Facolt`a di Scienze Matematiche Fisiche e Naturali Dipartimento di ...

Facolt` a di Scienze Matematiche Fisiche e Naturali Dipartimento di Fisica Laurea Magistrale in Fisica Nucleare e Subnucleare

Study of the timing reconstruction with the CMS Electromagnetic Calorimeter Thesis Advisor:

Candidate:

Dr. Daniele del Re

Claudia Pistone matricola 1162469

Anno Accademico 2011-2012

Al mio fratellone.

“L’importante è non smettere di fare domande.” Albert Einstein

“Carpe, carpe diem, seize the days, boys, make your life extraordinary.” Dead Poets Society

Contents Introduction

1

1 The CMS experiment at the LHC

3

1.1

The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2

The Compact Muon Solenoid . . . . . . . . . . . . . . . . . . . . . .

7

1.2.1

Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.2.2

Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.3

Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . 12

1.2.4

Hadronic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . 12

1.2.5

Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2.6

Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3

The ECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3.1

Layout and geometry . . . . . . . . . . . . . . . . . . . . . . . 16

1.3.2

Lead tungstate crystals . . . . . . . . . . . . . . . . . . . . . . 18

1.3.3

Photodetectors . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.3.4

Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.3.5

Photon reconstruction . . . . . . . . . . . . . . . . . . . . . . 22

2 Time reconstruction in the ECAL 2.1

29

Time reconstruction study with data from the test beam . . . . . . . 30 2.1.1

Time extraction with ECAL crystals . . . . . . . . . . . . . . 30

2.1.2

Time measurement resolution . . . . . . . . . . . . . . . . . . 32 iii

2.2

Time reconstruction study with collision data . . . . . . . . . . . . . 34 2.2.1

Event samples and selection criteria . . . . . . . . . . . . . . . 35

2.2.2

Reconstruction of time of impact for photons . . . . . . . . . . 38

3 Study of time development of electromagnetic showers

43

3.1

Electromagnetic showers propagation in the ECAL . . . . . . . . . . 44

3.2

A new variable for discrimination between signal and background . . 50

4 Vertex reconstruction using ECAL timing information

55

4.1

Vertex reconstruction with the tracker . . . . . . . . . . . . . . . . . 56

4.2

Vertex reconstruction using ECAL timing . . . . . . . . . . . . . . . 58 4.2.1

Analysis of Z → ee events . . . . . . . . . . . . . . . . . . . . 65

5 Search for new physics using timing information 5.1

5.2

69

Theoretical framework . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1.1

The Standard Model and its limits . . . . . . . . . . . . . . . 71

5.1.2

Models with long-lived particles . . . . . . . . . . . . . . . . . 73

Search for long-lived particles using timing information . . . . . . . . 76

Conclusions

87

Ringraziamenti

89

Bibliography

91

iv

Introduction The Large Hadron Collider at CERN near Geneva is the world’s newest and most powerful tool for Particle Physics research. It is a superconducting hadron accelerator and collider and it is designed to produce proton-proton collisions at a centre of mass energy of 14 TeV and an unprecedented luminosity of 1034 cm−2 s−1 [1]. There are a lot of compelling reasons to investigate the TeV energy scale. The prime motivation of the LHC is to elucidate the nature of the electroweak symmetry breaking for which the Higgs mechanism is assumed to be responsible. The experimental study of the Higgs mechanism can also shed light on the mathematical consistency of the Standard Model (SM) at energy scales above about 1 TeV. Another goal of LHC is to search for alternative theories to the SM that invoke new symmetries, new forces or costituents. In addition, there is the possibility to discover the way toward a unified theory. One of the four LHC experiment is the Compact Muon Solenoid (CMS). It is a general purpose apparatus, and its design meets very well the goal of the LHC physics programme: its main distinguishing features are a high-field solenoid, a fullsilicon-based inner tracking system, a homogenous scintillating-crystal-based electromagnetic calorimeter (ECAL), a 4π hadron calorimetry, and a redundant efficient muon detection system. This thesis is concentrated on the ECAL. The ECAL is a hermetic homogeneous calorimeter made of 61200 lead tungstate (PbWO4 ) crystals mounted in the barrel region, closed by the 7324 crystals in each endcap. The main purpose is the energy reconstruction of photons and electrons. In addition to this, the combination of the scintillation timescale of the PbWO4 , the 1

2

Introduction

electronic pulse shaping and the sampling rate allow for an excellent resolution in time reconstruction. The goal of this thesis is to study the performance of the timing reconstruction. First of all, the behavior of the timing is investigated in terms of biases and resolution, after comparing collision data with Monte Carlo simulation. Secondly, the time correlation among different crystals belonging to the same photon shower is investigated with the aim of exploiting the difference between photon showers and calorimetric deposits due to jets. Finally, constraints on the position of the primary interaction are obtained by exploiting the time measurement of two high momentum photons. This feasibility study is to check if the timing information can offer additional handles to determine the primary vertex in events with small tracker activity, like H → γγ events. The thesis is organized as follows: • In chapter 1 the LHC and the CMS detector, focusing on the ECAL, are described. • In chapter 2 the time reconstruction using ECAL is illustrated. Collision data are compared to test beam data. • In chapter 3 the time propagation of the photon shower is studied. • In chapter 4 a feasibility study on the vertex reconstruction using timing is detailed by using collision data with both diphoton and Z → ee events and Monte Carlo simulation. • Finally, in chapter 5 results from a search for long-lived neutralinos χ˜01 decaying into a photon and an invisible particle are presented. This is the first physics analysis of the CMS experiment in which the ECAL time is used to search for an excess of events over the expected background.

Chapter 1 The CMS experiment at the LHC This chapter is dedicated to the description of the Large Hadron Collider (LHC) at CERN (section 1.1) and of the Compact Muon Solenoid (CMS) experiment (section 1.2), with particular emphasis on the Electromagnetic Calorimeter (ECAL) as it represents the main topic of this thesis (section 1.3).

1.1

The Large Hadron Collider

The LHC has been installed in the existing 26.7 km tunnel previously hosting the LEP accelerator (Figure 1.1) that lies between 45 m and 170 m below the surface. The tunnel has eight arcs flanked by long straight sections, which host detectors, RF cavities and collimators. The four interaction points are equipped with the four principal LHC experiments: • ALICE (A Large Ion Collider Experiment); • ATLAS (A Toroidal LHC ApparatuS ); • CMS (Compact Muon Solenoid ); • LHCb (Large Hadron Collider beauty).

4

The CMS experiment at the LHC

ATLAS and CMS are two general purpose experiments, designed in order to reconstruct the greatest possible number of phisics processes; ALICE is an experiment to study heavy ion physics; LHCb is dedicated to bottom quark physics.

Figure 1.1: The LHC ring.

Being a particle-particle collider, there are two separate acceleration rings with different magnetic field configuration. The beams are focused by 1232 dipole magnets and 392 quadrupole magnets cooled down to 1.9 K by means of liquid Helium. Protons are accelerated three times before entering the LHC ring (Figure 1.2): the LINAC brings them to 50 MeV, the Proton Synchrotron (PS) to 1.4 GeV, and finally the Super Proton Synchrotron (SPS) injects them into the LHC at 450 GeV. The LHC then completes the acceleration by bringing them to 8 TeV.

Figure 1.2: The LHC proton injection chain.


5

The number of physics events produced in pp collisions is N = σ · L, where σ represents the cross section of the particular process and L the luminosity. The LHC luminosity is defined as: L=

Np2 · fBX · k 4π · σx · σy

(1.1)

where Np is the number of protons per bunch, fBX the frequency of bunch crossing, k the number of bunches, and σx and σy are the transverse spread of the bunches. So, the high luminosity is obtained by a high frequency bunch crossing and a high number of protons per bunch. The two proton beams contain each about 1368 bunches. The bunches, with a number of about 1.5 · 1011 protons each, have a very small transverse spread (about 20 µm) and are about 7.5 cm long in the beam direction. The bunches cross at the rate fBX = 20 MHz, i.e. there is a collision each 50 ns.

Figure 1.3: Parton collision. A sketch of a pp collision is shown in Figure 1.3. When two protons collide at energies greater than their masses, the interaction involves their costituents, the partons: they carry only a momentum fraction xi of the proton momentum. The Parton Distribution Function (PDF) f (xi , Q2 ) describes the xi distribution for different partons, where Q2 is the four-momentum exchanged during the interaction.

6


The effective energy available in each parton collision is: √ sˆ =

√

xa xb s

(1.2)

where s = 4E 2 is the centre of mass energy of the pp system (E is the energy of the both protons), and xa and xb are the proton energy fractions carried by the two interacting partons (a and b). The cross section of a generic interaction pp → X can be written as: σ(pp → X) =

XZ

dxa dxb fa (xa , Q2 )fb (xb , Q2 )ˆ σ (ab → X)

(1.3)

a,b

where σ ˆ (ab → X) is the cross section of the elementary interaction between partons √ a and b at the centre of mass energy sˆ, and fa (xa , Q2 ) and fb (xb , Q2 ) represent the PDFs for the fraction xa and xb , respectively. √ For a centre of mass energy of s = 14 TeV at LHC, the total cross section is estimated to be σ ' (100 ± 10) mb. The inelastic collisions can be divided in two types: • big distance parton collisions, in which a small Q2 is exchanged. These are soft collisions where the majority of particles is produced at small momentum pT and so it escapes from the detector along beam line. These events are the so-called minimum bias events and they are the majority of the pp collisions. • small distance parton collisions, in which a high Q2 is exchanged. In these interactions high masses particles are produced with high momentum pT . These events are the rare events. It needs a higher luminosity in order to have an appreciable statistics of this kind of events. Unfortunately, increasing luminosity means that many parton interactions overlap in a same bunch crossing. In fact, given the instantaneous luminosity L and the minimum bias cross section σmb , the average number of interactions in each bunch


7

crossing (i.e. the number of the so-called pileup events) is given by: µ=

L · σmb fBX

(1.4)

At the nominal luminosity and for a minimum bias cross section of σmb = 80 mb, the average number of inelastic collisions per bunch crossing is about 20, i.e. there are 109 interactions per second. This implies that the products of a selected interaction can be confused with those of simultaneous interactions in the same bunch crossing. The pileup effect can be reduced using a fine granularity detector with a good time resolution. Moreover, since the maximum data storage rate sustainable by the existing device technology is of O(100) Hz, a strong online event selection is needed in order to reduce the event rate. The detector must also have a fast time response (about 25 ns). In addition to this, the high flux of particles coming from pp interactions implies that each component of the detector has to be radiation resistant. These are the general characteristics for a detector at LHC. The next section will illustrate the specific features of the CMS experiment.

