for a Highly Granular Hadron Calorimeter
Diploma Thesis of Christian Soldner Ludwig-Maximilians-Universit¨at
Department of Physics
Max-Planck-Institut f¨ ur Physik
Supervisor: Prof. Christian Kiesling
September 17, 2009
1 Introduction
2 Physics Motivation
2.1 The Fundamental Forces of Nature . . . . 4
2.1.1 Electromagnetism . . . . 5
2.1.2 The Particle Zoo and the Strong Force . . . . 6
2.1.3 The Weak Interaction . . . . 7
2.2 The Standard Model . . . . 8
2.3 Beyond the Standard Model . . . . 9
2.3.1 The Grand Unified Theory . . . . 9
2.3.2 Supersymmetry . . . 11
3 The ILC Detector and the Calorimetric Concept 3.1 The International Linear Collider . . . 13
3.1.1 Reasons for a Linear Collider . . . 14
3.1.2 Outline of the Collider . . . 16
3.1.3 Detector Concepts for the ILC . . . 17
3.1.4 Detector Requirements. . . 17
3.1.5 The International Large Detector . . . 18
3.1.6 Particle Flow . . . 20
3.2 Basics on Calorimetry . . . 22
3.2.1 The Passage of Charged Particles through Matter. . . 24
3.2.2 Electromagnetic Showers. . . 26
3.2.3 Hadronic Showers . . . 28
3.2.4 Calorimetric Concepts. . . 29
3.2.5 The Energy Resolution of Sampling Calorimeters . . . 31
3.3 The Calice Experiment . . . 32
3.3.1 Current Setup of the CALICE AHCAL . . . 34
3.3.2 Demands on the Tile Architecture . . . 35
3.3.3 Proposal of Tile Improvement . . . 38
4 The Impact of Non-Uniformity on the HCAL En- ergy Resolution 4.1 Toy Monte Carlo Study . . . 41
4.2 Full GEANT4 Study . . . 43
i
5.1.1 The Silicon Photo Multiplier . . . 56
5.1.2 Scintillator Material . . . 62
5.2 The Experimental Setup . . . 67
5.2.1 Core Setup - The SiPM Signal. . . 68
5.2.2 First Extension - The Tile Signal . . . 70
5.2.3 Final Setup - The Tile Scan. . . 74
5.2.4 The Software Chain. . . 76
5.3 Test Stand Run Modes and Results. . . 79
5.3.1 Preparative Measurements . . . 79
5.3.2 Tile Precision Measurements . . . 86
6 Uniformity Improvement through Tile Modifica- tion and SiPM Positioning 6.1 The Reflectivity of the Tile Faces . . . 101
6.2 Development of an advanced Tile Architecture . . . 104
6.2.1 Variation of the SiPM Coupling Position. . . 104
6.2.2 Tile Optimization with the Dimple Concept . . . 104
6.3 Tolerances and Mechanical Stability . . . 113
6.4 Proposal of a Tile Architecture for the next HCAL Prototype . . . 116
7 Conclusion and Outlook
Acknowledgments
Figures . . . 119
A small pile of sand can set off the greatest sandstorm if the wind blows into the right direction. Let us accompany this pile a bit on its journey during which it might help to unravel some fundamental characteristics of nature.
The most common constituent of sand is silicon dioxide (SiO
2) bound in the form of tiny quartz crystals. With the right refinement procedure silicon can be extracted and condensed to form a high purity crystal of macroscopic size (some 10 cm in diameter), the valuable base material, called a wafer, for most semi-conducting electronics components of the modern world [Enc]. Microscopic structures can be formed out of a small slice of this mono-crystal wafer by advanced etching and photolithographic processes.
The advanced processing methods of Si wafers cleared the way for the creation of an array of more than thousand photosensitive avalanche diodes positioned on an area of only 1 × 1 mm
2. Our small pile of sand has undergone metamorphosis to a silicon photomultiplier (SiPM) which can convert impinging single photons into an electrical signal. A SiPM operates at a relatively low voltage (< 80 V) de- livering a gain of about 10
6electrons for an incident photon [Ham07]. Moreover, it remains unaffected by high magnetic fields making it an ideal photosensor for the application in high energy physics in which strong magnets are crucial.
In the next step, our sand nugget learns how to detect high energetic particles.
A blue sensitive SiPM (new development of Hamamatsu [Web]) can be coupled directly to a plastic scintillator tile of a size of e.g. 3 × 3 × 0.5 cm
3. If a charged particle traverses such a tile it generates a few thousand photons (with a wave- length usually in the blue part of the visible spectrum) and a small fraction of it hits the SiPM which triggers an electric detection signal of the particle [Ott07].
Hundreds of those tiles can detect a complete particle shower if assembled close together to a two dimensional layer and to dozens of successive layers with massive absorber plates between them. A particle shower is a cascade of particles started when, e.g., a high energetic hadron impacts on a dense material and develops into a cascade of secondary hadrons by inelastic nuclear processes. In a calorimetric system, one intends to detect ideally all secondary particles of a shower to reconstruct the energy of the original particle. In an advanced concept, tile layers can be utilized as the active layers of a hadronic sampling calorimeter.
Such an option is currently tested as a calorimetric physics prototype by the CALICE collaboration [CALb].
By now the necessary number of sand nuggets has multiplied and we have arrived
1
in the regime of high energy physics. If the concept of a tile hadron calorimeter is accepted for the hadron shower detection within a large accelerator project, one needs a few million of them [Gro09]. In a modern accelerator experiment of high energy physics bunches of particles are accelerated and brought to collision at one or more interaction points. The collision can create jets of particles each of which ought to be detected by a large cylindrical detector which surrounds the interaction point and is supposed, in the ideal case, to reconstruct each particle track with energy and momentum within the jets. It turns out that an unprecedented jet energy resolution can be achieved by a fine segmentation of the calorimeter into small individual cells (“imaging calorimeter”) which then permits to reconstruct individual particles in a jet (particle flow approach, [Gro09]). Such a calorimeter is planned at the future International Linear Collider (ILC) by the detector concept of the International Large Detector (ILD).
The ILC will be able to perform precision measurements of the Higgs particle which is the origin of the mass of all particles, and of possible supersymmetric particles whose existence is necessary for a grand unification of the fundamental interactions of nature [ES07]. Supersymmetry is currently the favoured theory to extend physics beyond the Standard Model.
