Hadron Production from e+e-Collisions around the Z0 Mass
by
Yuan-Hann Chang
B.S. (physics), Taiwan University
(1983)
Submitted to the Department of Physics
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
at the
Massachusetts Institute of Technology
June, 1990
3 Massachusetts
Signature of Author
Certified by
Institute of Technology 1990
Signature redacted
6-I/
Department of Pfysics
April 6, 1990
Signature redacted
Saruel C. C. Ting
Thomas Dudley Cabot Institute Professor of Physics
Thesis Supervisor
Signature redacted
Accepted by
George F. Koster
Ch airman, Departmental Graduate Committee
Department of Physics
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HADRON PRODUCTION FROM e+e-COLLISIONS AROUND THE Z' MASS
by
Yuan-Hann Chang
Submitted to the Department of Physics on April 10, 1990
in partial fulfillment of the requirements
for the Degree of Doctor of Philosophy in Physics
ABSTRACT
The properties of the Z' particle are studied with hadronic events taken by
the L3 detector at LEP. 14,352 events at ten different center of mass energies are
used to calculate the hadronic cross section. From a fit to the Z0 resonance line
shape, the Z0 mass, total width, and the hadronic cross section are measured to be
Mz = 91.14 0.025(experiment) 0.030(LEP) GeV, I7z = 2.529 0.053 GeV and
Ch(Mz) = 29.5 0.7nb. rinvisible is also fitted to be 0.548 0.029GeV, corresponds
to 3.30 0.18 species of light neutrinos. The possibility of four or more neutrino
flavors is ruled out at 4a confidence level.
The production of b-hadrons is studied through their semi-leptonic decay. A
sample of 80% b-event purity is selected. With this sample, the partial width of
Zo -- bb decay is measured to be 356.8 50MeV. The charge asymmetry at Zo peak
is measured to be 18.8 13.9%.
Thesis Supervisor: Samuel C. C. Ting
Title: Thomas Dudley Cabot Institute Professor of Physics
1
ACKNOWLEDGEMENTS
My interest in experimental physics started when I met Professor Samuel C.
C. Ting for the first time six years ago. Since then, his view of physics and method
of performing experiments deeply influenced my study of physics. His outstanding
leadership and his rigorous scientific requirements made the construction of L3
possible. I would like to express my highest respect and thanks to him, and hope I
have learned at least some of his knowledge.
I have very much enjoyed working in the L3 collaboration. I would like to
thank all the members of this outstanding group.
I thank Professor Ulrich Becker, from whom I have learned how an experiment
is actually done. His deep understanding of physics and broad knowledge of instrumentation are the key factors to the success of the L3 Muon Chambers, on which I
have been working as a graduate student. I especially appreciate his ability to think
of everything in terms of fundamental physics laws, even when fixing a broken car.
Many thanks to Dr. D. Antreasyan, Dr. B. Wyslouch and Prof. G. Herten.
I learned from them about the practical work in an experiment. They also guided
me in data analysis, on which this thesis work is based.
Working with Dr. J. Burger has been a most pleasant experience. He showed
me how important patience and complete devotion are for an experimentalist. His
continuous attention to the detector makes the experiment run smoothly. I own
him a lot of thanks.
During the construction of the Muon chambers, I benefitted a lot from Dr. M.
White, P. Berges, and I. Clare, for their excellent work in making the chambers.
Through them, the meaning of "precision" was understood.
I thank Professors M. Chen and J. Branson for inspiring discussions and their
guidance in my analysis work.
I am grateful to Professor A. Kerman and Dr. F. J. Eppling, the director and
vice director of LNS of MIT, for their strong support of the L3 experiment. I also
thank the L3 A&C group: Dr. S. Ting, Dr. P. Lecomte, Dr. M. Steuer and Dr. H.
Rykaczewski, for effective administration of the experiment.
Special thanks to T. Wenaus for his handling of the software. My study was
largely simplified through his nice job of providing an efficient computing environment.
I greatly enjoyed working with the L3 trigger group, under the leadership of
Dr. M. Fukushima. I appreciate their achievements in the extremely difficult job
of triggering and data acquisition.
I wish to express my gratitude to CERN, for its hospitality and help. The
excellent achievements of the LEP division of CERN have made this experiment
possible, and they also deserve a special acknowledgement.
I would also like to thank Ms. P. Slade, Ms. J. Hudson and Ms. G. Kogler for
their administrative assistance. The help from Ms. P. Harris is especially unforgettable. Without her help, life at CERN would have been much more difficult.
Last but not least, I would like to thank my family, and especially my parents,
for their continuous support and encouragement.
2
Table of Contents
A bstract
..................................................................
1
A cknow ledgem ents............................................................
2
Chapter 1 Introduction .....................................................
4
Chapter 2 Theoretical Predictions ........................................
6
2.1
The spectrum of fundamental particles .............................
6
2.2 The Z ' line shape .................................................
7
2.3
Partial and total decay width of Z 0 ........ . . . . . . . . . . . . . . . . . . . . . . . . 9
10
2.4 Charge asymmetry of ZO -+ ff decay .............................
12
Chapter 3 The Experim ent ...............................................
12
3.1
L E P .............................................................
:..12
LEP m ain ring .........................................
3.1.1
13
LEP injection chain .......................................
3.1.2
13
Energy resolution of LEP .................................
3.1.3
13
L3 detector .......................................................
3.2
14
BGO electromagnetic calorimeter .........................
3.2.1
15
Hadron calorim eter .......................................
3.2.2
15
M uon spectrom eter .......................................
3.2.3
17
3.2.4 Trigger ...................................................
17
The luminosity measurement .....................................
3.3
Chapter 4 Z 0 line shape ...................................................
4.1
The analysis m ethod .............................................
4.2 Event selection ...................................................
4.3
Backgrounds .....................................................
4.4
The line shape fitting .............................................
20
20
21
23
23
Chapter 5 b-quark production ............................................
Method of identifying heavy quarks ...............................
5.1
M onte-Carlo simulation ...........................................
5.2
Event selection ...................................................
5.3
5.4 ZO -+ bb partial width ............................................
bb asym m etry ....................................................
5.5
25
25
25
26
28
31
Chapter 6 C onclusion .....................................................
33
...............................................................
R eferences
Figure C aptions.............................................................38
...............................................................
Figu res
35
3
41
Chapter 1
Introduction
The Z 0 particle is one of the most interesting objects in particle physics. It
is one of the gauge bosons carrying the weak force. Its mass is generated when
the gauge symmetry is broken by the Higgs field. A study on the properties of
the Z' can improve our understanding of the gauge symmetry and the mechanism
of symmetry breaking, which are the fundamental principles underlying modern
particle physics. This thesis presents some measurements on the basic parameters
of the Z.
The Z 0 particle was predicted, with a detailed description of its properties, in
a theory of electroweak interactions by Glashow, Weinberg and Salam [1-1]. The
GWS theory is a quantum field theory based on SU(2)L x U(1) gauge symmetry and
spontaneous symmetry breaking (commonly known as the Higgs mechanism) [1-2].
It successfully unified the electromagnetic and weak interactions, and is supported
by experimental data [1-3]. The theory predicts the existence of four vector bosons,
W , Z 0 and a photon, together these particles were assumed to mediate the unified
electroweak interaction. After the confirmation of the existence of W and ZO particles by UA1 and UA2 at CERN in 1984 [1-4], this theory became the "Standard
Model" for high energy physics.
A precise measurement of the basic parameters of Z 0 is very important because
of the following reasons:
(1) Knowing the mass of Z0 helps to verify the Standard Model by confirming the
fundamental equation relating the masses of W and Z0 :
=
cos 2
W
(1.1)
Mz
where 6 w is the weak interaction angle, which determines the extent of mixing
between electromagnetic and weak interactions. The relationship between particle masses and interaction strength in this formula is an important feature
of the standard model. It is a result of the spontaneous symmetry breaking,
which is responsible for the masses of all the particles. Any deviation from
this relationship will indicate the failure of the standard scheme for symmetry
breaking. It is thus important to verify this relation by precise measuring of
independently.
Mz, Mw and cos2
(2) The standard model groups fundamental fermions into families, but does not
predict how many families exist. Because each family contains exactly one
massless neutrino, we can determine the number of particle families by counting
the number of neutrino types from Z 0 decay. Although not directly detectable,
every neutrino type with a mass less than half the ZO mass contributes - 166
MeV partial width to the total Z' resonance width. A precise measurement of
4
the width of Z 0 therefore gives the number of different neutrino species, hence
the number of fermion families. This measurement is also sensitive to any new
particle which does not interact with the detector material.
(3) A "Z0 factory" is a rich resource for both new particle searches and detailed
studies of known phenomena. When decaying, the Z 0 interacts with some predicted but not yet observed particles like Higgs particles and top quarks. It also
interacts with most new particles predicted by theories that are enlargement of
the standard model [1-5]. Since the production rates of these processes depend
explicitly on the mass Mz, and sometimes the width 'z, of the Z 0 , a good
knowledge of these parameters is highly desired.
(4) Independent from the standard model, measurements on the weak coupling
constants gv and gA are also interesting. These constants determine the relative strength of vector and axial-vector coupling of weak interactions. At the
Z 0 peak, since the contribution to the total cross section from photon exchange
is relatively small, the measurements of g and gv are direct and free of QED
effects. In the hadronic channel, the coupling constants for b and c quarks can
be measured and provide information on the weak interactions of the unobservable quarks. Comparing the weak coupling constants from the quarks to
that from the leptons also provide an important test to the standard model.
Even though UA1 and UA2 discovered the Z 0 particle, they were not able
to fulfill these purposes. Their experiments were based on ZO's from pP collision
which, due to the complicated structure of protons, is not suitable for precision
measurement. The signals of hadronic decay from the ZO's produced in pP collisions
are obscured by the large background hadrons. The observation of the Z 0 from pP
collisions is therefore limited to leptonic decay channels, which comprise only 10%
of the produced Z 0 . The energy carried by the produced Z 0 is also not equal to
the beam energy, which is known with good precision, and has to be measured less
precisely by the detector.
Compared to pP collisions, e+e-collisions have the advantages of a simple and
well understood initial state, a clean final state and a high ZO production rate
at the resonance peak. Hadronic Z0 decays become accessible in e+e-collisions
and they provide high statistic measurements on certain parameters. Currently,
two e+e-facilities have been constructed: SLC at SLAC and LEP at CERN. The
former is a linear collider and the latter a storage ring. During 1989, both SLC and
LEP succeeded producing ZO's for physics study.
This thesis work is based on the Z 0 events taken by the L3 detector at LEP,
concentrating on hadronic decays of Z 0 around its resonance. The ZO mass and
width will be determined by line shape fitting. The number of neutrino types will
be derived from the width measurement. The partial width and charge asymmetry
of Z 0 -+ bb decay will be measured through the leptonic decay of b-quarks.