1.2

The Compact Muon Solenoid

The CMS detector [2] is a general purpose apparatus due to operate at LHC. The detector requirements for CMS to meet the goal of the LHC physics programme are the following: • good muon identification and momentum resolution over a wide range of momenta in the |η| ≤ 2.5, good dimuon mass resolution (' 1% at 100 GeV), and the ability to determine unambiguously the charge of muons with p < 1 TeV/c; • good charged-particle momentum resolution and reconstruction efficiency in the inner tracker. Efficient triggering and offline tagging of τ ’s and b-jets,

8

The CMS experiment at the LHC requiring pixel detectors close to the interaction region; • good electromagnetic energy resolution, good diphoton and dielectron mass resolution (' 1% at 100 GeV), wide geometric coverage, π 0 rejection, and efficient photon and lepton isolation at high luminosities; • good missing-transverse-energy and dijet-mass resolution, requiring hadron calorimeters with a large hermetic geometric coverage and with fine lateral segmentation.

The design of CMS meets all these requirements. The main distinguishing features of CMS are a high-field solenoid, a full-silicon-based inner tracking system, and a homogenous scintillating-crystal-based electromagnetic calorimeter. CMS has a cylindrical shape, symmetrical around the beam direction, with a diameter of 14.6 m, a total length of 21.6 m, and weighs about 12500 tons. It is divided into a central section, made of several layers coaxial to the beam axis (the barrel ), closed at its ends by two hermetic discs orthogonal to the beam (the endcaps). The overall layout of CMS is shown in Figure 1.4. Moving outside starting from the beam position, it presents a silicon tracker, a crystal electromagnetic calorimeter, a hadronic calorimeter, and the superconducting solenoidal magnet, in the return yoke of which there are the muon drift chambers. The coordinate system adopted by CMS has the origin centered at the nominal collision point inside the detector: • the x-axis pointing radially inward toward the center of the LHC; • the y-axis points vertically upward; • the z-axis points along the beam direction toward the Jura mountains from LHC Point 5.


9

Figure 1.4: A perspective view of the CMS detector. The azimuthal angle φ is measured from the x-axis in the x − y plane and the radial coordinate in this plane is denoted by r. The polar angle θ is measured from the z-axis. However, since parton interactions are typical boosted along the beam direction, quantities which don’t depend on longitudinal boost are used, such as the pseudorapidity: θ η = − ln tan 2

(1.5)

The momentum and energy transverse to the beam direction, pT and ET , respectively, are computed from the x and y components. The imbalance of energy in the transverse plane is the missing transverse energy, denoted by 6ET .

1.2.1

Magnet

At the heart of CMS sits a 13-m-long, 6-m-inner-diameter, 4-T superconducting solenoid [2] providing a large bending power (12 Tm) before the muon bending

10


angle is measured by the muon system. The return field is large enough to saturate 1.5 m of iron. The bore of the magnet is large enough to accommodate the inner tracker and the calorimetry.

1.2.2

Tracker

The main goal of the inner tracking [2] is to reconstruct isolated, high-pT electrons and muons with efficiency greater than 95%, and tracks of particles within jets with efficiency greater than 90%, within a pseudorapidity coverage of |η| < 2.5. It surrounds the interaction vertex and has a length of 5.8 m and a diameter of 2.5 m. Since it is so close to the interaction region, the particle flux is such that cause severe radiation damage to the detector. The main challenge in the design of tracking system was to develop detector components able to operate in this harsh environment for an expected lifetime of 10 years. In order to satisfy this requirement the tracker is completely made of silicon and it constitutes the first example in highenergy physics of an inner tracking system entirely based on this technology. By considering the charged particle flux at high luminosity of the LHC, three regions can be distinguished: • the closest region to the interaction point where the particle flux is the highest (' 107 /s at r ' 10 cm), and there are pixel detectors. The pixel size is 100 × 150 µm2 ; • the intermediate region (20 cm < r < 55 cm), where the particle flux is low enough to enable the use of silicon microstrip detectors with a minimum cell size of 10 cm × 80 µm; • the outermost region (r > 55 cm), where the particle flux has dropped sufficiently to allow the adoption of larger-pitch silicon microstrips with a maximum cell size of 25 cm × 180 µm. A section of the CMS inner tracker system is shown in Figure 1.5. It has three


11

Figure 1.5: Longitudinal view of the inner tracker system.

cylindrical pixel layers in the barrel region, placed at radii 4.7 cm, 7.3 cm and 10.2 cm respectively, and two closing-discs, extending from 6 cm to 15 cm in radius, and placed on each side at |z| = 34.5 cm and 46.5 cm. This design ensures that each charged particle produced within |η| = 2.2 releases at least two hits in the pixel detector. The pixel layers are enveloped by a silicon microstrip detector. The barrel microstrip detector is divided into two regions: the inner and the outer barrel. The inner barrel is made of four layers (the two innermost of which are double-sided), and cover the depth 20 cm < r < 55 cm. The outer barrel counts six layers (the two innermost double-sided) and reach up to the radius of 110 cm. In order to avoid that particles hit the sensitive area at too small angles, the inner barrel is shorter than the outer one, and three additional disc-shaped layers have been inserted between the inner barrel and the endcaps. The endcap detector is made of nine layers of discs, up to a maximum distance of |z| = 270 cm. The first, second and fifth layers are double-sided. The measurement precision of the pixels is of 10 µm for the x and y coordinates, and of 20 µm for the z coordinate. The microstrips have a resolution depending on cell thickness; however it results better than 55 µm in the transverse plane. The transverse momentum resolution obtained with the CMS inner tracker system is shown in Figure 1.6.

12


Figure 1.6: Resolution of transverse momentum for single muons (with transverse momentum of 1 GeV, 10 GeV and 100 GeV) as a function of pseudorapidity η [2].

1.2.3

Electromagnetic Calorimeter

The electromagnetic calorimeter [2] of CMS (ECAL) is a hermetic homogeneous calorimeter made of lead tungstate (PbWO4 ) crystals. The use of high density crystals has allowed the design of a calorimeter which is fast, has fine granularity, and is radiation resistant. One of the driving criteria in the design was the capability to detect the decay into two photons of the Higgs boson. This capability is enhanced by the good energy resolution provided by a homogeneous crystal calorimeter. The ECAL will be described in detail in the section 1.3.

1.2.4

Hadronic Calorimeter

The hadronic calorimeter (HCAL) [2] is particularly important to contain the hadronic showers, and therefore measures the jet four-momenta and, in combination with the ECAL, the missing transverse energy of events. The features for these tasks are: • a high hermeticity; • a good transverse granularity;


13

• a good energy resolution • a sufficient longitudinal containment of the showers.

Figure 1.7: Longitudinal view of CMS showing the location of the hadron barrel (HB), endcap (HE), outer (HO) and forward (HF) calorimeters. The HCAL is a sampling calorimeter made of copper layers (with a thickness of 5 cm) and plastic scintillators (3.7 cm). The barrel granularity is ∆η × ∆φ = 0.087 × 0.087, which corresponds to a 5 × 5 crystals tower in the ECAL. The Figure 1.7 shows a longitudinal view of CMS. The hadron calorimeter barrel and endcaps sit behind the tracker and the ECAL as seen from the interaction point. The hadron calorimeter barrel is radially restricted between the outer extent of the ECAL (r = 1.77 m) and the inner extent of the magnet coil (r = 2.95 m). This constraints the total amount of material which can be put in to absorb the hadronic shower: it has a thickness of about 7 radiation length (λi ), not sufficient to fully contain a hadron shower. Therefore, an outer hadron calorimeter or tail catcher is placed outside the solenoid complementing the barrel calorimeter with a thickness of 3λi . Beyond

14


|η| = 3, the forward hadron calorimeters placed at 11.2 m from the interaction vertex extend the pseudorapidity coverage down to |η| = 5.2 using a Cherenkovbased, radiation-hard technology.

1.2.5

Muon System

The muon system [2] has three functions: muon identification, momentum measurement, and triggering. Muons are the only particles which are able to pass through calorimeters without being absorbed. Therefore, the muon system is placed in the outermost region of the detector, behind the calorimeters and the solenoid, and cover the pseudorapidity range |η| < 2.4. A longitudinal view of the muon system is shown in Figure 1.8. It is subdivided in a barrel and two endcaps. The two regions are both made of four layers of measuring stations, embedded in the iron of the magnet return yoke. However, they use different technologies.

Figure 1.8: Longitudinal view of the CMS muon system. The system are made of three different kinds of detector: • in the barrel region (|η| < 1.2) there are drift tubes (DTs), each of which is made of 12 planes of tubes, for a total of 195000 tubes;


15

• in the endcaps (1.2 < |η| < 2.4) there are cathode strip chambers (CSCs), organized in six-layer modules. They are multi-wire proportional chambers in which the cathode plane has segmented into strips, and provide measurement of precision in high magnetic fields; • both in the barrel and in the endcaps resistive plate chambers (RPCs) have been placed in order to supply a very fast trigger system. They are organized in six barrel and four endcap stations, each of which is a parallel-plate chamber with an excellent time resolution (3 ns). The muon identification is provided by muon stations, while the measurement of muon momentum is made by combining the information of the track in the muon system with the information of the track in the inner tracking system, which has an excellent resolution.

1.2.6

Trigger

At the present LHC luminosity the event rate is about 109 Hz, so the storage is not possible for all pp collisions. However, not all the events are useful for the CMS physics programme: in fact, the majority of the interactions is soft collisions. Therefore, the aim of the trigger system [2] is to lower the rate of acquired events to manageable levels (∼ 100 Hz), retaining at the same time most of the potentially useful events. The CMS trigger system consists of two consecutive steps: the first is a Level-1 Trigger (L1), and the second is a High-Level Trigger (HLT). The L1 trigger reduces the rate of selected events to 50-100 kHz. It has to decide whether taking or discarding data from a particular bunch crossing in 3.2 µs: if the event is accepted, the data are moved to be processed by the HLT. Being the decision time so short, then L1 can’t read data from the whole detector, but it employs only the calorimetric and muon information, since the tracker algorithm is too slow for this purpose. Therefore, the L1 trigger results organized in a Calorimetric Trigger

16


and a Muon Trigger, whose information are transferred to the Global Trigger which takes the final accept-rejection decision. The HLT trigger is a software system and reduces the output rate to about 100 Hz. It employs various strategies, the guiding principle of which are a regional reconstruction and a fast event veto. Regional reconstruction tries to avoid the complete event reconstruction, which would take time, and focuses on the detector regions close where L1 trigger has found an interesting activity. Fast event veto means that uninteresting events are discarded as soon as possible, therefore freeing the processing power for the next events in line.

