Universidad Autónoma de Madrid (UAM)
Departamento de Fı́sica Teórica
Electron Energy Reconstruction in the
ATLAS Electromagnetic End-Cap
Calorimeter using Calibration Hits
D.E.A:
Supervisor:
Eduardo Nebot del Busto
Dr. Jose Del Peso Malagón
2
Contents
1 Introduction
5
2 The ATLAS detector
2.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Review of calorimetry
3.1 Sampling calorimeters . .
3.2 Electromagnetic showers .
3.2.1 Shower generation
3.2.2 Energy resolution .
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4 The
4.1
4.2
4.3
4.4
4.5
ATLAS EMEC
Introduction and Calorimeter requirements
The EndCap Electromagnetic Calorimeter.
Spatial granularity . . . . . . . . . . . . .
High Voltage . . . . . . . . . . . . . . . .
Presampler . . . . . . . . . . . . . . . . .
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5 The
5.1
5.2
5.3
5.4
5.5
5.6
Calibration Hits method
Cluster Energy . . . . . . . . . . . . . . . . . . . . . . .
Description of the method . . . . . . . . . . . . . . . . .
Corrections for energy depositions in the calorimeter . .
Correction for lateral leakage out of the cluster . . . . . .
Corrections for longitudinal leakage . . . . . . . . . . . .
Corrections for the energy loss in front of the Calorimeter
5.6.1 Region with presampler η < 1.8 . . . . . . . . . .
Region without presampler η > 1.8 . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . .
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5.7
5.8
6 Results
6.1 Energy resolution and linearity . . . . . .
6.1.1 Linearity . . . . . . . . . . . . . . .
6.1.2 Energy resolution . . . . . . . . . .
6.1.3 Uniformity of the response . . . . .
6.2 Contribution from the different corrections
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2
CONTENTS
6.3
6.4
Systematics . . . . . . . . . . . . . . . . . . .
6.3.1 Effect of the cross talk . . . . . . . . .
6.3.2 Effect of an imperfect knowledge of the
Front method vs X method . . . . . . . . . .
7 Conclusions
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death material
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63
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66
70
71
Agradecimientos
Me gustaria aprovechar esta oportunidad para dar mi mas sincero agradecimiento a
todas las personas que me han estado apoyando durante mi formación.
En primer lugar quiero agradecer a Jose del Peso por haberme acogido como su
estudiante y por todo el conocimiento que me ha permitido adquirir el estar bajo
su supervisión. El trabajo que se presenta aqui, asi como muchas otras tareas, no
hubiesen sido posibles sin su orientacion, comentarios y entusiasmo por mejorar.
Mi presencia en el grupo de altas energı́as se la debo también a Fernando Barreiro. Le quiero agradecer el interés que ha mostrado tanto por mi trabajo, en el
que ha contribuido compartiendo sus conocimientos, como por mi bienestar en todo
momento.
A Luis Labarga, primera persona que conocı́ en la Universidad Autónoma, le
tengo que agradecer su acogida y el tiempo que me ha dedicado siempre que he
solicitado su ayuda.
No quiero olvidarme de agracer al resto del grupo: Juanjo, Juan, Claudia, Mara,
Theodota, Luis Fernando, Pablo y Pachi, que siempre estan dispuestos a echar una
mano en lo que se necesite. Y a los que se marcharon: Matti y Conchi.
Por supuesto a todos mis viejos amigos, compañeros de carrera y de doctorado
con los que he pasado muy buenos momentos y que siempre me han empujado a
seguir adelante. En especial a Carolina, que ha sido compañera de licenciatura, de
doctorado y con la que he estado trabajando codo con codo durante los dos uĺtimos
años. Ella siempre ha estado ahı́ para mi y se que segirá estando si la necesito. Y a
los nuevos amigos, en especial a Gabe, que ha sido un gran apoyo en los momentos
difı́les.
Dejo para el final lo que pienso ha sido mas importante en mi formación como
fı́sico y como persona, mi familia. Ellos siempre han estado a mi lado e incluso ahora,
separados por unos cuantos miles de kilómetros, todavı́a siento su apoyo como si
estuviesen conmigo. Nunca estaré lo suficientemente agradecido a mis padres por
haber tenido una vida de sacrificio para que yo haya podido llegar hasta aquı́. En
muchas ocasiones he escuchado a personas decir lo orgullosas que están de sus hijos.
Pues yo lo estoy de mis padres y por eso esta trabajo va dedicado a ellos.
4
CONTENTS
Chapter 1
Introduction
The Large Hadron Collider, the most powerfull proton-proton collider existing so far,
it is being installed at CERN (Conseil Europeen pour la Recherche Nucleaire) and
will start running summer 2008.
The high center of mass energy, high luminosity and several physic channels
present at the LHC put several requirements in the expected performance of the
ATLAS detector.
The Liquid Argon Electromagnetic End-cap Calorimeter (EMEC), which is basically used to identify and measure the energy and direction of electrons and photons,
will be very important on the LHC since many of the physic events have electrons
and photons in their final states. The LAr Calorimeter has been mounted and
commissioned since last year in the ATLAS cavern and some problems have been
encountered and solved already. Furthermore, previous tests with electron beams of
known energy showed that the different calorimeter requirements were fulfilled for
the few modules tested (3 out of 16 modules for the EMEC). However, the nominal ATLAS set-up it is different compared to the one at the beam tests. Electrons
and photons coming from the interaction point will go through the inner detector,
cables, boards, cryostat walls, etc, before reaching the electromagnetic calorimeter.
In addition, they will feel the effect of a 2 Tesla magnetic field, which may bend
the trayectory, specially of the low energetic electrons, making miss the calorimeter
cell cluster. These conditions in ATLAS will affect the energy reconstructed in the
calorimeter for incident electrons and photons as well as the energy resolution with
respect to the Beam Tests. The correction for this energy loss was done in the past
using some weighting procedure in the different calorimeter compartments. It was
shown that this procedure was not satisfactory to reconstruct the energy at the level
required.
A new method to reconstruct the energy of electrons and photons, called Calibration Hits Method (CHM), was devised almost two years ago and has been developed
and tested for the Electromagnetic Barrel calorimeter (EMB) thereafter [12]. Simultaneously, the author of this ”tesina” has adapted and tested the method for the
Electromagnetic End-Cap Calorimeter (EMEC) and perform some further developments to the method demanded by some peculiarities of the EMEC. This is the work
done in this ”tesina”.
5
6
CHAPTER 1. INTRODUCTION
The Calibration Hits Method is named after a special Monte Carlo simulation
which records not only the energy depositions in the active parts of the calorimeter
but also in the inactive parts and death materials. This allows to compute correction
functions for all the different sources of energy loss independently. The parameters of
these functions depend on the following measurable quantities: the energies deposited
in the 3 calorimeter compartments and in the presampler, and both the barycenter
in depth and along the direction of the polar angle. The simulation of the electron
samples to develop the method an extract the coefficients require a large CPU time,
so the grid computing facility at the UAM high energy physics laboratory was used.
Chapter 2 will give and overview of the LHC and ATLAS detector. Chapter
3 introduces the basics of electromagnetic calorimetry paying special attention to
sampling calorimeters. In Chapter 4 a description of the Endcap electromagnetic
Calorimeter is given, with emphasis in the topics of interest for this work. In Chapter
5 a description of the Calibration Hits method and the work to obtain the different
corrections is presented. Finally, Chapter 5 presents the achieved results by the
method in terms of energy resolution, energy scale and linearity, and some systematic
errors are studied.
Chapter 2
The ATLAS detector
In this chapter the motivation and the main characteristics of the Large Hadron
Collider (LHC) as well as the ATLAS detector are discussed. In the first section the
most important accelerator parameters are reviewed. In the second section a brief
overview of the ATLAS detector is done.
2.1
The Large Hadron Collider
The LHC is a proton-proton and heavy ion collider with a center of mass energy
of 14 T eV when operating in p-p mode. The accelerator, being mounted in the
∼ 26.7Km circular LEP tunnel, is currently on the last installation stages: the first
proton-proton collisions are expected in summer 2008. The accelerator is basically
formed by 1232 superconducting dipoles, providing a magnetic field of 8.4T which
will keep the protons circulating. Bunches of protons separated by 25ns will intersect
at the four interaction points where the four different detectors (ATLAS, ALICE,
CMS and LHCb) are placed, figure (2.1). ATLAS and CMS are general purpose
experiments designed for searches of new physics and precision measurements; LHCb
is a B physics oriented detector while ALICE is a heavy ion experiment trying to
study the behavior of nuclear matter at very large energies.
In the first LHC runs a luminosity of 2 × 1033 cm−2 s−1 is expected, which will be
increased afterwards to its nominal value of 1034 cm−2 s−1 equivalent to an integrated
luminosity of 100 f b−1 a year. The design of the LHC makes it possible to explore
an unprecedented physical region, where new physics phenomena may appear.
2.2
The ATLAS detector
The ATLAS (A ToroidaL ApparatuS) is a multi-purpose detector designed to exploit
the physics potential of the LHC. The detector, figure 2.2, is a cylinder 44 meter long,
11 meters radius and an overall weight of 7000 tons [1]. The ATLAS coordinate
system is a spherical system defined in terms of the beam direction, which is the z
axis, and the polar (θ) and azimuthal (φ) angle. However, the polar coordinate it is
usually expressed in terms of the pseudo-rapidity which is defined as:
7
8
CHAPTER 2. THE ATLAS DETECTOR
Figure 2.1: Diagram of LHC ring.
θ
η = −ln(tan
)
2
The detector is made of four major components:
• The Inner detector (ID). It is a tracking detector located in the most inner
part of ATLAS, which is enclosed within a cylinder that has a length of 7m
and a radius of 1.15m (see figure 2.3). It is designed to measure the trajectory
(track) of charged particles with a very good efficiency in the coverage range
−2.5 < η < 2.5. It is immersed in an axial magnetic field of 2 T for the
measurement of the momentum of charged particles. It consists, from inner
to outer volume, of three parts: two types of Silicon semiconductor (Pixel
and SCT) and straw-tube tracking detectors (TRT). The combination of Pixel
and SCT allows for the reconstruction of particle decay length for unstable
particles, while the TRT implements an identification of electrons through the
transition radiation effect. Some of the measurements which can be performed
using the ID signals are: identification of the primary vertex or interaction
point, determination of the trajectory and momentum of charged particles,
decay length reconstruction, electron identification and measurement of charge
sign.
• The Calorimeters.The system of calorimeters can be seen in figure 2.4.
– The Electromagnetic (EM) Calorimeter is used to identify electrons and
photons, and to measure their energy and direction. It is also part of the
hadronic calorimeter when measuring the energy of jets and the missing
9
2.2. THE ATLAS DETECTOR
Figure 2.2: View of the atlas detector.
Barrel SCT
Forward SCT
TRT
Pixel Detectors
Figure 2.3: View of the Inner detector.
10
CHAPTER 2. THE ATLAS DETECTOR
transverse energy (ETmiss ) of some processes. The EM calorimeter is a lead
- liquid Argon sampling calorimeter with fine granular cells, which covers
a pseudo-rapidity range −3.2 < η < 3.2 and the whole range along the
azimuthal (φ) direction. It is divided in one barrel (−1.475 < η < 1.475)
and two end-caps (−3.2 < η < −1.375 , 1.375 < η < 3.2) [2].
– The hadronic Calorimeter will be used to measure the energy of jets and
missing transverse energy (ETmiss ). It is divided in one barrel and two EndCaps. The barrel part is a sampling iron - scintillator calorimeter readout
by optical fibers and photo-multipliers. The scintillator pieces are placed
normal to beam axis like ”tiles”, hence the name of Tile Calorimeter. The
End-Caps are sampling calorimeters with copper as absorber and liquid
Argon as sensitive material which share the cryostats with the EM EndCap and forward calorimeters.
– The forward calorimeter is realized to achieve a good hermeticity in ATLAS, hence to provide an excellent resolution in the measurement of missing transverse energy. It covers the region in pseudo-rapidity −4.9 < η <
−3.2 and 3.2 < η < 4.9. It is a sampling calorimeter, with liquid Argon
as sensitive material, segmented longitudinally in three compartments:
FCAL1, FCAL2 and FCAL3. As absorber material the first one uses
copper while the last two use tungsten inside copper tubes.
EM Accordion
Calorimeters
Hadronic Tile
Calorimeters
Forward LAr
Calorimeters
Hadronic LAr End Cap
Calorimeters
Figure 2.4: Schematic view of the ATLAS calorimeters.
• The muon spectrometer. It is a tracking detector for precise measurements
of muon trajectory and transverse momentum. It consists of gas proportional
11
2.2. THE ATLAS DETECTOR
chambers which surrounds the calorimeter and are immersed in a magnetic
field, with maximum value of 4 T , for the measurement of the muon transverse
momentum. There two types of chambers: MDT in the barrel location and
CSC in the End-Caps. Additionally there are fast response chambers to trigger
on muons, which are called RPC in the barrel region and TGC in the End-Caps.
Both chamber types for trigger purposes are capable of delivering the response
in a short time, between 15 ns and 20 ns, shorter than the crossing time of
LHC beam proton bunches. The chambers extend to the ATLAS dimensions,
for the barrel part to a radius of 11 m and for the the End-Caps to a length of
23 m from the nominal interaction point.
Resistive plate
chambers
Cathode strip
chambers
Thin gap
chambers
Monitored drift tube
chambers
Figure 2.5: View of the muon system.
• The magnet system. The ATLAS superconducting magnet system consists
of a central solenoid providing the magnetic field for the Inner Detector and
a system of large air-core toroids generating the magnetic field for the muon
spectrometer.
The solenoid magnet is place just in front of the Barrel Electromagnetic Calorimeter and it is cooled by helium at 4.5 K. It provides a magnetic field along the
z-direction of about 2 T . As a drawback it increases the material in front of
the EM Calorimeter causing electrons and photons showering before they reach
the active part of the calorimeter.
The toroid magnet is divided into one barrel part and two End-Caps. Both are
visible in the outer part of the ATLAS detector (figure 2.2).
12
CHAPTER 2. THE ATLAS DETECTOR
Chapter 3
Review of calorimetry
In this chapter an overview of the principles of calorimetry in high energy physics
is given. First the concept of sampling calorimeter will be explained and then the
electromagnetic particle showers or cascades.
3.1
Sampling calorimeters
Calorimeters currently used in high energy physics are either homogeneous or sampling. Homogeneous calorimeters consist of a single material, such as lead glass, NaI,
BGO, etc... When a fast particle enters the acceptance volume of a homogeneous
calorimeter its energy degrades and generates a measurable signal. On the contrary,
the tasks of absorbing the incident energy and generating a signal are, in sampling
calorimeters, done by two different materials: the passive material (Fe, Cu, Pb, U,
etc...) plays the role of energy absorber, whereas the active material (scintillating
plastic, LAr, silicon) gives rise to the signal. This work is focused on sampling
calorimeters.
The two materials present in a sampling calorimeter are tipically arranged in successive layers, so that the incident particle and the secondary ones generated by its
interaction with the detector, cross alternatively regions of active and passive material as they go deeper and deeper into the detector. The interaction just mentioned
usually produces a so called shower or cascade of secondary particles in which the
energy carried is degraded and part of it detected. Particle showers will be described
in 3.2.
The principles of the shower generation are of statistical nature. Therefore the
fraction of energy that an incident particle leaves inside the active medium can be
regarded as a random variable, subject to fluctuations. The geometry of a calorimeter
can be very complicated. For the sake of simplicity one can consider the simplest
plane-parallel layered structure as an example. In any case, the signal generated by
an incident particle must be, on average, proportional to its original energy.
In order to gain some insight into the features of the energy signals generated in
a sampling calorimeter, it is necessary to describe particle showers.
13
14
3.2
CHAPTER 3. REVIEW OF CALORIMETRY
Electromagnetic showers
We call electromagnetic showers to those generated by an electron, positron or photon
reaching a calorimeter. In this paragraph the mechanism of shower generation and
the resolution achievable in an energy measurement involving an electromagnetic
shower are discussed.