So in the end our grains of sand might help to bring us a little closer to a fair understanding of nature.
This thesis investigates the properties of SiPM coupling to scintillator tiles. The existing technique, developed for the CALICE physics prototype, encounters practical difficulties, if applied on a large scale. This thesis tries to find an alternative concept and to optimize these scintillator cells for the application in a highly granular imaging calorimeter planned for the ILC. Especially the consequences of a non-uniform photon readout of such a cell were studied and a cell modification was developed which restores uniformity partially.
For this thesis, we designed and constructed an experimental test stand which was used to quantify some characteristic properties of a SiPM. The test stand was also adapted to measure the SiPM signal of electrons from a radioactive source penetrating a plastic scintillator tile. An important task was also to study and categorize the non-uniform readout of different tile architectures.
Chapter 2 gives an overview of the fundamental physics concepts of the Standard Model. Furthermore, it explains the theory of grand unification and supersym- metry at a basic level.
Chapter 3 motivates the need for the ILC and presents the concepts of the ILC as well as of the ILD. It also gives an introduction to the working principle and the key properties of a hadronic calorimeter. Finally, the general outline of the CALICE physics prototype is explained along with its requirements to the cell architecture of a finely segmented analogue hadron calorimeter (HCAL). We propose how an improvement of the cells could be achieved.
In Chapter 4, we illustrate details on the energy reconstruction principle of
a HCAL. With a Monte Carlo simulation using the GEANT4 framework we studied how a non-uniform cell readout deteriorates the energy resolution of a test HCAL. We propose a simple method to minimize this degradation.
Chapter 5 starts with an introduction to SiPMs and to plastic scintillators. It then explains the advantages and limitations of the test stand along with three different configurations used for data taking. Finally, it describes the working principle and first results of the various performed run modes.
Chapter 6 shows how cell properties can be optimized by a modification of the cell architecture. The SiPM coupling position, the tile face reflectivity and the implementation of a dimple into the tile was investigated as a means to restore the uniformity of the cell readout.
Finally, Chapter 7 provides a conclusion and an outlook on further optimization
options.
The biggest achievement of particle physics in the last century is the formulation of the Standard Model. It describes three of the four fundamental forces of na- ture and defines the elementary particles the forces interact with and all matter is made of [Gri08]. The Standard Model proved to be very robust against exper- imental probing and describes the observed phenomena of particle physics more than thirty years after its first formulation still with outstanding accuracy. But it is certainly not the end of the story. The Standard Model relies on about twenty significant input parameters (like the values of elementary particle masses, the Weinberg angle or the CKM parameters) which have to be determined empiri- cally and the Standard Model cannot predict [Cah96]. But most importantly, the Standard Model does not include gravity, nor does it address the questions of dark matter or the huge matter-antimatter asymmetry observed in the universe.
New theories like Supersymmetry, Grand Unified Theories and String Theory al- low a glimpse how the future of particle physics might look like. Up to now those theories are only well-founded thoughts for which an experimental proof could not be delivered yet. But very innovative experiments in astro-particle and accel- erator physics are on the way to get a step closer and answer the questions that all particle physicists pursue: What is the universe made of? How did it begin?
What holds it together?
2.1 The Fundamental Forces of Nature
The modern quantum-mechanical formulation of the fundamental forces of nature started with Max Planck (1858-1947) who introduced in his speech for the German physics society in the year 1900 the revolutionary concept of the quantization of the electromagnetic field [Yan61]. He himself was not very fond of the idea, but as it turned out, it set off a new era of physics while it was generally thought at that time that all basic physical laws were already discovered. The only two interactions known at that time were the classical electromagnetism as derived by Maxwell (1831-1879) and Newton’s (1643-1727) laws for gravitation.
Quantum mechanics opened up the idea that a force is not mediated by a field but by a ”messenger” particle. In that view the electrical repulsion of, say, two electrons is not attributed to the electrical field surrounding them, but to the
4
Force Theory Force Carrier Range
Strong Chromodynamics gluon < 1 fm
Electromagnetic Electrodynamics photon ∞
Weak Flavourdynamics W
±, Z
010
−3fm
Gravitational Geometrodynamics graviton ∞ Tab. 2.1: The fundamental forces of nature.
exchange of a stream of field quanta, the photons [Gri08]. The same concept was applied to the weak and the strong interaction after their discovery decades later. Their force carriers are the W
±and Z
0bosons and the gluons, respectively (see table 2.1). Today the existence of all mentioned ”messenger” particles has been experimentally verified.
But what can we say about gravitation? Albert Einstein’s (1879-1955) theory of general relativity is a classical field theory describing gravitation, but cannot be incorporated into the Standard Model of particle physics. In fact, there is no consistent quantum theory of gravitation yet. A mediating ”graviton” was postulated but up to now no one has ever discovered it. Gravitation is purely attractive, about 10
−29-times weaker than the weak force in all known atomic and subatomic processes and influences matter mainly on astronomical scales at which quantum mechanics can hardly be applied. All other interactions show strong microscopic manifestations (whereas the electromagnetic interaction has an infinite range as well). Hence, the next section focusses on the three
“microscopic” forces: The electromagnetic, the strong and the weak interaction.
2.1.1 Electromagnetism
As mentioned above, the electromagnetic interaction has an infinite range [Gri99].
If not, the world would be a pretty dark place. That is why it is accessible to
our every day experience. It was the first fundamental force to be investigated
from the quantum mechanical point of view. Every charged particle can take
part in electromagnetic processes, whereas its force carrier itself, the photon is
uncharged. In 1928 Dirac discovered a first-order linear differential equation which
describes the quantum mechanics of point-like spin
12particles (fermions) and
which predicted at the same time the existence of antimatter. The combined
theory, describing the interaction of the charged Dirac field with the quantized
electromagnetic field, is called quantum electrodynamics (QED). The concept of
local gauge invariance assigns the mathematical symmetry group U(1) to the
electromagnetic interaction and gives rise to a massless spin 1 gauge boson, the
photon. The electromagnetic coupling constant is the Sommerfeld fine-structure constant α ≈
1371(in the case of small energies). Its smallness allows a perturbative approach to the determination of the cross sections for electromagnetic processes, which was developed by Feynman [Gri08].