5
Chapter 2
The theoretical predictions
At center of mass energies near the Z 0 mass, the process e+e- -+ hadrons can
be separated into several steps. First, e+e-annihilate into a Z 0 , which decays with
a 70% probability to a quark-antiquark pair. This step is purely electroweak and
the cross section can be precisely predicted by perturbative expansion of the electroweak theory. The quarks produced in Z0 decay can sometimes radiate photons
or gluons. Photon radiation is well understood through QED (quantum electrodynamics) [2-1], and the gluon radiation can be estimated by perturbative QCD
(quantum chromodynamics) [2-2]. We do not observe directly the partons, because
the strong interaction does not allow them to exist except in a bound state. Partons has to go through a fragmentation process in order to produce hadrons which
are observed by particle detectors. The fragmentation is a non-perturbative strong
interaction process, about which our knowledge is limited.
An important feature of the hadron production in high energy e+e-collisions
is that parton production and fragmentation can be treated independently. This
is a result of the "asymptotic freedom" [2-3] of strong interaction, which states
that at very small distances, the strength of the strong interaction is reduced such
that perturbative predictions are possible. At energies around the Z0 mass, parton
production happens at a length scale much smaller than that of non-perturbative
strong interactions. The strong interactions at that stage can therefore be treated
with perturbation methods similar to the electroweak interaction. The fragmentation process happens at larger distance by which time the partons have already
been created, therefore does not interfere with parton production. Based on this,
we adopt the following view: The hadronic total cross section is determined only by
the production rate of partons, which is well understood through the electroweak
theory and perturbative QCD. The fragmentation, although poorly understood,
does not affect an inclusive measurement of the total cross section. we assume also
that the properties of the strong interaction are unchanged at the energy scale of
the Z0 mass and hence low energy measurements can be extended to model the
fragmentation process.
In this chapter, a brief description of the ZO line shape based on parton level
calculation is presented. We ignore the fragmentation process and rely on the
Monte-Carlo simulation to handle it.
2.1
The spectrum of fundamental particles
Presently three families of fermions are known. Each family consists of one
electron-like lepton, one neutrino, one up-type quark and one down-type quark.
The top (up-type) quark and the r-neutrino of the third family have not been
experimentally observed. Table 2.1 lists the particles and some of their quantum
numbers.
In addition to the fermions, there are also vector bosons which mediate the interactions. Table 2.2 lists these particles and their quantum numbers. The graviton
(G) is not well established theoretically and has not been confirmed by experiment.
The standard model also includes a neutral scalar boson, the Higgs particle. It
6
comes from the spontaneous symmetry breaking and is responsible for the mass of
all the massive particles. Higgs particle has not been observed experimentally.
Flavor
spin
charge
u,c,t (up-type quarks)
1/2
2/3
d,s,b (down-type quarks)
Ve,,Vp,. (neutrinos)
e,p,r (charged leptons)
1/2
1/2
1/2
-1/3
0
-1
I
13
color
1/2
0
triplet
-1/2
1/2
-1/2
0
0
0
triplet
singlet
singlet
Table 2.1 The fermions and their quantum numbers. IL and Ik are
the third component of weak isospin for left and right handed particles
respectively.
spin
1
1
1
1
2
Z0
(weak boson)
W+ (weak boson)
-y (photon)
gi (i = 1... 8 gluons)
G (graviton)
Table 2.2
charge
0
1
0
0
0
color
singlet
singlet
singlet
octet
singlet
The Bosons and their quantum numbers.
The Z 0 line shape
To the lowest order of perturbative expansion, the total cross section of e+e- _
where f indicates any fermion, is
2.2
2
o0 = sNcD(s) [
12 reerff
+
MZ2Nc
If
I(s
MZ)
-
+
ff,
S
47rQ a 2Nc
3s
(2.1)
where
s =EM
D(s) =
ree,
1
s - mz2 + imzrz
=
Z* propagator,
rff = partial width of e and f,
Nc = color factor = 1 for lepton and 3 for quarks,
Qf
= charge of fermion
f,
and I is a constant which determines the interference between photon and Z 0 propagation. The standard model gives:
=
27ra 2 2
sin9W cos 2 9
si2o2
Qe Qf [ggf +gegf +gegf +g g9]
with
gIf = j - Q sin29W
g
2
= -Qf sin o
7
.
where Qf is the charge of the fermion and I' is the third component of weak isospin
for left handed fermion f, the values can be found in Table. 2.1.
The three terms in (2.1) are contributions from Z0 exchange, interference and
y exchange, respectively. The corresponding Feynman diagrams are displayed in
Fig. 2.1
The total hadronic cross section is the sum of contributions from different
quarks:
Or
c+
=h 1 uu~d~s~
(2.2)
Oro
At center of mass energy around the Z 0 mass, equation (2.1) gives a BreitWigner form due to Z 0 resonance, as the photon exchange and interference terms
are comparatively small. However, it is not enough to include only the lowest order
expansion at this energy scale, the higher order corrections can contribute as much
as 25% to the total cross section. In estimating the contribution from higher order
terms, two categories of corrections are treated separately [2-4]:
(A) Corrections not from initial state radiation: including photon loops, fermion
loops, box diagrams and QCD corrections. The net effect can be summarized
as:
(1) A redefinition of Jr to account for final state radiation, final state QCD
corrections and vertex corrections. Details will be presented in section
( 2.2).
(2) Use an energy dependent total width in the propagator, i.e.,
D(s)
=
s
-
1
M2 + iMz z x (s/M )
(2.3)
(3) Use an energy dependant coupling constant, a(s). At ZO mass, a(Mk) is
about 1/128.
Items (2) and (3) are mainly from loop corrections to the ZO propagator and
higher order -y - Z' mixing.
Including all these effects, we obtain a line shape function
the peak position by about 35 MeV from that of oro.
7nr(S),
which shifts
(B) Radiative corrections: Initial state photon bremsstralung is by far the largest
correction to the total cross section, due to the large deceleration of e+e-before
collision. The net effect of the radiation is to reduce the available energy for
Z' creation, hence shift the production probability to a value corresponding
to lower energy. It is therefore proper to treat this correction by convoluting
the cross section without radiative corrections, 0 nr, with the probability of
bremsstralung radiation:
a(s) =
dzon,(zs)G(z)
8
(2.4)
where
z = the ratio of the invariant energy left after radiation
G(z) = the probability of radiating photons.
The form of G(z) is complicated. We have used an exponential approximation
of the leading log corrections to all orders, plus other terms from the lowest orders.
The importance of including the correction to all orders can be realized by the fact
that radiative correction results in a 26% reduction in the total cross section at Z'
peak, and about 120 MeV shift of the peak position. Detailed form of G(z) can be
found in reference [2-4].
2.3
Partial and total decay width of the Z0
As mentioned in the Introduction, the ZO can decay into any fermion antifermion pair if the fermion mass is less than half of its mass. To the lowest order
the partial width of each fermion flavor is:
=
N~~[(g,)
+ (g[) 2 ](25
where
G= Fermi's weak coupling constant measured from muon decay.
and the standard model gives
g= 'Lf - 2Qf sin2
(2.6)
f = 13f
they are the vector and axial-vector coupling constant of weak interactions, respectively.
Important higher order corrections include radiation and loops of photons or
gluons and vertex corrections [2-5]. Using the measured value of G,, the loop
corrections are largely absorbed. The remaining corrections can be taken care of
by:
(1) Multiply the QED correction (1+ 6QED), and the QCD corrections (1+ 6QcD)
in the case of quark final states. Where
6QED = 3aQ2 = 0.0017 x Q(.
47r ff(2.7)
6QCD = a,/3 + O(a2)
0.02[2-6]. Ina. is estimated based on low energy measurement to be 0.12
0.007. This
cluding higher order correction, 6QCD is estimated to be 0.040
correction comes from photon and gluon radiation.
9
(2) Replace sin2
by s2, where
-2
sin2
w + Cos2o
bp
(2.8)
3Gm2
87r2v/g
.
This correction comes mainly from top quark loops coupled with Z 0
Table 2.3 presents estimated partial widths according to the standard model,
assuming Mz = 91.14GeV, mt,, = 100GeV, mH = 100GeV and a, = 0.12.
The variation due to different top quark mass and Higgs mass is less than 10MeV
for 60 < mt,, < 200GeV and 10 < mH < 1000GeV.
Peel
83.4
r.,
166.2
Puul
PddI
381.4
295.8
Ph
1734.4
bbl
378.5
ff
Table 2.3 The expected partial width of Z 0 -+
decay in MeV.
The total Z 0 width can be expressed as:
r =
NP, + 3Pee + 3Pdj+ 2ua
(2.9)
where we have included every known fermions and have assumed universality between fermion families. With the same assumptions as above, (2.7) gives Pz =
2.483GeV for three neutrino species.
The number of light neutrino species can be measured by solving (2.9):
Nv = Pinvisible/i
3
= (P - 3ree -
Charge asymmetry of Z' -+
2.4
(.
rd; - 2Pru)/(2
ff
decay
The charge asymmetry is defined by:
Aff =7f
=9cf
(2.11)
-
+
ab
where
of = Cross section with the fermion being scattered to the forward region.
Ob
= Cross section with the fermion being scattered to the backward region.
On the Z 0 peak, the charge asymmetry for e+-
-+
ff
is predicted by the standard
model to be:3
AJ f(Mzo) =
10
AeAf
(2.12)
where
2gf
Af =~(g)2 +
f
f
(g a)2
(2.13)
The most important higher order corrections are initial state radiations. They
can be treated by convoluting the uncorrected differential cross sections with the
probability function of bremsstralung radiation. Numerically, we find Abb = 10.8%
for Mz = 91.14GeV.
B0 - f 0 mixing changes the charges of b-quarks in B0 mesons, results in an
opposite charge asymmetry for these events. The net effect is a reduction of the
measured asymmetry. Assuming the average ratio of charge-flipping mixing to be X,
the measured asymmetry becomes (1 - 2X)Abb. Using the experimentally measured
value of = 0.12 0.06 [2-7], the expected asymmetry is then 8.2%.
11
Chapter 3
The experiment
The experiment is performed by the L3 detector at the LEP e+e-storage ring.
In this chapter, the structure and functioning of LEP and L3 are briefly described.
LEP
3.1
LEP main ring
3.1.1
LEP (Large Electron Positron collider) is a storage ring designed to store and
accelerate electrons and positrons up to 100GeV energy. It is built by CERN at
the border of France and Swiss. The LEP tunnel is 26.7 km in circumference, 3.8
m bore and 50 to 70 meters underground. Fig. 3.1 shows the layout of LEP. Some
LEP parameters are listed in table 3.1 [3-1].
