is a meson (quark-antiquark state) that is an excited state of the η meson and
decays to a π+π−η final state about 50% of the time. The η meson has a short lifetime
and decays to a variety of final states. This work uses the η → γγ and η → 3π0 decay
modes.
The large BaBar τ sample is used to search for the τ− → η′(958)π−ν
τ decay.
The algorithms developed in this work selects τ decays with three charged particles accompanied by either a pair of photons or three π0 mesons. In addition, other rare
or previously unobserved τ decay modes are measured. In particular, this study looks at decays to π−X0ν
τ where X0 is an f1(1285) or η′(958) meson ,and to (3π)−Y0 where
Y0 is an η or ω resonance. In many cases, the precision on the decay rate is improved
by an order of magnitude over previous measurements.
The Standard Model is discussed in Chapter 2. A quick review of the elementary groups of particles and forces will be made followed by a discussion of the particles and forces that contribute in our decay channels, and the physics that governs the interactions. Chapter 3 will outline the BaBar detector. The selection criteria for the study will be discussed in Chapter 4. This will outline what variables are used to select our data, and Monte Carlo (MC) samples. In Chapter 5 the general analysis methods will be discussed, which is followed by a specific discussion of the analysis of each measurement in Chapter 6. Chapter 7 concludes with a summary of all measurements.
Chapter 2
Theory
This chapter will begin with a brief introduction to the Standard Model (SM) of particle physics. The subgroups of the particles that make up the SM will be briefly discussed, which will continue with an overview of the particles and processes involved in this study.
2.1
Standard Model Overview
The classical theory of fields has been successful at describing interactions at the macroscopic scale. One needs to adjust the classical description to explain physics at the quantum scale. At the smallest sizes currently observable, the SM is highly successful description of elementary particles [1] through the excitation of a quantum field.
An elementary particle is one which, based on current observations, constitutes a primary building block of matter and cannot be further divided. The two groups of elementary particles that make up matter are leptons and quarks, which are referred to as fermions. A third group, known as vector bosons, mediate interactions between quarks and leptons and arise out of a requirement of local gauge invariance. The fermions have half-integer spin, and the vector bosons have integer spin. The leptons are listed in Table 2.1, the quarks are in Table 2.2, and the mediators are in Table 2.31.
The leptons are ordered into three generations. Each generation is made up of a charged lepton and its corresponding neutrino. Table 2.1 shows the leptons arranged
1
Lepton Charge Mass ( MeV/c2) Principal decays e -1 0.511003 -νe 0 < 3 -µ -1 105.659 eνµν¯e νµ 0 < 0.19 -τ -1 1777 µντν¯µ, eντν¯e, ¯udντ ντ 0 < 18.2
-Table 2.1: Leptons (spin 1/2)[2]. Flavor Charge Mass ( MeV/c2)
d -1/3 (4-8) u +2/3 (1.5-4) s -1/3 (80-130) c +2/3 (1.15-1.35) b -1/3 (4.1-4.4) t +2/3 (174.3±5.1)
Table 2.2: Quarks (spin 1/2).
in three generations. Since leptons do not carry a colour charge, they do not interact via the strong force. They do however carry a weak isospin charge and interact via the weak force, as well as the electromagnetic force for the charged leptons. The mediating particles for leptons are the photon and the W± and Z0 bosons.
Quarks are also spin 1/2, and are categorized in three generations. But unlike leptons, a quark has never been seen in isolation. Instead quarks always appear in groups of 2 or 3 which are classified as hadrons. Quarks carry a unique charge called “colour” which subjects them to strong interactions, in addition to the electroweak interaction. Strong forces in the quark sector of particle physics are mediated by the gluon vector bosons. The strong force is called Quantum Chromodynamics (QCD).
The forces in particle physics are mediated by the vector bosons, which have a spin of 1. These bosons arise out of the invariance of the Standard Model Lagrangian
Mediator Charge Mass ( GeV/c2) Force
gluon 0 0 strong
photon(γ) 0 0 electromagnetic
W± ±1 80.425 ± 0.038 (charged) weak
Z0 0 91.1876 ± 0.0021 (neutral) weak
under a SU(3)c × SU(2)L × U(1)Y local gauge transformation. The U(1)Y group
relates the weak hyper-charge Y to the electric field. It is associated with photons, which mediate the electromagnetic force, and couple only to particles that carry an electric charge. The strength of the coupling is determined by the electric charge e. The electromagnetic interaction is the simplest and oldest of the dynamical models, and serves as a template for the others. The SU(2)L describes the weak sector of
the standard model, specifically the W± and Z0 bosons which mediate the charged
and neutral weak forces, respectively. The strength of the couplings for the W±
boson is determined by the weak coupling constant, g, which couples the W± to
leptons and neutrinos, or to quark-antiquark pairs. The coupling strength of the Z0
is determined by the weak coupling constant gZ, which determines the strength of
the coupling of fermion-antifermion pairs. All fermions can interact via the weak process, although not exactly in the same manner. The decays examined in this study are mediated by the W±. The SU(3)
c group describes the coupling of strongly
interacting particles by the exchange of mass-less gluons. Gluons mediate strong forces in hadronic interactions, and only couples to objects which carry a colour charge. This means that not only can the gluon couple to quarks but also to itself.
Another boson (Higgs), arises out of electroweak symmetry breaking [4]. The sym-metry breaking is predicted to be responsible for giving mass to the various particles. In the simplest model the boson is a scalar field (spin = 0) which assigns non-zero expectation values to the vacuum with which the bosons and fermions interact. The Higgs field spontaneously breaks the local SU(2)L× SU(1)Y gauge symmetry, which
assigns masses to the W± and Z0 bosons. Although vital in the understanding of the
SM, the Higgs field does not play an active role in this study.