1.3

The ECAL

The ECAL [3] is the subdetector dedicated to energy reconstruction of photons and electrons. It plays a fundamental role in the Higgs search, especially in H → γγ channel, and in the search for physics beyond the Standard Model. In this section, the layout, the crystals and the energy resolution of the ECAL are described.

1.3.1

Layout and geometry

A 3-dimensional representation is shown in Figure 1.9(a). There are 36 identical supermodules, 18 in each half barrel, each covering 20◦ in φ. The barrel is closed at each end by an endcap. In front of most of the fiducial region of each endcap is a preshower device. Figure 1.9(b) shows a transverse section through ECAL. The barrel part of the ECAL (EB) covers the pseudorapidity range |η| < 1.479. The barrel granularity is 360-fold in φ and (2 × 85)-fold in η, resulting in a total of 61200 crystals. The truncated-pyramid shaped crystals are mounted in a quasiprojective geometry so that their axes make a small angle (3◦ ) with respect to the vector from the nominal interaction vertex, in both the φ and the η projections. The crystal cross-section corresponds to approximately 0.0174 × 0.0174 in η − φ plane or


17

(a)

(b)

Figure 1.9: Layout of the CMS ECAL: (a) a 3-dimensional view; (b) transverse section, showing geometrical configuration. 2.2 × 2.2 cm2 at the front face of crystal, and 2.6 × 2.6 cm2 at the rear face. The crystal length is 23 cm corresponding to 25.8 X0 . The centers of the front faces of the crystals in the supermodules are at a radius of 129 cm. The crystals are contained in a thin-walled glass-fibre alveola structures (submodules) with 5 pairs of crystals (left and right reflections of a single shape) per supermodule. The η extent of the submodule correspond to a trigger tower. The endcaps (EE) cover the rapidity range 1.479 < |η| < 3.0. The longitudinal

18


distance between interaction point and the endcap envelop is 315.4 cm. The endcap consists of identically shaped crystals grouped in mechanical units of 5 × 5 crystals (supercrystals or SCs) consisting of a carbon-fibre alveola structure. Each endcap is divided into 2 halves or Dees. Each Dee comprises 3662 crystals. These are contained in 138 standard SCs. The crystals and the SCs are arranged in a rectangular x − y grid, with the crystals pointing at a focus 130 cm beyond the interaction point, so that the off-pointing angle varies with η. The crystals have a rear face cross section of about 3 × 3 cm2 , a front face cross section of about 2.86 × 2.86 cm2 and length of 22 cm (24.7 X0 ). The preshower detector (ES) covers the pseudorapidity range 1.653 < |η| < 2.6. Its principal aim is to distinguish photons and π 0 s. In fact, the latter rapidly decay in two photons which are very close at high energy and so hardly separable. The ES also helps the identification of electrons and photons with its superior granularity. It is a sampling calorimeter with two layers: lead radiators initiate electromagnetic showers from incoming photons/electrons, whilst silicon strip sensors placed after each radiator measure the energy deposited and the transverse shower profiles.

1.3.2

Lead tungstate crystals

The characteristics of the PbWO4 crystals (Table 1.1) make them an appropriate choice for operation at LHC. parameter

value

density

8.28 g/cm3

X0

0.89 cm

RM

2.2 cm

Table 1.1: Principal characteristics of PbWO4 . The radiation length X0 is the longitudinal distance within which an electron traversing the material loses on average 1/e of its energy through diffusion processes.


19

The ECAL has to ensure the complete restraint of the electromagnetic shower within energy of TeV. For these energies the 98% of the longitudinal development is contained in 25X0 . The Molière radius RM is a quantity used to describe the transversal development of an electromagnetic shower, and it is defined as: RM =

21.2 MeV · X0 EC [MeV]

(1.6)

where EC represents the critic energy at which the ionization energy loss is equal to Bremsstrahlung energy loss. The 90% of the shower is contained in a cylinder with a radius of RM builded around the shower axis. The choice of PbWO4 has been mainly driven by its short X0 and its small RM which result in a compact calorimeter and a fine granularity necessary to distinguish γ−π 0 and for the angular resolution. Moreover, PbWO4 crystals have excellent hardradiation resistance and a scintillation decay time of the same order of magnitude as the LHC bunch crossing time. This last property allow to collect the 85% of the light in the interval between two successive pp intercations.

1.3.3

Photodetectors

The photodetectors need to be fast, radiation tolerant and be able to operate in the longitudinal 4-T magnetic field. In addition, because of the small light yield of the crystals, they should amplify and be insensitive to particles traversing them (nuclear counter effect). The configuration of the magnetic field and the expected level of radiation led to different choices: avalanche photodiodes (APDs) in the barrel, and vacuum phototriodes (VPTs) in the endcaps. The lower quantum efficiency and internal gain of the VPTs, compared to the APDs, are offset by their larger surface coverage on the back face of the crystals.

20


1.3.4

Energy resolution

The energy resolution of a homogeneous calorimeter can be expressed as a sum in quadrature of three different terms: S N σ(E) =√ ⊕ ⊕C E E E

(1.7)

where E is the energy expressed in GeV, and S, N and C represent the stochastic, the noise and the constant terms, respectively. Different effects contribute to these terms: • the stochastic term S is a direct consequence of the Poissonian statistics associated with the development of the electromagnetic shower in the calorimeter and the successive recollection of the scintillation light. This term represents the intrinsic resolution of an ideal calorimeter with infinite size and no response deterioration due to instrumental effects. The original energy E0 of a particle detected by a calorimeter is linearly related to the total track length Ltrack , 0 defined as the sum of all the ionization tracks produced by all the charged paris proportional to the number ticles in the electromagnetic shower. Since Ltrack 0 of track segments in the shower and the shower development is a stochastic process, the intrinsic resolution from purely statistical arguments is given by: p σ(E) Ltrack 1 0 ∝ ∝√ track E L0 E0

(1.8)

For a real calorimeter, this term also absorbs the effects related to the shower containment and the statistical fluctuations in the scintillation light recollection; • the noise term N accounts for all the effects that can alter the measurements of the energy deposit independently of the energy itself. It includes the electronic noise and the physical noise due to energy released by particles coming


21

from multiple collision events. Electronic noise is mainly caused by the photodetectors, that contribute basically via two components: one is proportional to its capacitance, the other is connected to the fluctuations of the leakage current; • the constant term C dominates at high energy. Many different effects contribute to this term: the stability of the operating conditions such as the temperature and the high voltage of the photodetectors, the electromagnetic shower containment and the presence of the dead material, the light collection uniformity along the crystal axis, the radiation damage of PbWO4 crystals, the intercalibration between the different channels.

Figure 1.10: ECAL energy resolution σ(E) as a function of electron energy as meaE sured from a test beam. The energy was measured in an array of 3 × 3 crystals with an electron impacting the central crystal. The points correspond to events taken restricting the incident beam of 120 GeV electrons to a narrow (4 × 4 mm2 ) region. The stochastic S, noise N and constant C terms are given [2]. The design goal for the CMS ECAL are about 2.8% for S, 0.12 GeV when adding the signal of 3 × 3 crystals for N and 0.3% for C (Figure 1.10). Measurements conducted on the ECAL barrel with electron test beam at CERN show that ECAL perform consistently with the design goals of the experiment. This result was obtained in the absence of magnetic field, with almost no inert material in front of the

22


calorimeter and with the beam aligned on the centers of crystals. The result is in good agreement with the design-goal performance expected for a perfectly calibrated detector. The first 7 TeV LHC collisions recorded with the CMS detector have been used to perform a channel-by-channel calibration of the ECAL [4]. Decays of π 0 and η into two photons as well as the azimuthal symmetry of the average energy deposition at a given pseudorapidity are utilized to equalize the response of the individual channels in barrel and endcaps. Based on an integrated luminosity of up to 250 nb−1 , a channel-by-channel in-situ calibration precision of 0.6% has been achieved in the barrel ECAL in the pseudorapidity region |η| < 0.8. The energy scale of the ECAL has been investigated and found to agree with the simulation to within 1% in the barrel and 3% in the endcaps.

1.3.5

Photon reconstruction

Photon showers deposit their energy in several crystals in the ECAL. Approximately 94% of the incident energy of a single unconverted photon is contained in 3 × 3 crystals, and 97% in 5 × 5 crystals. Summing the energy measured in such fixed arrays gives the best performance for unconverted photons. The presence in CMS of material in front of the calorimeter results in photon conversions. Unconverted and converted photons are distinguished from each other by means of the variable R9 =

E9 , Eγ

where E9 is the energy collected by a 3 × 3 crystals array, and Eγ is

the photon energy. In fact, unconverted photons or photons converted very close to the ECAL have values of R9 towards unity, whereas lower values of R9 describe an increase of the energy spread. Because of the strong magnetic field the energy reaching the calorimeter is spread in φ. The spread energy is clustered by building a cluster of clusters, a so-called supercluster, which is extended in φ. The supercluster position (i.e. the impact point of the photon) is obtained by calculating the energyweighted mean position of the crystals in the cluster.


23

The triggering photons selected by the HLT provide the starting point for offline reconstruction and selection of prompt photons. These selected photons already have transverse energy above the HLT selection thresholds and have passed the isolation criteria of the L1 and HLT selection (for details about photon trigger, see section 10.2 of [3]). Fake photons are due to electromagnetic component of a jet, mainly due to neutral pions. To reject such a background, isolation criteria are applied, both at trigger and analysis level. They are based on the presence of additional particles in a cone around the reconstructed ECAL cluster. Charged pions and kaons can be detected with the tracker or in the HCAL. Neutral pions and other particles decaying into photons can be detected in the ECAL. The size of the veto cones is optimized to take into account the energy spread in the calorimeter due to showering and magnetic field. The basic isolation variables considered are based on charged tracks reconstructed in the tracker, electromagnetic deposits observed in the ECAL, and hadronic energy deposits in the HCAL. These variables are combined to have a global isolation information. • Tracker Isolation: scalar sum of the transverse momentum pT of all tracks within a cone of radius ∆R = 0.35 from the photon direction, normalized to the photon transverse momentum. ∆R is defined as: ∆R =

p

(ηSC − η)2 + (φSC − φ)2

(1.9)

where ηSC and φSC are the coordinates of the supercluster position on the ECAL surface: they have been defined as a weighted average of the crystals coordinates, where each weight depends on crystal energy. Figure 1.11 shows a sketch of a photon in the CMS detector. • ECAL isolation: sum of the ECAL reconstructed energy not belonging to the photon cluster within a ∆R = 0.4 cone around the photon candidate and

24

The CMS experiment at the LHC normalized to the photon energy. • HCAL isolation: sum of the HCAL reconstructed energy within a ∆R = 0.4 cone behind the photon candidate and normalized to the photon energy.