Table 3.1 Main LEP parameters (phase 1)
Circumference (including sagitta in dipoles)
Average radius
Bending radius in the Dipoles
Field in dipole magnets
Nominal current per beam
Revolution Time
Accelerating Frequency
Injection Energy
Number of bunches per beam
Number of interaction points
Horizontal betatron wave number
Vertical betatron wave number
Number of RF cavities
Synchrotron radiation power
Accelerating Gradient
Nominal luminosity
26658.883 m
4242.893 m
3096.175 m
0.06T
3 mA
88.9245 ps
352.2 MHz
20 GeV
4
4
70.44
78.37
128
1.6 MW
1.47 MV/m
1.7 x 10 3 1 cm
2 s'
LEP has 3400 bending magnets, with maximal bending field 0.13 tesla. This
low field allows an unusual steel-concrete mixed core, in which the 1.5mm thick
steel laminations are spaced by 5.5 mm thick concrete filling. This design saves
the construction cost and improves the mechanical rigidity. In addition, LEP has
760 quadrupole and 512 sextupoles. Except for the mini-beta quadrupole, all the
magnets are made of conventional (non-superconducting) materials.
Due to synchrotron radiations, 50 GeV electrons lose 120 MeV of energy every
turn. To compensate for this loss, 128 RF cavity units are used to accelerate the
beams. Each cavity has 5 slot-coupled cells. Each group of 16 cavities are powered
by 2 coupled Klystrons of 1 MW output each. To lower the energy consumption,
every cavity is coupled with a spherical storage cavity with low energy dissipation.
RF energy oscillates between the 2 cavities, on average spending half the time in the
12
low-loss storage, and thus maintains a lower average energy loss. For the second
stage of LEP, superconducting cavities will be installed to achieve 100 GeV per
beam.
Four bunches of electrons and four bunches of positrons are stored in the vacuum beam pipe for collision. The vacuum is kept at 3 x 10-9 Torr for a proper life
time. During 1989 running period, luminosity of 3 x 10 30 cm-2 s-1, with 1.2 mA
current each beam, has been achieved at beam energies between 88 GeV and 94
GeV. Beam lifetime averages about about 20 hours.
3.1.2
The LEP injection chain
Fig. 3.2 shows the LEP injection chain. A high intensity electron beam is
created by an electron gun and accelerated to 200 MeV by the electron Linac LIL.
The 200 MeV electron beam produces positrons in a tungsten converter target. The
electrons for filling LEP are produced by another electron gun near the converter.
The electrons and positrons are further accelerated to 600 MeV by LIL, then transmitted to EPA (the Electron-Positron Accumulator). EPA stores and accumulates
the beam and transmits it to the PS (Proton Synchrotron). PS accelerates the
beam to 3.5GeV and then sends the bunches to SPS (Super Proton-antiproton Synchrotron), where they are accelerated to 20 GeV and finally injected into the LEP
main ring.
3.1.3
The energy resolution
The absolute beam energy is measured by integration of the bending magnet
field. Uncertainty in the absolute energy measured by this method is 0.1%, with
a reproducibility of 2 x 10-. By injecting a 20 GeV proton beam to the LEP
main ring and measuring the frequency of circulation, the absolute energy scale is
calibrated to 30 MeV precision. The relative energy difference between different
beam energies is precise to 10 MeV, and the energy spread within one bunch is 40
MeV [3-2].
3.2
The L3 detector
The L3 detector (Fig. 3.3 ) [3-3] is designed to measure with high precision
the momentum of muons, electrons and photons. It also measures the energy flow
of hadronic jets. L3 locates in a cavern 50 meters underground at LEP interaction
point 2. The whole detector is installed inside a solenoid magnet which provides 5
kG uniform magnetic field. All detector components are supported by a 32 m long,
4.5 m diameter steel tube. The major detector components, from interaction points
outwards, are:
- A vertex chamber, which measures the track of charged particle with 40 pm
precision.
- 22 radiation lengths of electromagnetic calorimeter made of BGO crystals, measuring energy of electrons and photons with 1% resolution.
- A layer of thirty scintillation counters for cosmic ray rejection and trigger decision.
- A hadron calorimeter made of Uranium absorber plates interleaved with sampling proportional chambers.
13
- A Muon filter made of brass plates with proportional chambers.
- Three layers of drift chanmbers, which measure the momentum of a 50GeV muon
with 2% resolution.
- A pair of luminosity monitors at small angle, consisting of planar drift chambers
and BGO crystals.
.
The detector covers 97% of 47r solid angle for electron, photon and hadron
detection, and 70% for high precision muon detection. In the following, BGO electromagnetic calorimeter, hadron calorimeter and muon chambers, which are used
in this study, are described.
3.2.1
BGO electromagnetic calorimeter
The electromagnetic calorimeter is designed to meet the following goals:
(1) Good (- 1%) energy resolution for e and y from 5 to 50 GeV.
(2) Good angular resolution for y.
(3) Hadron rejection around 103 for electrons above 1 GeV.
To achieve these goals, a high resolution, total absorption, fine granularity
calorimeter was required. Furthermore, to leave room for a long lever arm muon
detector, the available space was limited. Bismuth Germanate (BGO, Bi 4 Ge 3 012),
with its short radiation length, was the best choice. Other advantages of BGO
include very good intrinsic resolution (1% for E > 1 GeV) and it's high radiation
hardness.
The central calorimeter is made of 7680 BGO crystals, arranged in 48 rings of
160 crystals each (Fig. 3.4 ). Each crystal is a truncated pyramid pointing to the
interaction point. The two end surfaces are of dimensions 2 x 2cm2 and 3 x 3cm2
The length is 24 cm, corresponding to 22 radiation lengths. Since every crystal
has to point to the interaction point, the shape of the crystals varies slightly for
different rings. The crystals are mounted in a carbon fiber structure which supports
the weight of the crystals, fixes their positions and minimizes gaps between crystals.
Since the BGO operates in a 5.1 kG magnetic field, and because of the limited
space available, conventional phototubes are not used. Instead the light output of
the crystals is collected by two 1.5cm 2 photodiodes. A microcomputer controlled,
large dynamic range ADC is used to read the signal from each crystal, rendering
21 bits equivalent range with 10 bits resolution. The system is also used to read
1280 temperature sensors, which are used to monitor the temperature in order to
maintain a stable running environment.
Every crystal in the calorimeter has been calibrated within two fully equipped
half barrels. Electron beams with 2, 10 and 50 GeV were employed to measure
the calibration constants. The effect of different impact points and temperature
variations were also measured. Cosmic muons are used in situ to monitor the
calibration constants measured at the test beam. The electronic gain is further
monitored by a Xenon light source distributed to each crystals by optical fibers.
The overall energy resolution achieved in the test beam was 1.6% at 2GeV and
0.62% at 50GeV [3-4].
14
The hadron calorimeter
3.2.2
The Uranium hadron calorimeter consists of a barrel and endcaps. (Fig. 3.5).
The barrel covers the central region (450 < 0 < 135*) with 9 rings of 16 modules
each. The endcap covers the polar region 5.5* < 9 < 450 and 1350 < 9 < 174.5*
with three rings in each side of the interaction point. The barrel and endcap together make a 99.5% coverage of the 47r solid angle with a minimum of 3.5 nuclear
absorption length.
The barrel modules are made of depleted uranium absorber plates interspersed
with wire chambers operating in proportional mode. The "long" modules in the
central three rings contain 60 planes of proportional chambers and 58 uranium
plates of 5mm thick. The "short" modules of the outer 6 rings have 53 planes of
chambers and 51 planes of uranium absorbers. The stack of absorber/chambers
is supported by four spacer bar in between two stainless steel plates, which also
function as shielding from the natural radioactivity of uranium.
The chamber planes are made of arrays of brass tubes with 0.3mm thick walls
and inner dimensions of 5mmx10mm. The 50 pm gold-plated tungsten anode
wires are crimped into gold-plated brass jacks, which in turn are fitted into plastic
end pieces. To minimize the dead regions due to end structure, the chambers
are operated with the anode wire at ground potential. The chamber walls are at
negative high voltage. Wire plane orientations alternate layer by layer, and are
either parallel or perpendicular to the beam line.
Signal wires are grouped into towers for readout. The wires in each tower are
connected in parallel. Signal from each tower is amplified by a preamplifier, sent
through 40 meters of twisted pair cable and digitized by a charge integrating ADC.
The total number of charge sensitive readout channels in the barrel is 23,040.
The endcap hadron calorimeter has the same basic design of uranium absorber
with proportional chamber sampling. The structure is inside a stainless steel container of half ring shape. The wire planes are perpendicular to the beam line.
Within a half ring, a chamber layer consists of four chambers, each covering an interval of A4 = 45*. The wires are stretched azimuthally to measure the polar angle
9 directly. Neighboring chamber layers are rotated by 22.50 to allow measurement
of the 0 angle. The towering scheme groups the chamber wires to towers pointing
to the interaction region. In total 3960 tower signals are digitized and read out.
The response of the hadron calorimeter modules to hadron and electron beams
has been measured between 1GeV and 50GeV in a test beam. The response as a
function of energy is linear. The resolution is measured to be (55/VEK + 5)% [3-5]
(Fig. 3.6 ). As is shown in Fig. 3.6, this result agrees with the resolution observed
in hadronic Z0 events from e+e-collisions in LEP. Calibration with cosmic rays and
the y rays from radioactivity of uranium has been performed regularly in situ.
3.2.3
The Muon spectrometer
The L3 muon detector is designed to measure high energy muons with an accuracy of Ap/p = 2% at 45 GeV. Three layers of high precision drift chambers between
the supporting tube and the magnet coil are used to measure the curvature of the
muon tracks. This design has the following advantages:(1) The inner detectors filter
15
6
1
out most of the particles originating from the interaction point except for muons.
This makes the identification of muons very easy even within a hadronic shower.
(2) The space available allows a lever arm of 2.9 meters between the inner and outer
chambers. With the 5.1 kG magnetic field, a 45 GeV muon track deviates from a
straight line by a sagitta of 3.55 mm, making it possible to reach 2% momentum
resolution.
Since the volume filled by the muon detector is very large (1000 M 3 ), it is
important to modulize the detectors. The system consists of two ferris wheels,
each having 8 independent units called "octant"s. Each octant consists of two
outer chambers (MO), two middle chambers (MM) and one inner chamber (MI),
supported in a special mechanical structure (Fig. 3.7 (a)). MO and MI contains
a volume which is divided electrically into 19 (MI) and 21 (MO) drift cells. Each
cell has 16 sense wires measuring the track coordinate in the bending plane. The
volume is closed on top and bottom by drift chambers for polar angle measurement.