For completeness it should be noted that there is also the gravitational force, that is thought to be mediated by the spin 2 graviton. The force is very weak, and the role it plays in elementary particle physics is negligible at energies far below the Planck scale (1019 GeV).
2.2
The τ Lepton
The τ is the heaviest lepton in the SM, and resides in the third generation of the lepton family. It was discovered in 1974 by Perl et al. [5] and is massive (Mτ = 1776.99+0.29−0.26
MeV/c2)[2] enough to be able to decay into one or more hadrons. If a τ decays purely
-τ
τ
ν
W
Χ
-Figure 2.1: Semi-leptonic decay of a τ− lepton into a hadronic state (X). The circle
with horizontal lines through it represents the hadronization process for quarks, which is not well understood.
hadrons in the final state, then the decay is classified as semi-leptonic. The τ decays by emitting a ντ and a W± gauge boson. In our study we observe a semi-leptonic τ
decay as shown in figure 2.1. The W decays into a pair of quarks which hadronize into one or more particles (represented by X, where X is a meson). In many cases the single meson X is not directly observed, but instead the observed state is composed of many mesons which are often presumed to be decay products of the X-meson.
2.3
Probability of Decay
By studying large samples of a particular decay it is possible to determine the average probability of the decay or decay-rate which in turn can be used to test the SM. The following three subsections present the decay width, decay rate, and branching fraction.
2.3.1
Decay Width
The partial decay width (Γ) is defined to be the probability per unit time that a given particle will decay into a particular final state. This width is proportional to the transition rate from an initial to final state. This is derived from Fermi’s Golden Rule [6] and can be summarized as:
TransitionRate ∝ |M|2× (PhaseSpace)
where M is the matrix element that contains information about the dynamics of the process, and the phase space term contains kinematic information. The phase space factor is determined by how much energy is taken to build the final state, and how many final state particles are produced. For the decay of a particle into two other particles (1 → 2 + 3) the decay width can be written as (see, for example, [7]):
dΓ = |M| 2 2m1 d3p 2 (2π)32E 2 d3p 3 (2π)32E 3 × (2π)4δ4(p1− p2− p3)
In the above equation pi = (Ei, pi) is the four momentum of the ith particle, m1 is the
mass of the decay particle. By integrating, the two body decay amplitude simplifies to: dΓ = |M| 2 32π2 |p1| m2 1 dΩ
The matrix element is determined from Feynman rules [8]. For leptonic decays this is well understood, but for semi-leptonic decays this is complicated by the hadronization of the W± decay products.
2.3.2
Decay rate for τ Semi-Leptonic Decays
The matrix element for a two-body semi-leptonic τ decay (τ− → X−ν
τ) can be written as [1]: M = gw 8M2 W [¯uντγµ(1 − γ5)uτ]FXµ
where the γµ(1 − γ5) are the vector and axial vector components of the weak charged
current, the γ’s are Dirac matrices, gw is the weak coupling constant, FXµ is a form
factor that describes the coupling of the X resonance to the W boson, MW is the W
mass and ¯uντ and uτ are the ντ and τ spinors. The X in the subscript of the form factor
denotes the resonance into which the quarks hadronize. The determination of the form factors is a complicated matter, as a result they are determined by experimental measurements.
A well studied example is that of a τ− → π−ν
τ decay. The pion form factor has
the functional form
Fµ = fπpµ
fπ = 131.74 ± 0.125 MeV
where pµis the π 4-momentum, and f
π is the pion decay constant which is determined
from experimental measurements of the π+ → µ+ν
τ and π+ → µ+γντ decays [2].
Substituting the form factor into the amplitude equation gives the decay width for τ− → π−ν τ: Γ(τ− → π−ν τ) = G2 Ffπ2cos2(θc)m3τ 16π 1 − m 2 π m2 τ 2 GF = √ 2 8 gw MW 2
where mπ is the pion mass, θc is the Cabibo angle and GF is the Fermi coupling
constant. Although this procedure is analogous to the decay presented in this thesis, it cannot be carried out when the intermediate state or states (X) is not known.
2.3.3
The Branching Fraction
One computes the branching fraction by taking the decay width of the desired mea-surement and dividing it by the total decay width of the τ lepton. One of the branch-ing fractions presented in this work is τ−→ π−π+π−ην
τ which can be written as:
B(τ− → π−π+π−ην τ) = Γ(τ− → π−π+π−ην τ) Γτ Γτ = 1 ττ
where ττ = (290.6 ± 1.1) × 10−15s is the τ lifetime [2].
The branching fraction is calculated with: B(X) = Nsel
2Nstart
where Nsel is the number of events after all of the selections have been applied, and
Nstart is the number of events before selection. However, our selection algorithms are
not 100% efficient and despite optimization of selection criteria, we retain a small background. We therefore must correct the equation:
B(X) = Nsel 2Nstart
1 − fbkg
ǫ
where fbkg is the fraction of background in the measurement, and ǫ is the efficiency
for selecting the decays.
2.4
Hadronic τ Decays
The τ lepton is an interesting particle to study, as its mass and charge allow it to decay into low lying hadrons (mesons). A hadronic τ decay occurs via the weak process by coupling to the W± boson. The W± subsequently decays by coupling to a mesonic
state “X±” which is composed of a d′u pair, where d¯ ′ can be either a d or s quark.
The amount of each combination is proportional to the cosine or sine of the Cabbibo angle, respectively. The pair of quarks hadronize into mesons, where the types of mesons produced are limited by the τ mass. The coupling of the weak current to the hadronization process is defined by form factors often denoted as F(Q2). These
during the hadronization process which have a non-negligable contribution due to the relatively large value of the strong coupling constant in the energy range relevant in these studies. The form factors are therefore determined experimently, usualy by comparing the ratios of similar decays. A generic τ decay is shown in Figure 2.1. The allowed τ decays can be classified by their symmetry properties. Of particular interest in this study are decays that are suppressed by G-parity conservation, known as second class currents. G-parity is symmetry that involves isospin rotation and charge conjugation.