2.1.2 The Particle Zoo and the Strong Force
With the construction of the first modern particle accelerator, the Brookhaven Cosmotron, particle physicists discovered a large set of strongly interacting par- ticles (hadrons) in the laboratory between 1947 and 1960. They are produced on a timescale of ∼ 10
−23sec but some of them disintegrate relatively slowly within
∼ 10
−10sec indicating that there are two fundamentally different mechanisms in- volved [Pai52]. In modern language, these particles are produced by the strong force and decay by the weak force. But also another class of particles was found, which decayed ”too slowly” for the standard weak force. These particles accord- ingly were called ”strange particles”. Gell-Mann assigned a new property to these particles which he called ”strangeness” and observed that it is conserved in strong interactions but not in weak ones [GM53]. Like Mendeleev in chemistry, Gell- Mann created a ”periodic system” of all hadrons in which they are categorized by their isospin and strangeness, the so-called Eightfold Way [MGM64]. The re- sulting pattern of hadrons was explained by the existence of three quarks (and their anti-quarks) whose multiple combinations assemble all hadrons: The up, the down and the strange quark. Only the ”strange” quark carries the quantum number ”strangeness”.
The quark model had a difficult start and was not widely accepted at the begin- ning. It had two major problems: If all baryons consist of three quarks and all mesons of a quark and an antiquark, why could they never be observed freely?
In other words, why are they confined into a bound state? Secondly, if, e.g., the observed ∆
++particle really consists of three up quarks which are all in an iden- tical quantum state, does the quark model then violate the Pauli Principle? In 1964, Oscar W. Greenberg proposed an additional quantum number, the color (red, green and blue) which is assigned to every quark [Gre64]. All free hadrons are consequently colorless (if the hadron contains quarks with all three colors or a color and the corresponding anticolor). But to many physicists this assumption came as a purely mathematical construction at that time.
The breakthrough of the quark model came actually not from a satisfactory ex- planation to those questions, but from deeply inelastic scattering of electrons on protons, which revealed the quarks within the proton beyond any doubt [Tay91].
Some years later (1974) the J/ψ was discovered (historically known as the Novem-
ber Revolution), an electrically neutral extremely heavy meson with extremely
long lifetime ( [Aub74], [Aug74]). The only consistent explanation could be pro-
vided by the quark model introducing a fourth quark, the charm quark c and
identifying the J/ψ as a bound cc state. With a fourth quark a whole new set of hadron combinations is possible, most of which were discovered until today (e.g. [E.G75]). In the next two decades two more quarks were found (b: 1977, t:
1995) leaving us with the (up to now) complete set of quarks: the up and down (1
stgeneration), the strange and charm (2
ndgeneration) and the bottom and top quark (3
rdgeneration). This is the order of discovery (within hadron compounds) and dictated by the drastically increasing mass of the quarks which affords always more powerful particle accelerators.
On this basis the theory of the strong force has evolved to our current under- standing: The strong force affects all colored particles, i.e. all quarks. Thus the corresponding quantum theory is very fittingly called quantum chromodynamics (QCD). As there are three colors, the mathematical symmetry group is SU(3)
C. The force between two quarks is mediated by eight gluons corresponding to the eight allowed combinations of three colors and their anticolors. Since each gluon carries two colors they can couple directly to other gluons. When in a hadronic compound, gluons carry a substantial fraction of the hadron momentum as proved by deep inelastic scattering experiments of protons with electrons [HK71].
Coming back to the questions from above: One of the great triumphs of QCD was the discovery that the strong coupling constant, and therefore the strength of the strong force increases with the separation distance between two quarks.
This phenomenon is known as asymptotic freedom [D.J87] and the reason why quarks can exist exclusively in confined colorless hadronic compounds. If a quark is struck out of such a compound by a high energetic collision, the potential en- ergy is increased drastically until the creation of an additional quark-antiquark pair splits the compound into two individual hadrons. But from the theoretical point of view the problem is that confinement involves the long-range behaviour of the strong interaction and that is precisely the regime in which the perturbative Feynman Calculus fails [Reb83].
2.1.3 The Weak Interaction
In 1930 a problem had arisen in the study of the nuclear beta decay [Bro78]. The apparently fundamental process observed at that time was:
A → B + e
−(2.1)
A is the decaying nucleus, B the nucleus left over and e
−an emitted electron.
Now the problem was that the detected energy spectrum of the emitted electron was continuous, which is impossible for a two body decay. The fundamental con- servation of energy was in danger. Thus Pauli (1900-1958) proposed the existence of a neutral, ”invisible” particle. It was later named neutrino. The fundamental process of the beta decay could then be reduced to:
n → p + e
−+ ν
e(2.2)
where n is a neutron, p a proton and ν
ean anti electron neutrino.
In fact every process which involves the emission or absorption of a neutrino is a weak process. But the weak force affects leptons as well as quarks. In general there are two types of weak interactions: charged and neutral ones mediated by the very heavy W
±(∼ 80
GeVc2) and Z
0(∼ 91
GeVc2), respectively [G.A83].
Weak hadronic decays are changing the flavour. That means, e.g., that a down quark can transform into an up quark under the emission of a W
−-boson at a fundamental vertex. Moreover weak decays can be cross-generational (e.g.
s → u + W
−) meaning that the conservation of strangeness, charm and beauty is not valid in weak interactions. The theory of Nicola Cabibbo [Cab63] which states that the weak interaction acts upon an admixture of different quark sorts was published in 1963 and could explain the decay of “normal” and
“strange” particles (consisting of u, d and s quarks) for the first time. Kobayashi and Maskawa generalized the theory in 1973 to handle three generations of quarks [MK73]. This happened before the charm quark was discovered, and long before there was any experimental evidence for a third generation.
In 1967, Glashow, Weinberg and Salam formulated the idea that the weak and the electromagnetic force can be unified in a mathematical way. They proposed a theory which uses again the concept of gauge invariance to assign the mathemati- cal symmetry group SU (2)
L× U (1)
Yto an electro-weak force [C.H81]. It resulted in 4 force carriers out of which 3 (the W
+, the W
−, the Z
0) acquire mass by the Higgs mechanism (explained below), while one remains massless (the photon).