The MM chambers are divided into 15 cells, with 24 wires each for momentum
measurement, and closed by honeycomb panels to reduce the multiple scattering.
Fig. 3.7 (b) shows the structure of an outer chamber.
The P-chambers are filled with a mixture of Ar/ethane (61.5%:38.5%). With
the nominal voltage setting (4150 volts on anode sense wires and -3050 volts on
cathode mesh), in a 5.1 kG magnetic field and at 740 mmHg pressure, the gas gain
is about 8 x 104. After an electronic amplifier with 24 mV/pA gain, the signals
are discriminated with a threshold of 10% average pulse height and digitized by
Fastbus TDCs. The drift velocity is 51 pm/nsec, and the Lorentz angle is 19*. The
single wire resolution is measured to be less than 220Im throughout the entire drift
region[3-6].
To measure the sagitta of a muon track with high precision, the alignment
between different chamber layers is of critical importance. High energy muon tracks
will pass through only one octant, therefore only the internal alignment within
one octant is relevant to the momentum measurement. An optical system [3-7] is
built into each octant to define an octant central line and measures the position of
the wires within an octant relative to it. The optical system has been verified by
cosmic rays and a UV laser system built on the octants to fulfill the 30pm alignment
requirement in the sagitta measurement. The relative position of the octants to the
LEP central line is measured by optical survey to within 2mm.
The resolution of the momentum measurement depends on the intrinsic chamber resolution, the alignment error and the multiple scattering. From a full MonteCarlo simulation, assuming 250 Mm single wire resolution and 30 pm alignment
precision, Ap/p for a 50 GeV muon is 2.4%. Where 1.7% are from the chamber
resolution, 1.3% from the multiple scattering and 1.1% are from the alignment errors. During 1989 running period, 2.4% resolution has been achieved in measuring
ZO -_, p+p- decay.
Z chambers [3-8) consist of two layers of drift cells offset by one half cell with
respect to each other to help resolve the left-right ambiguity. Each cell has two
parallel aluminum I-beams connected to -2.4kV, with one gold plated molybdenum
16
wire with 50 pm diameter at 2.05 kV. The drift velocity in the non-explosive Argon
(91.5%) / Methane (8.5%) gas mixture is about 30 pm/nsec.. Single wire resolution is typically 500 pm. Since there are Z chambers on top and bottom of inner
and outer chambers, a charged particle originating from the interaction point with
-0.7 < cos 9 < 0.7 leaves eight Z chamber signals for track reconstruction. A total
of 7680 wires are connected to the same amplifier-discriminator system as the P
chambers and digitized by Fastbus TDCs.
3.2.4
Trigger
The primary trigger used for hadronic events is a energy trigger in the calorimeters which requires 15 GeV total energy or 12 GeV clustered energy. An independent
trigger, which requires six out of sixteen 0 sectors of the scintillation counters, is put
in "OR" with the energy trigger. Comparing the trigger result in accepted events
shows that the energy trigger is at least 99.9 % efficient and the scintillator trigger
is 93% efficient. For inclusive muon events, a fast track finder for muon chamber
hits provides another independent trigger. From the inclusive muon events accepted
by muon trigger, the energy trigger is found to be better than 99.5% efficient.
During the start-up phase of the hadron calorimeter end caps, an inefficiency
of 6 i 0.3% was found in the end cap region. For the cross section measurements,
the number of hadronic events has been corrected for this trigger inefficiency.
3.3
The luminosity measurement
The integrated luminosity is measured by counting small angle Bhabha events
in two luminosity monitors located on each side of the interaction point, at z =
2765mm. The luminosity monitor consists of eight layers of cylindrical rings of
BGO crystals, covering the region 14.7mrad < 0 < 69.3mrad. Azimuthally, the
crystals are arranged in 16 sectors of 19 crystals each. Fig. 3.8 shows the layout
of the crystals. The light output of the BGO is measured by photodiodes mounted
on the rear of each crystal, and read out through an ADC system identical to that
used in barrel BGO calorimeter.
The luminosity trigger is based on the analog sum of signals from each sector.
The trigger is defined by the 'OR' of the following three conditions [3-9]:
(1) Back-to-back coincidence between the sum of two adjacent sectors, with E >
17GeV in each side.
(2) Coincidence between the two BGO arrays, with E > 23GeV in each side.
(3) Asymmetric coincidence between the BGO arrays, requiring E > 30 GeV in
either one of the two arrays and E > 7.5GeV in the other array.
The internal comparison between the symmetric and asymmetric trigger shows
a 1.4 0.2% inefficiency, due to a small geometric region found to be inefficient.
Outside this region, the efficiency is at least 99.9%. A 0.2% systematic error is
therefore assigned to the luminosity due to trigger inefficiency.
The Bhabha event selection is based on the reconstructed shower variables 9,
4 and E. The selection conditions are:
(1) 1700 < AO < 190*.
(2) 30.1mrad < 1,2 < 63.9mrad and 24.7mrad < 92,1 < 69.3mrad
17
(3) E 1 ,2 > 0.33fi.
Fig. 3.9 shows the distribution of AO. The background is estimated from the
side-bands(140* < AO
1600) and found to be about 0.1%.
Two fiducial volumes are defined in the asymmetric cut condition (2): "loose",
24.7 < 9 < 69.3mrad, and "tight", 30.1 < 9 < 63.9mrad. The fiducial limits correspond to the boundary between two crystal rings. Two data sample are selected:
(1) "tight" fiducial volume in +Z side and "loose" fiducial volume in -Z side, and (2)
vice-versa. To reduce the sensibility to the non-perfect geometry and finite position
resolution, the average of these two samples is used in the luminosity calculation.
To asset the systematic uncertainty in the event selection, different cut conditions are applied. The result variations in the integrated luminosity are shown
in Table 3.2. The value of the integrated luminosity is very stable. Even in the
case where the acceptance is 59% reduced, the integrated luminosity changes by
less than 0.2%. Based on Table 3.2, we estimated a 0.8% systematic error in the
integrated luminosity due to event selection.
Cuts
< 63.9mrad
170* < z4 < 190'
std
Emin
0.33 /s
std
-
-
-35.43
-35.35
+0.12
1740 < AO K 186*
165* < AO K 1950
std
std
std
0.28V/s
+0.25
-0.32
+2.11
+0.31
-0.40
+2.88
+0.06
-0.08
+0.77
AO
M.C.
-
"tight" fiducial
30.1 < 9 < 63.9mrad
35.6 < 9 K 63.9mrad
std 41.1 <
std -59.24
K
-59.30 -0.15
std
std
std
Change in Percent
Data
Data/M.C.
Table 3.2 Sensitivity of Bhabha sample to event selection cuts. First line gives the
standard cut.
Additional systematic errors from the Monte Carlo statistics (0.8%), internal
detector geometry (0.8%), and the theoretical uncertainty of 0.6% must also be
taken into account. Including the trigger efficiency and selection errors, and adding
all errors in quadrature, the overall systematic uncertainty is 1.7%.
During 1989, a total of 1 pb- 1 integrated luminosity was collected, of which
759(nb- 1 ) was used in the analysis for this thesis. Data were at 10 different center of
mass energies around Z0 resonance, with about half on the peak. Table (3.3) shows
the energy, number of Bhabha events and the corresponding integrated luminosity.
18
v/s (GeV)
88.279
89.277
90.277
91.030
91.278
91.529
92.280
93.276
94.278
95.036
NBhabha
7822
5703
4256
10681
8938
10111
4030
4664
3962
813
f Ldt (nb-)
86.93 0.98
67.45 0.89
52.98 + 0.81
124.06 1.20
118.93 1.26
129.06 1.28
55.60 + 0.88
60.53 + 0.89
52.64 + 0.84
11.03 + 0.39
Table 3.3 Number of small angle Bhabha events and the corresponding
integrated luminosity. The errors quoted are statistical error only.
19
Chapter 4
The Z0 line shape
The goal of this chapter is to measure the total hadronic cross section of
e+e-collisions near the Z 0 mass to a precision of 2%. With the measured cross
section, the Z 0 line shape is then fitted with an analytic formula based on the
standard model. Physics parameters like the Z0 mass and width and number of
neutrino types are extracted from the fit.
The analysis method
The analysis of hadron events is based entirely on the energy measured in
the BGO and hadron calorimeter. Hits in BGO crystals and hadron calorimeter
towers are grouped into clusters by finding isolated local energy maxima and the
hits associated with them. The clusters within 0.65 radian of a jet axis are further
grouped into a "Jet", while the jet axis is determined by maximizing the sum of
the projected cluster energy along that axis. Since the central tracking chamber is
not used in this analysis, the clusters are our closest approximation to individual
particles, and a Jet is the reconstructed object that corresponds to a real hadron
jet. Fig. 4.1 shows a typical two jet event recorded by the L3 detector.
The nature (hadronic or electromagnetic) of each cluster is determined by the
extent of geometrical spread of the energy deposit and by the ratio of energy deposits
between BGO and hadron calorimeter. Different calibration constants are then
applied accordingly to calculate the cluster energy. The angular direction of a
cluster is defined by the energy weighted sum of the directions of individual hits in
the cluster. The total visible energy (Ev,,) is the scalar sum of the energy of all
reconstructed clusters, and the energy imbalance is obtained from the vector sum of
the energy of the clusters. The energy and axis of the jets are similarly calculated.
The event shape is described by Thrust, Major, Minor and Oblateness defined
as follows:
(4.1)
IEi -ei l/Evi,
Thrust = T = max
4.1
in which the sum is over all the reconstructed clusters and el is the direction to
maximize the projected energy flow;
IjEi - e 2 Evis
Major = Fmajor = max
in which e 2 is perpendicular to el and is the direction which maximizes the energy
flow in the plane perpendicular to the thrust (el);
IEi e 3 I/Evi,
Minor = Fminor
in which e 3 is perpendicular to both el and e 2 ;
Oblateness = 0 = Fmajor
20
Fminor-
II
Thrust axis (ei) defines the direction of energy flow. T, Fmajor and Fminor measure
the spatial distribution of energy flow. The oblateness 0 measures the event flatness.
The effects of hadron fragmentation and detector acceptance are calculated
through Monte-Carlo simulation. Events are generated by the LUND parton shower
program, JETSET 6.3 [4-1], using the Peterson fragmentation functions for b and cquarks. These events were then passed through a complete L3 detector simulation,
based on GEANT 3.13[4-2]. The effects of energy loss, multiple scattering, interactions and decays in the detector materials are included. The simulated events are
analyzed with the same program used to analyze the data.
4.2
The event selection
The hadronic events are selected with the following criteria:
< 1.5.