2.4.1
Isospin, Charge Conjugation and G-Parity
Werner Heisenberg introduced isospin in 1932 as a mechanism for understanding the nearly degnerate mass of the proton and the neutron and the equality of the strong interactions between any pair of nucleons, whether they be protons or neutrons [9]. It was convenient to treat the neutron and proton as the differnet states of the same particle, where the proton carried an isospin project of +1/2 and the neutron -1/2. Upon the discovery of quarks isospin was extended into the classification of the u and d quarks, which are nearly degenerate in mass.
The u and d quarks form an isospin doublet (I=1/2), and can be symbolized with Dirac bra-ket notation vectors in “isospin space”
u = |1/2, +1/2i d = |1/2, −1/2i
where the first number in the ket is the isospin value of the doublet and the second is the third component (I3) for the u and d quarks, respectively. With the above
notation, I3=1/2 and -1/2 for the u and d quarks, respectively 2.
Particles can be grouped in an octate formation according to their I3 values (see
Fig. 2.2) and quark content. This discussion focuses on the central line in the octet which groups the pions and the η meson, which are composed from u and d quarks. These arrangements are refered to as multiplets, where the pion multiplet contains three particles (π+, π0, π−) and the η exists as a singlet. The triplet is refered to
having an isospin value of 1 and the singlet is refered to as having an isospin value of 0. Certain decays can be classified according to the isospin value of a multiplet in
2
conjunction with the decays charge conjugation value.
Charge conjugation operation transforms a particle into its anti-particle, for ex-ample,
C|π+i = |π−
i
where the C operator acts on a positive pion state and transforms it into its negatively charged counterpart. Only particles which are their own anti-particles are eignestates of C. The eigenvalues of a system composed of a particle and its anti particle (i.e. π0
and η) the eigenvalue is -1l+s where l is the angular momentum of the state and s is
the spin. For the pseudo-scalars l=0 and s=0, leading to a C eigenvalue of +1. The restriction to neutral particles makes the functionality of the C operation somewhat limiting, untill combined with a rotation in isospin space.
Figure 2.2: Octet arangement of the pseudo-scalar mesons.
G-parity is a combination of charge conjugation and isospin rotation about the number 2-axis. The G-Parity operator is written as
G = CR2
R2 = eiπI2
This means that applying the G-Parity operator rotates the particle wave function by 180◦ in isospin space and then applies a charge conjugation. The combination of an
W
-τ
τν
-π
0π
W
-τ
τν
-π
η
Figure 2.3: The top figure shows a Feynman diagram for the τ− → π−π0ν
τ decay and
the lower Feynman diagram shows the second class τ−
→ ηπ−ν
τ decay. The circle
with horizontal lines through it represents the hadronization process for quarks, which is not well understood.
isospin rotation with the charge conjugation operation includes the charged members of the pion multiplet as eigenstates of the G operation. The G-Parity eigenvalue of a particle can be determined with the following formula
G(X) = (−1)IC
where I is the isospin value for its multiplet and C is the charge conjugation value of the neutral member of the multiplet.
It is possible to assign the G-parity for decays based on the decay products. The top diagram of Fig.2.3 illustrates a τ−→ π−π0ν
τ decay and the lower diagram shows
a τ− → π−ην
τ decay. For the τ− → π−π0ντ decay
and,
G = G(η)G(π±) = (1)(−1) = −1, for the τ− → π−ην
τ decay. The difference in G-Parity values arises because the
neutral pion belongs to a triplet of particles with isospin value I = 1 and the η is a singlet with isospin I = 0. G-Parity can be used to help categorize first class and second class currents.
2.4.2
Second Class Currents
The final states in τ decays can be ordered by the spin, parity, and G-Parity of the “X” state in the τ− → X−ν
τ (see Figure 2.1) decay, where X− is an allowed mesonic
state (consider ¯ud). The quarks that make up the meson can be found in either a “vector” spin J=1 or “scalar” spin J=0 state. The spin 1 state forms when the spins of the two quarks allign, and the spin 0 state forms when the spin of one of the quarks points in the opposite direction of the motion of that quark. The latter can be achieved in two ways, with either the ¯u quark with the anti-alligned spin, or the d quark. The J=0 spin state can therefore be represented in two configuration with either the two previously mentioned ways summed, or as the difference. The difference forms the |0+i state and the sum forms the |0−i state, which can be denoted
as JP = 0+ and JP = 0− respectively. The former is refered to as the scalar state,
and the latter as the pseudo-scalar. Final states can be further classified according to JPG. In τ decays, the allowed first class currents are (JPG = 0−−, 1+−, 1−+) and
the suppressed second class currents are (JPG = 0+−, 1++, 1−−).
The pseudo-scalar (JP= 0−) and scalar (JP= 0+) final states can be approximated
by md+ mu √ 2mhad |0− i +m√d− mu 2mhad |0+i ≈ |Ψhadi
where higher order terms are ignored. To calculate a decay rate one can multiply the state against its hermetian conjugate and square the factors which gives the following proportions for the |0−i and |0+i states
|hf|0−
i|2 ∝ (md+ mu)2
|hf|0+i|2 ∝ (m
d− mu)2.
η′(958)π−ν
τ decay, is proportional to the difference in the masses of the u and d
quarks. In the limit of equal u/d quark masses (isospin symmetry), it is clear that the |0+i does not form. This representation assumes free quarks, which is an
over-simplification at energies where quarks are strongly bound into mesons. For a more complete description one must consider a hadronic coupling to the W± boson.