3.2.1
Shower generation
Several mechanisms contribute to the energy loss of electrons and photons incident on
matter. However at high energies (well above 10 MeV ) the fraction of energy lost per
unit depth of material is almost energy independent and only due to bremsstrahlung
(electrons or positrons) and pair creation (photons). The secondary particles produced in the cascade carry successively less energy until they reach the range where
several other effects become important. If the whole shower is absorbed inside the
calorimeter, the energy deposited is obviously equal to that of the primary particle.
For electrons and positrons the processes that become relevant in the sub-GeV
range are Bhabha and Compton scattering and ionization. Positrons in addition
suffer annihilation. Ionization is in fact the dominant process and the reason why
all particles finally get absorbed. For photons the Compton and photoelectric effect
are the ones that compete with pair production at low energies.
At high energies (E > 1 GeV ) the absorption can thus be characterised in a
material-independent way by introducing the so called radiation length (X0 ) of the
substance. It is defined as the material thickness to be travelled by an electron so
that it looses on average 63.2% of its energy through bremsstrahlung; i.e. the electron
energy decreases by a factor 1/e each radiation length. This obviously means that
the typical shower particle energy at a given depth z (given in cm) is
− Xz
E = E0 · e
0
= E0 · e−t
where E0 is the initial energy of the incident electron or positron. Obviously t is the
depth measured in units of X0 .
At low energies, energy losses are dominated by collisions. The critical energy ǫ0
of a material is the energy value at which the mechanisms of bremsstrahlung and
ionization are equally important. It represents the limit where the growth of the
shower stops and the particle multiplicity starts to decrease. Its value in MeV is
given approximately by [3]:
ǫ0 =
550
Z
This approximation is accurate to 10% for an atomic number Z > 13.
A very simplified model of shower developement can provide some insight into
electromagnetic calorimetry, assuming that the only dominant processes at high energies are bremsstrahlung and pair production and describing these two mechanisms
by asymptotic formulae.
15
3.2. ELECTROMAGNETIC SHOWERS
An electron entering a calorimeter with energy E much larger than the critical
energy ǫ0 , after having crossed one radiation length of material (X0 ), will have lost
63% of its initial energy into photon. We can say that on average the photon and
the electron will carry each half of the original energy, E/2. After another radiation
length of material the photon will create an e+ e− pair and the electron will emit
another bremsstrahlung photon. The energy of each of the four particles will be
on average E/4. The multiplication process proceeds. When the shower particles
reach an energy below ǫ0 they are completely absorbed by collisions and the shower
terminates. The model is equally valid if the original particle is a photon, except for
a small shift in depth.
The number of particles doubles after each radiation length. Therefore at a depth
t (in units of X0 ) the number of shower particles is
N = 2t
The mean energy of a particle will then be
E
= E · 2−t
N
The depth at which the mean energy ǫ equals the critical energy ǫ0 is where the
shower reaches its maximum particle multiplicity, that is:
ln (Nmax ) = ln (E/ǫ0 ) ⇒ ln 2tmax = ln (E/ǫ0 )
ǫ=
Hence,
ln (E/ǫ0 )
(3.1)
ln2
The average total distance covered by all the particles of the shower is called the
average total track length T . Since each particle travels on average a distance X0
before splitting into two, the quantity T , in units of X0 , is equal to the total number
of particles in the shower.
As the showering process occurs, a small part of the energy is lost by ionization
and this fraction is proportional to the total track length, because each energetic
particle of the shower deposits an amount of energy per unit length independent of
the energy it carries. That is:
tmax ≃
E
ǫ0
This linear relation between the incident energy and the total track length or
energy loss by ionization makes calorimeters useful devices.
In general the whole track length will not be detectable, but only a fraction of it,
Td . Only shower particles above a certain energy threshold η will be detected, so we
can write
Evisible = Eionization ∝ T =
Td ≃ F (η) · T = F (η) ·
E
ǫ0
16
CHAPTER 3. REVIEW OF CALORIMETRY
In order to ensure the full containment of the shower in the calorimeter, both
experimental information and some calculation can be used [4]. The length necessary
to ensure a 98% energy shower containment can be parametrized as
< L98% >≃ tmax + 4λatt
where the quantity λatt comes from the exponential decay of the shower energy
density deposition (following e−t/λatt ) after reaching the maximum (see 3.1). This
λatt turns out to be approximately energy-independent and can be characterized in
terms of the radiation length as λatt ≃ (3.4±0.5)X0 . Notice that the depth necessary
for a calorimeter to fully contain and measure a shower grows only logarithmically
with the energy (see eq. 3.1).
Figure 3.1: Average longitudinal energy deposition of electromagnetic showers for
three types of materials: Lead (blue), Iron (green) and Aluminum (red).
The shower also develops transversally to the primary particle direction due to
the scattering angle of the different interaction processes. Averaging to enough number of events, the transverse energy deposits of the shower can be parametrized by
two decreasing exponential functions in the polar variable r, with different length
parameters [5]. The first exponential with a small mean length represents the core
of the shower, while the second one with a larger mean-length takes into account
the spread of the low energy particles in the last stages of the shower development
(mainly the multiple scattering process). The fluctuations around this average transverse profile are estimated to be small. The Moliére radius (RM ) is a characteristic
constant of a material giving the scale of the transverse dimension of the shower in
units of radiation lenghts. By definition, a cylinder with axis the direction of the
incident electron and radius 2RM contains on average 95% of the shower energy. An
approximate relation for RM is:
RM = 0.0265X0 (Z + 1.2)
For example, for lead RM = 12.3 mm and for liquid Argon RM = 71.2 mm.
3.2. ELECTROMAGNETIC SHOWERS
3.2.2
17
Energy resolution
The processes of energy deposition, detection and read out are of statistical nature.
The relative precision of the energy measurement can be obtained as:
σ (Evisible )
Evisible
where σ(Evisible ) is the standard deviation of the variable Evisible .
Intrinsic fluctuations
Two kinds of uncertainties enter the energy measurement. First, the showering is
in itself a statistical process, of almost gaussian character. Landau fluctuations [6]
due to ionization processes with large energy transfer to the electrons of the detector
material, lead to asymmetric spectra. They are however not quantitatively significant
in the case of the ATLAS calorimeter.
The visible energy is, as shown above, proportional to the number of particles
produced (N), but also to the number detected (Nd ). Both are large numbers √
that
will follow normal distributions. The standard deviation will thus scale as σ ∼ N .
Then
√
σ(E)
Nd
σ(Nd )
1
1
∼
=
=√
∝√
E
Nd
Nd
Nd
E
The relation stated above sets a lower limit to the accuracy of the energy measurement, i.e. the intrinsic fluctuations. The best homogeneous calorimeters made
of scintillating
crystals or noble liquids achieve energy resolutions of order σ/E ≃
√
1%/ E [4].
Sampling fluctuations
In the case of a sampling calorimeter only the fraction of the particle track that is
inside the active part will contribute to the visible signal. Hence, we need to decrease
Td by a factor to consider only the active part. However, we will follow in this section
an alternative approach, which uses the sampled (or visible) energy instead, Let Es
be the sampled energy, s the thickness of one calorimeter active layer and (dE/dx)s
the energy deposited by minimum ionising particles in the active layers per unit
length. Hence, the number of crossing through the active medium layers will be:
Ns =
Es
(dE/dx)s s
The visible energy can approximately be computed as:
dE
s
Es
∼ dE dx s dE E
s + dx d d
dx s
18
CHAPTER 3. REVIEW OF CALORIMETRY
where d is the thickness of the absorber layers, and both s and d are expressed in
units of radiation lengths.
d >> dE
s , we can write the following approximation:
Since normally dE
dx d
dx s
dE
s
Es
dx s
∼ dE E
d
dx d
Hence,
Ns ∼
E
dE
dx d
Therefore,
σs
1
=√
=
Es
Ns
s
d
dE
dx d
d
E
If d is in units of X0 :
dE
dx
d
∼
E
= ǫ0
T
where ǫ0 is the critical energy of the absorber material, then,
r
σs
ǫ0 d
=
Es
E
where d is given in units of X0 .
Expressing the critical energy ǫ0 in units of MeV and the energy E in GeV ,
previous relation becomes:
r
r
ǫ0 d
d
σs
= 0.032
=R
Es
E
E
√
where R = 0.032 ǫ0 .
The formula above must be corrected for multiple scattering. Once the passive
material is fixed, this correction can be reabsorbed in the constant R. The sampling fluctuations of the ATLAS Electromagnetic
Calorimeter followed the previous
√
approach, hence, the decrease law as 1/ E.
Other fluctuations.
There are other sources of degradation of the energy resolution like non-uniformities,
mechanical imperfections, energy leaking behind the calorimeter (in case the depth
is not enough), misscalibrations, etc.
In general this type of imperfections do not follow the same scaling law as the
sampling fluctuations, generating a constant term that dominates the energy resolution at high energies.
3.2. ELECTROMAGNETIC SHOWERS
19
To sum up, the energy resolution of a sampling calorimeter can be parametrized
by the formula 1
a
σE
= √ ⊕b
E
E
where the symbol ⊕ stands for the quadratic sum, that is:
r
σE
a2
=
+ b2
E
E
The presence of noise, for instance in the readout chain, introduces an additional
term which scales as 1/E, since the σ(noise) does not depend on the energy of the
incoming particle. Hence,
c
a
σE
= √ ⊕b⊕
E
E
E
1
Electronics noise is not taken into account at this stage.
20
CHAPTER 3. REVIEW OF CALORIMETRY
Chapter 4
The ATLAS EMEC
4.1
Introduction and Calorimeter requirements
Electromagnetic Calorimetry will play a main role in the understanding of the physics
outcoming from proton-ptoton collisions in the LHC, since many processes will manifest themselves through photonic and electronic final states. The main task of the
atlas electromagnetic calorimeter is to meassure energy and position of electrons,
photons and jets (portion of jets), measurement of the transverse momentum (pT ) of
the event and particle identification (specially electrons and photons). It is the only
device to identify photons, since they do not leave any track in the Inner Detector.
Several benchmark physics channels such as H → γγ, H → 4e or Z’or W’ identification put the most tight constrains on the construction of the calorimeter. In this
document we just describe those requirements of interest for the understanding of
the presented work:
• Search for rare processes require a very good η coverage, as well as the measurement of the missing transverse energy of the event.
• The strongest constrains in terms of energy resolution are based on higgs
searches. The channels H → γγ and H → 4e need a mass resolution of
1% in the region 114GeV < MH < 219GeV which requires a sampling term
of about ∼ √ 10%
and a constant term lower than ∼ 0.7%. In addition the
E(GeV )
energy scale must be controlled at the level of 0.1%.
• It is necesary to obtain a linearity better that 0.1%.
• Electron reconstruction capability from 1 GeV to 5 T eV . The lower limit comes
from the need of reconstructing electrons from b quark decay. The upper one
is set by heavy gauge boson decays.
• The total thikness of at least 24 radiation lenghts (X0 ) such that the resolution, linearity and energy scale are not affected by energy leaked behind the
calorimeter for high energy particles (E > 500GeV ).
21
22
CHAPTER 4. THE ATLAS EMEC
• Excelent electron/jet and photon/jet separation. The main source of missidentification of electrons and photons is hadronic jets. For example, a high pT π 0
decays in two high pT photons, which, going very close together, may look as
one photon of a Higgs decay channel H → γγ. To distinguish the two photons
of the π 0 decay, a fine lateral (granularity) in the calorimeter is required.
4.2
The EndCap Electromagnetic Calorimeter.
The ATLAS Electromagnetic End-Cap Calorimeter, is a sampling calorimeter with
lead as absorber or passive material and Liquid ARgon (LAR) as an active material
[2]. An accordion shape is given to all plates in order to avoid crack regions due
to cables and boards of the readout. A picture of the accordion shape is shown in
figure 4.1. Particles, which are incident onto the calorimeter from left to right of the
picture, perceive the alternate Lead-LAr structure of the sampling calorimeter.
Figure 4.1: Accordion shape in EMEC inner wheel
The Argon is kept liquid at a temperature of ∼ 89o K through a cryogenic system,
being the EMEC inside a cryostat vessel, which has two walls separated by vacuum
for better thermal isolation.
There are two EMEC, in their respective cryostats, located at the two mirror EndCap positions, one at z ∼ −350 cm (EMEC-C) and the other one at z ∼ 350 cm
(EMEC-A) of the nominal ATLAS interaction point (see figure 2.2). Each EMEC
End-Cap has a cylindrical (wheel) form being the internal and external radii of
about 30 cm and 200 cm respectively, and about 63 cm thick. In Figure 4.2 a picture
of one EMEC inside the cryostat, seen from the back, is shown, together with a
schematic drawing of the EMEC cylinder with some absorbers in it. The readout
cables (orange-color) coming from the back side are seen in the picture as well as
the 30cm-radius hole in the center to accommodate the beam pipe (as well as to
leave place to the forward calorimeter behind). In order to acomodate the acordion
4.2. THE ENDCAP ELECTROMAGNETIC CALORIMETER.
23
geometry the absorber plates are arranged radially like the spokes of a bicycle wheel
and the accordion waves are paralel to the front and back edges of the wheel and
run in depth (see drawing of figure 4.2).
(a) Picture of an EMEC wheel inside the End- (b) Arrangement of absorbers in an EMEC
Cap Cryostat.
cylindrical wheel
Figure 4.2: EMEC figures
Since the EMEC is a cylindrical wheel, the amplitude of the accordion waves
decreases when η increases (when the radious decreases).
Due to mechanical constraints demanded by this accordion shape, a second independent wheel is needed to extend the coverage to η = 3.2. Hence, there are two
wheels, the outer wheel from η = 1.375 to η = 2.5 and the inner wheel from η = 2.5
to η = 3.2. In the picture of figure 4.2 a metal ring is clearly seen separating the
two outer and inner wheels, which is shown in the drawing as well. A discontinuity
in the accordion wave shape is seen in the drawing of figure 4.2 when going from the
outer to the inner wheel, and can be clearly seen in figure 4.3 where a detail picture
of the outer-inner boundary is shown.
The lead is cladded by 0.2 mm thick steel to give it enough rigidity. For the
outer wheel, the thickness of the lead plates is 1.7 mm while the LAR gap thickness
between two absorbers decreases continously from 5.6 mm (at η = 1.375) to 1.8 mm
(at η = 2.5). For the inner wheel, the thickness of the lead plates is 2.2 mm (see
figure 4.3) while the LAR gap thickness between two absorbers decreases continously
from 6.2 mm (at η = 2.5) to 3.6 mm (at η = 3.2).
The LAR ionization is collected by electrodes (at high voltage) situated in between two absorbers (at ground) as can be seen in figure 4.3 for the inner wheel as
an example. To keep the electrode in the right place, honeycomb spacers are located
24
CHAPTER 4. THE ATLAS EMEC
Figure 4.3: Stacked layer of the inner wheel. The electrode is placed in between two
absorbers.
in between the absorber and the electrode, which are also distinguished in figure 4.3.
Hence the liquid Argon gap between two absorbers is divided in two parts, the ionization of both being readout by the same electrode. A picture of an outer-wheel
electrode is shown in figure 4.4. In the thickness of 0.25mm there are 3 copper layers
separated by Kapton isolation, namely two layers on top and bottom holding the
High Voltage and one layer in the middle to readout the ionization signal by the
effect of capacitance coupling. The thicknesses of these layers are given in figure 4.4.
The High Voltage (HV) held on the bottom and top electrode layers ranges between
1000 Volts and 2500 Volts depending on pseudorapidity (η) location. For such high
values of the voltage a very good isolator, like Kapton, is mandatory to avoid leak
current to the signal layer.
To facilitate handling and logistics each EMEC cylinder is divided into 8 octants
or modules (see figure 4.5), hence there are 16 modules in total for the two EMEC
End-Caps. One half of the modules have been stacked at the CPPM 1 and the other
half at UAM 2 under strict clean conditions. These clean conditions are important
to avoid short-circuits due to any dust particle entering in the gap between electrode
and absorber where the electric field may be higher than 1000 V /mm.
One module consists of 96 (32) layers for the outer (inner) wheel stacked one
on top of each other along the azimuthal direction (φ). Each layer is a sandwich of
absorber, spacer (gap), electrode, spacer (gap). Figure 4.5 represents a picture of a
module at the stacking frame of the UAM clean room.
The design is symmetrical in φ.