(1) 0.5 < EvisI
(2) Energy imbalance along the beam direction (Ell) and in the transverse direction
(E ) are both less than 37% of E.i,
(3) Number of jets above 5GeV > 2.
(4) Ncluster > 10.
(5) Evis/Nhit > 0.10GeV
(6) E BGO < 0-3 ss.
Cuts (1) and (2) reject dimuon events, beam gas, cosmic ray background and
part of the r events. Cuts (3) and (4) reject di-electron and rr events, since these
events generally have low multiplicity. Noise events are removed by condition (5),
which requires the average energy from each hit elements to be large. Cut (7) rejects
the remaining e+e-final state events in the BGO electromagnetic calorimeter.
The simulated events are subjected to the same selection criteria, and compared
to data. Fig. 4.2 shows that the data distributions of Ev,/Is, 1ElI/Evi, and
EI/Ei, are in good agreement with the Monte-Carlo prediction. Fig. 4.3 shows
the scatter plot of EBGO versus the number of clusters (Ncister) for a loosely
selected data sample in the barrel region. The contributions from ee, pp and rr
events are clearly separated from hadronic events. Conditions (4) and (6) reject
most of these events. Fig. 4.4 shows the distributions of EBGO and Nciuster from
.
selected hadron events, data and Monte-Carlo again agree well.
The event shapes are checked with the distributions of the Thrust, Major,
Minor and Oblateness. Fig. 4.5 shows the comparison of data and Monte-Carlo
simulation. The simulation describes correctly the event shape. Fig. 4.6 shows
the angular distribution of the thrust axis. Our data shows inefficiency at small
polar angle. This is due to a trigger inefficiency during start-up period of hadron
calorimeter endcap. A 6% inefficiency during that period was estimated according
to Fig. 4.6
Since the energy and event shape have been demonstrated to be accurately
described by the simulation, the acceptance can then be calculated by the simulated
0
events. The result is a 96.90 t 0.1% (statistical) acceptance for Z to hadron decay.
Systematic error is checked by varying the cut conditions. Table 4.1 shows .he
change of cross section due to changes in the cuts on energy, energy imbalance and
21
the number of clusters. Based on this table, a total systematic error of 0.9% is
assigned to the calculated acceptance.
Evis Cut
<
<
<
<
>
>
>
>
1.6
1.4
1.3
1.2
0.4
0.6
0.7
0.8
Data Ae(%)
Monte Carlo Ae(%)
Azch(%)
0.25
-0.59
-2.44
-8.07
0.28
-0.74
-2.99
-9.16
0.33
-0.85
-3.20
-9.42
0.14
0.60
-2.49
-8.59
-0.08
0.26
0.76
1.54
0.14
-0.14
-0.50
-0.65
(a) Evj/ts_ cut.
E1 /Evi, Cut
< 0.5
< 0.4
< 0.3
< 0.2
Data Ae(%)
0.73
0.30
-0.92
-5.07
Monte Carlo Le(%)
0.38
0.17
-0.78
-5.15
Agh(%)
0.30
0.13
-0.15
0.09
(b) E 1/Evi, cut.
E /E,i, Cut
< 0.5
< 0.4
< 0.3
< 0.2
Data Ae(%)
0.80
0.34
-1.21
-6.02
Monte Carlo Ae(%)
0.65
0.23
-0.97
-5.78
Agh(%)
0.15
0.11
-0.25
-0.26
(c) EI/E,, cut.
Nc luter Cut
Data AE(%)
Monte Carlo Ae(%)
Azch(%)
> 9
> 12
> 13
> 14
0.32
-0.73
-1.28
-1.99
0.14
0.42
-0.78
-1.26
0.18
-0.32
-0.52
-0.76
(d) Neluster cut.
Table4.1 Change of acceptance (Ae) and the total hadronic cross section
with different cuts.
(Agh)
Adding the statistical and systematic errors in the acceptance, and the uncertainty in the trigger efficiency in quadrature, the overall systematic error in the
corrected number of hadronic events is 1.0%. Combining this error with the 1.7%
error on the luminosity in quadrature, the overall systematic error on the measured
hadronic cross section is 2.0%.
22
Background
The main background comes from dielectron and rr events. The rates of these
events are estimated by Monte-Carlo simulation. With the same selection, it is
found that 1.86t0.24% of the r events and less than 0.1% of the electron events
are selected. Since the cross section of e+e-and 7r is 4.8% of the total hadronic
cross section, this background is equivalent to a 0.09+0.01% contamination in the
hadron sample.
Backgrounds not from e+ e- collision were estimated by visual scan. The sources
of this background include beam gas interaction, synchrotron radiation, electronic
noise and high voltage break down in the hadron calorimeter. Sometimes high
energy cosmic rays passing transversely through the BGO crystals can emit bremsstralung photons and imitate the signature of a broad BGO shower. About 1,000
selected events were scanned and none of these events were selected. The rate of
these types of background are therefore estimated to be less than 0.3%.
In the hadronic line shape fitting, the r background is subtracted according to
the Monte-Carlo prediction. An error of 0.3% is included in the total systematic
error as a contribution from the background.
4.3
The line shape fitting
Data taken from October till December, 1989 are used in this study, corresponding to 759nb-1 integrated luminosity. A total of 14,352 hadronic events are
selected at 10 different energies. Runs with significant hardware problems were
rejected. Table 4.2 lists the number of events selected, the measured luminosity for
each energy point, and the calculated cross section after background subtraction
and acceptance correction.
4.4
88.279
89.277
90.277
91.030
91.278
91.529
92.280
93.276
94.278
95.036
Total
Number of
events
404
556
968
3494
3284
3447
1069
710
348
72
14352
Number of
corr. events
433.0
583.4
1008.5
3635.6
3450.1
3627.7
1113.6
740.5
368.3
74.2
Lumi.
(nbl 1
86.93
67.45
52.98
124.06
118.93
129.06
55.60
60.53
52.64
11.03
759.21
0
(nb)
4.981
8.649
19.035
29.305
29.009
28.109
20.029
12.234
6.997 +
6.730
Table 4.2 Measured cross section of e+e- -+ Hadrons
23
rh
)
Vs (GeV)
(01).
0.254
0.384
0.678
0.571
0.592
0.554
0.689
0.493
0.391
0.828
The data are fit with the analytic formula provided by Cahn[4-3]. Three different fits are made:
(1) Only the Z 0 mass and an overall scale factor are used as a free parameters.
All the other quantities are derived from the standard model prediction. The
number of neutrino type is set to three. The overall scale factor is allowed to
vary within the systematic error quoted above.
.
(2) The Zo mass and invisible width are taken as free parameters. This fit gives
the number of neutrino species.
(3) A model independent fit which leaves Mzo, Lzo and Peerh as free parameters
is made.
For the fits, we take mt,, = 100GeV, mHigg, = 100GeV and as = 0.12.
The result of fit 1 is Mzo = 91.139 0.025 GeV. In addition to the experimental
error, the absolute energy calibration of LEP contributes a 30 MeV systematic error.
Furthermore, including a point to point systematic error on beam energy of 0.015
GeV add an extra 0.006 GeV error to Mzo. Combine the experimental and LEP
energy errors, we obtain an overall error of 38 MeV. Fits 2 and 3 gives identical
results on the mass of Z 0
The invisible width is fitted to be 0.548 0.029 GeV using method (2). This
result corresponds to 3.30 0.18 light neutrino types, assuming the standard model
prediction of I,, = 166.1MeV. The possibility of four or more neutrino types is
ruled out at 4o confidence level. Fig. 4.7 shows the cross section data and the
fitted curve. The predicted curve for two and four neutrino types are overlaid. The
best fit to our data clearly favors three neutrino types.
The results of fit 3 are: Mzo = 91.143 0.025 GeV, Pzo = 2.529 0.053 GeV
and reehr = 0.1441 i 0.0063GeV 2 . From these results, the total hadronic cross
section at Vi = Mzo is oh(Mzo) = 29.5
0.7nb. Taking the average leptonic
partial width of 83.0
2.1 1.1 MeV from L3 [4-4], the hadronic partial width
is rh = 1736 90MeV. This result should be compared to the standard model
prediction of 1734 MeV, assuming Mz = 91.14 GeV. The number of neutrino
species can be calculated using eq. (2.7). We obtain N, = 3.28 0.31.
The results of the fit is summarized in table 4.3. 30 MeV systematic error in
the LEP energy scale must be added to the quoted experimental errors.
Table 4.3
Summary of the fit results.
Fit
1
2
3
Mz (GeV)
91.139 0.025
91.143 0.025
91.143 0.025
rz (GeV)
Pinvisible
0.548
2.529
0.053
(GeV)
0.029
NX X2/D.F.
3.30
3.28
0.18
0.31
12.4/9
8.0/8
8.0/8
In conclusion, the Z' mass is measured to be 91.14 0.025 (exp.) 0.030(LEP).
The number of light neutrino species is 3.30 0.18. The existence of forth family
of light neutrinos has been ruled out at the 4o confidence level.
24
Chapter 5
b-quark production
Method of identifying b-quarks
Free quarks and gluons have never been observed experimentally, instead, the
fragmentation process creates a collimated hadron jet. The jets of hadrons reflect
the energy and orientation of the original partons. It is necessary to identify the
original parton from the observed jets in order to study the properties of individual
partons. One powerful method of tagging heavy quarks is via their semileptonic
decays. The B-mesons created in a jet decay with ~ 11% probability into an
electron-like lepton, a neutrino and a c-quark meson. In the spectator model, this
decay corresponds to the process b --+ c + W, W -+ f + vi. The result is a lepton
accompanying the hadron jet. By observing lepton production, it is possible to
identify the original quark charge and mass.
Due to a strong Lorentz boost, the momentum of the lepton gives little information as to its origin. However, assuming that the thrust axis of a jet reflects the
direction of the original quark, the transverse momentum (PT) of the lepton relative
to the jet is independent of the boost, and therefore directly related to the mass
of the original quark. Ignoring the detector effect, the expected PT distribution
peaks at about 1/4 of the quark mass, and drops to close to zero around 1/2 of
the quark mass. Therefore, a PT cut at about 1 GeV effectively rejects events from
u, d, s and c quarks. In the absence of heavier quarks, this method then selects a
sample of high b quark purity. Furthermore, except for a small fraction of cascade
decays b - c -- f + hadrons, the charge of the decay lepton has the same sign as
the charge of the parent quark, and can be used to identify b from b.
In this chapter, b quark production is studied through its semi-muonic decay in
inclusive muon events. The goal is to measure the partial width I'bb and the charge
asymmetry of e+e- -+ bb.