The hadronic current couples to the W± boson and the decay products through
either a vector current or an axial-vector current. Vµ = hΨvac|F1(Q2)γµ+ iF2(Q2) 2|Q| σµνq ν |Ψhadi Aµ= hΨvac|G1(Q2)γµγ5+ iG2(Q2) 2|Q| σµνγ5q ν |Ψhadi
In the above equations Vµ is the vector current, Aµ is the axial-vector current, Ψ
represent the wave functions, F and G are the form factors, qν is the four-momentum
and Q2 ≡ m2
had ≡ s. By inserting the conserved vector current (CVC) hypothesis
[11], which states that ∂µV
µ = 0, into the vector current the equation collapses to
mhadF1(Q2)hΨvac|Ψhadi = 0.
Since the vacuum state is defined as spin zero and scalar, the CVC hypothesis will only hold if there are no scalar currents, or equivalently the |0+i state is not observed.
2.5
Existing Experimental Measurements
There have been experimental searches for second class currents in β decay studies, and τ decays. Although there have been claims of observation of these modes, none have been substantiated.
2.5.1
β Decays
A study measuring the β-ray emissions from polarized 12B and 12N nuclei supports
the potential existence of second class currents [10]. In the study samples of12B and 12N nuclei were generated and polarized. The decays studied were
12
12
N →12C + e++ ν.
The majority of these decays proceed through a first class current, but it is proposed that the decays may have a second class current component. Measurements were made of the e+ and e− (β-rays) energies and the decay angles relative to the polarization
direction of the nuclei. The experiment measured a decay asymmetry defined by A = [W+− W−]/[W++ W−]
where W+ is the number of β-rays aligned along the polarization vector of the nuclei
and W− is the number aligned against the polarization vector. The asymmetry is
approximately given by
A ∼=∓P (p/E)(1 + α∓E)
where P is the nuclear polarization, p is the momentum of the β-ray and E is the energy of the β-ray. In the study the coefficients “α∓” are tested against theoretical
predictions given by the CVC hypothesis. CVC theory predicts a dependence of the asymmetry on the β-ray energy as a higher order effect, however, a second class component of the decay can also affect the asymmetry energy dependence. The predicted CVC component of the coefficient is calculated to be (α− − α+)CV C =
0.27%/MeV whereas the experiment value is α−− α+ = (0.52 ± 0.09)%/MeV. It is
suggested that the excess asymmetry could be accounted for by a second class current. Similar tests have been conducted in β-ray emissions from polarized 19Ne nuclei
[12]
19
Ne →19F + e++ ν.
The results of this study also cannot be accounted for by CVC theory. It is proposed that a second class current contribution could make up the difference.
A smiliar study [13] has yeilded results which are consistent with no second-class current. This study relied on calculated inputs [14].
2.5.2
τ Decays
There have been experimental searches for second class currents in the τ−
→ π−ην τ
and τ−
→ η′(958)π−ν
τ decays. In 1987 the HRS Collaboration reported a branching
fraction of (0.051±0.015) for the τ− → π−ην
τ decay[15]. These claims were soon after
[17]. To date there has been no experimental observation of the τ−
→ π−ην
τ decay.
The best upper limit on the branching fraction of the τ−
→ η′(958)π−ν
τ decay has
been placed by BaBar [18] at the 90% confidence level (CL) to be 7.2×10−6. Searches
for second class currents in the τ− → π−ην
τ decay [19] have resulted in a 95% CL
upper limit on the branching fraction of 9.9 ×10−5. A study of the τ− → ωπ0ν
τ decay
[20], which has a component that may proceed through a second class current, has also yielded limits on second class current contribution.
The expected rate of a second class decay is proportional to the square of the up-down quark mass difference, (mu − md)2 [21]. Recent theoretical work on the
τ−
→ η′(958)π−ν
τ decay [3] has set the rate below 1.4 × 10−6. This prediction is
using a model that is dominated by the a0(980) meson. This result is highly sensetive
to chosen parameterization of the u and d quark masses and the radius of the enclosure bounding them.
Chapter 3
The BaBar Detector
This section gives a detailed description of the hardware and software used in ac-quiring the data sets at BaBar. The linear injector and PEP II storage ring will be discussed. This will be followed by an outline of the BaBar detector with main focus being on the components used for detecting our final state particles.
3.1
The SLAC Accelerator Complex
The linear accelerator at SLAC became operational in 1966. It is 3.2 km long, making it the longest linear accelerator in the world. A linear accelerator uses electromagnetic
Figure 3.1: SLAC linear accelerator and PEP-II [25].
waves to accelerate charged particles to velocities near the speed of light. The SLAC accelerator is shown in figure 3.1. At the left an electron gun produces the electrons by heating a filament to very high temperatures. These electrons are fed into the accelerator, and propelled with microwaves supplied by the klystron gallery. Part way
e+e−→ Cross-section (nb) b¯b 1.05 c¯c 1.30 s¯s 0.35 u¯u 1.39 d¯d 0.35 τ+τ− 0.92 µ+µ− 1.16 e+e− ∼40
Table 3.1: Production cross-sections at the Υ (4S) resonance [22] [23].
down the linac some of the electrons are diverted towards a tungsten target. When the diverted electrons collide with the tungsten target they produce, among other particles, positrons which are then fed back into the linac. The electrons and positrons are fed into separate damping rings where they radiate synchrotron radiation which reduces the motion of the particles in the plane transverse to their direction of motion. The particles are then fed from the linac into the PEP II storage rings.
The original PEP ring is used for storage of the high energy electrons (9 GeV). A secondary ring was built over top of the original ring and is used to store the lower energy positrons (3.1 GeV). This configuration of the rings makes it possible to have asymmetric beam energies for the study of CP violation of B mesons. The beams collide near the centre of the BaBar detector.