Figure 1.11: Photon signal in CMS: it is an isolated energy deposit in the ECAL. A cone of radius ∆R is builded around the photon direction in order to define the isolation criteria. In addition, the relative HCAL and ECAL isolation cuts are limited by absolute thresholds in order to prevent energy cuts which are tighter than the noise level of the calorimeters. In fact, cutting tighter than the average noise level does not bring significant improvement in the signal over background ratio, but rapidly decreases signal efficiency. The isolation criteria are very efficient in rejection of jets and electrons: the former release energy in the HCAL and so they don’t satisfy the HCAL isolation; whereas the latter have tracks in the central detector associated to the ECAL deposits, and so they don’t satisfy the Tracker isolation. Furthermore, the π 0 represents an important source of background. In fact, when a π 0 decays into two photons, they reach the ECAL surface in two points which are too close to each other: they are detected as a single energy deposit and then the π 0 is misinterpreted


25

as a photon of the same energy. In order to distinguish between photons and neutral pions, the isolation criteria are not sufficient: the γ − π 0 discrimination algorithm exploits the differences on the shape of γ and π 0 deposits, which can be described by the so-called cluster shape variables, defined later. A photon candidate has to satisfy a set of requirements (photonID) summarized in Table 1.2. In addition to the tracker, ECAL and HCAL isolation, there are specific requirements: • SM inor represents the minor axis of the ellipse for the ECAL cluster, and it is used to identify energy deposits compatible with an electromagnetic shower induced by an isolated photon. It is defined from the covariance matrix of the geometric shape of an electromagnetic deposit in the ECAL: 



σηη σηφ    COV (η, φ) =     σφη σφφ

(1.10)

with

σµν =

Nx X

wi (µi − µ ¯) · (νi − ν¯)

(1.11)

i=1

where Nx is the number of crystals in the deposit, µi and νi are the η and φ coordinates of the ith crystal, and (¯ µ, ν¯) is the average position obtained by means of the weights wi defined as:

Extal,i wi = max K + log ;0 Eγ

(1.12)

with Extal,i the energy of the ith crystal. The covariance matrix can be diago-

26

The CMS experiment at the LHC nalized in order to obtain the major axis SM ajor and the minor axis SM inor of the elliptic energy deposit: 



SM ajor 0    COV (η, φ) =     0 SM inor

(1.13)

where

SM ajor

q 1 2 2 (σφφ + σηη ) + (σφφ − σηη ) + 4σηφ = 2 (1.14)

SM inor

q 1 2 = (σφφ + σηη ) − (σφφ − σηη )2 + 4σηφ 2

The variables SM ajor and SM inor , together with the variable R9 defined before, are the cluster shape variables. • the spike veto is needed to reject the so-called spikes, which are very energetic hadrons hitting directly the APDs. This requirement is defined in terms of the energy of crystals arrays: – E1 is the energy of the most energetic crystal (the so-called first crystal ); – E2 is the energy of the array made of first crystal and the second most energetic crystal near the first one; – E4 and E6 are 2 × 2 and 2 × 3 crystals arrays, respectively, around the first crystal. Note that the selection used in this analysis is almost identical to the one described in [14], except for the removal of the timing cut to reject ECAL spikes.


27

criteria

requirements

SM inor

0.15 < SM inor < 0.3

Spike Veto

E6 > 0.04 and E4 > 0.04 log E1 − 0.024 E2 E1 P P HCAL < 0.05 or HCAL < 2.4 GeV Eγ P P ECAL < 0.05 or ECAL < 2.4 GeV Eγ P pT < 0.1 pT γ

HCAL Iso ECAL Iso TRK Iso

Table 1.2: Photon identification criteria.

Chapter 2 Time reconstruction in the ECAL The combination of the scintillation timescale of the PbWO4 , the electronic pulse shaping and the sampling rate allow for an excellent time resolution to be obtained with the ECAL. This is important in CMS in many respects. The better the precision of time measurement and synchronization, the larger the rejection of backgrounds with a broad time distribution. Such backgrounds are cosmic rays, beam halo muons, electronic noise, and out-of-time proton-proton interactions. Precise time measurement also makes it possible to identify particles predicted by different models beyond the Standard Model. Slow heavy charged R-hadrons, which travel through the calorimeter and interact before decaying, and photons from the decay of long-lived new particles reach the calorimeter out-of-time with respect to particles traveling at the speed of light from the interaction point. As an example, to identify neutralinos decaying into photons with decay lengths comparable to the ECAL radial size, a time measurement resolution better than 1 ns is necessary. To achieve these goals the time measurement performance both at low energy (1 GeV or less) and high energy (several tens of GeV for showering photons) becomes relevant. In addition, amplitude reconstruction of ECAL energy deposits benefits greatly if all ECAL channels are synchronized within 1 ns. Previous experiments have shown that it is possible to measure time with electromagnetic calorimeters with a resolution better than 1 ns [5].

30

Time reconstruction in the ECAL In this chapter a description of the time extraction with a single crystal (section

2.1) and a study of the time reconstruction for high transverse momentum photons (section 2.2) will be given.

2.1

Time reconstruction study with data from the test beam

2.1.1

Time extraction with ECAL crystals

When a photon hits a PbWO4 crystal, it releases an energy deposit (called rechit). The resulting scintillation light is collected by the photodetectors (APDs and VPTs), and their signal is amplified and shaped by the front-end electronics. The pulse is then digitized at 40 MHz by an analog-to-digital converter (ADC), and finally the energy measured in GeV is obtained from the ADC count. In Figure 2.1(a) the time structure of the signal pulse measured after amplification (solid line) is shown: the pulse amplitude A is plotted as a function of the time difference T − Tmax , where T is the time of a generic ADC sample, and Tmax is the time corresponding to the amplitude maximum Amax . The pulse amplitude A is calculated from a linear combination of discrete time samples:

A=

NS X

wi · Si

(2.1)

i=1

where NS is the total number of samples, Si the time sample values in ADC counts, and wi are the weights, which have been calculated in an electron test beam before collisions. The ECAL time reconstruction is defined as the measurement of Tmax using the ten available samples of pulse amplitude. The algorithm which measures Tmax uses an alternative representation of the pulse shape: Figure 2.1(b) shows the difference T − Tmax as a function of the ratio R(T ) between the amplitudes of two consecutive

Time reconstruction in the ECAL

31

digitizations, defined as: R(T ) =

A(T ) A(T + 25 ns)

(2.2)

This signal representation is independent of Amax and is described by a simple polynomial parameterization.

(a)

(b)

Figure 2.1: (a) Typical pulse shape measured in the ECAL as a function of the difference T − Tmax . The dots indicate ten discrete samples of the pulse, from a single event, with pedestal subtracted and normalized to Amax . The solid line is the average pulse shape. (b) T − Tmax as a function of R(T ) [5]. Each pair of consecutive samples gives a measurement of the ratio Ri = Ai /Ai+1 , from which an estimate of Tmax,i = Ti − T (Ri ) can be extracted with its relative uncertainty σi , where Ti is the time when the sample i is taken, and T (Ri ) is the time corresponding to the amplitude Ri as given by the parametrization in Figure 2.1(b). The time of the pulse maximum Tmax and its error are then evaluated from the weighted average of the estimated Tmax,i : X Tmax,i Tmax =

σi2 X 1 σi2 i

i

,

1 σT2max

=

X 1 σi2 i

(2.3)

32


2.1.2

Time measurement resolution

The time resolution can be expressed as the sum in quadrature of three terms:

2

σ (t) =

N σn A

2

+

S √ A

2

+ C2

(2.4)

where A is the measured amplitude, σn is related to the electronics noise, and N , S and C represent the noise, stochastic, and constant term, respectively. Monte Carlo simulation studies give N = 33 ns, when the electronic noise σn is ∼ 0.042 GeV in the barrel and ∼ 0.14 GeV in the endcaps. The stochastic term comes from fluctuations in photon collection times, associated with the finite time of scintillation emission. It is estimated to be negligible. The constant term takes into account effects due to the point of shower initiation within the crystal, and systematic effects in the time extraction, such as those due to small differences in pulse shape for different channels. The first determination of the time resolution has been obtained with test beam data, prior to collisions. The methods used the distribution of the time difference between adjacent crystals that share energy from the same electromagnetic shower. This approach is less sensitive to the term C, since effects due to synchronization do not affect the spread but only the average of the time difference. Then the spread in time difference between adjacent crystals is parameterized as: 2

σ (t1 − t2 ) =

N Aeff /σn

2

+ 2C¯ 2

(2.5)

p where Aeff = E1 E2 / E12 + E22 with t1,2 and E1,2 corresponding to the times and energies measured in the two crystals, and C¯ is the residual contribution from the constant terms. The extracted width is shown in Figure 2.2 as a function of the variable Aeff /σn . The fitted noise term corresponds to N = (35.1 ± 0.2) ns, and C¯ is very small: C¯ = (0.020 ± 0.004) ns. Note that the constant term C¯ takes into account of the error due to the so-called intercalibration between crystals, σintercalib .


33

Figure 2.2: Spread of the time difference between two neighboring crystals as a function of the variable Aeff /σn for the electron test beam. The equivalent singlecrystal energy scales for barrel (EB) and endcaps (EE) are overlaid in the plot [5].

As shown, for large values of Aeff /σn , which correspond to an energy greater than 10 GeV in the EB, σ(t) is less than 100 ps, demonstrating that, with a carefully calibrated detector, it is possible to reach a time resolution better than 100 ps for large energy deposits (E > 10 − 20 GeV in the EB). The time resolution is also determined with a sample of cosmic ray muons collected during summer 2008, when the ECAL was already inserted into its final position in CMS. The approach to extract the resolution is similar to that made at the test beam, but in this case the crystal with the maximum amplitude is compared with the other crystals in the cluster. Since different pairs of crystals are used, a constant term comparable with the systematic uncertainty of the synchronization (section 4 of [5]) is expected. The spread of the time difference between crystals of the same cluster as a function of Aeff /σn is shown in Figure 2.3. The noise term is found to be N = (31.5 ± 0.7) ns and is very similar to that obtained from test beam data. The constant term is C¯ = (0.38 ± 0.10) ns, which is consistent with the expected systematic uncertainty from synchronization.

34


Figure 2.3: Gaussian width of the time difference between two crystals of the same cluster as a function of the variable Aeff /σn for cosmic ray muons [5].

