Track simulation and reconstruction in LHCb

176 Pages·2005·9.53 MB·English

Track simulation and
reconstruction in LHCb
Cover: Condensation trails (contrails) in the sky.
ISBN: 90-6464-244-3
Printed by Ponsen & Looijen b.v., Wageningen.
Copyright ' 2005 by Jeroen van Tilburg. All rights reserved.
The work described in this thesis is part of the research program of ’het Nationaal In-
stituut voor Kernfysica en Hoge-Energiefysica’ (NIKHEF) in Amsterdam, the Nether-
lands. The author was financially supported by the ’Stichting Fundamenteel Onderzoek
der Materie’ (FOM).
VRIJE UNIVERSITEIT
Track simulation and
reconstruction in LHCb
ACADEMISCH PROEFSCHRIFT
ter verkrijging van de graad Doctor aan
de Vrije Universiteit Amsterdam,
op gezag van de rector magnificus
prof.dr. T. Sminia,
in het openbaar te verdedigen
ten overstaan van de promotiecommissie
van de faculteit der Exacte Wetenschappen
op dinsdag 11 oktober 2005 om 13.45 uur
in het auditorium van de universiteit,
De Boelelaan 1105
door
Jeroen Ashwin Niels van Tilburg
geboren te ’s-Gravenhage
promotor: prof.dr. M.H.M. Merk
Contents
1 Introduction 1
2 B physics 5
2.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 CP violation in the Standard Model . . . . . . . . . . . . . . . . . . . . . 7
2.3 B mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Mixing of neutral B mesons . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Decay of B mesons . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 CP violation with neutral B mesons . . . . . . . . . . . . . . . . . 15
3 LHCb experiment 21
3.1 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 General layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Vertex Locator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Trigger Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Inner Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.6 Outer Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 RICH detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.9 Muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.10 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.10.1 Level-0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.10.2 Level-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.10.3 High Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 Monte Carlo simulation 47
4.1 Introduction to LHCb simulations . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Framework and applications . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Event generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.1 Pythia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.2 B production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.3 Multiple parton interactions . . . . . . . . . . . . . . . . . . . . . 54
4.3.4 Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.5 B decay simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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Contents
4.3.6 Pile-up and spill-over . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.1 Geant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.2 Passage of particles through matter . . . . . . . . . . . . . . . . . 60
5 Outer Tracker simulation 67
5.1 Detector description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Particle distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Detector response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3.1 General overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3.2 Digitisation processes . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4 Detector performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4.1 Occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4.3 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6 Track reconstruction 87
6.1 Track fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1.1 Kalman formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.2 Resolution and pull . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1.3 Extended Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1.4 Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.1.5 Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1.6 Outlier removal and refit . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Pattern recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2.1 Track types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2.2 General strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.3 Matching tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3 Overall tracking performance . . . . . . . . . . . . . . . . . . . . . . . . 108
6.4 Track visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7 Selection and sensitivity studies 119
7.1 Decays of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2 Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.3 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3.1 Overview of the selection variables . . . . . . . . . . . . . . . . . 124
7.3.2 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.3.3 Optimisation of final selection . . . . . . . . . . . . . . . . . . . . 127
7.3.4 Event yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3.5 B decay times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.4 Flavour tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.5 Sensitivity studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.5.1 Likelihood fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.5.2 Sensitivity on ∆m . . . . . . . . . . . . . . . . . . . . . . . . . . 141
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7.5.3 Sensitivity on γ −2χ . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
A Kalman filter derivation 147
References 155
Summary 157
Samenvatting 161
Dankwoord 165
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Contents
viii
Chapter 1
Introduction
SincemanydecadesphysicistshavebeenintriguedbyNature’spreferenceformatterover
antimatter. Matter is what everything around us is made of, as for instance people, the
Earth, the Moon, and all the stars. Antimatter, on the other hand, is not so common.
The reason that it is uncommon in our daily lives is that it cannot survive in a matter-
dominated environment. Nevertheless, it is regularly created by Nature — and exists for
short periods of time — in radioactive decays and in collisions of cosmic particles with
the atmosphere. Today, antimatter is also created in particle accelerators, and even in
hospitals when making PET scans.