1
2
Centre de Physique des Particules de Marseille
Universidad Autónoma de Madrid
4.3. SPATIAL GRANULARITY
25
i(t)
R
HV
Figure 4.4: Picture of an EMEC electrode. The thin electrode has 3 layers separated
by Kapton isolation: two HV layers on the sides and one signal layer inbetween which
capture the ionization signal by capacitance coupling.
4.3
Spatial granularity
The EMEC is segmented along the two angular directions, η and φ, and along the
calorimeter depth.
The electrodes are longitudinally segmented in three (two) compartments, all
called samplings, in the outer (inner) wheel of the calorimeter:
• The first sampling (S1 or front) is about 4.4X0 thick in the outer wheel while
it is about 22X0 in the inner wheel.
• The second sampling (S2 or middle) is about 17X0 (2 − 8X0 ) in the outer
(inner) wheel. For particles hiting on the outer wheel most of the energy will
be deposited on this second sampling since.
• The third sampling (S3 or back) has a depth between 4 and 12 X0 , depending on η, in the outer wheel. Note that this compartment is not present in
the inner wheel. Sometime it is used to estimate the longitudinal leakage of
electromagnetic showers with the data themselves.
Figure 4.6 shows a picture of an electrode corresponding to the outer wheel. The
front and back sides correspond to the top and bottom parts of the picture respectively, while pseudorapidity η increases from right to left. The three compartments,
S1, S2, S3 can be distinguish by the different segmentation along η they have: the
S1 compartment on top of the picture, the S3 on the bottom part and the S2 in
between.
As showed in figure 4.6 the granularity along η is also defined in the electrodes
by mean of copper strips using kapton as electrical isolator between them. The size
26
CHAPTER 4. THE ATLAS EMEC
Figure 4.5: Picture of an EMEC module or octant at the stacking frame of the UAM
clean room.
of such strips depends on the compartment, being smallest in the S1 to allow for the
separation of the two photons from the decay of a π 0 . This separation must be done
before the cascade generated by the photons gets broader in the calorimeter material,
hence the fine segmentation is defined in the front, S1 , compartment.3 The values
of the cell size for the three compartments as a function of η are given in table 4.1.
The strips drawn in the electrodes point to the nominal ATLAS interaction point,
however the accordion geometry, for example the absorbers, is not projective to that
point.
Wheel
Outer
Inner
η range
1.375 - 1.425
1.425 - 1.5
1.5 - 1.8
1.8 - 2.0
2.0 - 2.4
2.4 - 2.5
2.5 - 3.2
Front
(0.050,2π/64)
(0.025,2π/64)
(0.003,2π/64)
(0.004,2π/64)
(0.006,2π/64)
(0.025,2π/64)
(0.1,2π/64)
Middle
(0.050,2π/256)
(0.025,2π/256)
(0.025,2π/256)
(0.025,2π/256)
(0.025,2π/256)
(0.025,2π/256)
(0.1,2π/64)
Back
(0.050,2π/256)
(0.050,2π/256)
(0.050,2π/256)
(0.050,2π/256)
Table 4.1: Transverse granularity (∆η, ∆φ) for each calorimeter sampling (Front,
Middle and Back).
3
Regions |η| < 1.5 and |η| > 2.5 do not have very fine longitudinal and transversal granularity
since they are out of the high precision measurement region. The former corresponds to the barrelendcap crack (where the large amount of materials in front will not allow to get as good energy
resolution as required) and the latter corresponds to very forward regions (with high noise coming
from proton remnant and soft interactions).
27
4.4. HIGH VOLTAGE
Figure 4.6: Picture of an EMEC electrode of the outer wheel. The segmentation
along η and the three compartments in depth, S1,S2 and S3, are clearly seen.
The granularity along the azimuthal φ direction is defined by connecting several
consecutive electrodes together using the so called summing boards. In principle one
could read the electrodes individually, defining a fine granularity along φ of 0.003
radians; however this is too much fine for the needs and would increase the number
of channels considerably. This is the reason for using Summing Boards (SB) to
group the signal of several electrodes together. In this way, for example, in the S2
compartment, three consecutive electrodes are connected (their signals are summed)
to obtain the desired granularity of ∆φ = 0.025 radians, while 12 electrodes are
connected for the S1 compartment given a granularity of ∆φ = 0.1 radians in this
compartment. A summary of the EMEC granularity is given in table 4.1.
Figure 4.7 shows some summing boards plugged in the electrode connectors for
the S1 compartment of an EMEC module. The φ direction goes from bottom to
top of the picture, while the η direction increases from left to right. The electrode
connectors can be distinguished in black between two absorbers. The summing
boards group the signals of 12 electrodes together in this example.
4.4
High Voltage
The relation between the signal (E) and the high voltage (U) applied on the gaps is:
E∼
fs b
U
g 1+b
(4.1)
where g is the liquid argon gap thickness and fs the sampling fraction (which is a
function of the gap thickness). The value for the exponent b was measured at beam
beam test of Module 0 to be close to 0.4 [9].
The argon gap of the EMEC decreases almost linearly when the pseudorapidity
28
CHAPTER 4. THE ATLAS EMEC
Figure 4.7: Picture the summing boards plugged in the front face of an EMEC
module.
HV region
η range
HV values
1
2
1.375-1.5 1.5-1.6
2500 V 2300 V
End-cap outer wheel
3
4
5
1.6-1.8 1.8-2.0 2.0-2.1
2100 V 1700 V 1500 V
6
2.1-2.3
1250 V
7
2.3-2.5
1000 V
Table 4.2: The high voltage regions of the end-cap outer wheel.
(η) increases. This makes the cluster signal changing along the pseudorapidity direction due to the explicit gap variation and the implicit change in the sampling fraction
according to equation 4.1. The sampling fraction (fs ) decreases when η increases,
but not fast enough to cancel the 1/g 1+b rise, as a result the response E increases
with η. This growth may be compensated by decreasing U continously when η increases. For practical reasons a decreasing stepwise function for U is chosen defining
seven HV sectors, the High-Voltage sector definitions is given in Table 4.2. for the
outer wheel 4 . Inside one sector the HV is constant and therefore the cluster signal
increases with η. To correct for the increase of the cluster signal inside HV sectors,
η-dependent weights (w (s) ) are applied on each cell:
w (s) (ηj ) = β (s) /(1 + α(s) (ηj − η (s) ))
(4.2)
where for a given sampling layer (front, middle or back) ηj is the cell pseudorapidity
and η (s) the pseudorapidity at the centre of the HV sector s. The parameter α(s)
is the slope of the energy dependence with η and the parameter β (s) accounts for
inaccurate high voltage settings. Both parameters were obtained from a fit to the
test beam data [10, 14].
4
There are two additional sectors in the inner wheel which are not given on the table
29
4.5. PRESAMPLER
4.5
Presampler
In figure 4.8 (a) a schematic view of a quadrant of the electromagnetic calorimeter
is shown. An electron, positron or photon created in one p-p collision will cross
different layers of material, of the inner detector, cables, boards, cryostat walls, etc,
before it enters into the End-Cap Electromagnetic Calorimeter (EMEC). The particle
may start a particle-shower (or particle-cascade) crossing these consecutive material
layers by the effect of the bremsstrahlung process ( photon emission by an electron or
positron) or the pair creation process (e+ e− creation by a photon). Every secondary
particle may suffer either the bremsstrahlung process (in case of e+ or e− ) or pair
creation (in case of γ) creating tertiary particles and so on. In this way a cascade
is developed. Every charged particle of this cascade will lose part of its energy by
ionization of the material. In addition, the 2T magnetic field may bent some of the
charged particles of the cascade such that they hit the calorimeter at an unexpected
position. The result is that the energy measured in the calorimeter will be smaller
than the initial particle energy as produced in the p-p collision.
6
ID services+cables
Presampler
scintillator
feedthrough
superconducting
solenoid coil
Al cryostat
Al cryostat
cold wall
warm wall
(tapered)
BARREL
Pb(1.5mm)
2.10cm/X0
Al cryostat
walls
warm
cold
BARREL
5
4
active accordion
active accordion
3
Presampler
ENDCAP
Pb(1.1mm)
2.65cm/X0
Scintillator
Warm cryo cone + flange
2
Presampler
)
.7mm
Pb(1
75 75
1.3 1.4
η= η=
8
.6
η=1
η=
0
.8
1m
B=2T
ENDCAP
η=1.8
η=2.5
INNER DETECTOR
η=3.2
2m
OUTER
WHEEL
INNER
Pb(2.2mm)
4m
Cold wall
Cold wall
1
Coil
Warm wall
0
Warm wall
ID to r=115 cm
ID to r=63 cm
0
0.5
1
1.5
2
2.5
3
Pseudorapidity
(a) Longitudinal view of a quadrant of the EM (b) Breakdown of the material in front of the
calorimeter
EM calorimeter
Figure 4.8: Description of the material in front of the calorimeter
The amount of material depends on the η direction, as can be seen in figure 4.8 (b),
where the amount of material is expressed in units of radiation lengths (X0 ) and it
goes up to about 3 − 5X0 in the region 1.5 < |η| < 1.8 degrading the measured
energy. In order to partially recover this resolution a presampler detector is placed
in front of the calorimeter in the region 1.5 < |η| < 1.8. The endcap presampler is
divided into 768 cells per endcap wheel with a transversal segmentation of ∆η×∆φ =
0.025×2·π/64. The quoted segmentation along φ is achieved by the modularity in 32
identical azimutal modules. Each module consist of two active Liquid Argon layers,
2 mm thick, formed by three electrodes paralells to the front face of the EMEC.
Figure 4.9 shows the material in front of the calorimeter for the η region studied
30
CHAPTER 4. THE ATLAS EMEC
X0
Amount of material in front of the calorimeter
Front sampling
40
Middle end
sampling
Entries 32000
Mean
2.026
Mean
y 32.59
Back
sampling
35
RMS
0.2748
RMS y 3.265
End of the active region
30
25
20
15
10
5
0
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
Figure 4.9: Total ammount of material in front of the different samplings of the
EMEC in the η region of interest.
in this document.
Chapter 5
The Calibration Hits method
An electron (or a photon) deposits energy in several cells of the calorimeter due to
EM shower created by the interaction with matter. A cluster of cells is then defined
to contain the energy deposits, or at least most of them, in order to compute the
electron (photon) energy. However, several effects distort this calculation, namely:
the energy lost by the electron (photon) in the matter in front of the calorimeter,
the energy leaked behind the calorimeter and the energy outside the defined cluster
of calorimeter cells. A method to correct for these energy losses and reconstruct
the electron (and photon) energies from the cluster energies deposited in the active
layers of the calorimeter and the presampler has been applied to the Barrel Electromagnetic Calorimeter (EMB) [12]. The method is built in a modular way and
the corrections are parametrized as a function of measurable quantities: energies in
presampler, front, middle and back calorimeter layers and the barycenter in depth.
The parameters are obtained from a special Monte Carlo simulation, labeled Calibration Hits, which includes the energy deposits in all materials of the detector and not
only in the active ones. In this document the method is applied to the EM EndCap
Calorimeter (EMEC), taken into account the peculiarities of this device: different
geometry, different dead material in front and the presampler does not cover the
whole range in pseudorapidity (η). These differences between the EMEC and the
EMB forced us to do some modifications in the Calibration Hits method, in particular in the region without presampler a new algorithm has to be developed to recover
the energy lost in front of the EMEC. For this work, electrons are simulated from
the nominal Atlas interaction point taken into account the magnetic field (which
deflects electrons) and the interation vertex spread (due essentially to the z-width of
the LHC proton bunches).
5.1
Cluster Energy
When an electron or photon goes thought the ATLAS Calorimeter it deposits part of
its energy in several cells of the different layers. In order to reconstruct the energy of
the incoming particle a cluster of cells in (η,φ) is define around the cell with maximum
deposit. The cluster size should not contain many cells to avoid introducing too much
31
32
CHAPTER 5. THE CALIBRATION HITS METHOD
χ2 / ndf
242.4 / 106
Constant
145.7 ± 1.9
Mean
1.765e+04 ± 30
Sigma
1903 ± 19.9
140
120
100
80
60
40
20
0
0
5000
10000
15000
20000
25000
30000
Figure 5.1: Cluster energy distribution for 100 GeV Monte Carlo electrons at η =
1.7125. Calibration Hits Method is not applied to the events. A gaussian fit is
superimposed.
noise in the signal, however it should contain enough energy of the electron or photon
cascade. There are two sources of noise: the readout electronics and the minimum
bias events, physics low energetic events which superimpose the hard process under
study. The choice of the cluster size is then a compromise between minimizing the
noise in the cluster and minimizing the cascade energy leaked out of the cluster. A
small amount of cascade energy leaking out of the cluster can be recovered using the
Calibration Hit method as illustrated in a subsequent section.
In the present work, three different choices of cluster size are studied: 3 × 5, 3 × 7
and 5 × 5. The first number refers to the number of cells of the middle compartment
of the calorimeter along the η direction, while the second number is the number
of cells of the middle compartment of the calorimeter along the φ direction. The
corresponding cells of the other two compartments, Front and Back, complete the
cluster definition.
The sum of the energies deposited in each cell of the cluster will be named ”cluster
energy”. As an example, a 3 × 7 cluster energy distribution for 100 GeV electrons is
represented in figure 5.1 before the Energy Reconstruction method (the Calibration
Hit method) is applied to perform the corrections mentioned above. A gaussian fit is
plotted as well to observed the deviation of the distribution from a guassian shape.
The clustering algorithms allow also to determine the psedorapidity of the incoming particle using only information from the calorimeter. This variable is computed
as the following barycenter along η:
ηcalo
P s
s ηc · Es
= P
s Es
where ηcs and Es are the central η value and the energy deposit on the sth cell and
s runs over all the cells forming the cluster. In this document we will reffer to this
magnitude as η since we are only using calorimeter information.
33
5.2. DESCRIPTION OF THE METHOD
5.2
Description of the method
When an electromagnetic cluster in the EM Calorimeter is identified, the energy
contained in this cluster of calorimeter cells is less than the energy of the electron (or photon). This is due to energy losses in the dead material in front of the
calorimeter and the leakage both lateral outside the cluster and longitudinal behind
the calorimeter. To recover the electron (photon) ”true” energy from the measured
cluster energy, corrections for the three energy losses are applied. This corrections
are functions of measured quantities such as the energies on the three layers of the
calorimeter, E1 , E2 , E3 , the energy on the presampler, Eps and η of the incoming
particle. The corrected cluster energy will be called Ereco and it is split in three
terms, namely:
Ereco = Einf ront + Ecalo + Ebehind
(5.1)
where Einf ront corresponds to the cluster energy corrected for the effect of the material in front of the calorimeter, Ecalo is the cluster corrected for two effects ocurring
inside the calorimeter, the lateral leakage outside the cluster and a small bias in
the sampling fraction, and Ebehind referes to the cluster energy corrected for the longitudinal leakage behind the calorimeter. This corrected energies are functions of
Eps , E1 , E2 , E3 , η, and the longitudinal barycenter X, defined as the following linear
combination:
P3
i=1 Xi · Ei
X= P
3
i=1 Ei
(5.2)
Xi , i = 1, . . . , 3 being the compartment, S1,S2,S3, geometrical centers in units of
radiation length (X0 ).
This functions are written along this document as:
•
Ecalo = fcalo (η, X) · (1 + fout (η, X)) ·
3
X
Ei )
i=1
where fout is the correction to recover the lateral leakage out of the cluster
and fcalo is a small correction to the sampling fraction taking into account in
E1 , E2 , E3 .
•
Ebehind = Ecalo · fleak (η, X)
where fleak referes to the correction for leakage behind the calorimeter
34
CHAPTER 5. THE CALIBRATION HITS METHOD
• For region with presampler:
2
Einf ront = a(η, Ecalo ) + b(η, Ecalo )Eps + c(Ecalo , η) · Eps
For region without presampler:
Einf ront = a(η, Ecalo ) + b(η, Ecalo )X + c(η, Ecalo )X 2
To determine the weights (or coefficients) entering the above formula for the
reconstructed energy, a Monte Carlo simulation of the ATLAS nominal setup is performed using ATHENA 12.0.3 (the official ATLAS software) which incorporate the
Monte Carlo program GEANT 4.7 for the simulation of the particle-matter interactions. This simulation includes the energy deposits in both passive and active parts
of the detector. Digitization and reconstruction 1 stages are included to profit from
extra information as the presence of tracks, to distinguish between electrons and
photons, or EM particle identification (IsEm), to determine the quality of electrons.