2.2

Time reconstruction study with collision data

The performance obtained prior to LHC collisions needed to be confirmed after the detector was installed and fully configured. With proton-proton collisions there are additional effects which were not present at the test beam and with cosmics events. They are determined by the fact that a collision consists of the crossing of two packages of protons, the bunches, with a finite size. The effects to be considered are then given by: • time of interaction (Figure 2.4). Given that the bunches are about 7 cm long, they cross each other in a finite amount of time, which corresponds to about 200 ps. The interaction between two protons can happen within this time interval. • interaction point position (Figure 2.5). The primary vertex could be in a point different from z = 0 and the time of flight of the particle considered depends on the interaction point position. It is important to note that the time is reconstructed subtracting an η-dependent offset so that crystals at different pseudorapidities result synchronous. This means


35

Figure 2.4: A sketch of the bunch crossing. The bunches are about 7 cm long and they cross each other in a finite amount of time, which corresponds to about 200 ps. The interaction between two protons can happen within this time interval. that for all particles which are coming from the geometrical centre of CMS, i.e. (vx, vy, vz) = (0, 0, 0), the time measured in ECAL is independent of η within uncertainties.

2.2.1

Event samples and selection criteria

In order to study the time resolution at the collisions, high transverse momentum photon samples are used. Since this thesis has started from the search for physics beyond the Standard Model using displaced photons with the Gauge Mediated Symmetry Breaking model [14] (chapter 5), data and Monte Carlo samples are the same of that analysis. The data here used are the proton-proton collision data at a center-of-massenergy of 7 TeV recorded by the CMS detector at the LHC, corresponding to an integrated luminosity of 2.4 ± 0.1 fb−1 . The data were recorded using the CMS two-level trigger system. Data sample consists of events selected by at least one of

36


Figure 2.5: Two different cases of the interaction point position. As shown in this sketch, two photons, which hit the same point on the ECAL surface but coming from different primary vertices (the first from z = 0 and the second from z 6= 0), have different times of flight. the triggers dedicated to photons, such as: • single photon with different pT thresholds (e.g. 25 GeV/c, 40 GeV/c, 70 GeV/c, 90 GeV/c); • photon and missing transverse energy above a minimum threshold (e.g. 70 GeV/c, 90 GeV/c); • photon and a minimum number of jets with pT over a given thresholds (e.g. 3


37

jets with pT > 25 GeV/c); • double photons with a pT threshold at 20 GeV/c on single photon and a minimum value of the invariant mass (e.g. 60 GeV/c, 80 GeV/c). Note that the different pT thresholds are motivated by the fact that during the data taking the triggers with the lower thresholds are prescaled1 due to the increasing luminosity. Moreover, in the trigger selection, isolation criteria, less restrictive than those required in the offline selection, are applied to photons. There is a non-negligible probability that several collisions may occur in a single bunch crossing due to the high instantaneous luminosities at the LHC. The average number of multiple interaction vertices (pileup) for this data sample is about 8 in each bunch crossing. The Monte Carlo samples are simulated with pythia 6.4.22 [6] or MadGraph 5 [7] with the CTEQ6L1 [8] parton distribution functions (PDFs). The response of the CMS detector is simulated using the Geant4 package [9]. The SUSY GMSB signal production follows the SPS8 [22] proposal, where the free parameters are the SUSY breaking scale Λ and the average proper decay length cτ of the neutralino. The χ˜01 mass explored is in the range of 140 to 260 GeV (corresponding to Λ values from 100 to 180 TeV), with proper decay length cτ = 1 mm, i.e. the point to the primary vertex. More details will be provided in chapter 5. Events satisfying trigger requirements have to pass additional selection criteria based on vertexing: events with a good vertex are selected, i.e. there is a primary vertex with at least 4 associated tracks (vndof ≥ 4), whose position is less than 2 p cm from the centre of CMS in the direction transverse to the beam ( vx2 + vy 2 < 2 cm) and 24 cm in the direction along the beam (|vz| < 24 cm), where vx, vy and vz indicate the x, y and z coordinates of the primary vertex, respectively. Then, 1

If the rate of a given trigger is too high, due to the luminosity increase, a prescale factor is fixed (e.g. 10: this means that for every 10 events, only one is stored).

38


the most energetic photon, satisfying the isolation criteria listed in Table 1.2, have to pass the criteria pT γ ≥ 20 GeV/c and ηγ ≤ 2.52 . criteria good vertex

requirements vndof ≥ 4 ,

p

vx2 + vy 2 < 2 cm , |vz| < 24 cm

|ηγ |

≤ 2.5

pT γ

≥ 20 GeV/c

Table 2.1: One photon events selection criteria.

2.2.2

Reconstruction of time of impact for photons

The time resolution of single crystal, σxtal,i , is studied. Note that σxtal,i , as detailed in section 2.1.2, is the squared sum of two terms: the noise term, which is inversely proportional to the energy of the crystal Extal,i , and the constant term, which takes into account of the intercalibration error σintercal : 2 σxtal,i

=

σn N Extal,i

2

2 + σintercal

(2.6)

From the electron test beam [5] the coefficients N and σn correspond to N = 35.1 ns and σn = 0.042 GeV in the EB and σn = 0.14 GeV in the EE. The validity of this parametrization has been verified using the spread of the time distribution of the selected photons as a function of the energy of the crystal. A 2-dimensional histogram of the time of the single crystal, Txatl,i , versus its energy Extal,i is plotted separately for EB and EE. The time spread is extracted in bins of Extal,i via a Gaussian fit as shown in Figures 2.6 and 2.7 (black markers). The resulting fitted values are then compared with the expected values [5] (red markers). As shown, there is a disagreement. For Monte Carlo, a full compatibility was not expected, 2

Note that the gaps between barrel and endcaps (i.e. the ranges −1.566 ≤ η ≤ −1.4442 and 1.4442 ≤ η ≤ 1.566) are excluded from the analysis, because some cluster energy can be lost in non-sensitive parts of the detector.


39

while on data the difference is due to hardware configuration compared to test beam, which results in a different detector noise. The noise term which best represents the data is reported in Table 2.2.

σn [GeV] (EB)

σn [GeV] (EE)

data

0.0378

0.175

Monte Carlo

0.0377

0.14

Table 2.2: The best coefficients σn for data and Monte Carlo in the EB and the EE.

The constant term, σintercal , can’t be extracted with this approach since it is not possible to decouple the effects due to the finite width of the beam spot and the time of interaction. They have been obtained from previous studies, and are listed in Table 2.3. The data values are compatible with those obtained prior to collisions [5]. For simulation, we also observe that the constant term is different from zero. This was not expected since no intercalibration uncertainty is simulated and it is still under study.

σintercal [ns] (EB)

σintercal [ns] (EE)

data

0.24

0.035

Monte Carlo

0.137

0.063

Table 2.3: The intercalibration errors σintercal for data and Monte Carlo in the EB and the EE.

At the first approximation, the time of the impact of a photon on the ECAL surface can be represented by the time measured in the most energetic crystal Tseed (since this crystal is also know as the seed of the clustering algorithm). A better measurement of the photon time is represented by the time averaged over the crystals of the supercluster, Tsig (i.e. the signal time). Each crystal is

40


(a)

(b)

Figure 2.6: The crystal time spread σxtal,i observed (black markers) and expected (red markers) as a function of Extal,i for data (a) and Monte Carlo (b) in the EB.

(a)

(b)

Figure 2.7: The crystal time spread σxtal,i observed (black markers) and expected (red markers) as a function of Extal,i for data (a) and Monte Carlo (b) in the EE.

weighted with the expected error following the formula: X Txtal,i Tsig

2 σxtal,i =X 1 2 σxtal,i i i

(2.7)

Only crystals which satisfy the requirement Extal,i > 1 GeV and −2.0 ns ≤ Txtal,i ≤


41

2.0 ns contribute to Tsig . Since Tsig uses the information of several crystals which are expected synchronous, it should have a better resolution compared to Tseed . This is confirmed by the direct comparison between the time distributions of Tsig and Tseed (Figure 2.8).

(a)

(b)

Figure 2.8: Tseed (black line) and Tsig (red line) distributions for data (a) and Monte Carlo (b). The corresponding RMS, indicated as σTseed and σTsig , is also reported. The measured time Tsig is studied as a function of the photon pseudorapidity ηγ and azimuthal angle φγ to check for biases and miscalibrations. To reduce possible effects due to shifts in the beam spot position along the z axis, the primary vertex reconstructed with tracks must satisfy the constraint |vztrk | < 0.5 cm. In Figure 2.9 the Tsig as a function of ηγ is plotted. For data it shows an average shift of about −0.5 ns and a clear η-dependence, while for Monte Carlo there is no significant deviation from zero. Based on the results shown in these plots, a correction (etaCorr) has been extracted. In the following the measured time will be then: etaCorr Tsig = Tsig − etaCorr

(2.8)

The same study performed as a function of the azimuthal angle is reported in Figure 2.10. It shows a clear miscalibration, maybe following the segmentation of the ECAL supermodules. For the time being, no correction is applied to recover for

42


this effect.

(a)

(b)

Figure 2.9: Tsig as a function of ηγ for data (a) and Monte Carlo (b). The etaCorr correction factor corresponds to the Tsig mean value extracted in bins of ηγ (gray line).

(a)

(b)

Figure 2.10: Tsig as a function of φγ for data (a) and Monte Carlo (b). The gray line corresponds to the Tsig mean value extracted in bins of φγ (gray line).

Chapter 3 Study of time development of electromagnetic showers Photon showers usually involve more than 20 ECAL crystals. For large photon energies (> 20 GeV) the time can be measured with a better than 1 ns resolution in many crystals. It is then possible to exploit this information to perform studies of the time propagation of the shower. Given that the size of crystals is about 20 cm × 3 cm × 3 cm, delays of a fraction of ns are expected in peripheral crystals. The goal of this study is to quantify this dependence. In addition, the idea is to exploit this time dependence to develop a discriminant for photon identification purposes. In this chapter the electromagnetic showers propagation dependence on the η and φ coordinates is studied (section 3.1), and it is used to build a new variable for photon identification purposes (section 3.2).

44

Study of time development of electromagnetic showers

3.1

Electromagnetic showers propagation in the ECAL

The study is first performed on simulation. This is because we want to start from a pure sample of photons identified using Monte Carlo truth information. Events with at least one photon with pT > 30 GeV/c and |η| < 1.4 (barrel) are selected. Since Monte Carlo truth matching is used, the isolation criteria in order to select photons are not necessary. We also build a sample of fake photons originated from misidentified jets. The definitions of the two samples are the following: • good photon − the reconstructed photon is compared with each generp ated photon, computing the variable ∆R(γreco , γgen ) = ∆η 2 + ∆φ2 for each γ γ γ γ ), φγreco (ηgen , ∆φ = φγreco − φγgen , and ηreco − ηgen (γreco , γgen ) pair. ∆η = ηreco

(φγgen ) are the pseudorapidity and the φ coordinate of the reconstructed (generated) photon, respectively. The reconstructed candidate with the minimum ∆R(γreco , γgen ) is chosen. If ∆R(γreco , γgen ) < 0.1 the photon is selected as a good photon. A further requirement on ∆R(γreco , jetgen ) > 0.3 is applied in order to minimize the combinatorial background from jets. • fake photon − the reconstructed photon is matched with a generated jet (∆R(γreco , jetgen ) < 0.1) and does not overlap with a generated photon (∆R(γreco , γgen ) > 0.3). In addition, the reconstructed photon must fail the HCAL isolation defined in section 1.3.5. When a photon hits the ECAL, it creates an electromagnetic shower. The resulting supercluster consists of a cluster of crystals and in each crystal the time is measured. We expect that the larger the distance of the crystal from the photon impact point, the larger the time difference compared to the crystal seed. In other words, the difference ∆Ti = Txtal,i − Tseed increases as the differences ηxtal,i − ηSC and φxtal,i − φSC increase.