There is no evidence for the presence of large quantities of antimatter in the Uni-
verse [1]. So why does the Universe consist of only matter, and not of antimatter? This
question arose after the discovery of antimatter in cosmic rays in the 1930s. Apparently,
there must be a fundamental difference between matter and antimatter.
ShortlyaftertheBigBang, whentheUniversewascreated, therewasahotanddense
phase. Cosmologists believe that in this phase there was an equal amount of matter
and antimatter. Somehow, the Universe must have developed an excess of particles
over antiparticles. In 1967, Sakharov [2] posed three conditions needed to explain this
imbalance. One of them is the violation of CP symmetry.
Symmetry is an important concept in physics. The laws of physics are invariant un-
der certain symmetry transformations. According to Noether’s theorem, a continuous
symmetry leads to a conservation law. For instance, time invariance leads to conser-
vation of energy and spatial translation invariance leads to conservation of momentum.
In general, physicists want to investigate whether the laws of physics obey certain sym-
metry principles. In 1956, Lee and Yang [3] pointed out that the discrete symmetry
of space inversion, also called parity (denoted by P), may not be conserved in all fun-
damental interactions. Soon thereafter, the first experimental evidence [4] showed that
parity is indeed violated in the weak interaction. It was a striking result that the weak
interaction would behave totally differently in a mirror-world. Other fundamental, dis-
crete symmetries are charge inversion (C), i.e., particle–antiparticle transformations,
and time reversal (T). Until 1964, it was thought that — instead of P symmetry — the
combined CP operation was a good symmetry. That year, violation of the CP symmetry
was observed [5] in the weak decay of neutral K mesons.
1
Introduction
Nowadays, the phenomenon of CP violation is described in the Standard Model of
particle physics. It is incorporated in the Cabibbo-Kobayashi-Maskawa (CKM) matrix,
which describes the quark transitions in the weak interaction. The aim for many particle
physicists is to accurately measure the matrix elements using the decay of B mesons.
CP violation can be observed when there is a difference between the decay of a B to
¯
some final state, f, and the decay of an anti-B to the CP-conjugated state, f. Some
decaychannelsareexpectedtoexhibitlargeCP-violatingeffects, whichcantheoretically
be interpreted in a clean and model-independent way. Measurements of these B decays
will provide insight into the question whether the observed CP violation is sufficient to
explain the current excess of matter in the Universe.
The first observation of CP violation with B mesons has already been made by the
two B factory experiments (BABAR and BELLE) using the decay B0 → J/ψK0 and
S
similar modes. Other experiments (CDF and DØ) have started running and also plan
to measure CP violation in the B system.
At the Large Hadron Collider (LHC), B mesons will be created abundantly in the
high-energy proton–proton collisions. This collider is currently being constructed at
CERN (European Organisation for Nuclear Research) in Geneva. One of the exper-
iments located around a collision point is LHCb, which is designed to detect these
B mesons. The aim of LHCb is to study CP violation and find rare decays using a
high-statistics sample of B decays. The two advantages of LHCb, compared to the
B factories, are the higher statistics of B decays, giving access to decay modes with
small branching fractions, and the possibility to study the heavier types of B hadrons,
most notably the B meson.
s
In the harsh hadronic environment of proton–proton collisions, not only B mesons,
but also many other particles are created, leaving many tracks in the detector. One of
the main challenges of LHCb is to find the B decays among the tracks emerging from
the collision. Therefore, LHCb requires a fast track reconstruction with high efficiency.
Simulation studies play a prominent role in the optimisation of the design of the
detector, as well as in the determination of the expected performance. Ultimately, the
performance is measured in terms of the sensitivity to the CP-violating parameters.
This requires both a realistic simulation and an efficient reconstruction of an event after
a proton–proton collision.
The remainder of this thesis is divided into the following chapters:
In Chapter 2, an overview of CP violation in the Standard Model is presented. Also,
themethodtoextracttheCP-violatingparametersintheCKMmatrixusingbenchmark
B decay channels is explained.
In Chapter 3, the LHCb detector is discussed. First, the characteristics of proton–
proton collisions in the LHC are summarised. Thereafter, the detector itself, its main
components, and their functionality are described.
In Chapter 4, the simulation procedure of proton collision events is explained. After
a brief introduction to the software framework, the B production mechanism and the
different types of particle interaction with the detector are explained.
In Chapter 5, the detection of particles in one of LHCb’s components, namely the
2