After these stages, cell energies are corrected by the effect of the gap size variation
with η inside high voltage regions of the EMEC (see equation 4.2).
In order to extract a full set o coefficients for every correction in the pseudorapidity region corresponding to the endcap a set of 220000 electrons per energy have
been generated, for the following energies: 25, 50, 75, 100, 200 and 500 GeV. The
CPU time needed per event simulated depends on the electron energy and it goes
from 7 minutes at 25GeV , up to 15 minutes at 500GeV . All of the events have been
produced using the Grid computing site of our Laboratory at UAM. To increase
statistical significance, all the fits of this work, were done taking into account only
histogram bins in which the number of events were higher that 0.5 percent of the
total.
5.3
Corrections for energy depositions in the calorimeter
The digitization+reconstruction step performed over the single electrons samples
used on this analysis allow to apply a correction factor taking into account the High
Voltage and sampling fraction variation with η, providing an approximation for energies, E1 , E2 , E3 , deposited in the front, middle and back compartments respectively.
The correction factor fcalo is then defined as the ratio between the total energy in
1
The simulation of ATLAS events is performed in five steps: Generation (where the cinematics
of the event is produced), Simulation (where GEANT emulates the interaction of every particle
with matter), Digitization (where the readout and all the electronics is simulated), Reconstruction
(where all variables of interest are computed from raw data) and ESD and AOD production (those
last steps produce standard object to work with when doing physics analysis). Even though we are
working at the simulation level, we run the two following steps to get the information needed for
particle identification.
5.3. CORRECTIONS FOR ENERGY DEPOSITIONS IN THE CALORIMETER35
the calorimeter given by the Monte Carlo over the total energy obtained after the
digitization+reconstruction step mentioned above, namely:
fcalo (η, X) =
P3
E abs + Eilar
P3i
i=1 Ei
i=1
1.4
25 GeV
50 GeV
75 GeV
1.3
χ2 / ndf
17.43 / 18
p0
1.005 ± 0.003
p1
-0.005359 ± 0.000634
p2
0.0002594 ± 0.0000286
1.01
f calo
f calo
where Eiabs (Eilar ) is the energy deposited on the absorbers (LAR) of the ith compartment of the calorimeter. In figure 5.2 (left) this factor is represented versus X
for two values of η, 1.7125 and 1.9125, for all the energies. It can be observed a small
deviation, of about 2 %, respect to unity reflecting an overestimation of the energy
in the digitization+reconstruction step.
1
100 GeV
200 GeV
500 GeV
1.2
0.99
1.1
0.98
1
0.97
0.9
0.96
0.8
6
8
10
12
14
16
X Barycentre
0.95
6
8
10
12
14
16
X Barycentre
1.2
25 GeV
50 GeV
1.15
75 GeV
100 GeV
1.1
200 GeV
χ2 / ndf
22.89 / 13
p0
1.022 ± 0.011
p1
-0.00932 ± 0.00178
p2
0.0004601 ± 0.0000714
1.04
f calo
f calo
(a) fcalo versus X for the various energies at (b) fcalo versus X (energy averaged) at η =
η = 1.7125
1.7125
1.02
500 GeV
1
1.05
1
0.98
0.95
0.96
0.9
0.94
0.85
0.8
7
8
9
10
11
12
13
14
15
16
X Barycentre
0.92
7
8
9
10
11
12
13
14
15
16
X Barycentre
(c) fcalo versus X for the various energies at (d) fcalo versus X (energy averaged)at η =
η = 1.9125
1.9125
Figure 5.2: fcalo correction as a function of the longitudinal barycenter of the shower
The distributions shown in figure 5.2 correspond to a profile of the factor fcalo
versus X, i.e, we fixed a certain number of X bins and for each of those bins we build
a fcalo distribution. The final plots show the mean value of the distribution versus
the center of the X bin.
The correction is parametrized as a function of the barycenter of the shower X.
The sligh deviation from one shows that the estimated sampling fraction and H.V
correction applied at the construction step is overestimated.
36
CHAPTER 5. THE CALIBRATION HITS METHOD
The correction is rather independent of energy, hence an average over all energy
points is obtained and fitted to a second order polynomial (figures 5.2 b and d) with
coefficients being η dependent2 :
fcalo (η, X) = q0 (η) + q1 (η) · X + q2 (η) · X 2
2
(5.3)
The η dependence means that a set of parameters has been determined for each η-middle-cell
value
37
35
100 × f out
100 × f out
5.4. CORRECTION FOR LATERAL LEAKAGE OUT OF THE CLUSTER
25 GeV
50 GeV
75 GeV
30
100 GeV
200 GeV
35
25 GeV
50 GeV
75 GeV
30
100 GeV
200 GeV
500 GeV
500 GeV
25
25
20
20
15
15
10
10
5
6
8
10
12
5
14
16
X Barycentre
7
8
9
(a) η = 1.7125
10
11
12
13
14
15
16
X Barycentre
(b) η = 1.9125
Figure 5.3: fout correction as a function of X for the different particle energies
5.4
Correction for lateral leakage out of the cluster
The second factor which contributes to the term Ecalo in (5.1) is (fout ) which is
determined by the energy leaked out transversally of the cluster. It is defined by
(5.4):
fout (η, X) =
P3
out
i=1 Ecl,i
P3
abs
act
i=1 (Ecl,i + Ecl,i )
(5.4)
out
where Ecl,i
is the energy out of the cluster in the ith layer and i runs to the three
layers (Front, Middle and Back). In contrast to the fcalo correction, fout shows an
energy dependence (see figure (5.3)) due to the fact that the low energy electrons
are more deflected by the magnetic field. However, the energy independence of this
corrections is recovered by treating the distributions of fout belonging to a determined
X bin in a special way. As it is shown in figure (5.4), the distributions have really
long tails in the low X bins while they are gaussian-like distributions when we look
at higher X bins. The adopted approach is to fit all distributions with a landau-like
function and use the Most Probable Value (MPV) + one standard deviation (σ)
as a function of X (where X refers to the center of the bins specified). It can be
observed in figure 5.5 (a) that using MPV+σ the correction is rather independent of
energy. This procedure also prevents for underestimation of the reconstructed energy
specially at low values of the generated electron energy.
An average over all energies is represented in figure 5.5. The points are fitted by
the following function:
fout (η, X) = p0 (η) + p1 (η) · X +
p2 (η)
X
(5.5)
In this procedure it was assumed that the particle is incident at the center of the
central cell of the cluster. This is obviously not always the case and must be taken
38
CHAPTER 5. THE CALIBRATION HITS METHOD
nombre_bin2
Entries
403
χ2 / ndf
61.63 / 81
Prob
0.9463
Constant
86.86 ± 8.05
10.25 ± 0.17
MPV
Sigma
1.338 ± 0.110
25
20
nombre_bin3
Entries
2878
χ2 / ndf
83.86 / 73
Prob
0.1809
Constant
928.6 ± 28.2
9.277 ± 0.043
MPV
Sigma
1.021 ± 0.026
200
180
160
140
120
15
100
80
10
60
40
5
20
0
0
5
10
15
20
25
30 35
40
45
50
% Energy out of the cluster
0
0
5
(a) 6 < X < 7
10
15
20
25
30 35
40
45
50
% Energy out of the cluster
(b) 7 < X < 8
nombre_bin4
Entries
8637
χ2 / ndf
69.75 / 52
Prob
0.05065
Constant
3741 ± 61.5
MPV
8.301 ± 0.019
Sigma
0.7888 ± 0.0104
700
600
500
nombre_bin5
1200
1000
400
800
300
600
200
400
100
200
0
0
5
10
15
20
25
30 35
40
45
50
% Energy out of the cluster
Entries
13274
χ2 / ndf
85.09 / 39
Prob
2.812e-05
Constant
7772 ± 104.5
MPV
7.6 ± 0.0
Sigma
0.5868 ± 0.0064
1400
0
0
5
(c) 8 < X < 9
nombre_bin6
1800
1600
1400
15
20
25
30 35
40
45
50
% Energy out of the cluster
(d) 9 < X < 10
Entries
13635
χ2 / ndf
85.51 / 28
Prob
9.826e-08
Constant 1.138e+04 ± 152
MPV
7.052 ± 0.008
Sigma
0.4112 ± 0.0045
2000
10
nombre_bin7
2500
Entries
11548
χ2 / ndf
168.9 / 19
Prob
0
Constant 1.348e+04 ± 206
MPV
6.653 ± 0.006
Sigma
0.2918 ± 0.0038
2000
1500
1200
1000
1000
800
600
500
400
200
0
0
5
10
15
20
25
30 35
40
45
50
% Energy out of the cluster
0
0
5
(e) 10 < X < 11
10
15
20
25
(f) 11 < X < 12
nombre_bin8
Entries
7208
χ2 / ndf
289.2 / 14
Prob
0
Constant 1.067e+04 ± 176
MPV
6.338 ± 0.006
Sigma
0.2252 ± 0.0027
1800
1600
1400
1200
30 35
40
45
50
% Energy out of the cluster
nombre_bin9
Entries
2543
χ2 / ndf
271 / 13
Prob
0
Constant
4454 ± 141.6
6.127 ± 0.008
MPV
Sigma
0.176 ± 0.004
800
700
600
500
1000
400
800
300
600
200
400
100
200
0
0
5
10
15
20
25
30
35
40
45
50
% Energy out of the cluster
0
0
5
(g) 12 < X < 13
10
15
20
25
(h) 13 < X < 14
nombre_bin10
Entries
357
χ2 / ndf
20.73 / 5
Prob
0.0009128
Constant
610 ± 44.7
MPV
5.936 ± 0.024
Sigma
0.2025 ± 0.0110
100
80
30 35
40
45
50
% Energy out of the cluster
nombre_bin11
Entries
25
χ2 / ndf
1.737 / 4
Prob
0.7839
Constant
37.42 ± 14.16
MPV
5.866 ± 0.110
Sigma
0.2208 ± 0.0838
7
6
5
4
60
3
40
2
20
0
0
1
5
10
15
20
25
30
35
40
45
50
% Energy out of the cluster
(i) 14 < X < 15
0
0
5
10
15
20
25
30 35
40
45
50
% Energy out of the cluster
(j) 15 < X < 16
Figure 5.4: fout distributions per X bin at η = 1.7
39
26
25 GeV
24
50 GeV
75 GeV
22
100 GeV
200 GeV
20
500 GeV
18
16
14
12
% Energy out of the cluster
cluster sampling fraction
5.5. CORRECTIONS FOR LONGITUDINAL LEAKAGE
χ2 / ndf
Prob
p0
p1
p2
30
25
0.04546 / 6
1
-6.4 ± 6.664
0.358 ± 0.2945
106 ± 36.95
20
15
10
10
5
8
6
6
8
10
12
14
16
X Barycentre
(a) All six energies
6
8
10
12
14
16
X Barycentre
(b) Energy averaged
Figure 5.5: MP V + σ of the fout distributions as a function of the Barycenter of the
shower X
(a) η modulation of the energy scale
(b) phi modulation of the energy scale
Figure 5.6: η and φ modulations observed on the beam test.
into account in a second step of the Calorimeter Reconstruction Algorithm. In order
to be more clear, figure 5.6 shows the obseved η (left plot) and φ modulation during
beam tests. The η modulation shows clearly the increase of energy underestimation
when the incident electron hits farther away from the center of the cluster. In
the φ modulation plot a combination of leakage and irregularity effect due to the
acordion geometry is shown. Notice that these corrections are appied in a step after
the calibration hits method using the information extracted from the test beam.
Therefore, all results presented in subsequent sections still need to be corrected by
those modulations.
5.5
Corrections for longitudinal leakage
The small fraction of the energy that is deposited behind the calorimeter is computed
by applying to the reconstructed energy in the calorimeter the factor fleak , defined
40
CHAPTER 5. THE CALIBRATION HITS METHOD
by (5.6):
fleak (η, X) =
Eleak
Eacc
(5.6)
1.8
25 GeV
50 GeV
1.6
75 GeV
100 GeV
1.4
200 GeV
100 × f leak
100 × f leak
where Eleak accounts for all the energy deposited behind the calorimeter and Eacc
for all the energy depositions in the calorimeter (active and pasive materials). As
shown in figure (5.7 a and c), fleak is again fairly energy independent when it is
parameterized as a function of the longitudinal barycenter of the shower.
500 GeV
χ2 / ndf
1
72.83 / 19
p0
0.01065 ± 0.00013
p1
1.826e-07 ± 6.931e-09
0.8
1.2
1
0.6
0.8
0.4
0.6
0.4
0.2
0.2
0
4
6
8
10
12
0
14
16
X Barycentre
4
6
8
10
12
14
16
X Barycentre
25 GeV
1.4
50 GeV
75 GeV
100 GeV
1.2
200 GeV
100 × f leak
100 × f leak
(a) fleak versus X for the various energies at (b) fleak versus X (energy averaged) at η =
η = 1.7125
1.7125
χ2 / ndf
1
15.94 / 14
p0
0.006125 ± 0.000170
p1
1.316e-07 ± 6.546e-09
0.8
500 GeV
1
0.6
0.8
0.6
0.4
0.4
0.2
0.2
0
8
10
12
14
16
X Barycentre
0
8
10
12
14
16
X Barycentre
(c) fleak versus X for the various energies at (d) fleak versus X (energy averaged) at η =
η = 1.9125
1.9125
Figure 5.7: fleak correction as a function of the longitudinal barycenter of the shower
The weights that corrects for the longitudinal leakage are extracted by fitting the
energy averaged fleak distributions to the following function (figure 5.7 b and d ):
fleak (η, X) = l0 (η) · +l1 (η) · eX
(5.7)
The η dependence of these parameters reflects the variation of the calorimeter depth
with η.
5.6. CORRECTIONS FOR THE ENERGY LOSS IN FRONT OF THE CALORIMETER41
5.6
Corrections for the energy loss in front of the
Calorimeter
In [12] is demonstrated that the energy lost in front of the calorimeter (inner detector,cryostat, boards, cables, material between presampler and S1) can be successfully
parameterized as a function of the energy deposited in the presampler detector of the
EM Barrel Calorimeter. However, in the EMEC only the region η < 1.8 is equipped
with a presampler. For the region η > 1.8 a new procedure has been developed in
the present work.
5.6.1
Region with presampler η < 1.8
As in the case of fout a special treatment of the distributions of energy in front
of the calorimeter per presample energy (Eps ) bin was done. In figure 5.8 we can
see that the distributions of energy in front of the calorimeter are landau-like at
low energy depositions in the presampler while they are more gaussian-like when
the energy deposit is higher. The treatment consist on taking the most probable
value of the distributions (instead of the mean value) by using a gaussian fit in the
interval (1.0 · σ, 1.5 · σ) around the maximum. The fit is also represented in the
figure. Figure 5.9 shows the difference between considering the most probable value
of the distributions and considering the mean for 25GeV electrons being incident at
η = 1.7. The proper choice in this approach has an impact on the energy resolution
and energy scale.
The energy in the dead material in front of the calorimeter, obtained as the most
probable value fit described above, is represented versus the energy deposited in the
presampler at η = 1.6125 in figure 5.10. The six different plots correspond to the six
different electron energies.
The points are fitted using the following second order polynomial:
2
Einf ront = a(Ecalo , η) + b(Ecalo , η) · Eps + c(Ecalo , η) · Eps
(5.8)
The fit includes a quadratic term, which is absent for the EMBarrel, due to the
larger variation of material in front for the EMEC. We notice a dependence with
energy which is considered by making the coefficients of the polynomial dependent
on Ecalo .
Similar plots are represented in figure 5.11 for a different value of pseudorapidity,
η = 1.7125. There are small variations with respect to η = 1.6125, which results on
different paramaters for the fit using the polynomial 5.8.
Figure 5.12 represents the parameters of the previous fit as a function of Ecalo .