45

∆Ti is studied as a function of two variables defined as: ∆ηi =

ηxtal,i − ηSC 0.0174

,

∆φi =

φxtal,i − φSC 0.0174

(3.1)

where 0.0174 × 0.0174 correspond to the dimensions of the crystal front face in the η − φ plane. Then, ∆ηi and ∆φi result to be the distance of the crystal from the impact point position in terms of number of crystals. The study is performed in strips of η and φ in order to disentangle the effects along the η and φ coordinates. Then, the requirement that φxtal,i = φSC is applied when studying the dependence in ∆ηi and the requirement that ηxtal,i = ηSC is applied when studying the dependence in ∆φi . The study is done for the barrel and also repeated in different bins of pseudorapidity. The results are shown in Figures 3.1, which demonstrate the time development of the shower. The points are fitted with a quadratic polynomial and the fit results are reported on the plots. The dependence in ∆ηi is very similar in all η bins. The different minimum position is probably due to the different staggering of ECAL crystal, which is η dependent and flips between positive and negative η’s. The dependence in ∆φi is less evident, because of the large fraction of converted photons in the sample and the effect of the magnetic field which bends the shower constituents only along φ.

46


Figure 3.1: ∆Ti = Txtal,i −Tseed mean value as a function of ∆ηi (left) and ∆φi (right) for Monte Carlo in the pseudorapidity ranges, from top to bottom, −1.4442 ≤ η ≤ −0.7, −0.7 ≤ η ≤ 0, 0 ≤ η ≤ 0.7 and 0.7 ≤ η ≤ 1.4442, respectively.

We repeated the same study on data. To select a pure sample of photon the isolation criteria defined in section 1.3.5 are applied. In addition, tighter criteria on cluster shape are used:


47

• SM inor < 0.3 • SM ajor < 0.4 • R9 > 0.94 As shown in Figure 3.2, data and Monte Carlo show a similar dependence along both η and φ. Residual differences are maybe due to the fact that the data sample is contaminated by fake photons from jets (80-90% purities are expected), which dilute the effect.

(a)

(b)

Figure 3.2: ∆Ti = Txtal,i − Tseed mean value as a function of (a) ∆ηi and (b) ∆φi for Monte Carlo (red markers) and data (blue markers) in the pseudorapidity bin 0 ≤ η ≤ 0.7. The proper dependence of time as a function of ∆ηi and ∆φi can be used to better determine the time of the photon, which is represented by the minimum of the parabola shown in Figure 3.1. A 2-dimensional fit has been set for this purpose. The ∆Ti delay in 2D has been modeled by assuming as uncorrelated the delays versus η and φ, fitted in bins of pseudorapidity as in Figure 3.1. The ∆ηi and ∆φi variables have been rescaled in order to make the 2D dependence as a pure rotational unit paraboloid by means of a change of variables: ∆ηi0 =

∆ηi − Aη Bη

,

∆φ0i =

∆φi − Aφ Bφ

(3.2)

48


The fitted parabolas in Figure 3.1 correspond to:

Txtal,i = aη + bη ∆ηi + cη (∆ηi )2 for ∆φi = 0 (3.3) 2

Txtal,i = aφ + bφ ∆φi + cφ (∆φi ) for ∆ηi = 0 where the coefficients aη , bη and cη (aφ , bφ and cφ ) are obtained by the fit. After the translation in equation 3.2, they become:

Txtal,i = (∆ηi0 )2 for ∆φ0i = 0 Txtal,i =

(∆φ0i )2

for

∆ηi0

(3.4)

=0

The final 2D parametrization is then: Txtal,i = (∆ηi0 )2 + (∆φ0i )2 + Tf it

(3.5)

where Tf it corresponds to the time of the photon. We use this parametrization to perform a fit based on a χ2 minimization where the only free parameter is Tf it (Figure 3.3). The χ2time is defined as: χ2time

=

exp 2 X (Txtal,i − Txtal,i ) i

2 σxtal,i

(3.6)

where i indicates the crystal of the supercluster, Txtal,i is the measured time in that exp crystal, Txtal,i is the expected time as in equation 3.5 and σxtal,i is the expected time

uncertainty as in equation 2.6. This minimization is run for each photon, thus obtaining the time of the photon Tf it and the value of the χ2time for the minimum. The probability of the χ2time is reported in Figure 3.4(a) and shows a reasonable behavior. The peak at zero is maybe due to either fake photons or converted photons, where the time dependence is jeopardized by the presence of a e+ e− pair, which distort the ∆Ti along the


49

Figure 3.3: A map of the crystals in the supercluster in an event. The height of the columns is the time measured by the crystals Txtal,i . The red line is the fit function given by equation 3.5. φ direction. The resulting Tf it distribution is then compared with Tsig in Figure 3.4(b). As shown, there is some improvement in resolution by using this alternative approach.

(a)

(b)

Figure 3.4: (a) The P (χ2time ) distribution. (b) The comparison between the distribution of Tf it (red line), Tseed (blue line) and Tsig (green line).

50


3.2

A new variable for discrimination between signal and background

The time development is not the same between real and fake photons. When the electromagnetic shower is produced by a misidentified jet, it is due either to a hadronic shower or to multiple hits due to hadrons at minimum of ionization or to neutral pions. Each of these contributions give crystal energy deposits which are more synchronous compared to the case of a single electromagnetic particle hitting the calorimeter (see the sketch in Figure 3.5).

(a)

(b)

Figure 3.5: A sketch of the shower propagation in the ECAL for (a) signal and (b) background. This is confirmed by the comparison of the ∆Ti versus ∆ηi and ∆φi for good and fake photons, as shown in Figure 3.6. Based on this observation, the time measured in the crystals of a supercluster offers some separation power to reject fake photons. We use the best χ2time described in equation 3.6 as discriminating variable. Note that, as mentioned before, the signal is given by the good photons, which are photons matched to a generated photon within ∆R < 0.1, and the background


(a)

51

(b)

Figure 3.6: ∆Ti mean value as a function of (a) ∆ηi and (b) ∆φi for Monte Carlo in the pseudorapidity range 0 ≤ η ≤ 0.7. The mean values are extracted in bins of ∆ηi [∆φi ] from the 2-dimensional histogram of ∆Ti versus ∆ηi [∆φi ] for signal (red markers) and background (blue markers). consists of fake photons, which are photons matched to a generated jet within ∆R < 0.1 and fail the HCAL isolation. In Figure 3.7 the χ2time distributions normalized to the degrees of freedom are plotted for good photon sample (red line) and fake photon sample (blue line).

Figure 3.7: The χ2time distributions normalized to the degrees of freedom for good photon sample (red line) and fake photon sample (blue line). Figure 3.8 shows the plot of the background rejection as a function of the signal efficiency. Each point of the curve is obtained for a given cut on the variable χ2time :

52


for example, with a cut of χ2time < 1.3, when the signal efficiency is about 0.69, the background rejection is about 0.72.

Figure 3.8: The ROC curve. Note that, with a χ2time < 1.3 cut, when the signal efficiency is about 0.69, the background rejection is about 0.72. The discriminating power of this new variable has been also checked when the full photon selection is applied. This is because the isolation criteria enrich the fake photon sample of isolated neutral pions, whose shower properties are very similar to photons. Figure 3.9 shows the χ2time distribution and the ROC curve when the requirements SM inor < 0.3 and SM ajor < 0.4 are applied to both the signal sample and the background sample. These plots show that a correlation between χ2time and the cluster shape variables may exist. In fact, when only χ2time is used, when the signal efficiency is about 0.75, the background rejection is about 0.67, whereas with the additional requirement on the cluster shape variables the background rejection decrease to about 0.5. In summary, this new variable may help in the photon identification, even though it looks correlated with the shape of the electromagnetic cluster.


(a)

53

(b)

Figure 3.9: (a) The χ2time distributions normalized to the degrees of freedom for good photon sample (red line) and fake photon sample (blue line) when cut on cluster shape variables SM inor and SM ajor are applied. (b) The ROC curve. Note that, when the signal efficiency is about 0.75, the background rejection is about 0.5.

Chapter 4 Vertex reconstruction using ECAL timing information The identification of vertices plays an important role in the event reconstruction. Precise coordinates of the primary event vertices are needed to assign tracks to collisions and to determine the event kinematics. Furthermore, the determination of secondary vertices is used to determine the presence of particles decaying in flight, not only Standard Model particles like taus or B hadrons, but also possible new states [10]. In this work a novel and alternative method is developed to determine the position of the vertex. The time of arrival measured with the ECAL is used. This method is completely decoupled from the tracking. It may offer an important alternative handle in events where there is a small track activity, like H → γγ, and to reject noise from pileup. In this chapter the vertex reconstruction exploiting the timing information from the ECAL is described. First, the vertex reconstruction algorithm using tracks is presented (section 4.1). Then, the novel method is discussed (section 4.2). Finally, an application of this method to the case of Z → ee events is shown (subsection 4.2.1).

56

Vertex reconstruction using ECAL timing information

4.1

Vertex reconstruction with the tracker

Vertex reconstruction made by the tracker [3] [11] usually involves two steps, vertex finding and vertex fitting. Vertex finding is the task of identifying vertices within a given set of tracks, such as the track of a jet in case of flavor tagging or the full event in case of primary vertex finding. So the vertex-finding algorithms can be very different depending on the physics case. Vertex fitting on the other hand is the determination of the vertex position assuming it is formed by a given set of tracks. The goodness of fit may be used to accept or discard a vertex hypothesis. In addition, the vertex fit is often used to improve the measurement of track parameters at the vertex. Track selection, which aims to select tracks produced promptly in the primary interaction region, imposes requirements on the maximum allowed transverse impact parameter significance with respect to the beamspot, its number of strip and pixel hits, and its normalized χ2 . To ensure high reconstruction efficiency, even in minimum bias events, there is no requirement on the minimum allowed track pT . The selected tracks are then clustered, based on their z coordinates at the point of closest approach to the beamspot. This clustering allows for the possibility of multiple primary interactions in the same LHC bunch crossing. The clustering algorithm must balance the efficiency for resolving nearby vertices in cases of high pileup against the possibility of accidentally splitting a single, genuine interaction vertex into more than one cluster of tracks. The primary vertex resolution along the z axis is shown in Figure 4.1 as a function of the number of tracks: the lower the number of tracks using for vertex reconstruction, the worse the resolution on the primary vertex position. In such cases additional information are needed in order to be able to reconstruct the vertex. For example, in H → γγ events, the reconstructed primary vertex which most probably corresponds to the interaction vertex of the diphoton event can be identified using the kinematic properties of the tracks associated with the vertex and their corre-


57

lation with the diphoton kinematics. In addition, if either of the photons converts and the tracks from the conversion are reconstructed and identified, the direction of the converted photon, determined by combining the conversion vertex position and the position of the ECAL supercluster, can be used to point to and so identify the diphoton interaction vertex.