2.2 The Standard Model
In the current view all matter is made out of two kinds of elementary particles:
Leptons and quarks. The forces between the matter particles are established by the exchange of field quanta (gluons, photon, W
±and Z
0). As seen in table 2.1, there are six leptons. They are classified by their charge and three generation dependent lepton numbers L
e, L
µand L
τ. Similarly, there are six quarks classified by charge, up, down, strangeness, charm, bottom and top (beauty and truth are the old-fashioned names). For all quarks and leptons corresponding antiparticles exist and every quark or antiquark can have three different colors. So altogether this leaves us with 12 leptons and 36 quarks, adding up to 48 elementary particles.
The list is nearly completed by 12 mediators for the microscopic fundamental forces: 8 differently colored gluons, the photon and the heavy W
±- and Z
0-boson.
Each force is described by its renormalizable symmetry group derived in view of
the concept of local gauge invariance. The conclusive group of all interactions is
SU (3)
C× SU (2)
L× U
Y(1) with respect to QCD and the GWS theory. All this
makes up the Standard Model [Wil97] which has been validated multiply over
u
up2.4 MeV
⅔
½
c
charm
1.27 GeV
⅔
½
t
top
171.2 GeV
⅔
½
down
d
4.8 MeV
-⅓
½
s
strange
104 MeV
½
-⅓
b
bottom
4.2 GeV
½ -⅓
ν e
electron neutrino
<2.2 eV
0
½
ν μ
neutrinomuon
<0.17 MeV
0
½
ν τ
neutrinotau
<15.5 MeV
0
½
electron
e
0.511 MeV
-1
½
μ
muon
105.7 MeV
½
-1
τ
tau
1.777 GeV
½ -1
γ
photon 0 0 1
g
gluon 0 1 0
Z 0
91.2 GeV
0 1
weakforce
W
±80.4 GeV
1
±1 weakforce mass→
spin→
charge→
QuarksLeptons
Three Generations of Matter (Fermions)
Bosons (Forces)
I II III
name→
Fig. 2.1: The elementary fermions and bosons in the Standard Model [Wik09].
the last decades, except for one missing link: The Higgs particle. The concept of gauge theory works, however, only for massless particles: It could never account for the massive nature of the W
±and the Z
0. Until the year 1964 in which Peter Higgs, an until then unknown young physicist, published his theory of the Higgs mechanism [Hig66]. He postulated a massive scalar field with infinite extension, present everywhere in the universe, the Higgs particle ( [Hig64a], [Hig64b]). The idea of spontaneous symmetry breaking assigns a potential to the Higgs field which assumes a non-zero vacuum ground state. The particle masses arise almost naturally when this potential is incorporated into the gauge theories and interacts with the spin 1 field of bosons and the spin
12field of fermions. Nevertheless, only the discovery of this massive Higgs particle (m
H> 114
GeVc2determined at LEP by exclusion [ewg]) can confirm all this.
2.3 Beyond the Standard Model
2.3.1 The Grand Unified Theory
At one time, electricity and magnetism were two distinct subjects. When physi-
cists realized that an accelerated electric charge can create a magnetic field or
that a moving magnet can generate electric current in a nearby loop of wire, it became suggestive that electricity and magnetism are two different manifes- tations of one single fundamental interaction. Years later James Clerk Maxwell (1831-1879) found a theoretical access to the unified theory of electromagnetism with his famous set of equations [Gri99].
A similar line of reasoning was used when the electromagnetic and the weak force became unified in the GWS-theory to the more fundamental underlying elec- troweak force. In the current universe the electromagnetic force is about 10
−11orders of magnitude stronger than the weak force [Gri08] but this can be at- tributed to the huge mass of the W
±- and Z
0-bosons (see section 2.1.3). The intrinsic strengths of the weak and electromagnetic force are quite similar, but this becomes only apparent at energies above M
Wc
2at which weak processes are no longer suppressed.
The next logical step is the integration of the strong force, known as the theory of grand unification (GUT). Investigating the energy dependence of the coupling constants within the Standard Model, which determine the strengths of the three fundamental interactions, we find that the strong coupling constant decreases at short distances or in other words, at high collision energies. So too does the weak coupling, but at a slower rate. The electromagnetic coupling constant, on the other hand, increases with increasing energy. It turns out that grand unifi- cation can only occur above energies of the order 10
16GeV and with a further extension of the Standard Model, like Supersymmetry ( [Gri08], see Figure 2.2).
GUTs suggest an overarching symmetry group (e.g. SU(5) in the first developed GUT [GG74]) which contains the SU(3)
Cand the SU (2)
L× U
Y(1) of the Stan- dard Model as subgroups. It involves the existence of twelve more mediators, the X and the Y particles (coming in 3 colors and two different charges each), with a mass similar to the GUT scale (m
X,Y> 10
16GeVc2). They couple quarks to anti- quarks and leptons to quarks which is why they are commonly called “diquarks”
or “leptoquarks”.
The consequences would be most dramatic: Leptoquark couplings allow for non- conservation of lepton and baryon number and hence permit the decay of the proton (i.e. p → e
++ π
0). Fortunately, this is immensely suppressed due to the huge mass of the X and Y, resulting in a proton lifetime orders of magnitude higher than the age of the universe. Otherwise the world could have ceased to exist long ago.
Proton decay is one of the “measurable” key predictions of GUTs, but until today
it has never been observed [Shi98], leaving grand unified theories in the state of
speculative assumptions beyond the Standard Model. On the other hand GUTs
claim to be able of giving an explanation for the relation between quark and
lepton charges and moreover the quantization of charge itself for the first time.
2 4 6 8 10 12 14 16 18 0
10 20 30 40 50 60
log10 μ/GeV
Standard Model
a)
α3−1 (μ) α2−1 (μ) α1−1 (μ)
2 4 6 8 10 12 14 16 18
0 10 20 30 40 50 60
log10 μ/GeV
mSUSY = 1 TeV α3−1 (μ)
α2−1 (μ) α1−1 (μ)
b)
Fig. 2.2: Energy development of the three coupling constants of the fundamental interactions within the Standard Model a) and the Minimal Supersym- metric Model b) [pdg08].