The PEP II rings were designed to provide high luminosities (3 × 1033 cm−2s−1)
needed to do B meson studies. The high luminosity also produces a large sample of τ pairs. Table 3.1 shows the various production cross-sections at √s = 10.58 GeV. The energy of the colliding beams is tuned to the Υ (4S) resonance, which is on the threshold for B ¯B meson production. PEP II has delivered a total integrated luminosity of 557 fb−1, of which 531 fb−1 was recorded by the BaBar detector. The
majority of this sample is collected at the Υ (4S) resonance with a small amount collected at the Υ (3S) and Υ (2S) resonances which are not used in this work.
3.2
The BaBar Detector
The BaBar detector [22] was specifically designed to accommodate the asymmetric beam energies provided by PEP II. This meant that the interaction point (IP) would not be centered within the detector and that some of the components in the detector
would be arranged asymmetrically. The closest component to the IP is the Silicon Vertex Tracker (SVT). This is a charged track detector whose primary purpose is to detect low energy charged particles, reconstruct decay vertices, and precisely measure the position of charged tracks along the z-axis. The next component is the Drift Chamber (DCH) which also measures charged tracks, and contributes to particle identification by measuring the energy lost by the particle as it traverses the DCH. Encircling the track detectors is the Detector of Internally Reflected Cherenkov light (DIRC), which is used to distinguish charged pions and kaons. Once the particles leave the DIRC they pass through the Electromagnetic Calorimeter (EMC), which uses crystals to measure the energy of electromagnetic showers. The last component system in the detector is the magnet and Instrumented Flux Return (IFR). The magnet supplies a high magnetic field (1.5 T) along the axis of the beam-pipe, which bends tracks in the transverse plane of the detector and gives a measurement of the momentum of the charged particles. The IFR provides a return path for the magnetic field as well as providing muon and hadron separation.
3.3
Tracking Components
The measurement of charged tracks is an important part of this analysis. Tracking detectors measure the position and momentum of charged particles. The two tracking detectors, SVT and DCH, are the innermost components of the detector. The magnet provides a high magnetic field that bends the tracks in the tracking chambers allowing the measurement of the particles’ momentum.
The SVT is shown in figure 3.3, and is the sole tracker for charged particles with a momentum transverse to the beam direction of pt < 100 MeV. It is composed of
five double sided active layers of silicon centred on the beam pipe, where the first layer is set at a radius of 32 mm from the IP. As a charged particle moves outward from the interaction point (IP), it deposits charge in the silicon layers. Its trajectory is reconstructed using the deposited charge as reference points. The point resolution ranges from 10-15 µm for the inner layers to 30-40 µm for the outer layers. The pulse height of the charge is then used to infer the amount of energy deposited (dE/dx) as the particle passed through the silicon. Since each layer is double sided this allows up to 10 independent dE/dx measurements per track. The SVT has a resolution of 14% on dE/dx measurements for minimum ionizing particles, which allows for a 2σ separation of kaons and pions up to momentum of 500 MeV/c.
Figure 3.3: The silicon vertex tracker [27].
The DCH tracks particles with transverse momentum greater than 100 MeV/c. The tracker is a 280 cm long cylinder with an outer radius of 80.9 cm, and an inner radius of 23.6 cm, and surrounds the SVT and beam pipe. A cross section of the DCH is shown in figure 3.4.
10
4
10
3
10
–1
1
10
e
µ
π
K
p
d
dE/dx
Momentum (GeV/c)
1-2001 8583A20Figure 3.5: Plot of dE/dx in the DCH as a function of track momenta [26] . The volume of the DCH contains 7140 hexagonal drift cells arranged in 10 super layers, of 4 layers each. The chamber is pressurized with (4:1) helium - isobutane gas mixture. As the charged particles traverse the DCH, they ionize the gas. The resulting ionization is detected by wires which run along the entire length of the detector. The wires are clustered into hexagonal orientations with six shared field wires on the perimeter and a central sense wire. The nominal voltage settings of the sense and field wires are 1960 V and 340 V respectively. As the charged particles move outward in radius, they traverse the alternating layers which return information about the position and particle identification by energy loss dE/dx. Figure 3.5 shows the energy loss for various particles as a function of their momentum in the DCH.
sys-tems. Five parameters define each track (d0,φ0,w,z0,tanλ). The point of closest
approach in the x-y plane defines d0 and the point on the z-axis where this occurs
defines z0 2, φ0 is the azimuth of the track, w is the curvature defined as 1/pt, and
λ is dip angle relative to the transverse plane. The reconstruction algorithms con-nect the tracks in the DCH with the tracks in the SVT, as well as discriminate false tracks. The tracking efficiency in the DCH is defined as the ratio of reconstructed DCH tracks to the number of reconstructed tracks in the SVT which exceed pt> 100.
The average efficiency for the DCH is about 98% per track [26].
The momentum measurement in the tracking chambers is made possible by a superconducting solenoid. The solenoid is 3.8 m long and 3.0 m in diameter. The coil is cooled to 4.5 K with liquid helium and cold gas. When activated, the solenoid provides a 1.5 T magnetic field, which bends all charged tracks in the detector. The radius of curvature and dip angle in the charged tracks along with the magnetic field information can be used to calculate the momentum of the charged particles. Using cosmic ray muons, the resolution of the transverse momentum was measured to be:
σpt/pt = (0.13 ± 0.01)% · pt+ (0.45 ± 0.03)%
where the transverse momentum pt is measured in GeV/c.
3.4
Electromagnetic Calorimeter
The Electromagnetic Calorimeter (EMC), shown in figure 3.6, measures the energy of electromagnetic showers. The EMC consists of a cylindrical barrel, with an end cap in the forward direction. Ninety percent coverage of the solid angle is provided in the centre mass system, with (15.8 − 141.8)o degree coverage in the lab polar angle
and full coverage in the azimuthal angle.