Figure 4.1: Primary vertex resolution inz as a function of the number of tracks, for two different kinds of events with tracks of different average transverse momentum [12]. The performance of the vertex reconstruction has been assessed using samples of tt¯H with H(mH = 120 GeV/c2 ) → b¯b and H → γγ (produced through gg and vector-boson fusion). All samples are simulated at low luminosity pileup (L = 2 · 1033 cm−2 s−1 ). The efficiency of finding and selecting the vertex with the largest P 2 pT within ±500 µm around the Monte Carlo signal primary vertex reaches about 99% for tt¯H events, whereas for H → γγ events it can go down to about 76% [3]. Hence, it is important to implement alternative methods for vertex reconstruction, which do not make use of the tracker information, in order to improve the performance in low multiplicity track activity cases, like H → γγ.

58

4.2


Vertex reconstruction using ECAL timing

In order to reconstruct the primary vertex position exploiting the ECAL timing etaCorr and the vertex coinformation, a relationship between the measured time Tsig

ordinate vz should be found. To do this, we have to first find the relation between the time expected Texp and the position of the vertex along the z axis, vz. Since the ECAL time is reconstructed by subtracting an offset so that all crystals result synchronous for photons coming from the geometrical centre of CMS, i.e. (vx, vy, vz) = (0, 0, 0), Texp is defined as: Texp (vz) =

1 (Sγ (vz) − S0 ) = Tγ (vz) − T0 c

(4.1)

where Sγ (vz) is the flight length of the photon produced in the primary vertex with a coordinate along the z axis corresponding to vz, while S0 is the flight length expected when the photon is produced in the geometrical center of the detector vz = 0 (Figure 4.2); Tγ (vz) = 1c Sγ and T0 = 1c S0 . Note that Texp = 0 when vz = 0.

Figure 4.2: A graphic definition of the flight length.


59

etaCorr can be correlated with Texp via the following formula: The measured time Tsig

etaCorr Tsig = Texp (vz) + t˜

(4.2)

where the term t˜ takes into account additional time jitter due to the time of the interaction, electronics and trigger. The linearity of the time measurement has been verified by studying the depenetaCorr dence of Tsig versus Texp . The results are reported in Figure 4.3. In plots are

listed the linear fit results (where p0 is the intercept and p1 the slope). Since slope is not exactly equal to unit, a correction factor slopeCorr, corresponding to the reverse etaCorr of the slope p1, will be applied to Tsig .

(a)

(b)

etaCorr Figure 4.3: Tsig as a function of Texp for data (a) and Monte Carlo (b). The correction factor slopeCorr is the reverse of the slope obtained by the linear fit (red etaCorr line) of the gray markers, which are the Tsig mean values extracted in bins of Texp . Corr Finally, the measured time Tsig after applying etaCorr and slopeCorr correc-

tions is defined as: Corr etaCorr Tsig = slopeCorr · Tsig ≡ slopeCorr · (Tsig − etaCorr)

(4.3)

Corr For a given measured Tsig there are two unknowns which need to be measured

60


event by event: the position of the primary interaction vz and the time of the interaction t˜. In events with two high momentum photons, there are two measured times and two equations for two unknowns:   γ1 T γ1 ,Corr = Texp (vztime ) + t˜ sig

(4.4)

 T γ2 ,Corr = T γ2 (vztime ) + t˜ exp sig and the system can be solved. Only events with a good reconstructed vertex are selected. This is done because the performance of the vertex reconstruction will be obtained by comparing with the vertex reconstructed with tracks. The selection criteria applied to each of the two most energetic photons are the same seen before in section 2.2. From the system 4.4, the two equations can be subtracted and, after some math, a quadratic equation in vztime is obtained: 2 a vztime + b vztime + c = 0

(4.5)

γ1 ,Corr γ2 ,Corr where the a, b and c terms depend on the difference Tsig − Tsig and on the

ηγ1 and ηγ2 coordinates of the two photons. Thus, there is a two-fold ambiguity in good the measurement of vztime . The resulting vztime closest to zero will be called vztime , good bad while the other one vztime . As shown later, the choice of vztime gives much better good performance in terms of resolution. The expected uncertainty on vztime , σ(vztime ),

is obtained via error propagation. The measured resolution, which is indicated as σ m (vztime )1 , is provided by the Gaussian fit of the vztime − vztrk distribution (Figure 4.4). The resulting resolutions,

1

The superscript m stresses that this is the measured resolution, which must not be confused with expected one, σ(vztime ).


61

integrated over the full η range, for data and simulation, correspond to:

data : σ m (vztime ) = (11.61 ± 0.24) cm (4.6) m

Monte Carlo : σ (vztime ) = (4.959 ± 0.034) cm

(a)

(b)

Figure 4.4: The distribution of vztime − vztrk for data (a) and Monte Carlo (b) from which the resolution σ m (vztime ) is extracted by a Gaussian fit. The vertex resolution depends on the geometry and, in particular, on the difference in polar angle of the two photons. The closer the two photons in η, the smaller the handle to determine the vertex. Then, an additional requirement on ∆ηγ1 γ2 between the two photon directions to be larger than 0.5 is applied. Such a criterion assures that the resolution in the vertex does not diverge. Figure 4.5 shows how the good bad resolution depends on ∆ηγ1 γ2 , for both vztime and vztime . Note that the resolution bad worsens with the decrease of ∆ηγ1 γ2 . Moreover, since the vztime resolution result good much worse than the vztime one, the criterion used to pick the best solution seems

to be reasonable.

62


(a)

(b)

Figure 4.5: The vztime −vztrk resolution as a function of ∆ηγ1 γ2 for the good solution good bad vztime (red markers) and the bad one vztime (blue markers), in data (a) and in Monte Carlo (b). Pulls of the measured time are verified to check that there is no bias and that the resolution is evaluated correctly. Pulls are defined as: pull =

vztime − vztrk σ(vztime )

(4.7)

where σ(vztime ) is the error on vztime computed by means of the statistical error propagation. Ideally, pulls should be distributed following a unit normal distribution. As shown in Figure 4.6(a), the distribution is almost Gaussian, the bias is negligible but the width is larger than one, indicating that the error is over-estimated. At the moment there is no full understanding on why this happens. It is maybe due to an underestimate of the constant term of the time resolution (section 2.2). Further checks are ongoing.


(a)

63

(b)

Figure 4.6: The pulls distribution for data (a) and Monte Carlo (b). Another validation of the method is represented by the the correlation plot between vztime and vztrk (Figure 4.7). Ideally one would expect a linear correlation, with slope 1 and null intercept. The study shows that for both data and MC (Figure 4.7(a) and 4.7(b)) the intercept is compatible with 0 and the slope is very close to 1, whereas data and MC slightly differ. There are two possible explanations on why this happens. The average beam spot position in the transverse plane, shown in Figure 4.8, is different between data and simulation. This would introduce a slight bias in the vertex determination. In addition the data sample is very different from the one used for simulation in terms of tracker activity. While the MC SUSY events are rich in number of jets, two-photon data events are quite empty. Then the efficiency and the resolution of the vertex determination with tracks is very different (as discussed in section 4.1). This would impact the vztime and vztrk correlation.

64


(a)

(b)

Figure 4.7: The correlation plot between vztime and vztrk for data (a) and Monte Carlo (b). The gray markers are the mean values extracted in bins of vztrk and the red line is the linear fit of these markers.

(a)

(b)

Figure 4.8: The beam spot position for data (a) and Monte Carlo (b). After solving the system in equation 4.4, also t˜ can be extracted. The resulting values of t˜ are reported in Figure 4.9.


(a)

65

(b)

Figure 4.9: The t˜ distribution for data (a) and Monte Carlo (b).

4.2.1

Analysis of Z → ee events

The performance of the vertex determination using timing has been verified using a different dataset represented by a sample of reconstructed Z bosons decaying in electrons. The calorimetric deposits of the electrons are reconstructed as photons, while the electron tracks are used to determine the primary vertex position. Hence, compared to the photon sample used before, the vertex mistag rate is much smaller. Electrons reconstructed as photons in Z → ee events are selected with almost the same selection criteria of the diphoton case, with the exception of the tracker isolation request in Table 1.2, which is inverted. In addition, it is required that the invariant mass of the two electrons system is close to the Z mass, precisely in the range 85-97 GeV/c2 (Figure 4.10). The selection criteria are listed in Table 4.1. After applying the corrections etaCorr and slopeCorr to Tsig and solving the system in equation 4.4, we get the following: • The resulting vertex position resolution corresponds to (Figure 4.11):

σ m (vztime ) = (10.930 ± 0.074) cm

(4.8)

66


criteria

requirements

good vertex

vndof ≥ 4 , d0 < 2 cm , |z| < 24 cm

|ηe1 ,e2 |

≤ 2.5

pTe1 ,e2

≥ 20 GeV/c the same for photons

photonID(e1 , e2 )

except for TRK Iso:

P

pT pT γ

> 0.1

mee

≥ 85 GeV/c2 and ≤ 97 GeV/c2

∆ηe1 e2

> 0.5

Table 4.1: Z → ee events selection criteria.

Figure 4.10: The two electrons invariant mass distribution. The azure lines show the mass values window of selected events. • The pulls standard deviation (Figure 4.12(a)) is larger than 1 and quite consistent to the diphoton result. • The study of the correlation with vztrk (Figure 4.12(b)) shows an intercept which is zero within the error, and a slope which differs from the diphoton result, whereas it is more similar to the MC one. Part of this effect is maybe due to a bias in the computation of Texp : electrons are bent by the magnetic field and the measured times would slightly differ from the expected one. In addition, the kinematics of these events, and in particular the opening angle between the two electrons, is different from the diphoton case, thus affecting


67

the performance of the method.

Figure 4.11: The distribution of vztime − vztrk for Z → ee data. The resolution σ m (vztime ) is extracted by a Gaussian fit (red line).