2.3.2 Supersymmetry
The final goal is to unify all fundamental forces of nature within a single universal theory, a Theory of Everything (TOE), including not only the microscopic forces, but gravity as well. Formulating a quantum theory of gravity is a most difficult task and faces severe theoretical difficulties until today [Gri08]. For example, String Theories are promising candidates for a TOE. But most TOEs have in common that they require another underlying symmetry of nature, called Supersymmetry (SUSY).
SUSY is a symmetry that transforms bosons and fermions into each other. In other words, in a supersymmetric theory, for every type of boson there exists a corresponding type of fermion which is its superpartner, and vice versa. So in one step the whole set of elementary particles known in the Standard Model gets doubled [Mar]. As of now no supersymmetric particles have been discovered, so one suggests that Supersymmetry is strongly broken and SUSY particles are extremely heavy and therefore beyond the range of current particle accelerators.
Nevertheless there are strong indications that at least some of them should be accessible to the next big accelerator project, the Large Hadron Collider at CERN which is about to be commissioned in the near future (see section 3.1).
But what is so tempting about this theory? First of all, if Supersymmetry can
be found at the Terascale (∼ 1 TeV) within a minimal extension to the Standard
Model, the so-called Minimal Supersymmetric Standard Model (MSSM), a
perfect convergence of the three running coupling constants at the GUT scale
is possible (see Figure 2.2, right). Apart from this, the lightest supersymmetric
particle is colorless, neutral and stable, making it an attractive candidate for dark matter. Dark matter makes up the largest part of all matter in the universe and it remains still unclear what it is made of. Moreover, as mentioned above, attempts to formulate a quantum theory of gravity do require Supersymmetry.
There are many other extensions to the Standard Model not mentioned
here which try to provide answers to the open questions of particle physics, but
in the end only experiments have the power to validate or disprove even the
most ingenious theory. An overview can be found, e.g., in [Gri08].
Calorimetric Concept
It is the aim of particle physicists to test the Standard Model as well as extensions to it, like Grand Unified Theories and Supersymmetry, on an experimental basis.
The generation and detection of, e.g., the postulated Higgs particle or the lightest supersymmetric particles requires the application of the most modern technology and often the development of completely new technologies. The expenses and expertise needed for such an experiment are usually immense and can only be provided by an international collaboration of many institutions and physicists.
In this Chapter we will explain such a large-scale experiment: The International Linear Collider (ILC) is a planned future 31 km long linear e
+e
−collider. Its Ref- erence Design Report [ES07] was published in August 2007. The International Large Detector (ILD) is one of the detector concepts discussed for the ILC with its Letter of Intent published at the end of March 2009 [Gro09]. The goal of the ILC and its detector is the precise measurement of physics at high energy scales (∼ 1 TeV). It will study Standard Model physics including top physics, heavy flavour physics and physics with Z/W bosons as well as physics beyond the Stan- dard Model including the search for the Higgs and the lightest supersymmetric particles.
In the first section we will present the International Linear Collider and the phys- ical principles of a particle detector on the example of the ILD. We will in the following go into detail on calorimetric concepts. Therefore, we explain physical basics of the working principle of a calorimeter and specifications on the CALICE experiment, an existing calorimetric prototype which tests the requirements to calorimetry given by the ILC physics programme.
3.1 The International Linear Collider
Particle accelerators are our tool to probe new physics at high energies. Charged particles (e.g. protons, nuclei, electrons) are accelerated to a velocity very close to the speed of light and brought to collision with a suitable target. In the collision the energy of beam particles can be converted into new particles, following Einsteins famous equation E = mc
2. Collider experiments, in which two beams
13
of particles travelling in opposite direction collide at a common interaction point, are used if a high center of mass energy shall be achieved for the generation of new particles in a so far unexplored mass region.
The Large Hadron Collider (LHC), which will be commissioned at the end of 2009, is such a collider. It is designed to collide protons at a center of mass energy of 14 TeV, accessing the so-called Terascale which means “physics in the TeV regime”. One of the heavy particle candidates that shall be explored is the Higgs (see Chapter 2.2). If the Higgs particle exists, the LHC will most probably discover it. If supersymmetric particles exist at a mass scale of about one TeV, the LHC has a good chance to observe them. Nevertheless, the physics at the LHC has some limitations which lead to the development of a complementary collider concept. The International Linear Collider (ILC) will enable high precision measurements by colliding electrons and positrons at a center of mass energy of up to 1 TeV. The highest energy reached up to now was a center of mass energy of 209 GeV at the Large Electron-Positron collider (LEP) at CERN, which terminated operation in the year 2000 to make space for the LHC. At LEP, no signs of the Higgs or Supersymmetry were found, so that the mass scale of such particles clearly required more powerful accelerators.
3.1.1 Reasons for a Linear Collider
Hadrons, such as the proton, consist of quarks and gluons (“partons”), each of which carries a fraction of the total momentum. If hadrons are brought to collision, the initial state of the colliding partons is not accurately known. The “interesting”
final states result from the collision of two partons. Due to confinement, all other hadronic fragments form further particles which are emitted into the detector system simultaneously, so-called “underlying events”. Therefore, the collision of quark-gluon compounds gives always rise to many background particles which accompany an “interesting” event and disguise its signal.
Leptons on the other hand are, according to our current knowledge, elementary particles without substructure. Electron-positron collisions are therefore clearly defined concerning the center of mass energy and the quantum numbers of the initial state. The precision measurements of parameters like spin and parity of fi- nal state particles (e.g. at pair produced SUSY particle or Higgs radiation events) can be performed only in an electron-positron collider experiment. The contribu- tion of underlying events is small and the physics signals can be extracted more clearly.
One can only profit from these advantages if the collider is capable of accelerating the leptons to a energy high enough to access Terascale physics. One finds that this can only be achieved for a linear e
+e
−-collider.
Two basic types of colliders are used in particle physics: Synchrotrons such as
the LHC accelerate particles along a circular path, whereas linear colliders use a straight path. Circular accelerators have many advantages over linear ones. They are capable of accelerating to high energies by gradually building up the energy over many revolutions and thus a multiple use of the same accelerating cavities.
Strong dipole magnets keep the particles “on-track” on the way around the ring.
Only a small fraction of all beam particles actually collide. The non-interacting particles remain in the ring and are available for future collisions. As a result, a higher collision rate can be reached for a synchrotron than for a linear collider.