5.1
Monte-Carlo simulation
Due to the complicated nature of hadron fragmentation, direct interpretation
of the data is difficult. Monte-Carlo methods are therefore employed to simulate
the process and facilitate extraction of physics parameters. In the simulation of
heavy quark (b and c) events, the spectrum of the muon momentum is directly
related to the production of the mesons which contains the primary quarks, since
the muons are the decay product of these mesons. Fig. 5.1 depicts the bb event
production and subsequent semileptonic decay. The fragmentation process b -+
bq + q, where b-hadron is produced, is characterized by a fragmentation function
f(z). This fragmentation function gives the probability of finding a b-hadron with
energy equal to z times the primary b-quark energy. In this study, the fragmentation
function developed by Peterson et. al. [5-1] is used for the hadronization of b and
c quarks. The function form is:
5.2
1C
f(z)
Z
-
25
-T)
2
(5.1)
where z is defined as [5-2]:
_
(E + P )hadron
(E + P)quark
The parameter eq determines relative "hardness" of the fragmentation. Based on
the measurement at lower energy [5-2], the following values of eq are selected for
the standard Monte-Carlo events:
eb = 0.02
Cc = 0.07
=
0.07(5.2)
For the fragmentation of light quarks (u,d and s), the standard Lund string
fragmentation is used. The branching ratio of semileptonic decay Br(b-hadron -+
y + v, + c-hadrons) was set to 11.2%. 30,000 events were generated under these
conditions and analyzed with the same analysis program used in data analysis.
5.3
The event selection
Inclusive muon events, Z 0 -- p + X, were selected from the hadronic event
sample used in the line shape measurement. We required in addition at least one
track in the muon chambers. To avoid reconstruction errors, the muon track was
required to have reconstructed track segments in two of the three P-chambers and
in both Z-chambers of inner and outer layers. This requirement resulted in a 2.2%
loss in acceptance, due to dead drift cells. Fig. 5.2 shows a typical selected inclusive
muon event. The selected sample includes three categories of events:
(a) Prompt muon events, where the track is a muon originating from the interaction
point, mainly due to semi-muonic b and c decays.
(b) Decay muon events, where the track is a muon originating from hadron decays
in the detector. These events are characterized by their vertex being off the
interaction point.
(c) Punch through events, where the track is not a muon, but rather a hadron
originating either from the interaction point or from a hadronic shower in the
detector, and was not absorbed by the inner detectors.
Category (a) contains the real signal, while the other two categories are background to be reduced. To distinguish prompt muons from the background, the
closest approaching distance to the interaction point from the extrapolated track in
x - y plane (RT) and z direction (Rz) were used. Fig. 5.3 shows the distribution
of RT versus Rz, as well as the contributions from prompt muons and background
predicted by Monte-Carlo simulation. While the prompt muons concentrate near
the interaction point, the background has a wider distribution extended to large
distance. Fig. 5.4 shows the projection to RT and Rz. The simulation is in
good agreement with the data. Based on this, a requirement of RT < 160mm and
IRzJ < 160mm was chosen to select the prompt muon events. 674 events were
selected with this cut, corresponding to 4.7% of the total hadronic events.
26
Fig. 5.5 shows the momentum distribution after the vertex cut. The absence of
events with P < 2GeV is the result of energy loss when muons pass through inner
detectors. Due to the large curvature, tracks with momentum less than 4GeV are
not well reconstructed. We therefore selected events with the additional requirement
that P > 4GeV. After vertex and momentum cuts, 523 inclusive muon events were
selected, corresponding to 3.68% of the total hadronic events. From Monte-Carlo
simulation, 73.5% of this sample are prompt muon events.
As described in 5.1, a cut on the transverse momentum of the muons relative
to the jet axis, PT, facilitates separation of the quark flavor. Fig. 5.6 shows the PT
distribution of the selected inclusive muon events. The Monte-Carlo predictions of bquark and c-quark contributions are also shown. To avoid c-quark contamination, a
PT cut at 1.3GeV is chosen. 184 events were selected after this cut. The composition
of this event sample from Monte-Carlo study is listed in Table 5.1. Assuming the
branching ratio Br(b --
to 0.0437
) = 11.2%, the b-quark content in the sample corresponds
0.0018(statistical) of total produced b-events.
b-+
74.9 t 2.5
b -+ c --+ y
4.9
1.1
C
/I
4.9 + 1.1
Table. 5.1The composition of b-sample in %.
decays and
punch throughs
15.3 1.8
Statistical error only.
The systematic error in event selection is estimated with the following effects:
(1) Different cut conditions are applied for event selection. Table 5.2 lists the ratio
of the number of selected events from data to that from Monte-Carlo for various
cut conditions, normalized to the ratio with standard cuts. Assuming that the
variations are from the systematic error in the number of b events only, we
determined a 3% systematic error to the b purity. This result corresponds to
an error of 0.0013 in the tagging efficiency.
(2) The systematic error on the number of background events was estimated by low
PT events. As is shown in Fig. 5.6 , events in the low PT region is dominated by
background. The number of events in that region is therefore sensitive to variations in the background rate. We require that the number of events predicted
by Monte-Carlo with PT < 1GeV should agree, within statistical error, with
the number of events in the data sample. This requirement limits the variation
of backgrounds to be less than 13% from the central value. A systematic error
of 13% is therefore assigned to the predicted number of background events.
27
-A
P cut (GeV)
4.0
3.0
5.0
6.0
8.0
std
std
std
std
std
std
std
std
std
std
R cut (mm)
160.
std
std
std
std
std
std
std
std
std
std
std
120.
200.
240.
PT cut (GeV)
1.3
std
std
std
std
0.8
1.0
1.2
1.4
1.6
1.8
2.0
std
std
std
Nd
jNM C
1.000
0.989
1.022
1.028
0.998
0.945
0.985
0.995
1.031
1.014
0.970
0.972
1.019
0.981
0.964
Table 5.2 Ratio of number of events from data to that from Monte-Carlo prediction.
First line gives the standard cut condition. "std" means standard value.
(3) The contribution from c-events depends on the branching ratio Br(c -+ u)
and the fragmentation function for c-quark. We assume a 10% error for these
effects.
Combining the systematic and statistical errors in quadrature and including
2.2% inefficiency due to the number of required track segments, we find the following
results:
b tagging efficiency = (4.27 0.22)%
b purity = 79.8 3.0%
(5.3)
ratio of c events = 4.9 1.2%.
ratio of background events = 15.2 2.7%
5.4
bb partial width rbb
Table 5.2 shows the number of events in the selected b sample, the luminosity
and the measured e+e- -+ bb cross section. The backgrounds are subtracted according to the Monte-Carlo predictions which have been normalized to total number of
hadronic events. The remaining events are then used to calculated the cross section
assuming 4.27% tagging efficiency. The errors quoted for O-bb are statistical error
only, the systematic errors will be included after the fit.
28
Average Vs
(GeV)
89.50
91.28
93.00
number of
events
20
138
26
Table 5.3
number of equivalent b events
358.3 107.4
2639.3 244.8
480.1 121.7
Measured e+e
integrated
Lumi. (nb-1)
201.97
369.39
180.65
-+
a-bb
(nb)
1.777 0.53
7.145 0.66
2.656 0.67
bb cross section.
To include the effect of photon exchange and interference contributions in the
total e+e- - bb cross section, the measured cross sections are fitted with the
0.030
analytic formula given by Cahn [2-4]. In the fit, Mz = 91.147 0.024
measurement
section
GeV and rz = 2.527 0.054 from the total hadronic cross
were used. The only free parameter is the overall normalization factor, which is
proportional to I eelbbBr(b -- y). The fit gives
Fee'bbBr(b -+
) = 3733 t 304(statistical)MeV 2 .
(5.4)
with x 2 = 1.75 per two degrees of freedom.
Fig. 5.7 shows the data points and the fitted curve.
Using the measured F11 = 83 2 MeV [5-4], and including 6% systematic error
due to tagging efficiency and 1.7% luminosity error, we obtain:
FbbBr(b -
) = 44.9
3.6(statistical)
+ 3.0(systematic)
-
This method, however, does not include the effect of the fragmentation functions. Since the fragmentation function is directly related to the momentum distribution of the muons, the tagging efficiency is expected to depend on the relative
hardness of the fragmentation. In order to measure accurately FbbBr(b -+ P), it
is necessary to study the variation due to different fragmentation functions. We
therefore determined rbbin a fit to the data which allow both the fragmentation
and Frbto vary. In the fit, we also normalized the distributions by the total number
of hadronic events, hence included the uncertainty due to Fee automatically. Furthermore, we lifted the PT cut to allow fitting to the whole spectrum, thus reduced
the statistical error.
To characterize the fragmentation function, we used the scaled energy xE
2Ehpdrp instead of z defined in (5.1). This is because that the the gluon radiation
in the parton shower model changes the energy of the primary quark, rendering
a different z value, which often exceeds 1. xE , on the other hand, is well defined
and measurable. The distribution of
xEis
described by Peterson form, with a single
Because of the parton shower model used, the distribution of x is
parameter J.
in general softer than that of z. From our Monte-Carlo, events generated with
Eb = 0.02 gives ex
0.08.
29
We performed a maximal likelihood fit to the two-dimensional dN/dPdPT distribution. Three parameters were determined from the fit: (1) PbbBr(b -- p). (2)
Judc, which is sum of the partial widths of u,d,s and c quarks. (3) ef. Pb and Pudsc
are subject to the further constrain of rbb + rudsc = Ph, where Ph is taken from
the measured result in 4.4. In varying ef, we reweighted the events such that the
resulting distribution agrees with the Peterson form with the new e.
The direct results of the fit is rbbBr(b --+ p) = 42.1 3.5 MeV, and e =
0.97 0.035. Fig. 5.8 shows the contour plot of constant probability of the fit in
the plane of Pbband e'. We found that PbbBr(b -+ p)is insensitive to q.
To asset the systematic error in the fitting, the following checks were make:
(1) We applied different cuts on P and PT and repeated the fit, the results are
shown in Table 5.4. From the table, we observed a typical 4% variation in
PbbBr(b -- y).
P cut (GeV)
3.
2.
4.
5.
6.
3.
3.
3.
3.
PT cut (GeV)
0.0
0.0
0.0
0.0
0.0
0.4
0.8
1.2
1.6
FbbBr(b
-+
p)/(M.C. value)
0.992
1.025
0.979
1.014
0.959
1.003
0.951
0.941
0.958
e
0.096
0.100
0.110
0.107
0.088
0.092
0.061
0.056
0.074
Table. 5.4The fit result of rbbBr(b - pt)and ef under different cut conditions.
(2) Including the partial width of Z 0 -+ ce, rCc, and e' of the c-quark fragmentation
function as additional free parameters, the fit result of rbb changes by 4%.