The left column of plots refers to η = 1.6125 and the second one to η = 1.7125. The
points are fitted to the following functions:
a(Ecalo , η) = O0 (η) + O1 (η) · Ecalo + O2(η) ·
p
Ecalo
(5.9)
42
CHAPTER 5. THE CALIBRATION HITS METHOD
25GeV_bin1-From0.000-To0.800
25GeV_bin1-From0.000-To0.800
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
14
12
10
185
2476
1287
7.133 / 8
12.56 ± 1.61
2009 ± 148.3
631.6 ± 136.7
25GeV_bin2-From0.800-To1.600
25GeV_bin2-From0.800-To1.600
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
50
40
703
3522
1372
13.93 / 11
40.24 ± 2.65
2896 ± 125.2
1079 ± 185.8
30
8
6
20
4
10
2
0
0
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(a) 0GeV < EP S < 0.8GeV
25GeV_bin3-From1.600-To2.400
25GeV_bin3-From1.600-To2.400
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
100
80
1602
4539
1559
17.84 / 15
85.5 ± 3.5
3847 ± 46.7
1073 ± 64.7
0
0
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(b) 0.8GeV < EP S < 1.6GeV
25GeV_bin4-From2.400-To3.200
25GeV_bin4-From2.400-To3.200
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
160
140
120
2867
5493
1561
27.01 / 17
136.7 ± 4.0
4931 ± 50.4
1303 ± 67.8
100
60
80
40
60
40
20
20
0
0
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(c) 1.6GeV < EP S < 2.4GeV
25GeV_bin5-From3.200-To4.000
25GeV_bin5-From3.200-To4.000
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
180
160
140
3340
6360
1516
26.68 / 16
162.9 ± 4.6
5838 ± 46.8
1271 ± 65.9
120
0
0
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(d) 2.4GeV < EP S < 3.2GeV
25GeV_bin6-From4.000-To4.800
25GeV_bin6-From4.000-To4.800
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
120
100
2522
7237
1521
23.04 / 19
110.6 ± 3.5
6749 ± 63.3
1536 ± 97.1
80
100
60
80
60
40
40
20
20
00
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(e) 3.2GeV < EP S < 4.0GeV
25GeV_bin7-From4.800-To5.600
25GeV_bin7-From4.800-To5.600
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
70
60
50
1323
7963
1507
25.96 / 23
58.86 ± 2.38
7676 ± 55.2
1361 ± 64.8
00
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(f) 4.0GeV < EP S < 4.8GeV
25GeV_bin8-From5.600-To6.400
25GeV_bin8-From5.600-To6.400
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
25
20
454
8648
1492
31.19 / 21
21.87 ± 1.51
8223 ± 79.7
1126 ± 78.9
40
15
30
10
20
5
10
0
0
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(g) 4.8GeV < EP S < 5.6GeV
25GeV_bin9-From6.400-To7.200
25GeV_bin9-From6.400-To7.200
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
6
5
80
8939
1371
21.34 / 26
2.457 ± 0.453
8902 ± 423.9
1996 ± 593.6
4
0
0
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(h) 5.6GeV < EP S < 6.4GeV
25GeV_bin10-From7.200-To8.000
25GeV_bin10-From7.200-To8.000
Entries
Mean
RMS
χ2 / ndf
Constant
Mean
Sigma
2
1.8
1.6
1.4
15
8995
1778
0.8869 / 10
1.12 ± 0.36
9092 ± 6625.0
7518 ± 9805.7
1.2
3
1
0.8
2
0.6
0.4
1
0.2
00
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(i) 6.4GeV < EP S < 7.2GeV
00
2000
4000
6000
8000
10000
12000 14000 16000
E in front (MeV)
(j) 7.2GeV < EP S < 8GeV
Figure 5.8: Distributions of energy in front of the calorimeter per EP S bin at η = 1.7
for 25GeV electrons
5.6. CORRECTIONS FOR THE ENERGY LOSS IN FRONT OF THE CALORIMETER43
χ2 / ndf
0.06371 / 7
p0
1585 ± 1384
p1
1.659 ± 0.863
p2
-8.463e-05 ± 0.0001097
Graph
E in front (MeV)
18000
16000
χ2 / ndf
0.06573 / 7
p0
1306 ± 831.7
p1
1.37 ± 0.7201
p2
-3.286e-05 ± 0.0001104
14000
Peak.
12000
Mean
10000
8000
6000
4000
2000
00
1000
2000
3000
4000
5000
6000
7000
8000
EPS (MeV)
Figure 5.9: Energy in front of the calorimeter versus EP S for the two different approaches. The blue points represent the mean of the E in front distributions for EP S
while red points represent the peak of the distributions..
b(Ecalo , η) = S1 (η) + S2 (η) · Log(Ecalo ) + S2 (η) ·
c(Ecalo , η) = R1 (η) + R2 (η) · Ecalo −
p
R3 (η)
2
Ecalo
Ecalo
(5.10)
(5.11)
The fact that the offset a is not negligible means that there can be energy lost in
the material in front and however no energy deposited in the presampler. This effect
has two sources:
i) the material between the presampler and the S1-compartment of the calorimeter, electronics and cables,is considered as material in front of the calorimeter, but
it is behind the presampler;
ii) absorption of very low energy photons and electrons present in the early shower.
According to equation 5.9 this offset increases with Ecalo .
Parameter b is a kind of ”gain” factor to convert from Eps signal to Einf ront .
Parameter c takes into account small non-linearities or saturation effects.
44
CHAPTER 5. THE CALIBRATION HITS METHOD
E in fronf (MeV)
10000
χ2 / ndf
11.89 / 11
p0
254.2 ± 504.8
p1
1.802 ± 0.1717
p2
-4.112e-05 ± 1.397e-05
50GeV
20000
E in fronf (MeV)
χ2 / ndf
18.41 / 12
p0
1590 ± 504.7
p1
1.344 ± 0.2823
p2
-3.063e-05 ± 3.843e-05
25GeV
12000
18000
16000
14000
8000
12000
6000
10000
8000
4000
6000
4000
2000
2000
00
1000
2000
3000
4000
5000
6000
0
0
7000
8000
EPS (MeV)
2000
(a) E = 25GeV
8000
10000
12000
14000
EPS (MeV)
χ2 / ndf
17.24 / 17
p0
1442 ± 518.1
p1
1.307 ± 0.1163
p2
1.42e-06 ± 6.195e-06
100GeV
45000
E in fronf (MeV)
E in fronf (MeV)
35000
6000
(b) E = 50GeV
χ2 / ndf
28.09 / 16
p0
411.9 ± 424.9
p1
1.596 ± 0.1198
p2
-1.441e-05 ± 7.91e-06
75GeV
40000
4000
40000
35000
30000
30000
25000
25000
20000
20000
15000
15000
10000
10000
5000
0
0
5000
2000
4000
6000
0
0
8000 10000 12000 14000 16000 18000
EPS (MeV)
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
EPS (MeV)
(c) E = 75GeV
(d) E = 100GeV
E in fronf (MeV)
60000
50000
40000
χ2 / ndf
9.321 / 14
p0
3668 ± 476.9
p1
1.081 ± 0.04305
p2
3.991e-06 ± 8.762e-07
500GeV
E in fronf (MeV)
χ2 / ndf
14.29 / 16
p0
2171 ± 606.5
p1
1.175 ± 0.08426
p2
4.665e-06 ± 2.741e-06
200GeV
×10
3
160
140
120
100
80
30000
60
20000
40
10000
0
0
20
5000
10000
15000
20000
25000
(e) E = 200GeV
30000
35000
EPS (MeV)
0
0
10000
20000
30000
40000
50000
60000
EPS (MeV)
(f) E = 500GeV
Figure 5.10: Energy in front of the calorimeter versus energy in the presampler for
different electron energies at η = 1.6
5.7
Region without presampler η > 1.8
As explained before, the Calibration Hits method in the η < 1.8 region is basically an
adaptation of the already existing method for the EMBarrel. However, for η > 1.8 a
new approach has been developed trying to use variables sensitive to the upstream
material, since no presampler is present in this region. Two different procedures have
been tried and compared: a parameterization of the energy lost as a function of X,
and the use of the S1 compartment as a kind of presampler.
5.7. REGION WITHOUT PRESAMPLER η > 1.8
E in fronf (MeV)
12000
χ2 / ndf
13.42 / 15
p0
1398 ± 298.3
p1
1.254 ± 0.1145
p2
-5.806e-06 ± 1.061e-05
50GeV
20000
E in fronf (MeV)
χ2 / ndf
4.551 / 12
p0
931.1 ± 279.7
p1
1.507 ± 0.1899
p2
-6.739e-05 ± 3.076e-05
25GeV
14000
45
18000
16000
10000
14000
12000
8000
10000
6000
8000
6000
4000
4000
2000
2000
0
0
1000
2000
3000
4000
5000
6000
0
0
7000
8000
EPS (MeV)
2000
(a) E = 25GeV
8000
10000
12000
EPS (MeV)
χ2 / ndf
15.92 / 15
p0
1334 ± 244.8
p1
1.169 ± 0.06279
p2
7.24e-06 ± 3.772e-06
100GeV
E in fronf (MeV)
E in fronf (MeV)
25000
6000
(b) E = 50GeV
χ2 / ndf
24.29 / 14
p0
1427 ± 230.6
p1
1.182 ± 0.07251
p2
6.001e-06 ± 5.341e-06
75GeV
4000
35000
30000
20000
25000
20000
15000
15000
10000
10000
5000
5000
00
2000
4000
6000
0
0
8000 10000 12000 14000 16000 18000
EPS (MeV)
2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
EPS (MeV)
(c) E = 75GeV
(d) E = 100GeV
E in fronf (MeV)
80000
70000
60000
50000
×10
3
160
140
120
100
40000
80
30000
60
20000
40
10000
0
0
χ2 / ndf
25.42 / 11
p0
3545 ± 403.7
p1
0.98 ± 0.03731
p2
5.854e-06 ± 7.871e-07
500GeV
E in fronf (MeV)
χ2 / ndf
7.864 / 13
p0
1661 ± 206.5
p1
1.102 ± 0.0355
p2
7.646e-06 ± 1.425e-06
200GeV
20
5000
10000
15000
20000
25000
(e) E = 200GeV
30000
35000
EPS (MeV)
0
0
10000
20000
30000
40000
50000
60000
70000 80000
EPS (MeV)
(f) E = 500GeV
Figure 5.11: Energy in front of the calorimeter versus energy in the presampler for
different electron energies at η = 1.7
1. Parametrization of the energy lost in front of the calorimeter as a function
of X. The barycenter in depth X is expected to change by the presence of
upstream material due to the early start of the shower. More energy lost in
the upstream material would mean less value for X and vice versa, less energy
lost in front of the calorimeter would mean larger value for X. Figure 5.14
represents the energy lost in front as a function of the barycenter of the shower
X. The points are obtained as the most probable value of the distributions
following a similar procedure as described in previous section. From figure 5.14
46
CHAPTER 5. THE CALIBRATION HITS METHOD
Offset
4000
0.3332 / 3
-2184 ± 638.9
-13.7 ± 4.807
558.6 ± 122.2
χ 2 / ndf
p0
p1
p2
Offset vs Eacc
Offset
χ 2 / ndf
p0
p1
p2
Offset vs Eacc
4000
2.602 / 3
828.2 ± 521.8
5.753 ± 3.771
-2.294 ± 94.59
3500
3000
3000
2500
2000
2000
1000
1500
1000
0
500
100
200
300
400
χ 2 / ndf
p0
p1
p2
Slope
Slope vs Eacc
2.4
500
E acc reco (GeV)
2.037 / 3
4.681 ± 0.4547
-1.049 ± 0.1493
0.1331 ± 0.02251
0
100
200
300
1.8
1.7
2.2
1.6
2
1.5
1.8
1.4
400
χ 2 / ndf
p0
p1
p2
Slope vs Eacc
Slope
0
500
E acc reco (GeV)
1.596 / 3
1.961 ± 0.423
-0.1919 ± 0.1345
0.008587 ± 0.01978
1.3
1.6
1.2
1.4
1.1
1.2
1
1
0.9
100
200
300
400
χ 2 / ndf
p0
p1
p2
Secord vs Eacc
Secord
-3
×10
0.05
500
E acc reco (GeV)
0.4589 / 3
1.659e-05 ± 2.376e-06
-2.722e-08 ± 5.542e-09
0.06126 ± 0.007054
0
100
200
300
400
χ 2 / ndf
p0
p1
p2
Secord vs Eacc
-3
Secord
0
×10
0.02
500
E acc reco (GeV)
0.5046 / 3
1.046e-05 ± 2.172e-06
-8.006e-09 ± 5.185e-09
0.02958 ± 0.009237
-0
0
-0.02
-0.05
-0.04
-0.1
-0.06
-0.08
-0.15
-0.1
0
100
200
300
400
500
E acc reco (GeV)
0
100
200
(a) η = 1.6
300
400
500
E acc reco (GeV)
(b) η = 1.7
Figure 5.12: Parameters a, b, c of equation 5.8 as a function of Ecalo . The left side
column corresponds to η = 1.6, while the right side column corresponds to η = 1.7.
Correlation between b and c
Correlation between b and c
×10
×10
-3
c (MeV -1)
c (MeV -1)
-3
0.02
0.02
-0
-0
-0.02
-0.04
-0.02
-0.06
-0.04
-0.08
-0.1
-0.06
-0.12
-0.14
-0.08
-0.16
-0.1
-0.18
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
b
(a) η = 1.6
(b) η = 1.7
Figure 5.13: Parameter c versus parameter b of equation 5.8
1.7
1.8
b
5.7. REGION WITHOUT PRESAMPLER η > 1.8
47
it can be inferred the sensitivity of the variable X to the energy loss in front of
the calorimeter: the more energy loss the smaller the value of X. This relation
can be described by a second order polynomial, namely:
Einf ront = a(Ecalo , η) + b(Ecalo , η) · X + c(Ecalo , η) · X 2
(5.12)
The dependences of the a, b, c paramaters with Ecalo are shown in figure 5.15.
In contrast to the equivalent parameters in the region with presampler, discussed in previous section, this energy dependences is more simple and can be
parametrized using second order polynomials.
2. Method of Using the S1 compartment as a presampler. An increase of material
in front of the calorimeter would increase the probability of having an early
electromagnetic shower with a higher number of particles in its first stages. A
larger number of particles entering the S1 compartment would deposit more
energy in it, hence the energy in S1 may be sensitive to the amount of energy
lost in the upstream material. In general, the thinner a detector layer is, the
more sensitive will be to the energy lost in front of it3 . The sensitivity is related
to the ratio between the energy lost in dead material and the energy deposited
in the layer. In the case of the S1 compartment the thickness is about 4.4 X0 ,
hence it is expected some sensitivity.
The energy lost in front of the calorimeter as a function of the energy in the S1
compartment (E1 ) is shown in figure 5.16. Similarly to the previous sections,
the points are produced using the most probable value of the distributions,
according to the procedure described in section 5.6.1. It can be observed that
the sensitivity of E1 to the energy loss in front is similar to the sensitivity of
X, discussed in previous section, except for the low energy point E = 25 GeV
(lower slope in the plot). We saw a much larger sensitivity at E = 25 using
the presampler for η < 1.8, as shown in figure 5.11. This means that at low
energies like 25 GeV the approximation of using the S1 compartment as a
presampler is not valid anymore. The reason is related to the position of the
maximum of the electromagnetic cascade in the calorimeter. At low input
energy this maximum is located closer to the S1 layer, hence two much energy
of the cascade is deposited in this compartment to be consider as a ”thin”
presampler layer. For high input energies less energy, relative to the total, is
deposited in S1, hence more sensitivity to the small energy lost in the upstream
material.