However, regarding e
+e
−-colliders, there is a disadvantage that prohibits the con- struction of a circular collider to access the Terascale. The emission of electro- magnetic radiation limits the maximal reachable energy of electrons or positrons in circular accelerators. If a high energetic particle of energy E, charge q and mass m is circularly accelerated it emits electromagnetic radiation. This radia- tion is called synchrotron radiation. The energy loss
dWdtof a particle in a circular accelerator with radius R due to this radiation is:
dW
dt ≈ 2cq
23
γ
4R
2= 2cq
23
E
4m
4c
8R
2(3.1)
where γ is the relativistic Lorentz factor and c is the speed of light.
Acceleration power has to compensate for this energy loss. Note that the loss scales with the mass to the power of four. As protons are approximately 2000 times heavier than electrons, a circular accelerator could be realized for the LHC.
The synchrotron radiation for an accelerated electron at the same energy is much larger:
(
dWdt)
e(
dWdt)
p= 1.6 · 10
13· R
2pR
2e(3.2)
For protons, the maximum energy is limited by the costs and performance of the
dipole magnets that keep the protons on their circular track. Circular machines
are not an option for an electron-positron collider at the Terascale. The LEP ex-
periment, accelerated electrons and positrons circularly and achieved an energy
of about 100 GeV. The planned ILC is going to accelerate the same particles to an
energy at least 2.5 times higher. This would mean the energy loss by synchrotron
radiation is at least 2.5
4≈ 39 times higher. The radius of the ring contributes
only with a power of two (see equation 3.1). A reasonable energy loss could only
be achieved by increasing the radius to a few hundred kilometers. This is not
affordable. Building a linear electron-positron collider with a high acceleration
gradient, thus avoiding the emission of synchrotron radiation, is the only remain-
ing option. Nevertheless, reaching an acceleration gradient as high as 31.5
MVmplanned for the ILC affords the development of novel acceleration structures.
3.1.2 Outline of the Collider
Figure 3.1 shows the basic outline of the ILC. It consists of two separate accelerator systems: One for positrons depicted in green and one for electrons depicted in magenta. The interaction point (IP), where the beam particles collide head-on, is located in the center of the machine. The design of the interaction region is capable of hosting two detectors which shall detect all final state particles (ideas for such detectors are described in the following sections). A complementary detection system enables the vital cross-checking of discoveries.
As two interaction regions bring no gain in a linear collider setup in terms of the total integrated luminosity and the beam delivery system is a major cost driver of a linear accelerator, the two detectors will probably operate in a “push-pull”
system scenario, sharing the beam time in regular intervals [ES07].
Main Linac
Damping Rings
Main Linac 31 km
e+ e−
e−
Positrons
Electrons
Undulator
Detectors Electron
Source
Beam Delivery System
Fig. 3.1: Outline of the International Linear Collider.
In order to achieve the planned center of mass energy of 500 GeV [ES07], the two linear accelerators (linacs) will have a total length of about 30 km. Beam pro- duction starts with a laser which detaches electrons from a photocathode. They are then preaccelerated in a preliminary linear accelerator to an energy of 5 GeV before being injected into the electron damping ring (see Figure 3.1).
Positron production is initiated in a so-called undulator. An undulator contains an magnetic dipole field with alternating poles at very short periodic distances. An injected electron beam undergoes transverse oscillations and emits synchrotron radiation by this acceleration. While the electron beam returns to the main ac- celerator, the generated synchrotron photons hit a titanium-alloy target and are converted to electron-positron pairs. The positrons are collected, accelerated to 5 GeV, and then injected into a second damping ring.
The electron and positron damping rings have a circumference of 6.7 km and are housed in a common tunnel at the center of the ILC complex. They are mainly used to store the electron and positron beam. In the following, the electrons and positrons are delivered from the damping rings to their respective main linacs.
The linacs contain super conducting radio frequency (SCRF) cavities which ac-
celerate each bunch by a high electromagnetic field to a final energy of 250 GeV.
They operate at an average gradient of 31.5
MVm. The achievable peak luminosity of this design amounts to 2× 10
34cm
−2s
−1. To upgrade to a machine with a center of mass energy of 1 TeV, an extension of the linacs and the beam transport lines from the damping rings by another ∼ 11 km will be required [ES07].
3.1.3 Detector Concepts for the ILC
The interaction point of the ILC will be enclosed by a cylindrical detector which is optimized to identify and determine the four-vector of all particles produced in a collision. The four-vector holds information about the direction of flight, energy and momentum of a particle.
There are currently three different detector concepts which are under intense study for the ILC: The International Large Detector (ILD), the Silicon Detector (SiD) and the so-called 4th detector concept (4th). The investigations for this thesis were performed in view of the ILD concept.
3.1.4 Detector Requirements
The physics programme of a linear collider imposes stringent demands on the performance of a detector for the ILC. Some main performance requirements can be summarized as follows:
The most precise reconstruction of kinematic quantities is achieved in final states with charged leptons. Therefore, excellent momentum resolution is re- quired [ES07]:
σ
pp
2∼ 5 · 10
−5GeV
−1(3.3)
This momentum resolution is a factor of ten better than that achieved at LEP.
Many of the interesting physics processes will show multi-jet final states originat- ing from decays of heavy particles into the weak gauge bosons W
±and Z
0. An example is the top quark which decays into a W boson and one of three possible quarks s, d or b. Further examples can be found in [ES07]. The intended analyses require a clear separation of the jets resulting from W
±→ qq and Z
0→ q
0q de- cays. Only detectors with an unprecedented jet energy resolution can make that distinction. For the success of the physics programme the jet energy resolution of the detector system is required to be better than:
σ
EJ etE
J et∼ 30 %
q
E
J et[GeV]
(3.4)
This aim can be achieved by various concepts one of which is the particle flow
algorithm (PFA) approach (see section 3.1.6). This jet energy resolution is more
than a factor of two better than the best jet energy resolution achieved at LEP [Cea95].
3.1.5 The International Large Detector
Common particle detectors consist of a tracking system close to the interaction point, surrounded by an electromagnetic calorimeter (ECAL), a hadron calorime- ter (HCAL) and a superconducting magnet which provides a high magnetic field.