(3) Changing the ratio of punch through and decay events by t20%, Fbschanges
by 3%.
From these variations, we estimated a relative systematic error of 6.4% in
rbbBr(b -+ p). The final result from the fit is therefore:
FbbBr(b --+ u) = 42.1
3.5(statistical)
2.7(systematic)MeV.
(5.6)
This result agrees with the previous result based on event counting.
Using the measured value Br(b -+ p) = 11.8
rbb =
356.8
30(stat.)
30
1.1% [5-5], we obtained
40.4(sys.)(MeV)
(5.7)
The value of rbb is related to the weak coupling constants, as described by eq. (2.5).
One can extract the following result from the measured value of Fbb:
(gb)
2
+ (g,)2 = 0.349
0.029
Inserting the Standard Model value gb = -1/2,
(5.8)
0.039.
the vector coupling constant was
solved to be:
(5.9)
0.011(sys).
0.008(stat)
= 0.099
(g,)2
= 0.23.
This agrees with the Standard Model prediction (g) 2 = 0.12, for sin2
One can also assume the Standard Model predictions of rbb and derive the
average branching ratio of semi-leptonic decays of B-mesons, Br(b - p). With
rbb - 378.5 MeV, we obtained
Br(b --+ ) = 11.1
0.9(stat.)
0.7(systematic)%
(5.10)
bb asymmetry
5.5
The forward-backward charge asymmetry of e+e- -+ bb is measured with the
collected b sample. The sign of the charge of the b quarks is determined by the
charge of the measured muon. The 9 angle of the quark is determined by the thrust
axis of the event. The cos 0 distribution of b-quark is shown in Fig. 5.9 . Defining
the number of events with cos 0,- > 0 or cos 0,+ < 0 as Nf, and number of events
with cos 0.- < 0 or cos 0,+ > 0 as Nb, and assuming that, except for the charge
of the muon, the cascade decay b
b - y decay, we find:
-
c -* y bears the same asymmetry as that of
Nf = (1 - a)N + aN + Nb + Nackgroun
Nb
=
(1
b)Nt
+ &N(+ N/ + Nackground
-
(5.11)
where
=number of events with b (c) quark in the forward region.
b,(,) = number of events with b (-) in the forward region.
-(c)
a = ratio of accept b -* c --+ p events to the total accepted b events.
To get the b-quark charge asymmetry, we made the following assumptions:
- Background events are charge symmetric, i.e.,
Nbfackground = Nbackground =
Nbackground
- c-quark asymmetry is as the standard model prediction, i.e.,
Nf
_
Nb
= Acc(Nf + N b) = Acc Nc
31
where Acc is the predicted c-quark asymmetry.
- The'number of background and c-quark events (Ne,
by the simulations.
Nbackground)
are predicted
With the measured Nf and Nb, and including Nc, Nbackground and a from
Monte-Carlo prediction, we can solve equation (5.11) to get the asymmetry:
Abb =
Nf -NNb
b
N
N1
b
b
1 - 2a Nf + Nb
b
-
+ A
(5.12)
Nc - Nbackground
-
Due to our Z-chamber segment requirement, the acceptance of muon tracks is
limited to Icos 01 < 0.7. This angular cut reduced the measured value of asymmetry.
We therefore modified (5.12) to:
e()Abb =
NJ' - Nba + Acce(9)Nc
N -Nb+AO)c(5.13)
1 - 2a N! + Nb - Nc - Nbackground
1
1
where e(9) is the correction factor of the asymmetry due to the angular cut.
Since the asymmetry depends strongly on the center of mass energy, only the
138 events around the Z 0 peak are used. We find:
Nf =77
Nb = 61.
Monte-Carlo prediction of the background is:
Nc = 6.2 t 1.5
19.1
0.023
Nback ground =
a = 0.061
3.4
(5.14)
and
e(Icos(9)| < 0.7) = 0.858
0.071.
Using Acc = 6.5%, we find
Abb =
18.8
13.9%
This result agrees with the predicted value of 8.2%, assuming 12% [5-6] B 0 -B 0
mixing.
32
Chapter 6
Conclusion
.
In this study, fundamental parameters related to the Z 0 are measured with
events recorded by the L3 detector in the LEP e+e-collider. The mass and width
of ZO, the hadronic partial width, and the bb production rate are determined by
hadronic Z 0 decay. The number of neutrino types and the weak coupling constant
in Z' -+ bb vertex were derived from the measured parameters.
The mass of Z 0 , Mz, was determined by fitting the resonance peak of e+e
Z' -+ hadrons cross section to the theoretical formula. The hadronic events used
are selected according to the energy deposit in the BGO electromagnetic calorimeter
and the uranium hadron calorimeter of L3. Cross sections of ten different center
of mass energy are measured, and fitted with analytic formula including the effect
of radiative corrections. The results of the fit are Mz = 91.143 0.025GeV, J'z =
2.529 0.053 Gev and ]PeeFh = 0.1441 t 0.0063GeV 2
The number of light neutrino types can be determined from the Z0 width. In
this case, we limit the fit to within the scope of the Standard Model, leaving only
Mz and the invisible width as free parameters. The results are Mz = 91.143+ 0.025
GeV and "invisible = 0.548+0.029 GeV, corresponding to 3.30+0.18 neutrino types.
This result ruled out the possibility of four neutrino types with 40- confidence level.
With 95% confidence level, this result also imply that any new decay channel which
is not predicted by the Standard Model will have a partial width less than 109 MeV.
The coupling between Z 0 and b-quarks was studied with inclusive muon events
selected from hadron sample. The transverse momentum of the muon related to
the closest jet is used to separate b-events from the lighter quarks. The selected
sample contains 80% of b-events, with a 4.4% tagging efficiency. With this sample,
we determined the Z' -* bb partial width rbb to be 356.8 + 50 MeV, in agreement
with the prediction of the Standard Model. The weak vector coupling constant was
derived from the measured Fbb to be (gl) 2 = 0.099 + 0.008 + 0.011, assuming the
axial vector coupling constant gb to be the predicted value of 1/2.
If we use instead the Standard Model prediction of F6b, then the high transverse
momentum inclusive muon events can be used to determine the averaged branching
ratio of semi-muonic decay from B mesons. The value was found to be Br(b --+ P) =
11.1 + 0.9 + 0.7%, in agreement with measurements done at lower center of mass
energy.
bb charge asymmetry was also measured with the selected b-sample. We found
18.8 + 13.9% asymmetry at Z 0 peak. Combining the measurement of rbb and the
charge asymmetry, it is possible to determine both ga and gV, independently from
the Standard Model. Due to the large statistical error presented in the charge
asymmetry, however, we are not able to extract useful results by this method now.
Looking ahead, high luminosity run of LEP in 1990 and 1991 should provide a
0
Z sample of about 106 events. With this sample, the methods used in this study can
identify about 6000 b-events. A precise measurement of both bb partial width and
charge asymmetry will then be possible. gb and gb derived from this measurement
are the most important parameters in understanding the weak interactions of the
quarks. They also provide another channel of measuring 0,, the weak mixing
33
angle. Comparing Ow measured from leptonic Z 0 decay and b> decay will be a
stringent test to the Standard Model, and will hopefully improve our knowledge on
the electroweak interactions.
34
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UA1 Collaboration, C. Albajar et al., Phys. Lett. B186(1987) 247;
MAC Collaboration, H. Band et al., Phys. Lett. B200(1988) 221;
Mark II Collaboration, C. K. Jung et al., SLAC-PUB-5136 (1989).
37
~
I
FIGURE CAPTIONS
Fig. 2.1 The lowest order Feynman diagrams for the process e+e
Fig. 3.1 A schematic view of LEP.
Fig. 3.2 The LEP injection chain.
Fig. 3.3 (a)The L3 detector.
(b)End view of L3 detector.
(c)Side view of L3 detector.
_ f.
Fig. 3.4 The BGO electromagnetic calorimeter. Left side shows the end view. Right
side shows the side view.
Fig. 3.5 Perspective view of the L3 hadron calorimeter.
Barrel hadron calorimeter module.
Fig. 3.6 Energy resolution of hadron calorimeter. The solid points are obtained with
BGO in front of the test module.
Fig. 3.7 (a)Perspective view of an octant of the muon system.
(b)An exploded view of an MO chamber.
Fig. 3.8 (a)Side view of the luminosity monitor.
(b)End view of the luminosity monitor.
Fig. 3.9 Distribution of the acoplanarity of small angle Bhabha events, AO.
Fig. 4.1 (a) The end view of a typical two jets hadronic event. The squares in the
hadron calorimeter show towers with some energy deposit, the size of the square
is proportional to the energy deposit. The bars drawn on the BGO represents
crystals with energy deposits. The length of the bar is proportional to the
energy.
(b) The side view.
Fig. 4.2 (a) Total visible energy of hadronic events. The shift of the distribution near
the peak is from an incorrect calibration constant applied to events in the
endcap region, where the BGO calorimeters are not installed yet. This shift
does not affect the selection efficiency because the applied cuts are at the tails
where the discrepancy is not significent.
(b) Transverse energy imbalance of hadronic events.
(c) Longitudinal energy imbalance of hadronic events.
Fig. 4.3 Energy in the BGO calorimeter versus number of clusters. The events here
are selected with only total energy and energy imbalance cuts. The cluster of
events on the left top corner are dielectron events. The events on left bottom
corner are dimuon and cosmic ray events. rr events scatters between ee and
pp events, with small number of clusters. The hadronic events are distributed
in the middle, shows clear separation from ee, pp and rr events. Cut on the
number of clusters shown in this picture effectively removes the backgrounds.
Fig. 4.4 (a) Total BGO energy, normalized by beam energy. The peak near 0 BGO
energy corresponds to small angle events, since there is no BGO calorimeter
38
in the endcap region. The slight discrepancy in the distribution is due to our
limited knowledge about the composition of a the hadron jets. Presently we
assume 1/3 of the energy in a jet is of electromagnetic nature. Since only
very few events have BGO energy above 80GeV after the cluster cut, this
discrepancy dose not affect the selection efficiency.
(b) Number of clusters.
Fig. 4.5 (a)
(b)
(c)
(d)
The distribution
The distribution
The distribution
The distribution
of Thrust.
of the values of Major.
of the values of Minor.
of oblateness.
Fig. 4.6 cos 9 distribution of the thrust axis. Discrepancy in the small angle region is
due to endcap trigger inefficient during some of the runs. The inefficiency was
estimated according to this picture and corrected in the cross section calculations.
Fig. 4.7 Total hadronic cross section and the fitted line shape. Expected line shape for
two and four neutrino type is also shown.
Fig. 5.1 Feynman diagram corresponds to the production of an inclusive muon event,
from the point of view of spectator model.