The barrel of the EMC is lined with 5760 trapezoidal CsI(Tl) crystals, which are arranged in 48 polar-angle (θ) rows. The crystals are oriented towards the interaction point. The crystals increase in length from (16-17)X03 in steps of 0.5X0 every 7
crystals as you move from the IP to the front of the EMC. The forward end cap contains 820 crystals, and spans a solid angle corresponding to 0.893 ≤ cos θ ≤ 0.962
2
Within the BaBar coordinate system, the positive z-axis is in the direction of the electron path, the y axis is oriented along the vertical, creating a right handed coordinate system
3
X0is the radiation length and is defined as the distance over which the electron energy is reduced
Figure 3.6: A cross section view of the electromagnetic calorimeter with only the top half being shown [26]. Distances are shown in mm.
in the laboratory frame.
The energy and angular resolution of the EMC are: σE E = (2.32 ± 0.30)% 4 pE(GeV) ⊕ (1.85 ± 0.12)% σθ,φ = (3.87 ± 0.07) mrad2 pE(GeV)
where the ⊕ means that the two numbers are added in quadrature [26]. The energy resolution of the EMC is measured by monitoring decays of the π0 and the η into
two photons, using radioactive sources, and by observing Bhabha scatterings at high energies. The angular resolution is determined by measuring the decays of a π0 or η
into two approximately equal energy photons.
3.5
DIRC Particle Identification
The DIRC uses Cherenkov light to distinguish high energy charged π from charged K mesons as well as aiding in identifying electrons and muons. A particle that is traveling faster than the speed of light in a medium will radiate a cone of light known as Cherenkov Radiation. It is possible to determine the velocity of a particle in a medium by measuring the angle of the Cherenkov cone. The velocity of the particle can be used to determine the mass which is used to distinguish between the lighter
charged π from the heavier charged K. Figure 3.7 is a schematic of the DIRC system. As charged tracks pass through quartz bars in the barrel section, cones of Cherenkov light are emited. The light cones are internally reflected towards an array of photo multipliers that measure the Cherenkov angle. Figure 3.8 shows the relation of the Cherenkov angle to the laboratory momentum for different types of particles.
Figure 3.7: A schematic of the DIRC detector system [26]. Distances are shown in mm.
3.6
Superconducting Coil and IFR
The superconducting coil provides a means to measure charged particle momentum and the IFR system provides a way to do hadron/µ discrimination. The supercon-ducting coil supplies a 1.5 T magnetic field which bends charged tracks in the plane transverse to the beam direction. The arc of the bend is used to determine the mo-mentum of the charged tracks. Muons of energies above 0.6 GeV and hadrons are identified with the IFR. The IFR is composed of layers of steel and iron with active detectors sandwiched in between. The efficiency for identifying µ and π candidates is shown in figure 3.9
Figure 3.8: The plot displays the angle of the Cherenkov radiation as a function of lab momentum of charged tracks. [26].
Momentum (GeV/c)
Efficiency
Efficiency
0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 3-2001 8583A44 a) b)Polar Angle (degrees)
0.0 0.2 0.4 0.6 0.8 1.0 0 40 80 120 160
Figure 3.9: The left scale shows the µ identification efficiency and the right scale shows the π misidentification probability as a function for the laboratory track momentum (top) and polar angle (bottom) [26].
3.7
The BaBar Trigger
The trigger is a series of systems which work together as a primary filter that accepts events of interest and rejects unwanted events. The BaBar trigger is set up in two stages. First the events are passed through the hardware-based Level 1 trigger, and then they are passed through the software-based Level 3 trigger.
Each detector subsystem is prone to unwanted signals which are often referred to as noise. The source of the noise varies from fluctuations in the hardware, to cosmic background radiation or background from the beams. It is the job of the Level 1 trigger to discriminate background from physics events [26]. The Level 1 trigger filters events based on charged tracks in the DCH, showers in the EMC, and tracks in the IFR, each of which has its own trigger. The DCH and EMC triggers are primarily responsible for the identification of physics events in the detector, and the IFR trigger is responsible for rejecting events from cosmic ray background and triggering on µ+µ− events.
The Level 3 trigger reconstructs the events and classifies them according to their topology. Decisions on whether to keep or reject the event are made based on the entire event data available, which includes the Level 1 trigger information. The reconstructed quantities from the DCH and EMC are subjected to more stringent demands which reduces the amount of beam background and Bhabha ( e+e− → e+e−
scattering ) contamination. The selection in the Level 3 trigger proceeds through three phases. The first phase involves very generic classifications based on the DCH and EMC trigger information from the fast control and timing system responsible for discrimination of read out data from the front end of the detector. A second phase classifies the events further according to scripts which contain well measured and understood parameters from the current understanding of the SM. The third phase outputs logical statements based on the results from the first two phases.
Trigger results are then fed into the BaBar data acquisition system. This dedi-cated computing system has to meet fast timing requirements stipulated by the fast triggering done at Level 1, as well as provide controls for the BaBar detector. The computing system can handle rates of up to 2 kHz with an average event size of 32 kB. In addition to data acquisition and detector control, the computing system runs routine calibrations. Conditions important to data quality such as beam luminosity, gas purity, and voltage supplies are recorded for each event.
Chapter 4
Selection
The decays in this analysis are reconstructed from one of two final decay states, τ−→ π−π−π+η
γγντ or τ− → π−π−π+3π0ντ. The selection for both final states is
similar, where ηγγ and the π0s are reconstructed from two photon candidates. Other
differences in optimization of selection arise when selecting different intermediate resonances and are discussed in the following sections.