All three detecting components are capable of measuring the energy or momen- tum of particles. The accuracy and detection efficiency of the components depends on the particle energy and type.
The Calorimetric System
The calorimetric system is explained in detail in section 3.2. Here, it shall suffice to say that certain high energetic particles (electrons, photons, hadrons) gener- ate a so-called shower of secondary particles (also called particle cascade) when incident to a massive target material. Calorimeters reconstruct the energy of an incident particle by measuring the energy that is deposited in the material by the generated shower particles. The energy resolution
σ(E)Eof a calorimeter improves with increasing impact energy E as:
σ(E)E∝
√1E
. The Tracking System
The tracking system determines the momentum of charged particles by measuring the curvature of their tracks. The magnetic field B which penetrates the detector forces a charged particle on a bent track due to the Lorentz force F
Land the radial force F
r:
F
L= F
r⇒ p
r = qB (3.5)
where p is the momentum of the particle, q its charge and r the radius of its curve.
For a given magnetic field B, the transverse momentum p
tof a particle can be
determined if the associated track of the particle with radius r is detected. The
tracking system reconstructs the track of a charged particle by measuring a set of
three dimensional points N at distinct positions on the track. It makes use of the
fact that a charged particle deposits energy by excitation and ionization processes
when traversing matter (details in section 3.2.1), in this case the material of the
tracking system. Thus, neutral particles can traverse the trackers without leaving
a trace.
The momentum resolution of the detector can be expressed as [Glu63]:
σ(p
t)
p
t∝ σ(x) B
s
720
N + 4 p
t(3.6)
Where σ(x) is the spatial resolution of the measured points.
Note that the momentum resolution
σ(ppt)t
is deteriorated with increasing momen- tum p
tof the particle, in contrast to the development of the the energy resolution which improves with increasing particle energy.
Outline of the ILD
In the following we present the general configuration of the ILD. Figure 3.2 shows an overview of the ILD design. A detailed description of all subdetector compo- nents is out of the scope of this thesis but can be found in the ILD Letter of Intent [Gro09].
Fig. 3.2: Outline of the International Large Detector: Vertical cut through one quarter of the ILD (left). Schematic 3D-view of the cylindrical design concept (right).
The overall layout of the International Large Detector is optimized for the use
of the particle flow algorithms (explained in section 3.1.6). We explain its com-
ponents from the interaction point outwards. A multilayer silicon pixel vertex
detector is positioned close to the interaction point. It is surrounded by layers of
silicon strip detectors in the barrel and in the forward regions. A time projection
chamber (TPC) encloses the inner trackers. The tracking system is completed by
a second set of silicon strip detectors outside the TPC.
The calorimetric system consists of an electromagnetic calorimeter surrounded by a hadron calorimeter. ECAL and HCAL are designed as sampling calorimeters which consist of alternating layers of active and passive absorber material (see section 3.2.4). The ECAL will use tungsten as absorbing material, the HCAL iron. Silicon or scintillator cells are discussed as active material for the ECAL and scintillator cells or gas detectors for the HCAL. Both systems achieve good imaging capabilities through a fine segmentation of the active layers. The calori- metric system is explained in detail in section 3.2 on calorimetry.
A large superconducting coil on the outside penetrates the whole detector system described so far with a strong magnetic field of 3.5 Tesla. An iron yoke returns the magnetic flux of the solenoid. It will be instrumented with either scintilla- tor strips or resistive plate chambers, which serve as muon trackers as well as hadronic shower tail catchers.
3.1.6 Particle Flow
The concept of Particle Flow is guided by the idea that the momentum of each particle in a jet is reconstructed in the subdetector which provides the best reso- lution. The accuracy of the momentum measurement below ∼ 100 GeV is better in the tracking system than the accuracy of energy measurement in the calorime- ters [Mol08]. However, neutral hadrons and photons traverse the trackers without leaving a trace. Their energies can only be measured in the HCAL and ECAL, respectively. Figure 3.3 schematically shows the detector response to different particle types.
From LEP measurements, detailed information on the average particle composi- tion of jets is known ( [KL97], [MGW]). The jet composition varies on an event- to-event basis, but on average, charged particles account for ∼ 62 % of the energy of a jet, photons contribute with ∼ 27 % and long lived neutral hadrons (e.g. neu- trons or K
L0) with ∼ 10 %. The rest is energy lost to the detector by the emission of neutrinos which interact only weakly and traverse the detector unaffected.
Therefore the energy resolution of a jet depends on the individual energy mea- surement resolutions of charged particles σ
h±, photons σ
γand neutral hadrons σ
h0:
σ
2J et= σ
h2±+ σ
h20+ σ
γ2+ σ
conf2(3.7) where σ
confis the confusion term, to be explained shortly.
The PFA requires in particular a high granular calorimetric system (see the
energy depositions in the calorimeter in Figure 3.3), which means that it is
finely segmented into independent active cells where the deposited energy is
measured. The confusion term arises from wrong assignment of the deposited
Fig. 3.3: The detector response to different particle types: hadrons (h
+, h
0), electrons (e), muons (mu) and photons g. Neutral particles (dashed lines) cannot be detected in the tracker. The curvatures come from the solenoidal magnetic field. The detector schematics is drawn in the direc- tion of the colliding beams.
energy in the calorimeters when the particle showers of two or more jet particles
are so close that they overlap. Figure 3.4 shows two cases in which the clustering
algorithms which assign showers, or more precisely calorimeter cells, which
detected a traversing shower particle, to incident particles fail. The energy of the
charged particle, labelled h
+in Figure 3.3 and 3.4, is in both cases reconstructed
accurately in the tracking system and the information of the calorimeters is not
needed. Its track is bent by the magnetic field and it has a distinct momentum,
so that its particle shower overlaps significantly with the shower of a neutral
particle, labelled h
0, g. By chance, part or all of the energy deposited by the
neutral particle is assigned to the cascade of the charged particle (see fig. 3.4,
(left)). If this happens, the energy of the neutral particle is reconstructed wrongly
and thus it might be identified as another neutral particle or if all energy is
assigned to the charged particle it might not be detected at all. On the other
hand, it can happen that the shower of a charged particle develops in a way that
the clustering algorithm assigns a fraction of it to an incident neutral particle
which in fact never existed (see fig. 3.4, (right)). Both cases contribute to the
confusion term and can result in a significant deterioration in the overall jet
energy resolution.