Fig. 5.2 (a) End view of a high PT inclusive muon event. Muon chamber registered a
high energy muon with large angle relative to the hadron jets. This event was
selected as a b-event.
(b) Side view of the same event.
Fig. 5.3 (a) The distribution of RT versus Rz from Z 0 events. RT (Rz) is the closest
approach distance from the muon track to the interaction point in transverse
(longitudinal) direction. These quantities gives the position of reconstructed
vertex.
(b) Monte-Carlo prediction of the same distribution from Prompt muon events.
(c) The same distribution for punch-through events.
Fig. 5.4 (a) Extrapolated vertex of muon track in the x-y plane (RT). Shaded area
shows the contribution from prompt muon events.
(b) Extrapolated vertex in z direction (Rz).
Fig. 5.5 The distribution of muon momentum. Shaded area shows the Monte-Carlo
predicted contribution from b-events.
Fig. 5.6 The transverse momentum related to the nearest jet. With Monte-Carlo prediction of b and c events overlaid. As expected, the b distribution peaks at
about 1.25 GeV (1/4 of the quark mass), and c contribution become relatively
small above 1 GeV.
Fig. 5.7 Measured cross section of the process e+e- --+ bb, fitted with the theoretical
prediction.
Fig. 5.8 The countour plot of constant probability in the fit for lb and E. The three
curves correspond to one, two and three standard deviation from the minimal
value.
39
-A
U
Fig. 5.9 Angular distribution of the selected b events. ,- is the expected angle of bquark, determined by the thrust axis of the event and the charge of the observed
muon. A clear asymmetry is observed.
40
e+
z0
e-
f
e+f
e~
Fig. 2.1 The lowest order Feynman diagrams for the process e+e-
41
LEP
e
njec t ion
Fig. 3.1 The LEP collider
LINACS
(LIL)
200 MeV e-
e- *4 converter
600 MeV
e* or e-
EPA 600 MeV
PS
3,5 GeV
LEP
3
h
ic
TT 70
LSS
5
rtn
'0
yas
SPS
'
LSS
IT
6
20 GeV
-LSS I
Fig. 3.2 The LEP injection chain.
42
MAGNET YOKE
MAGNE T (OIL
MUON
CHAMBER
SUPPORT TUBE.
HADRON
BGO
VERTEX CHAMBER
\LUMINO SI TY MONI TOR
Fig. 3.3a The L3 detector.
CALORIMETER
4AGW
T YOKE
muon chamber
calr
rtex hambadron
vertex chambBO
BGO
uminosity monitor
endcap hadron calorimeter
Fig. 3.3c Side view of L3 detector.
Hadron calori-eter
Tig. 3.3b End view of L3 detector.
44
Ift
CAP
Lf
*z
mes sp
I.'
---
N
ii
~I
Fig. 3.4 The BGO electromagnetic calorimeter.
45
Fig. 3.5a Perspective view of the L3 hadron calorimeter.
Fig. 3.5b Barrel hadron calorimeter module.
46
I
-
60
TEST BEAM DATA
50
4
0
30
0
0
30
+
-112
5)%
(55xE
20
10
two jet ZO-events 91.16Gev
0
A
t
I
I
J
I
I
I
I
1
2
4
10
20
50
Pion momentum (GeV/c)
Fig. 3.6 Energy resolution of hadron calorimeter.
47
I
I
Z CHAMBERS
P CHAMBER
AMPoFIERS-
P CHAMBER
GA
SSYSTEM
--
ARRAY
STAND
--
Fig. 3.7a Perspective view of an octant of the muon system.
48
7 CtJAMBER.
ENDFRAME
Fig. 3.7b An exploded view of an MO chamber.
IL ,
4
w
Hadron CaLorimeter Endcaa
Planar
Chamoers
8 G.0
Fig. 3.8a Side view of the luminosity monitor.
Fig. 3.8b End view of the luminosity monitor.
50
I
II
I
I
10 4[0
0O
+
c;)
Se
103
W
Cut
Cut *
Ir 4 1 I
Ii
10 2k-
Sideband
10 1
i
o
Sideband
3'
1
1141
130
155
180
205
11{
o
230
Ap (degrees)
Fig. 3.9 AO distribution for small angle Bhabha events.
51
101906 Event # 19564 Total Energy: 99.83 GeV
Run #
1L_____________________________________________
~
Tranwverm Imboeance : 5.17 GeV
Thrust:.9843
Longtmunal Imbaance: -8.81 GeV
Majr:.0754 Mnor:.0620
Fig. 4.1b The side view.
Run #
101906 Event #19564 Total Energy: 99.83 GeV
Transverse imbaiance: 5.17 GeV
Thrusr:.9843
Lonpuidinal Imatanm: -8.81 GeV
Majr-.0754
nor:.0620
Fig. 4.1a A typical two jet hadronic event.
52
# of events
Iuuu
{
800
Data
M.C.
600
400
200
-
-
--
0
0.6
-
-
0.8
1
1.2
1.4
E i 5 /Vs
Fig. 4.2(a) Total visible energy
53
# of events
Data
600
M.C.
400
-
-
02
200
0
0
-
-
0.1
0.2
0.3
0.4
EJEv,
Fig. 4.2(b) Transverse energy imbalance.
54
# of events
1000
--
}
800
600
Data
M.C.
400
200
0
-0.4
-0.2
0
0.2
0.4
Eg/Ev,
Fig. 4.2(c) Parallel energy imbalance.
55
Utz
o
+
+Z
+
+~
+
+i
~
++
-t+
++
+
+
++
+
tA
+++
+
+ + +t.+~*
+0
++
++
i+++
-t
+ +:+ +*
+ ++++++++
++
+W
+
0
00
+
+
+
+
++
+
*0
+-+
++
* f#+H
+
+
+
4+ -+
+
+
+
+1
+
++
1
+++
+
(GeV)
+++
+
I++:
+
+ ++
+
o.+ &+
-+F +
++4
+
+~ V+
+ + 44
++
+s
+) +
.+
+ ++
+
+++
+
43'
4-
1-
EBGO
+
,+ +
+c
C
# of events
600
Data
400
M.C.
2001
0
0
0.2
0.4
0.6
Fig. 4.4(a) BGO energy.
57
0.8
EBGO/Vs
# of events
600
-
500
Data
M.C.
400
300
200
-
-
100
0
0
20
40
60
80
Nciuster
Fig. 4.4(b) Number of clusters.
58
1
# of events
11
I
I
7 7
1 -
1
1
1
1
1
1
1 1--
1
1
1
1 1
I
D ita
M .C.
102
I
0.5
0.6
0.7
0.8
Fig. 4.5(a) Thrust.
59
0.9
1
"
101
T
# of events
Data
M.C.
102
101
100
0
0.4
0.2
0.6
Fmajor
Fig. 4.5(b) Major.
60
II
# of events
103
Data
M.C.
102
101
100
0
0.1
0.2
0.3
0.4
Fminor
Fig. 4.5(c) Minor.
61
of events
I
I
103
Data
M.C.
102
-
101
I
I
H
100
n
0
I I
0.2
0.4
I________________I
I
Fig. 4.5(d) Oblateness.
62
0.6
0
1/50 dN/dcos()
500
Data
+
400
M.C.
300
200
0
'
-1
'
-
-
'
-0.5
0
-
-
100
0.5
1
cos(e)
Fig. 4.6 Polar angle distribution of thrust axis.
63
Uh
(nb)
Data
-
/-Fitted
30F
-- 4 neutrino types
-
-
line shape
\ -- 2 neutrino types
I'
201
%
~1
I%
I,%
If,%
I,%
-%
%%
/N
10I
0
88
90
92
94
Fig. 4.7 Total hadronic cross section.
64
Vs (GeV)
Ebe
F 51 e ff
e+~~
Ef(Z) bV
C
Fig. 5.1 The production of an inclusive muon event.
65
Run #
93208 Event # 34723 Total Energy: 81.50 GeV
Transverse imbaiance: 4.84 GeV
Thnru .9491
Run U
Longudinaf Imbahanc.: -2.47 GeV
MaWor:.1561
Anor:.0742
93208 Event# 34723 Total Energy: 81.50 GeV
Transverse Imbalance : 4.84 GeV
ThruM:.9491
Longftadm
Maor:.1561
Imbalance:
-2.47 GeV
Wrnor:.0742
Fig. 5.2 An inclusive muon event.
66
500
-
400
300
I-
0
-400
0
-200
200
Rz (mm)
(a) ZO events.
500
500
400
300
-*.5
I-
200
..
.
.
..
0
- - -
(b) From M.C. prompt muon events.
0
.
.
..
.
200
400
R( (mm)
(c) FRom M.C. punch through events.
Fig. 5.3 RT versus Rz.
67
......
- - - - -- ---- -a . ...
-2W
RZ (nm)
ug..
- - --- .- e ....
. .
-
-20
.
-.
**
-4
s..
100
40
0
.
.
-..
.
*
# of events
25U 1
Data
200
- oll
.
M .C
150
Prompt muon events
100
cut
50
:: ::.
0
0
100
200
300
400
500
RT (mm)
Fig. 5.4(a)Vertex position of muons in x-y plane.
68
M116
I
-0--
C
4)
-0
CQ
V-4
U
00
U
0
-V-4
00
0
.9-4
r%4
0
dN/dP
1 11i
II
i
I
I
I II II I
j II
I I I
_
R, Rz ;
Data
r
160 mm
-
II
50
Lm-c-
40
b -events
I'
30
1
-7
(
20
i.l.
10
Li
n'
-30
-20
0
-10
10
Fig. 5.5 Muon momentum.
70
20
30
P (GeV)
/
Nevens
0.25GeV
100
Data
M.C.
80
b-quarks
c-quarks
-
60
RT, Rz 5 160 mm
I
*
40
I
t
I
-
20
-
P 2 4GeV
-.
414-,
4i
*
*
-- 4*
0
0
1
3
2
4
Fig. 5.6 Muon transverse momentum.
71
5
6
PT (GeV)
(nb)
abb
br
61
4
2
C'
88
I
I
92
90
Fig. 5.7 e e~ -+ bb cross section.
72
Vs (GeV)
r
0.20
I
i
0.15
0.10
3.
1.2.
0.05
I I
0.8
0.9
1
1.1
1.2
r bbBr(b-->A)/(M.C. value)
Fig. 5.8 Contour plot of X 2 statitic of PbbBr(b-+pL) versus eb
73
-7
# of events
i
P
-
25
I4GeI
4GeV
1.3GeV
PT
20
160mm
Rz
-RT,
15
10
51
0
I
-1
I
I
I
I
I
I
I
I ~
0
-0.5
0.5
1
cos(OiL_)
Fig. 5.9 Angular distribution of selected b-events.
74