The energy lost in front of the calorimeter is parametrized by a second order
polynomial of the energy deposited in layer S1 (E1 ), as follows:
Einf ront = a(Ecalo , η) + b(Ecalo , η) · E1 + c(Ecalo ) · E12
3
(5.13)
Consider that the thickness must be above a certain threshold to get a clean signal out of the
detector
48
CHAPTER 5. THE CALIBRATION HITS METHOD
E in front (MeV)
5000
4500
4000
3500
χ2 / ndf
23.67 / 10
p0
2.321e+04 ± 2022
p1
-3170 ± 348.2
p2
112.7 ± 14.93
E in front of calo vs X (50GeV)
E in front (MeV)
χ2 / ndf
8.349 / 9
p0
1.629e+04 ± 2070
p1
-2450 ± 378.7
p2
97.41 ± 17.25
E in front of calo vs X (25GeV)
6000
5000
4000
3000
3000
2500
2000
2000
1500
1000
1000
500
0
8
9
10
11
12
13
0
14
15
X Barycentre
8
9
(a) E = 25GeV
8000
7000
6000
7000
6000
5000
4000
3000
3000
2000
2000
1000
1000
10
11
12
13
0
14
15
X Barycentre
10
(c) E = 75GeV
12
13
14
15
X Barycentre
χ2 / ndf
12.8 / 10
p0
1.802e+05 ± 1.733e+04
p1
-2.418e+04 ± 2566
p2
823.5 ± 94.89
E in front of calo vs X (500GeV)
25000
E in front (MeV)
E in front (MeV)
12000
11
(d) E = 100GeV
χ2 / ndf
18.32 / 12
p0
6.926e+04 ± 7968
p1
-9142 ± 1247
p2
308.5 ± 48.69
E in front of calo vs X (200GeV)
14
15
X Barycentre
χ2 / ndf
21.82 / 12
p0
3.987e+04 ± 4641
p1
-5291 ± 766.2
p2
180.6 ± 31.54
8000
4000
9
13
9000
5000
0
12
E in front of calo vs X (100GeV)
E in front (MeV)
E in front (MeV)
9000
11
(b) E = 50GeV
χ2 / ndf
13.77 / 12
p0
3.288e+04 ± 2481
p1
-4526 ± 417
p2
161.8 ± 17.45
E in front of calo vs X (75GeV)
10
20000
10000
8000
15000
6000
10000
4000
5000
2000
0 10
11
12
13
(e) E = 200GeV
14
15
X Barycentre
0
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
X Barycentre
(f) E = 500GeV
Figure 5.14: Energy in front of the calorimeter versus barycenter of the shower for
different electron energies at η = 1.9
The good quality of the fits can be seen in figure 5.16.
The dependences of the a, b, c paramaters with Ecalo are represented in figure
5.15, and can be fitted using the following functions:
Figure (5.17) shows the energy dependence of all three parameters in the previous fits. Again we observe that all points but the ones corresponding to
low energy (25GeV) follow a certain tendency. The adopted criterium is to
eliminate this low energy point from the fit in order to get the coefficients.
The extrapolation of the fit to low energies produces good results, as it will be
5.7. REGION WITHOUT PRESAMPLER η > 1.8
Offset
×10
220
200
0.8792 / 3
1.603e+04 ± 4970
279.2 ± 106.1
0.132 ± 0.2508
220
×10
200
2.014 / 3
-950 ± 7856
330.7 ± 172.9
-0.05142 ± 0.4079
180
180
160
160
140
140
120
120
100
100
80
80
60
60
40
40
20
20
100
200
300
400
χ 2 / ndf
p0
p1
p2
Slope
Slope vs Eacc
0
0
500
E acc reco (GeV)
0.8959 / 3
-2787 ± 866.1
-31.35 ± 17.65
-0.02773 ± 0.04019
100
200
300
400
500
E acc reco (GeV)
χ 2 / ndf
p0
p1
p2
Slope vs Eacc
Slope
0
0
χ 2 / ndf
p0
p1
p2
Offset vs Eacc
3
Offset
χ 2 / ndf
p0
p1
p2
Offset vs Eacc
3
49
0
2.02 / 3
214.7 ± 1316
-42.49 ± 27.7
0.006541± 0.06341
-5000
-5000
-10000
-10000
-15000
-15000
-20000
-20000
-25000
-25000
-30000
100
200
300
χ2
Secord vs Eacc
Secord
400
/ ndf
p0
p1
p2
1000
500
E acc reco (GeV)
0.9357 / 3
123.5 ± 37.64
0.8228 ± 0.7327
0.001331± 0.001614
0
100
200
300
400
χ2
Secord vs Eacc
Secord
0
/ ndf
p0
p1
p2
500
E acc reco (GeV)
2.024 / 3
-6.888 ± 55.02
1.381 ± 1.107
-0.0002164 ± 0.002466
800
800
600
600
400
400
200
200
0
0
100
200
300
(a) η = 1.9
400
500
E acc reco (GeV)
0
100
200
300
400
500
E acc reco (GeV)
(b) η = 2.0
Figure 5.15: Parameters a, b, c of equation 5.12 as a function of Ecalo . The left side
column corresponds to η = 1.9, while the right side column corresponds to η = 2.0.
shown in next sections. The functions used to fit the parameters are:
a(Ecalo , η) = O0 (η) + O1 (η) · Ecalo + O2 (η) ·
p
b(Ecalo , η) = S1 (η) + S2 (η) · Log(Ecalo ) + S2 (η) ·
c(Ecalo , η) = R1 (η) + R2 (η) · Ecalo −
Ecalo
(5.14)
p
(5.15)
R2 (η)
Ecalo
Ecalo
(5.16)
The point at 25 GeV has not been considered in the fit for the reason explained
above; the extrapolation of the fit to these low energy produces good results,
as it will be shown in next sections.
The energy dependence of a, b, c in this case is similar to the dependence obtained using the real presampler (see equations ??), which is another proof of
the presampler capabilities of the S1 compartment. This dependence is more
complicated than the one seen using variable X. On equivalent performance (it
will be discussed in next chapter) variable X will be preferred for the correction
of the energy lost in front for η > 1.8.
Also observed is the fact that there is an offset a different from zero, which
means there can be energy loss in front but no energy detected in S1. This is
50
CHAPTER 5. THE CALIBRATION HITS METHOD
again interpreted as the absorption of very low energy photons and electrons
present in the early shower.
25GeV
Entries
Mean
Mean y
RMS
RMS y
χ2 / ndf
p0
p1
p2
4000
3500
3000
2500
3434
8172
1445
1767
600
44.74 / 13
1104 ± 200.8
0.03561 ± 0.04824
6.659e-07 ± 2.840e-06
50GeV
E in front of calo vs E str reco (50GeV)
E in front (MeV)
E in front (MeV)
E in front of calo vs E str reco (25GeV)
2000
Entries
Mean
Mean y
RMS
RMS y
χ2 / ndf
p0
p1
p2
6000
5000
4000
3434
1.465e+04
2021
3318
881.4
11.97 / 13
805.9 ± 247.4
0.06128 ± 0.03498
1.391e-06 ± 1.202e-06
3000
1500
2000
1000
1000
500
0
0
2000
4000
6000
8000
10000
12000
0
0
14000 16000
ESTR (MeV)
5000
10000
(a) E = 25GeV
75GeV
6000
5000
3434
2.017e+04
2415
4820
1060
11.37 / 14
1100 ± 247.6
0.02234 ± 0.02561
1.987e-06 ± 6.405e-07
25000
30000
ESTR (MeV)
100GeV
E in front of calo vs E str reco (100GeV)
Entries
Mean
Mean y
RMS
RMS y
χ2 / ndf
p0
p1
p2
10000
E in front (MeV)
E in front (MeV)
Entries
Mean
Mean y
RMS
RMS y
χ2 / ndf
p0
p1
p2
7000
20000
(b) E = 50GeV
E in front of calo vs E str reco (75GeV)
8000
15000
9000
8000
7000
6000
4000
5000
3000
4000
3434
2.492e+04
2698
6000
1159
10.34 / 13
1176 ± 189.3
0.01199 ± 0.01674
1.854e-06 ± 3.570e-07
3000
2000
2000
1000
00
1000
5000
10000
15000
20000
25000
30000
00
35000 40000
ESTR (MeV)
10000
(c) E = 75GeV
14000
12000
10000
3434
4.075e+04
3472
1.071e+04
1577
11.11 / 12
2373 ± 253.4
-0.04455 ± 0.01305
1.638e-06 ± 1.625e-07
40000
E in front of calo vs E str reco (500GeV)
50000
ESTR (MeV)
3434
7.466e+04
4936
RMS
2.167e+04
RMS y
2052
2
χ / ndf
35.09 / 16
p0
3697 ± 281.6
p1
-0.03142 ± 0.00797
p2
5.92e-07 ± 5.41e-08
20000
15000
8000
6000
500GeV
Entries
Mean
Mean y
25000
E in front (MeV)
E in front (MeV)
Entries
Mean
Mean y
RMS
RMS y
χ2 / ndf
p0
p1
p2
30000
(d) E = 100GeV
200GeV
E in front of calo vs E str reco (200GeV)
20000
10000
4000
5000
2000
×10
140
160
ESTR (MeV)
3
0
0
10000 20000 30000 40000 50000 60000 70000 80000 90000
ESTR (MeV)
(e) E = 200GeV
00
20
40
60
80
100
120
(f) E = 500GeV
Figure 5.16: Energy in front of the calorimeter versus energy in the front sampling
for different electron energies at η = 1.9
5.8
Summary
For the sake of clarity, the corrections of the Calibration Hits Method are summarized
in table 5.1.
51
5.8. SUMMARY
Offset
4000
1.458 / 2
-945.1 ± 975.2
-1.746 ± 5.096
248.8 ± 151.9
χ 2 / ndf
p0
p1
p2
Offset vs Eacc
Offset
χ 2 / ndf
p0
p1
p2
Offset vs Eacc
3500
3500
0.3406 / 2
-2147 ± 1239
-9.282 ± 6.562
445.1 ± 194.6
3000
3000
2500
2500
2000
2000
1500
1500
1000
1000
500
500
100
200
300
χ 2 / ndf
p0
p1
p2
Slope vs Eacc
Slope
400
0.1
0
0
500
E acc reco (GeV)
0.6305 / 2
0.6748 ± 0.2143
-0.1968 ± 0.06502
0.02312 ± 0.008679
100
200
300
0.08
400
χ 2 / ndf
p0
p1
p2
Slope vs Eacc
Slope
0
500
E acc reco (GeV)
1.599 / 2
0.8107 ± 0.2458
-0.2335 ± 0.07452
0.02775 ± 0.009953
0.15
0.06
0.1
0.04
0.02
0.05
-0
-0.02
0
-0.04
-0.06
-0.05
100
200
300
χ / ndf
p0
p1
p2
Secord vs Eacc
-6
Secord
400
2
×10
3
500
E acc reco (GeV)
0.1218 / 2
2.585e-06 ± 6.051e-07
-3.882e-09 ± 1.017e-09
3.445e-05 ± 5.94e-05
0
100
200
300
400
χ / ndf
p0
p1
p2
2
Secord vs Eacc
-6
Secord
0
×10
2
500
E acc reco (GeV)
4.909 / 2
2.389e-06 ± 6.308e-07
-3.548e-09 ± 1.059e-09
6.975e-05 ± 6.322e-05
2
0
1
0
-2
-1
-4
-2
-6
-3
0
100
200
300
400
500
E acc reco (GeV)
-8
0
100
(a) η = 1.9
200
300
400
500
E acc reco (GeV)
(b) η = 2.0
Figure 5.17: Parameters a, b, c of equation 5.13 as a function of Ecalo . The left side
column corresponds to η = 1.9, while the right side column corresponds to η = 2.0.
Correction
Einf ront
Ecalo
Ebehind
TOTAL
n0 params/cluster
9
6
2
17
Cl dependence
no (×1)
yes (×3)
no (×1)
total n0 params
9
18
2
29
Table 5.1: Summary of the parameters used by the calibration hits method in each
correction. The parameters corresponding to Einf ront refer a, b and c to equation 5.8
(equation 5.12 for η > 1.8)). Ecalo include the parameters of both fcalo (equation 5.3)
and fout (equation 5.5). Those parameters need to be computed for the three different
cluster sizes. Einf ront includes the three paramaters in equation 5.7.
52
CHAPTER 5. THE CALIBRATION HITS METHOD
Chapter 6
Results
The set of coefficients or parameters extracted in previous chapter are applied in
Monte Carlo samples of single electrons to check the peformance of the method in
terms of energy resolution, linearity, uniformity and energy scale. The Monte Carlo
samples differ from the ones used to obtain the parameters of the method. Some
systematic errors are also studied in this chapter.
6.1
Energy resolution and linearity
The energy of the incoming electron is reconstructed using the procedure described
in chapter 4, Ereco = Einf ront + Ecalo + Ebehind , where the three different terms
include the coefficients for the needed corrections. As an example, the distributions
of Ereco are represented in figure 6.1 for different generated electron energies and
for η = 1.7125. Under ideal conditions, perfect gaussian distributions for Ereco are
expected. However, a low energy tail is observed at low generated energies. This
is interpreted as the Calibration Hits Method (CHM), in the present release, is not
able to correct totally the energy lost in front of the calorimeter. The influence of the
dead material in front is less important for the highest energies, hence no tails are
distinguished. The gaussian mean (m) and standard deviation (σ) are obtained from
the gaussian part of the distribution by fitting the so called ”Cristal Ball” function.
It consists of a gaussian core portion and a power-law low-end tail below a certain
threshold:

2
− 21 ·( x−m
x−m
σ )

e
> −|a|

σ

f (x) =
1 ·a2
n n −2


 (n|a| ) ·e x−m n x−m ≤ −|a|
σ
( |a| −|a|− σ )
6.1.1
Linearity
The average reconstructed energy (m) as a function of the generated electron energy
is represented in figure (6.2) for two values of η, namely: 1.7125 (belongs to region
with presampler) and 1.9125 (belongs to region without presampler). Apparently for
53
54
A RooPlot of "Reco Energy"
A RooPlot of "Reco Energy "
Events / ( 110 )
Events / ( 200 )
CHAPTER 6. RESULTS
160
140
120
250
200
100
150
80
60
100
40
50
20
0
10000
15000
20000
0
25000
25000
30000
Reco Energy
30000
35000
(a) E = 25GeV
45000
50000
55000 60000
Reco Energy
(b) E = 50GeV
A RooPlot of "Reco Energy"
Events / ( 275 )
A RooPlot of "Reco Energy "
Events / ( 200 )
40000
250
200
350
300
250
200
150
150
100
100
50
50
×10
110
120
Reco Energy
3
0
50000
55000
60000
65000
70000
75000
0
70
80000 85000 90000
Reco Energy
80
100
A RooPlot of "Reco Energy "
Events / ( 525 )
(d) E = 100GeV
A RooPlot of "Reco Energy "
Events / ( 325 )
(c) E = 75GeV
90
300
250
300
250
200
200
150
150
100
100
50
50
×10
3
0
170
180
190
200
210
(e) E = 200GeV
220
Reco Energy
×10
520
530
Reco Energy
3
0
460
470
480
490
500
510
(f) E = 500GeV
Figure 6.1: Reconstructed energies at η = 1.7125
55
500
400
Ereco = e1 × Etrue + e2
e1 = 0.9998 ± 0.0002
e2 = -0.0398 ± 0.0270
Χ 2 /d.o.f = 19.66/4
Ereco (GeV)
Ereco (GeV)
6.1. ENERGY RESOLUTION AND LINEARITY
500
400
300
300
200
200
100
100
0
0
100
200
300
400
Ereco = e1 × Etrue + e2
e1 = 0.9994 ± 0.0003
e2 = -0.1355 ± 0.0336
Χ 2 /d.o.f = 286.84/4
0
0
500
Etrue (GeV)
100
200
(a) η = 1.7125
300
400
500
Etrue (GeV)
(b) η = 1.9125
Figure 6.2: Reconstructed energy versus true energy superimposed with a first degree
polinomial fit
both η values the relation is linear. However, to check the deviation from a linear
relation at the per mil level, the points are fitted using a first degree polinomial and
the following quatity is calculated for each point mi , i = 1, . . . , 6:
∆mi =
mi − Ef it
Ef it
where Ef it = e1 · Etrue + e2 being e1 and e2 the parameters of the fit.