4.1
Data/MC Samples
Table 4.1 lists all of the Monte Carlo samples used in this analysis, along with the corresponding number of events in each sample. The τ -pair production is simulated with the KK2F Monte Carlo event generator [28]. The τ decays, continuum qq events, and final-state radiative effects are modeled with Tauola [29], JETSET [30], and Photos [31], respectively. Dedicated samples of τ+τ− events are created using Tauola
or EvtGen [32] where one of the τ leptons can decay to any mode and the other τ decays to a specific final state. The detector response is simulated with GEANT4 [33]. All Monte Carlo simulation events are passed through a full simulation of the BaBar detector and are reconstructed in the same way as the data. The data consists of the entire Υ (4s) sample, the bulk of the BaBar data set, which corresponds to approximately 468 fb−1.
Table 4.1: Monte Carlo samples used in this work and corresponding generators. Generic refers to standard BaBar Monte Carlo sets used in many analyses. KK2F generates two τ ’s which are then allowed to decay according to any branching fraction in Tauola and EvtGen generates two τ ’s where one tau is allowed to decay according to any mode and the other τ decays according to the specified decay channel.
Decay Mode Events Generator
Generic uds 2379G JETSET
Generic cc 1237G JETSET Generic τ τ 931G KK2F/Tauola τ−→ π−2π0ην τ 2.062M EvtGen τ− → π−2π0ων τ 2.062M EvtGen τ− → π−π−π+ην τ 4.138M EvtGen τ−→ π−f 1ντ 4.138M EvtGen τ− → π−η′(958)ν τ 2.062M EvtGen τ− → K−η′(958)ν τ 2.062M EvtGen τ−→ π−η′(958)π0ν τ 1.871M EvtGen
4.2
Tau preselection
The data and generic MC samples are passed through a set of loose preselection criteria that selects events with desired properties in a process called skimming, which is a coordinated effort at BaBar. The skim selects events based on specific physics signatures such as topology and particle identification. The skim imposes loose energy and mass requirements which can later be tightened in a physics analysis. Babar produces 50-100 skim samples some of which can reach up to 20% of the total data sample.
The Tau1N skim is used, which is designed to select τ pair events where one τ decays to a single charged track and the other τ decays to N charged tracks where N≥3. The Tau1N selector requires the charged tracks to pass the Good Tracks Very Loose (GTVL) criteria (the GTVL criteria is discussed in Appendix A). The tracks are required to originate close to the primary vertex, which eliminates events with a long-lived Ks → π+π− decay in the final state.
In the centre-of-mass frame the τ ’s are produced in a back-to-back topology. The event is bisected into hemispheres according to a plane perpendicular to the Thrust axis. The hemisphere which has one track is called the tag hemisphere and the other is the signal hemisphere. Figure 4.1 shows a e+e−
to a µ and the other τ decays to three charged tracks. The thrust axis is defined below.
Figure 4.1: Shown is a e+e− → τ+τ− event that contains 3 charged tracks in one
hemisphere (right side), and is being tagged by a single charged track (left side), in this case a muon. The perspective is transverse to the beam direction.
The thrust is a measure of the alignment of the particles within an event along a common axis. The skim imposes a requirement on the magnitude of the thrust Thrust > 0.8 to reduce q ¯q background. The thrust is calculated with the following formula T = max PN i (|(A · pi)|) PN i pp2 i (4.1)
where N is the number of tracks and neutral clusters used in the calculation, A is the thrust 3-vector with unit length, and pi is the three momenta of a charged track.
are back-to-back and the latter describes events that are spherical.
Sections 4.3-4.5 outline the requirements imposed on the data and MC samples. These sections present a discussion of general event selection, which helps remove background from non-τ events, the criteria applied to the tag hemisphere, and the selection applied to the signal hemisphere.
4.3
Event Selection
Thrust 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Events 0 50 100 150 200 250 300 350 400 Thrust 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Events 0 50 100 150 200 250 300 350 400 Data Signal MC Tau MC qqbar MCγ
γ
Thrust 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Events 0 20 40 60 80 100 120 140 Thrust 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Events 0 20 40 60 80 100 120 140 Data Non-Res Resonant Background 0π
0π
0π
Figure 4.2: The top plot is thrust for the η → γγ selection and the bottom plot is for η → 3π0. The q ¯q MC is normalized to the data luminosity, as τ modes which are
not measured in this analysis. The signal MC and measured τ modes are scaled to measured branching fractions.
A tighter thrust cut of 0.92 ≤ T ≤ 0.99 is applied to the data and MC samples. The lower bound eliminates much of the qq background as these events tend to be distributed more isotropically than τ decays. The upper bound removes e+e− and
µ+µ− events. Figure 4.2 shows the thrust after all selections have been applied.
The points in the figures are data and the coloured histograms are Monte Carlo. Depending on the decay (τ− → (3π)−η
γγντ or τ− → (3π)−3π0ντ), the coloured
Monte Carlo histograms are composed of different samples. All plots related to the 3τ− → (3π)−η
γγντ selection have signal Monte Carlo displayed in white, the entire
generic τ sample shown in tan and the generic qq sample shown in green. Plots which show variables related to the τ−
→ (3π)−3π0ν
τ selection contain non-resonant signal
modes in the white histogram, resonant signal modes in the tan histogram and qq along with all other τ decays in the green histogram.
4.4
Tag hemisphere requirements
The track in the tag hemisphere is required to be an electron or a muon, which signif-icantly reduces the background from q ¯q events. We impose the following conditions:
• Only one track in the tag hemisphere.