HCAL ECAL
h0, g h+
IP
b)
HCAL ECAL
h0, g h+
IP
a)
Fig. 3.4: Problems of the particle flow algorithm caused by the overlapping par- ticle showers of a charged particle h
+and a neutral particle g, h
0: a) Part or all of the neutral energy deposition is assigned to the charged shower. b) The algorithm assigns a fraction of the shower to a neutral particle which never existed.
The aim of the particle flow algorithm is to keep this kind of confusion as low as possible. This challenge can be met by a calorimetric system with very fine segmentation (also referred to as high granularity) and a highly developed shower recognition. The capability of the calorimeters to resolve individual particles within a particle shower is called imaging capability and one of the crucial factors for the precision measurement of new particle sorts.
3.2 Basics on Calorimetry
Calorimetry for high energy physics means to measure the total energy of a given particle in the final state. When a high energetic particle traverses matter it loses energy due to several interaction processes. Before we discuss the details of the calorimetric measurement, table 3.1 gives an overview over the different particle types and their main interaction processes: All charged particles as well as photons are subject to excitation and ionisation processes. High energetic electrons loose energy by Bremsstrahlung. Additionally, hadrons are subject to elastic and inelastic scattering processes. All interactions will be explained in detail in the subsequent sections.
The dominant process is determined by the particle type, its energy and the
detector material it interacts with. Most high energy interactions with matter
Particle Type Interactions relevant for Particle De- tection:
Electromagnetic Interactions:
Heavy charged particles : → ionisation and excitation (M > m
electron)
Electrons → ionisation and excitation
→ Bremsstrahlung
Photons → excitation
→ ionisation: photo effect, Compton effect, pair production
Strong Interactions
Hadrons → elastic and inelastic scattering
Tab. 3.1: Overview over the different particle interactions sorted by the particle types.
generate secondary particles which interact further in the detector material. This multiplication repeats until the incident particle’s energy is no longer sufficient to create additional secondaries. The process of particle multiplication is called a shower, or a cascade. As the cascade evolves the energy of the secondary particles decreases progressively down to the threshold of further interactions. The final, very low energetic shower particles, being able to only scatter elastically, are either absorbed in the detector material or escape. The energy that all the secondary shower particles together deposit on their way through the detector is ideally proportional to the energy of the initial particle. By measuring the deposited energies, the incident energy of a high energetic particle can be reconstructed.
In general, there are two different types of cascades (or showers): Electromag- netic and hadronic showers. Charged electrons or positrons and photons interact electromagnetically and generate electromagnetic showers. Hadrons loose energy predominantly by strong processes and generate hadronic showers. Since neutral pions decay into electromagetic particles (mostly photons), hadronic showers may also have electromagnetic subshowers.
Electromagnetic and hadronic showers of the same energy can be distinguished by their transverse and longitudinal dimensions in the detector material. Elec- tromagnetic cascades are typically denser and stopped at a shorter penetration length than hadronic ones.
In the following we explain first the energy loss mechanism of charged particles.
Later we focus on the formation of electromagnetic and hadronic showers. The
properties of homogeneous and sampling calorimeters and the derivation of a
general expression for the energy resolution of a calorimeter is discussed at the end of this section.
3.2.1 The Passage of Charged Particles through Matter
Charged particles (with a mass higher than the electron mass) loose energy by the excitation and ionisation of electrons bound to atoms of the material they pass through. The Bethe-Bloch equation describes the mean energy loss dE per unit length dx that a particle of charge ze deposits in an absorber of atomic number Z and atomic mass A by the electromagnetic processes mentioned above.
− 1 ρ
dE
dx = const Z A
z
2β
2ln 2m
ec
2β
2γ
2I − β
2− δ 2
!
, (3.8)
Here:
const ≈ 0.307
MeV cmg 2A mass number of absorber Z atomic number of absorber
ρ density of absorber
z charge of incoming particle m
eelectron mass
β =
vcγ = √
11−β2
δ density correction factor I mean excitation potential
Figure 3.5 shows the energy loss distribution of muons traversing copper as ab-
sorber material. The range between ∼ 10
MeVcand ∼ 50
GeVcis well described by
the Bethe-Bloch equation. The energy loss
dEdxis high for low particle energies. It
decreases to a broad minimum around βγ ≈ 3 − 4. Particles with an energy in
this range are called minimum ionizing particles (MIPs). Due to this well-defined
energy deposition, MIPs are often used for detector calibration. After this min-
imum the energy loss increases slightly. This is called relativistic rise and the
Sternheimer correction function δ(βγ) accounts for it. The correction originates
from a polarisation of the absorber medium that shields the electric field of a
charged particle which traverses at relativistic energies. At very high energies
above βγ ≈ 1000 radiative losses become dominant:
Muon momentum 1
10 100
Stopping power [MeV cm2/g] Lindhard- Scharff
Bethe-Bloch Radiative
Radiative effects reach 1%
µ+ on Cu
Without δ Radiative
losses
0.001 0.01 0.1 1 10 βγ 100 1000 104 105 106
[MeV/c] [GeV/c]
100 10
1
0.1 1 10 100 1 10 100
[TeV/c] Anderson-
Ziegler
Nuclear losses
Minimum ionization
Eµc µ−
![Fig. 2.1: The elementary fermions and bosons in the Standard Model [Wik09].](https://thumb-eu.123doks.com/thumbv2/1library_info/4014074.1541292/15.892.273.602.174.559/fig-elementary-fermions-bosons-standard-model-wik.webp)
![Fig. 3.6: Energy and angle broadening of monoenergetic particles. Top: The Landau-Vavilov distribution: Probability for the energy loss of charged particles crossing a thin absorber [Gro08b]](https://thumb-eu.123doks.com/thumbv2/1library_info/4014074.1541292/33.892.202.671.225.929/broadening-monoenergetic-particles-vavilov-distribution-probability-particles-crossing.webp)
![Fig. 3.12: New integrated design of the AHCAL layers for the next CALICE prototype [Rei08].](https://thumb-eu.123doks.com/thumbv2/1library_info/4014074.1541292/43.892.137.679.478.919/fig-new-integrated-design-ahcal-layers-calice-prototype.webp)