The values of e1 and e2 are (e1 = 0.9998 ± 0.0002 , e2 = −0.0398 ± 0.0270) for
η = 1.7125 and (e1 = 0.9994 ± 0.0003 , e2 = −0.1355 ± 0.0336) for η = 1.9125. The
values of e2 , represented as a funtion of η in figure 6.3 (a), are close to zero, but not
compatible with this value. This fact indicates that the Calibration Hits Method is
a little biased at very low energies. The values of e1 (figura 6.3 b) are close to one,
this parameter being related with the energy scale (Ereco/E) of the calorimeter.
offset (GeV)
1
0.8
1.005
1.004
0.6
1.003
0.4
1.002
0.2
1.001
0
1
-0.2
0.999
-0.4
0.998
-0.6
0.997
-0.8
-1
SLOPE
Entries
38
Mean
2.027
RMS
0.2751
SLOPE
Slope
Offset
Entries
38
Mean
2.252
RMS
0.3117
Offset
0.996
1.6
1.7
1.8
1.9
2
2.1
2.2
(a) e1 versus η
2.3
2.4
2.5
η
0.995
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
(b) e2 versus η
Figure 6.3: Uniformity of the parameters e1 and e2
In figure 6.4 the quantities ∆mi as a function of the generated electron energy (E)
are shown. The left (right) raw correspond to η = 1.7125 ( η = 1.9125). The energy
lost in front of the calorimeter is corrected by using the parametrization function of
56
CHAPTER 6. RESULTS
0.02
0.02
∆m
∆m
the shower barycenter X (see section 5.4.2), which is taken as default. At η = 1.7125
the deviation from linearity is below 0.1 % except for the point at 25 GeV , which is
0.5 %. At η = 1.9125 the linearity is worse being the low energy points at the level
of 1%.
0.015
0.015
0.01
0.01
0.005
0.005
0
0
-0.005
-0.005
-0.01
-0.01
-0.015
-0.015
-0.02
0
100
200
300
400
500
Energy (GeV)
-0.020
100
(a) η = 1.7125
200
300
400
500
Energy (GeV)
(b) η = 1.9125
Figure 6.4: ∆m versus energy
To study the uniformity of the linearity as a function of η, one quantity representing the deviation from linearity at a given pseudorapidity must be defined. One
candidate is the maximum deviation from linearity defined as:
L = ∆mk
where k corresponds to the index which makes |∆mi | maximum.
This quantity L is shown as a funtion of η in figure (6.5). Except for three points,
the rest are clearly below the 1% level.
6.1.2
Energy resolution
As seen in chapter 3 the energy resolution
σ
m
is parameterized as:
a
σ(E)
=p
⊕b
m(E)
E(GeV )
(6.1)
where a and b are the sampling and constant term respectively and ⊕ means the
quadratic sum.
A term c/E is not considered here since the Monte Carlo simulation, used in this
study, does not include any noise.
In figure 6.6 the energy resolution as a function of the generated electron energy
(E) is shown. The left (right) plot correspond to η = 1.7125 ( η = 1.9125). The
energy lost in front of the calorimeter is corrected by using the parameterization
function of the shower barycenter X (see section 4.4.2), which is taken as default. The
points are fitted using equation 6.1 obtaining the following values for the sampling
and constant terms:
57
6.1. ENERGY RESOLUTION AND LINEARITY
L
DevL
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
Figure 6.5: Maximum deviation from linearity versus η.
0.045
χ2 / ndf
6.187 / 4
p0
0.2046 ± 0.002583
p1
0.007935 ± 0.0002464
0.04
p0
p1
σ
E
σ
E
χ2 / ndf
0.035
7.309 / 4
0.1237 ± 0.003736
0.00625 ± 0.000346
0.03
0.035
0.025
0.03
0.025
0.02
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
100
200
300
400
(a) η = 1.7125
500
Energy (GeV)
0
0
100
200
300
400
500
Energy (GeV)
(b) η = 1.9125
Figure 6.6: Resolution versus energy
a = 0.205 b = 0.0079 η = 1.7125
a = 0.124 b = 0.0063 η = 1.9125
In the region around η = 1.7 the dead material in front has a higher value and
larger variation than in the region about η = 1.9. This fact reflects on the different
values obtained for the resolution, much better at η = 1.9. Again the present release
of the Calibration Hits Method is not able to bring the sampling term to the level of
0.1 and the constant term to the level of 0.007 for the whole η region. To study the
uniformity of the energy resolution the sampling and constant terms are represented
as a function of η in figure (6.7). Both parameters show a flat behaviour in the η
58
CHAPTER 6. RESULTS
range between 1.8 and 2.4 with values a ∼ 14% and b ∼ 0.6%. However, there is
a large variation on the sampling and constant term on the region 1.55 < η < 1.8.
The former varies from 16% up to 38% and the later from 0.6% up to 1.2%. This big
variation, as we will discuss in the next section, is attributed to the huge variation
of the amount of material in front of the calorimeter in this area. In fact it can be
observed a correlation between the variation of the sampling term and the variation
of the dead material in front represented in figure 4.9. The values of the constant
term b for η = 1.6625 and η = 1.6875 are an artifice of the fit, namely for very high
values of the sampling term there is less sensitivity to the constant term in the fit. In
the region η > 2.4 both sampling and constant term increase again from 15% up to
20% and from 0.6% up to 1% respectively. This is probably due to the fact that in
this η region no electron quality cuts (isEM) are applied to extract the coefficients
due to low efficiency (see section ”Description of the method” in previous chapter).
6.1.3
Uniformity of the response
The uniformity of the response along η is represented in figure 6.8 for both m and
σ normalized to E. The normalization is performed to check the energy scale simultaneously. The ahieved uniformity is better than 0.5% for all energies but 25GeV
which goes up to 0.1% in severall cells. This is due to the fact that low energy
electrons are much more affected by energy loss in front of the calorimeter and by
the effect of the magnetic field. The magnetic field reflects the charged particles of
the pre-shower in the dead material, hence they missed the cluster of cells defined in
the calorimeter to evaluate the energy (see fout corrections in previous chapter).
Note also that an excelent energy reconstruction is achieved for electrons with
energy higher that 100GeV being mostly within 0.3% in the whole η range. Finally
we can see in figure 6.8b (also seen in figure 6.7) a small jump in the resolution at
η = 1.8, which is the transition between the two regions with and without presampler.
At this η cell the amount of material in front of the calorimeter is still big, as can
be seen in figure 4.9, and the absence of the presampler produces a worst correction.
This shows the advantage of having a presampler for recovering the energy lost in
the material in front.
6.2. CONTRIBUTION FROM THE DIFFERENT CORRECTIONS
59
sampling term (%)
Sampling term
45
40
35
30
25
20
15
10
5
0
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
2.3
2.4
2.5
η
(a) Sampling term versus η
Constant term (%)
constant term
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1.6
1.7
1.8
1.9
2
2.1
2.2
(b) constant term versus η
Figure 6.7: Resolution sampling and constant term over the whole η range
6.2
Contribution from the different corrections
First we would like to stress the necessity of applying a reconstruction method in
order to improve the energy resolution, energy scale and linearity. With this goal we
compare the energy scale and resolution , figures 6.9 and 6.10, when no corrections
are applied at all (dark blue points), called raw energy in the graphic, with the case in
60
CHAPTER 6. RESULTS
m/E
lin25
1.03
25 GeV
50 Gev
75 GeV
1.02
100 Gev
200 Gev
500 Gev
1.01
1
0.99
0.98
0.97
0.96
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
(a) Energy scale versus η
σ
E
res25
0.1
25 GeV
50 Gev
0.09
res25
Entries
38
Mean
1.984
RMS
0.2985
75 GeV
100 Gev
200 Gev
0.08
500 Gev
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
(b) resolution versus η
Figure 6.8: Energy scale and resolution for the various eneregies versus eta. Blue,
green, magenta, yellow, red and black points correspond to electrons of 25, 50, 75,
100, 200 and 500GeV
which the Calibration Hits Method is used (green points). The left plots correspond
to η = 1.7125 and the right ones to η = 1.9125. The abscissa refers to the generated
electron energy (or true energy) E. It can be seen, for example, that at η = 1.7125
61
6.2. CONTRIBUTION FROM THE DIFFERENT CORRECTIONS
1.2
Raw energy
f calo correction
1.15
∆m
Ereco/E true
the raw energy is unaceptable, about 78% of the true 50 GeV , while applying the
Calibration Hits Method to this raw energy leads to 99.999 % of the true energy.
Similarly for the energy resolution one sees the improvement applying the Method at
η = 1.7125. In contrast, at η = 1.9125 there is only improvement for the energy scale,
but no gain for the resolution. In the region η > 1.8 the distribution of upstream
material is flat and small so the corrections for energy in the calorimeter are expected
to be the most important ones, and in paticular the correction for lateral leakage.
However this depends basically on the fluctuations of the transversal section of the
electromagnetic shower that, as explained in chapter 3, is almost negligible.
As a second exercice, we discuss the contribution of the different corrections
applied in the Calibration Hits Method to obtain the reconstructed energy. The
modularity of the method allows to perform this kind of studies. Looking again at
figures 6.9 and 6.10 and starting from the raw energy, the corrections are applied
in an accumulative way following the order, fcalo (red points) thereafter fout (cian
points), next is fleak (yellow points) and last finf ront (green points) which shows the
performance of the full method.
f calo +f out corrections
1.1
Raw energy
f calo correction
f calo +f out corrections
1.1
f calo + f out + f leak corrections
f calo + f out + f leak corrections
All corrections
All corrections
1.05
1
1
0.9
0.95
0.8
0.9
0.7
0.60
0.85
100
200
300
400
0.8
0
500
Energy (GeV)
100
(a) η = 1.7125
200
300
400
500
Energy (GeV)
(b) η = 1.9125
0.1
Raw energy
f calo correction
0.09
f calo +f out corrections
0.08
All corrections
f calo + f out + f leak corrections
0.04
σ
E
σ
E
Figure 6.9: All different contributions to the Energy scale versus energy
Raw energy
f calo correction
f calo +f out corrections
0.035
f calo + f out + f leak corrections
All corrections
0.03
0.07
0.06
0.025
0.05
0.02
0.04
0.015
0.03
0.01
0.02
0.005
0.01
00
100
200
300
(a) η = 1.7125
400
500
Energy (GeV)
0
0
100
200
300
400
500
Energy (GeV)
(b) η = 1.9125
Figure 6.10: Al different contributions to the resolution versus energy
The following exercice consists in fixing a certain generated energy, 100 GeV in
62
CHAPTER 6. RESULTS
this case, and study the contribution of the different corrections as a function of
η. This is represented in figure 6.11 for the energy scale and figure 6.12 for the
resolution.
In the η interval (1.55, 1.8) the largest contribution to the energy scale as well as
the resolution is the correction by energy loss in front of the calorimeter, improving
the former up to 25% and the latter up to 55%. At η values above 1.8 that correction
becomes less important, having an impact only on the energy scale of a few percent.
The next significant correction is fout , that is the correction for the cascade energy
leaking transversally out of the defined cluster of calorimeter cells. It is hardly seen
in the figures (light blue points) since the points are behind the yellow ones. It can be
seen in figure 6.11 that the correction for the energy scale increases when η increases.
This reflects the fact that the cell size in cm decreases when η increases, hence more
lateral leakage is expected a larger η values. In addition to this effect, for the region
1.55 < η < 1.8, where the dead material is higher, low energetic electrons from an
early-cascade produced in the material are bent by the magnetic field, hence they
may hit out of the calorimeter cluster.
The factor fcalo has the effect of correcting a small overestimation applied at the
reconstruction level before the Calibration Hits Method. Finally, as expected, the
contribution of the energy behind the calorimeter (fleak ) is almost zero since the
fraction of energy deposited in this part of the detector never exceeds 1% of the total
energy for very high energies and 0.2% for low energy electrons.
m/E
Lraw
1.2
Raw energy
f calo correction
Lraw
f calo +f out corrections
1.1
f calo + f out + f leak corrections
Kurtosis -1.161
All corrections
1
0.9
0.8
0.7
0.6
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
Figure 6.11: Al different contributions to the energy scale (100GeV) versus η.
63
6.3. SYSTEMATICS
Rraw
σ
E
0.12
Raw energy
f calo correction
f calo +f out corrections
0.1
f calo + f out + f leak corrections
All corrections
0.08
0.06
0.04
0.02
0
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
Figure 6.12: Al different contributions to the energy resolution (100GeV) versus η.
6.3
Systematics
In this section two sources of sistemactic errors for the energy reconstruction are
studied, namely: i) cross talk between neighboring cells and ii) variations of the
material in front with respect to the one implementated in the present release of the
Monte Carlo simulation.
6.3.1
Effect of the cross talk
In several tests using charge injection and electron beams [13] it has been observed
the existence of cross talk between cells. A calibration signal is injected in one
individual cell and the neighborings are read out. Using this procedure it has been
found that the highest cross talk is produced between strips of the S1 compartment
(S1 → S1 cross talk) reaching up to 5 %, in the η region where the S1-cells are
smallest (see table 4.1 of η granularity). Cross talk was also observed from an S2
cell to the S1 and S3 compartments, S2 → S1 and S2 → S3 cross talks respectively,
being in this case less than 1 %.
A first study of the cross talk effect on the CalibHits method has been done faking
a cross talk not at the cell but at the cluster level, i.e., we moved a certain fraction of
the energy of the cluster either from one compartment to another (so the total energy
in the cluster remain constant) or from one compartment to outside the cluster. The
former case has been used to fake S2 → S1 as well as S2 → S3 cross talks while the
latter has been used to simulate energy underestimation due to S1 → S1 cross talk.
Figure 6.13 (left) shows, at η = 1.7125, the effect of the S2 → S1 cross talk on
the computation of the barycenter of the shower, ∆X = XXtalk − XN oXtalk , as a
64
-0
25 GeV
-0.05
50 Gev
75 GeV
100 Gev
-0.1
200 Gev
∆ Ereco (%)
0
∆ X (X )
CHAPTER 6. RESULTS
0.18
0.16
25 GeV
50 Gev
75 GeV
0.14
500 Gev
100 Gev
200 Gev
500 Gev
0.12
-0.15
0.1
-0.2
0.08
-0.25
0.06
-0.3
0.04
-0.35
0.02
-0.4
0
1
2
3
4
5
Percentual moved energy
(a) Barycenter of the shower variation
0
0
1
2
3
4
5
Percentual moved energy
(b) Energy variation
Figure 6.13: Effect of the Middle to Front cross talk at η = 1.7125
function of the percentual energy in the S2 sampling moved to the S1 compartment.
Since part of the S2 energy is moved to S1, the value of X decreases, therefore ∆X
is negative. It can be observed in the figure that for a 1 % cross talk, X drops 0.06
radiation lengths at 100GeV , which represents about 0.2 % of the total calorimeter
depth.
In Figure 6.13 (right) it is represented, at η = 1.7125, the effect of the S2 → S1
Xtalk
N oXtalk
cross talk on the reconstructed energy, ∆Ereco = Ereco
− Ereco
, as a function
of the percentual moved from S2 to S1. The reconstructed energy is modified by
the S2 → S1 due to its dependence on X. The term which dominates the energy
variation is fout , the correction for the energy leaked transversally out of the cluster.
An underestimation of X produces an overestimation of the percentual energy out
of the cluster (see figure 5.5), hence the reconstructed energy is overcorrected. For
example, it can be observed in figure 6.13 that a S2 → S1 cross talk of 1 % produces
an increase in the reconstructed energy of about 0.02% at 100GeV . On the other
hand, for low generated energies the longitudinal profile of the shower picks a lower
X values (see equation 3.1), hence the underestimation of X is lower in percentage
terms due to the non-linear behavior in figure 5.5, therefore a larger reconstructed
energy variation is expected. This is also observed in figure 6.13 where the largest
variation of the reconstructed energy corresponds to the lowest energy (25GeV ).
Even at 25GeV , a cross talk of 1% leads to a reconstructed energy variation of only
0.04 %, it is then a second order effect, hence we conclude that the S2 → S1 cross
talk does not affect the energy reconstruction.
Figure 6.14 shows the effect on X and Ereco of the S2 → S3 cross talk at η =
1.7125. The same variables, ∆X and ∆Ereco are ploted but now the abscissa refers to
the percentual energy moved from the S2 to the S3 compartment of the calorimeter.