• The track passes the eMicroTight or the µMicroTight selection. • Pcms < 4 GeV/c
• Nneutrals < 2
• Eneutrals < 1 GeV
The eMicroTight and µMicroTight selectors are BaBar utilites that identify elec-trons and muons and are discussed in Appendix A. Pcms is the magnitude of the
3-momentum of the track in the tag hemisphere in the centre-of-mass frame, and is implemented to remove background from Bhabha and di-muon events. Nneutrals is the
number of neutrals in the tag hemisphere and Eneutrals is the energy of those neutrals,
and these cuts help to remove background from q ¯q events. Figure 4.3 and Figure 4.4 show the data and Monte Carlo for the tag variables. The plots show a generaly good agreement between data and Monte Carlo.
Tag Neutral Energy (GeV) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Events 1 10 2 10 3 10
Tag Neutral Energy (GeV)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Events 1 10 2 10 3 10 Data Non-Resonant Resonant Background 0 π 0 π 0 π
Tag CMS Lepton Momentum (GeV/c)
0 1 2 3 4 5 6 Events 0 20 40 60 80 100 120 140
Tag CMS Lepton Momentum (GeV/c)
0 1 2 3 4 5 6 Events 0 20 40 60 80 100 120 140 0 π 0 π 0 π Tag Neutrals 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Events 0 200 400 600 800 1000 1200 1400 Tag Neutrals 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Events 0 200 400 600 800 1000 1200 1400 π0π0π0
Figure 4.3: Plots showing the energy of the neutrals (top), the center-of-mass mo-mentum of the track in the tag hemisphere (middle), and number of neutrals in the tag hemisphere (bottom) for the η → 3π0 selection. In each plot all selections have
Tag Neutral Energy (GeV) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Events 10 2 10 3 10
Tag Neutral Energy (GeV)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Events 10 2 10 3 10 Data Signal MC Tau MC qqbar MC γ γ
Tag CMS Momentum (GeV/c)
0 1 2 3 4 5 6 Events 0 50 100 150 200 250 300 350 400
Tag CMS Momentum (GeV/c)
0 1 2 3 4 5 6 Events 0 50 100 150 200 250 300 350 400 Data Signal MC Tau MC qqbar MC γ γ
Tag Num Neutrals
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Events 0 1000 2000 3000 4000 5000 6000
Tag Num Neutrals
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Events 0 1000 2000 3000 4000 5000 6000 Data Signal MC Tau MC qqbar MC γ γ
Figure 4.4: Plots showing the energy of the neutrals (top), the center-of-mass mo-mentum of the track in the tag hemisphere (middle), and number of neutrals in the tag hemisphere (bottom) for the η → γγ selection. In each plot all selections have been applied except the one being plotted.
4.5
Signal hemisphere requirements
The goal of this selection is to identify the signal decay mode while excluding back-grounds from other τ -decays and non-τ events. This analysis measures several dif-ferent decay modes. Some signal selection criteria is shared by all decay modes, but others are specific to certain decay channels. The following subsections will discuss the general selections and the specific selections to each decay.
4.5.1
General Signal Selection
Three charged tracks are required in the signal hemisphere. The tracks are required to be either a charged π or charged K, depending on the mode being studied. The charged π candidates are identified with the PionLHTight selector and the K can-didates are identified with the KaonMicroVeryTight selector (see Appendix A for additional details).
We reduce our background by requiring that there are no photon conversions, • Nconv = 0
• NVTE = 0
where Nconv is the number of conversions. The conversions in this analysis are
iden-tified with the standard BaBar conversion finder (see Appendix A). In addition, if Mee > 0.02 GeV/c2, or both Mee > .005 GeV/c2 and Eee > 1 GeV then the
can-didate is not considered to be a conversion, where Mee is the conversion mass and
Eee is the energy of the conversion. NVTE is the number of tracks that satisfy the
eMicroVeryTight selection criteria. This requirement removes residual conversions not identified by the standard conversion finder.
The upper limit on the signal mass is set at the τ mass (Msignal < 1.8 GeV/c2),
where Msignalis the mass of the charged tracks and all neutral candidates in the signal
hemisphere. Applying the cut ensures that the signal mass is less than the mass of the τ and reduces background from qq events. Figure 4.5 shows the signal mass for the 3π3π0ν
τ final state without the cut applied, as well as the invariant masses of
the π+π−π0 and 3π0 systems. The 3π3π0ν
τ shows some resonant τ decays above the
τ mass. This is due to a shift which is applied to the resonant MC sample, and is detailed in section 6.7. The agreement in all plots is considered good. The peaks in the π+π−π0 plot have the same ammount of events in the data and Monte Carlo.
) 2 Mass (GeV/c 0 π 3 π 3 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Entries 0 50 100 150 200 250 ) 2 Mass (GeV/c 0 π 3 π 3 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 Entries 0 50 100 150 200 250 τ-→ 2π-π+ 3π0ντ
]
2[GeV/c
0 π 3 π 3M
Non-Resonant
Resonant
Background
) 2 Mass (GeV/c 0 π 3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Entries 0 20 40 60 80 100 120 140 160 180 200 ) 2 Mass (GeV/c 0 π 3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Entries 0 20 40 60 80 100 120 140 160 180 200 τ-→ 2π-π+ 3π0ντ ) 2 Mass (GeV/c 0 π π 2 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 2 Entries/0.02 GeV/c 0 200 400 600 800 1000 1200 1400 1600 ) 2 Mass (GeV/c 0 π π 2 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 2 Entries/0.02 GeV/c 0 200 400 600 800 1000 1200 1400 1600 τ ν 0 π 3 + π -π 2 → -τFigure 4.5: Plot of the invariant mass of the 3π3π0 system (top), the invariant mass
of the 3π0 system (middle), and the invariant mass of all of the π+π−π0 combinations
(bottom). The middle plot is showing the η resonance, and the last plot is showing the η and ω resonances. In the top plot all selections have been applied except on the signal mass.