Again, the increase on ∆X is understood (figure 6.14 a) since we are moving a
certain fraction of energy to the last compartement. In this case the correction for
the energy leaked behind the calorimeter is potentially dangerous due to the exponetial function used to parameterize fleak (see figure 5.7). However, the large depth
of the calorimeter in the whole pseudorapidity region produces that the extracted
parameters l0 and l1 in (5.7) have a low value, being this fleak insensitive to small
65
∆ Ereco (%)
0.45
0
∆ X (X )
6.3. SYSTEMATICS
0.4
25 GeV
75 GeV
0.35
-0.04
100 Gev
200 Gev
0.3
0
-0.02
50 Gev
500 Gev
-0.06
0.25
-0.08
0.2
-0.1
0.15
-0.12
0.1
-0.14
0.05
-0.16
25 GeV
50 Gev
75 GeV
100 Gev
200 Gev
0
0
1
2
3
4
5
Percentual moved energy
(a) Barycenter of the shower variation
-0.18
0
500 Gev
1
2
3
4
5
Percentual moved energy
(b) Energy variation
Figure 6.14: Effect of the Middle to back cross talk at η = 1.7125
variations of X.It is again the behaviour of fout the one that dominates and with the
above argument we understand the energy variations shown in (6.14 b). In this case
the energy variation is on the oposite direction to the one produced by S2 → S1 but
affects quatitative at the same level.
Finally, in figure (6.15) the results refering to the S1 → S1 cross talk are presented. In contrast to previous types of cross talk, in S1 → S1 part of the S1
energy is moved out of the cluster, hence the cluster energy is not conserved. This
has two effects, first an increase of X, since E1 is decreased respect to E2 and E3 ,
second a decrease of Ereco . The amount of cross talk, abscissas in the figure, has
been stablished as follows: i) the cell to cell cross talk in S1 from measurements is at
the level of 5%; ii) only the S1-cell nearest to the cluster boundary will leak energy
outside the cluster. The most negative situation will be a cluster 3x3 middle cells
where the electron is incident on the edge of the central cell. The distance between
the incident point of the electron and the boundary of the cluster is the width of
one middle cell. According to the transverse profile of a electromagnetic shower at
the depth of the S1 sampling, order 1% of the shower energy will be deposited in
the S1-cell nearest to the cluster boundary. This estimation has been obtained by
transforming from Uranium to Lead the calculation of reference [5]. Then, the 5%
cross talk of 1% Front energy is 0.05 % of E1 to be moved out. This number must
be considered as orden of magnitude 0.1% , because of the rough calculation. It can
be observed in figure 6.15 that, for instance at 100 GeV , a decrease of 0.1% in E1
produces a reduction on Ereco of about 0.03%. The worst case being at 25 GeV were
the variation of Ereco is 0.04%, hence, this cross also produces a negligible influence
on the energy reconstruction.
For completeness, the same studies have been performed for the middle cell centered at η = 1.9125 in order to be sure that the different parameterizations used to
compute the energy losses in the upstream material is not more sensitive to the cross
talk. Figures 6.16, 6.17 and 6.18 show the effect of S2 → S1, S2 → S3 and S1 → S1
cross talk respectively for the cell placed at η = 1.9125. Notice that the variations
reach the same order of magnitud as in the cell centered at η = 1.7125.
66
0.002
0.0018
∆ Ereco (%)
0
∆ X (X )
CHAPTER 6. RESULTS
25 GeV
0.0016
0.0014
0
-0.005
50 Gev
75 GeV
100 Gev
200 Gev
-0.01
500 Gev
-0.015
0.0012
0.001
-0.02
0.0008
-0.025
0.0006
-0.03
0.0004
-0.035
25 GeV
50 Gev
75 GeV
100 Gev
0.0002
0
0
200 Gev
500 Gev
-0.04
0.02
0.04
0
0.06
0.08
0.1
Percentual moved energy
(a) Barycenter of the shower variation
0.02
0.04
0.06
0.08
0.1
Percentual moved energy
(b) Energy variation
-0
25 GeV
-0.05
50 Gev
75 GeV
-0.1
100 Gev
200 Gev
-0.15
∆ Ereco (%)
0
∆ X (X )
Figure 6.15: Effect of the Front to Front cross talk at η = 1.7125
0.6
25 GeV
50 Gev
75 GeV
0.5
100 Gev
200 Gev
500 Gev
500 Gev
0.4
-0.2
-0.25
0.3
-0.3
0.2
-0.35
-0.4
0.1
-0.45
-0.5
0
1
2
3
0
0
4
5
Percentual moved energy
(a) Barycenter of the shower variation
1
2
3
4
5
Percentual moved energy
(b) Energy variation
0.6
∆ Ereco (%)
0
∆ X (X )
Figure 6.16: Effect of the Middle to Front cross talk at η = 1.9125
25 GeV
50 Gev
0.5
75 GeV
100 Gev
200 Gev
0
-0.1
500 Gev
0.4
-0.2
0.3
-0.3
0.2
-0.4
0.1
-0.5
25 GeV
50 Gev
75 GeV
100 Gev
200 Gev
500 Gev
0
0
1
2
3
4
5
Percentual moved energy
(a) Barycenter of the shower variation
-0.6
0
1
2
3
4
5
Percentual moved energy
(b) Energy variation
Figure 6.17: Effect of the Middle to back cross talk at η = 1.9125
6.3.2
Effect of an imperfect knowledge of the death material
The Calibration Hits method extract all the correction coefficients based on a Monte
Carlo simulation, where the different properties of the ATLAS detector are implemented at a certain level of accuracy. In this subsection we try to quantify the
67
∆ Ereco (%)
0
∆ X (X )
6.3. SYSTEMATICS
25 GeV
0.0025
50 Gev
75 GeV
100 Gev
200 Gev
0.002
0
-0.01
500 Gev
-0.02
0.0015
-0.03
0.001
25 GeV
-0.04
0.0005
50 Gev
75 GeV
100 Gev
200 Gev
0
0
0.02
0.04
0.06
0.08
0.1
Percentual moved energy
(a) Barycenter of the shower variation
-0.05
0
500 Gev
0.02
0.04
0.06
0.08
0.1
Percentual moved energy
(b) Energy variation
Figure 6.18: Effect of the Front to Front cross talk at η = 1.9125
possible deviation on the energy scale due to an imperfect knowledge of amount of
materials in front of the Calorimeter.
As discused in chapter 5, the only inputs to the CHM are the energies on the three
samplings of the calorimeter plus the energy in the presampler. We have developed
a new approach to estimate the effect on the energy reconstruction of an inaccurate
knowledge of materials in front of the calorimeter.
In figure 6.19 the variation of the energy on the presampler and on the three
layers of the calorimeter is shown as a function of the amount of material in front
(M) for 100 GeV generated energy. The amount of material is expressed in units of
radiation lengths (X0 ). The points refer to the most probable value and the error
bars to the RMS of the energy distributions. These dependences are obtained from
the variation of the material in front along η organizing the Monte Carlo events in
bins of M. We observe how the energy in the presampler is the most sensitive to this
variation, changing its value up to a factor larger than 2 for ∼ 2·X0 of variation. The
fitted functions in figures 6.19) are second degree polynomials: Eif it (M), i = 0, . . . , 3,
where the index 0 refers to presampler. These polynomials are used to estimate the
energy depositions in a certain cell if the amount of material in front were different.
The energy out of the cluster is included in the calculation of the total energy for
the previous plots, hence the results are not biased by the possible differences in cell
size along η. Similar functions are obtained for each generated energy point, finding
that the parameters of the Eif it (M) polynomials dependent on the energy.
The cluster energy in the different compartments is rescaled, using the polynomials Eif it (M) for a certain variation of material in front respect to the nominal value,
and the Calibration Hits Method (CHM) is applied under these different conditions
(new values of E0 , E1 , E2 , E3 , E4 for a given η). More explicitly, the rescaling is
performed according to the following expression:
Einew
=
Eif it (M new )
Eif it (M nominal )
Ei (M nominal ) i = 0, 1, 2, 3
where Ei (M nominal ) is the cluster energy in compartment i for the nominal amount
of material in front, and M new refers to the new value for the amount of material.
68
CHAPTER 6. RESULTS
With these new values Einew i = 0, 1, 2, 3, the barycenter X new is computed and the
new corresponding corrections (functions of X new and Einew ) of the CHM are applied
new
to obtain Ereco
.
Eps (GeV)
18
0.05674 / 12
-16.15 ± 30.98
10.21 ± 16.94
-0.8117 ± 2.257
16
χ2 / ndf
p0
p1
p2
nombre3F
Efront (GeV)
χ2 / ndf
p0
p1
p2
nombre3PS‘
40
0.2882 / 12
12.01 ± 14.61
10.37 ± 8.992
-1.265 ± 1.313
35
14
30
12
25
10
8
20
6
15
4
2.8
3
3.2
3.4
3.6
10
3.8
4
4.2 4.4 4.6 4.8
Ammount of material in front (X 0)
1.5
2
2.5
3
3.5
4
4.5
5
Ammount of material in front (X 0)
(a) Energy in the presampler (100GeV) versus (b) Energy in the front (100GeV) versus
amount of material.
amount of material
Emiddle (GeV)
80
0.1733 / 12
87.91 ± 22.45
-9.747 ± 15.53
-0.172 ± 2.473
70
χ2 / ndf
0.4526 / 12
p0
0.9517 ± 0.4841
p1
-0.265 ± 0.2867
p2
0.0217 ± 0.04103
nombre3B
Eback (GeV)
χ2 / ndf
p0
p1
p2
nombre3M
1
0.9
0.8
0.7
60
0.6
0.5
50
0.4
0.3
40
0.2
30
0.1
1.5
2
2.5
3
3.5
4
4.5
5
Ammount of material in front (X 0)
1.5
2
2.5
3
3.5
4
4.5
5
Ammount of material in front (X 0)
(c) Energy in the middle (100GeV) versus (d) Energy in the back (100GeV) versus
amount of material
amount of material
Figure 6.19: Effect of the variation of the amount of material in front in the Calorimeter on the energy deposited in the calorimeter
new
Figures 6.20(a),(b) show the variation of X new and Ereco
respectively with a
change in the material in front respect to the nominal implementation. The figures
refer to a position η = 1.7125, in the region equipped with presampler. The following
new
nominal
definitions are used: ∆X = X new − X nominal and ∆Ereco = Ereco
− Ereco
. The
barycenter variation ∆X is negative, which means more contribution from the S1
compartment than for the S2,S3, and is less affected at low energies. More material in
front means that the maximum of the electromagnetic shower moves occurs earlier,
hence more energy in S1. The situation reminds the Middle to Front cross talk,
figure 6.13, where part of the Middle compartment energy was moved to the S1
compartment. The effect on the reconstructed energy depends much on the generated
energy being large, about 7% drop per X0 material increase, at 25 GeV . We can
also observe in figure 6.20 (b) that at 500 GeV the new extra material in front makes
the reconstructed energy to increase. This is an effect of the correction functions
in the CHM where different signs compete (see for instance figure 5.12 (b) for the
parameters a,b,c of the Einf ront correction). A similar reasoning can be made for the
69
6.3. SYSTEMATICS
region without presampler, as can be seen in figure 6.21 for η = 1.9125. However
at this location the reconstructed energy is more affected by the variation of the
amount of material in front, being about 16% drop per X0 material increase. This
may be explained by the fact that adding an extra X0 of material in front means a
larger relative increase at η = 1.9 than at η = 1.7.
In conclusion, a fair knowledge of the material in front of the calorimeter is
important to determine a precised reconstructed energy.
-0
Energy variation due to X0 var η = 1.9
Energy variation (%)
∆ X (X0)
X variation due to Middle-Back X-talk η = 1.9
-0.2
-0.4
-0.6
-0.8
2
0
-2
-4
-1
-6
-1.2
25 GeV
25 GeV
50 Gev
50 Gev
75 GeV
75 GeV
-1.4
-8
100 Gev
500 Gev
500 Gev
-1.60
0.2
100 Gev
200 Gev
200 Gev
0.4
-10
0
0.6
0.8
1
1.2
Variation in the ammount of material (X 0)
(a) Barycenter of the shower variation with the
amount of material in front
0.2
0.4
0.6
0.8
1
1.2
Variation in the ammount of material (X 0)
(b) Effect of the material in front on Ereco
Figure 6.20: Effect of the variation of the amount of material in front on the reconstructed energy for electrons hiting at η = 1.7125
-0
Energy variation due to X0 var η = 1.9
Energy variation (%)
∆ X (X0)
X variation due to FRont-Front X-talk η = 1.9
-0.2
-0.4
-0.6
5
0
-5
-0.8
-10
-1
25 GeV
-1.2
25 GeV
50 Gev
-15
75 GeV
100 Gev
-1.4
0
75 GeV
200 Gev
500 Gev
0.2
50 Gev
100 Gev
200 Gev
500 Gev
0.4
0.6
0.8
1
1.2
Variation in the ammount of material (X 0)
-20
0
0.2
0.4
0.6
0.8
1
1.2
Variation in the ammount of material (X 0)
(a) Barycenter of the shower variation with the (b) Effect of the material in front on Ereco )
amount of material in front
Figure 6.21: Effect of the variation of the amount of material in front on the reconstructed energy for electrons hiting at η = 1.9125
70
CHAPTER 6. RESULTS
Front method vs X method
6.4
In section 5.7 two different approaches were considered to recover the energy lost in
the material in front for η > 1.8, namely: i) the correlation of the energy loss with
X (X method); ii) the correlation of the energy loss with E1 (Front method). In
the present section we compare both procedures in terms of energy resolution and
linearity.
Figure 6.22 shows the constant term and sampling term (a , b respectively) of
the energy resolution, as well as the linearity (c) as a function of η. The red points
correspond to the Calibration Hits Method using the X method, while the blue
points refer to the use of the Front method. Both methods give compatible results
for the energy resolution, pehaps slightly more stable the X method than the Front
method for the linearity.
constantX
Entries
28
Mean
2.026
X paramet.
RMS
0.28
2
1.8
samplingX
Entries
28
Mean
2.043
X paramet.
RMS
0.2869
Sampling term
Sampling term (%)
Constant term (%)
constant term
STR paramet.
1.6
1.4
1.2
1
30
STR paramet.
25
20
15
0.8
10
0.6
0.4
5
0.2
0
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
0
2.5
η
(a) Resolution constant term versus η
1.6
1.7
1.9
2
2.1
2.2
2.3
2.4
2.5
η
(b) Resolution sampling term versus η
DevLX
Entries
28
Mean
2.066
X paramet.
RMS
0.3132
DevL
L
1.8
0.02
0.015
STR paramet.
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
η
(c) Maximumdeviation from linearity versus
eta
Figure 6.22: Comparation between the two posible methods in the region without
presampler and resolution achieved with the strips method for the various energies.
Chapter 7
Conclusions
A new method to reconstruct the energy of electrons and photons, called Calibration
Hits Method (CHM), applied sometime ago to the ATLAS Electromagnetic Barrel Calorimeter, has been adapted and tested with the Electromagnetic End-Cap
Calorimeter. Some further developments to the method had to be done due to some
peculiarities of the EMEC not present in the Barrel. The CHM corrects for the energy losses in material in front of the calorimeter as well as leakage, both transverse
out of cell cluster definition and longitudinal behind the calorimeter.
To obtain these energy losses a special Monte Carlo simulation of the ATLAS
response to single electron has been run, where the electrons are produced at the
nominal interaction point with 6 different energies ranging from 25 to 500 GeV. The
simulation included the nominal ATLAS geometry, taking into account the effect of
the magnetic field as well as the vertex spread at the interaction point.
The 17 parameters of the CHM are obtained as functions of measurable quantities,
namely: the energy in presampler, front, middle and back calorimeter compartments
and the pseudorapidity (η) of the electron impact point. Corrections are applied at
the cell cluster level, i.e. to the cluster energy, where several cluster sizes have been
studied.
The energy reconstructed using this CHM method is checked in terms of linearity
and energy resolution. For the region η > 1.8 the deviation from linearity es better
than 0.5%, except for two points that need to be understood, while the sampling and
constant terms of the energy resolution are a ∼ 14% and b ∼ 0.6% respectively. In
the region 1.55 < η < 1.8, more affected by the material in front of the calorimeter,
the linearity has been found better than 1% and the sampling and constant terms of
the energy resolution in the intervals a ∼ 15 − 35% and b ∼ 0.5 − 1%. The method
needs further developments to improve the results in the latter region.
Some sources of systematic errors have been studied, namely i) the influence of
the cell to cell cross talk, and ii) the effect of an inaccurate knowledge of the material
in front of the calorimeter. The former is not a concern for the energy reconstruction
using the CHM, while the latter may introduce variations at the level of 10% per X0
of material increase for low energies (25 GeV).
71
72
CHAPTER 7. CONCLUSIONS
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73