(a)

(b)

Figure 4.12: Z → ee data: (a) the pulls distribution; (b) the correlation plot of vztime and vztrk .

Chapter 5 Search for new physics using timing information In this chapter the search for long-lived particles in pp collisions at

√

s = 7 TeV

by the CMS experiment will be presented. It represents the first publication which makes use of the ECAL timing information [14]. This is done to identify photons which are produced from the decay in flight of supersymmetric particle, thus being displaced with the respect to photons produced at the beam spot and arriving at the calorimeter with O(ns) delay. This analysis uses several ingredients discussed and implemented in this thesis. The time as an average of the time measured in the crystals of the supercluster and the study of the different performance in data and simulation have been used in this analysis. In the following, we will briefly discuss the theoretical framework, explaining the reason why physics beyond the Standard Model is necessary, focusing the Gauge Mediated Symmetry Breaking (GMSB) model (section 5.1). This model foresees the existence of a long-lived, massive, neutral particle (the neutralino χ˜01 ), which ˜ + γ. Then, the search for the decays into a gravitino and a photon: χ˜01 → G ˜ + γ events will be described, and finally the results obtained and published χ˜01 → G by CMS will be presented (section 5.2).

70

Search for new physics using timing information

5.1

Theoretical framework

The Standard Model (SM) of elementary particles and their fundamental interactions provides a very elegant theoretical framework, and has been verified with high accuracy by several experiments, showing an excellent agreement between theoretical expectations and experimental results. Today, the SM is a well established theory applicable over a wide range of conditions. Despite the striking experimental success of the SM, this theory still has some unsolved problems, which range from the origin of particle masses to the nature of the Dark Matter in the Universe, and represents a strong conceptual indication for new physics in the TeV energy domain. Recent theoretical and experimental advances have brought a new focus on theoretical proposals for physics beyond the SM with massive and long-lived particles, which are common in several Supersymmetry (SUSY) models and also in more exotic scenarios. From an experimental point of view, models with long-lived particles decaying into an energetic photon are very accredited for early discoveries of new physics from the experiments at the LHC. The analysis discussed here regards SUSY theories with Gauge Mediated Supersymmetry Breaking (GMSB), since they have a relatively high production cross section and have a very distinctive experimental signature. According to the choice of the parameters, GMSB model foresees the existence of a long-lived, massive, neutral particle (the neutralino χ˜01 ), which decays ˜ Since the neutralino can have non-zero into a high energy photon and a gravitino G. ˜ + γ decay reaches the ECAL later than pholifetime, the photons from the χ˜01 → G tons produced at the bunch crossing, the so-called prompt photons. The gravitino is stable and weakly interacting, usually escaping from detection, and so it can be considered as a massive neutrino.


5.1.1

71

The Standard Model and its limits

The SM of particle physics [15] is the successful theory which describes three of the four fundamental forces, i.e. strong, weak and electromagnetic interactions (the gravitational one is not included in this model), and the basic constituents of matter. It has been carefully verified by experiments from the 60’s until now, in particular with measurements made by the LEP experiment of the CERN in Geneva. It is a gauge theory, namely a theory which is invariant under a set of space-time dependent transformations (called local transformations). According to the gauge principle, the forces are mediated by the exchange of the gauge fields, corresponding to a specific symmetry group. The mediators associated to the symmetry group are 12 spin-1 gauge bosons: 8 bosons (gluons) for SU (3)C , 3 bosons (Wi ) for SU (2)L , and 1 boson (B) for U (1)Y . The W ± bosons are obtained as a linear combination of W1 and W2 , while the Z boson and the photon γ can be seen as a linear combination of W3 and B. The gluons are massless, electrically neutral and carry color quantum number. The consequence of gluons being colorful is that they can interact with each other. The weak bosons W ± and Z are massive particles and also self-interacting. The photon γ is massless, chargeless and non-selfinteracting. Matter fields are represented by spin- 21 leptons and quarks, organized in three families with identical properties, except for mass. In Figure 5.1 is shown the three matter generations and the gauge bosons. In the SM mass terms are introduced by means of the so-called Higgs mechanism [16] [17], which predicts the existence of a new particle, the Higgs boson: gauge bosons (except photons), leptons and quarks acquire mass interacting with the Higgs field. The Higgs particle is an elementary particle, a massive boson which has no spin, electric charge or color charge. It is also very unstable, decaying into other particles almost immediately. Its existence is predicted for theoretical reasons, and it may have been detected by experiments at the Large Hadron Collider in Geneva. On 4

72


Figure 5.1: Standard Model structure. July 2012, the CMS and the ATLAS experimental teams independently announced that they each confirmed the formal discovery of a previously unknown boson of mass between 125 and 127 GeV/c2 , whose behavior so far has been consistent with a Higgs boson. If confirmed, this detection would further support the existence of the Higgs field, the simplest of several proposed mechanism for spontaneous electroweak symmetry breaking, and the means by which elementary particles acquire mass. Although the SM is the most successful theory of particle physics to date, it is not perfect. In fact, it isn’t able to answer some fundamental questions, such as: • if an energy scale to which all gauge interactions can be described by a single coupling constant exists; • how the gravity interaction can be included in the unified theory which describes the strong, electromagnetic and weak interactions; • how to solve the hierarchy problem concerning the radiative corrections to the Higgs mass; • how the matter-antimatter imbalance observed in the universe could be explained;


73

• which could be a good candidate to the dark matter, which is non-relativistic, non-barionic, non-luminous and weakly interacting. Then, answers to these lacks should be found. Different alternative models have been proposed to date, such as the String theory and the Extradimensions. Among these, the Supersymmetry is considered the most plausible theory to search for new physics. From an experimental point of view, the SUSY models are favored because they have non negligible cross sections and relatively small SM background.

5.1.2

Models with long-lived particles

Recent theoretical and experimental advances have brought a new focus on models beyond the SM with massive, long-lived particles. Such particles are common in several SUSY scenarios [18]. According to the characteristics of the long-lived particle, three main categories has been identified.

Charged particles In many SUSY models, charged particles with large lifetime, due to small decay phase space, are expected to exist. They mimic the case of very high momentum muons, crossing the detector with velocity significantly lower than the speed of light. This unique signature makes the search for it a model-independent search, based on measurement of both the time of flight and the energy loss by ˜ (the supersimmetric ionization. In this context, only those models with a gravitino G partner of graviton) in the final state are considered.

Colored particles A long-lived, colored gluino g˜ is a generic prediction of several models of physics beyond the SM. In this scenarios, g˜ decays into scalar particles are forbidden and gluinos acquire a macroscopic lifetime. During this time, they can hadronize into the so-called R-hadrons, bounds states of the gluino and quarks or gluons. R-hadrons live long inside the detector and, in case they are electrically charged, can lose all their momentum via ionization and come at rest.

74

Search for new physics using timing information These particles, commonly referred as stopped gluinos, can decay after a long

time via: g˜ → g + χ˜01

(5.1)

where χ˜01 is a massive and weak interacting exotic particle called neutralino, and g is a gluon which hadronizes into a jet. Stopped gluinos provide a striking experimental signature, established by a large amount of delayed hadronic activity without anything else.

Neutral particles The primary motivation to look for massive neutral particles with large lifetime is provided by the GMSB model, although they can also be present in other models, such as hidden valleys scenarios [19]. For what concern the analysis here presented, the attention will be focused on GMSB model with long-lived neutralino decaying into a gravitino and a high-energy photon: ˜+γ χ˜01 → G

(5.2)

The combination of displaced decay photons and significant energy imbalance in the transverse plane (due to gravitino which escapes from detection) generally leads to extremely clean, nearly background-free analysis. The GMSB model is one of the mechanism for soft supersymmetry breaking that produces the desired properties in the Minimal Supersymmetric Standard Model (MSSM) [20]. This is the natural extension of the SM to the supersymmetries which involves the smallest possible number of new particles: each SM particle has a supersymmetric partner, and they differ by a half unit of spin (Figure 5.2). If the SUSY were an exact symmetry of nature, particles and superparticles would have same masses. This would imply that also the superparticles have already been discovered. Not being so, then the SUSY is clearly a symmetry broken through some mechanism: the superpartners of the SM particles result much heavier and hence not yet discovered. Due to the symmetry breaking, the MSSM states can


(a) SM particles

75

(b) SUSY particles

Figure 5.2: Sketch of all MSSM particles. mix to form mass eigenstates. In particular, from the mixing of the neutral super˜ 10 , H ˜ 20 ) and (B ˜ 0, W ˜ 0 ), four mass eigenstates called neutralinos symmetric fermions (H are created and ordered by incrising mass in the following way: Mχ˜01 < Mχ˜02 < Mχ˜03 < Mχ˜04 .

(5.3)

In this model the states are represented by a further quantum number, the R-parity, which is a multiplicative number and is defined as R = (−1)3(B−L)+2s , where B, L and s are barionic number, leptonic number and particle spin, respectively. All SM particles have R = +1, whereas the supersymmetric ones have R = −1. The R-parity conservation ensure that there cannot be mixing between particles and superparticles. Moreover, due to the R-parity conservation: • The states created in laboratory have R = +1, then superparticles are always created in pairs. • Each superparticle decays into a state which contains another superparticle. • The lighter superparticle LSP is stable. If it is neutral, it interacts only weakly and it is not revealable by detectors: it would be an excellent dark matter candidate.

76

Search for new physics using timing information • The next lightest superparticle N LSP necessarily decays into two particels, one of which is the LSP and the other is an ordinary particle with R = +1. One of the techniques used to search for N LSP is exploiting decay channels in which the ordinary particle has a clear identificable kinematics. One of the most credited models for the spontaneous supersymmetry breaking is

the Gauge Mediated Supersymmetry Breaking (GMSB) model [21]. In this model all the superparticles acquire a mass higher than 100 GeV, whereas the gravitino has a mass of some keV, and so it results to be the LSP of the theory. In a particular scenario of the GMSB, called Snowmass Points and Slope 8 (SPS8) [22], the N LSP is the neutralino, which decays into a gravitino and a photon at 95% of the cases: ˜+γ . χ˜01 → G

(5.4)

This scenario is used as the reference in the search for long-lived particles made at CMS.

5.2

Search for long-lived particles using timing information

The interesting process at LHC is then the following: ˜ + 2γ + X 00 p + p → s˜1 + s˜2 + X → . . . → 2χ˜01 + X 0 → 2G

(5.5)

where s˜1 and s˜2 are two generic superparticles, and X i are systems of SM particles produced in the event. Figure 5.3 shows a possible sketch of an event with a GMSB decay. Note that the analysis here presented is an inclusive analysis. Hence, only one branch of the two decay chains in Figure 5.3 is studied, integrating over the rest of the event in order to be as general as possible. The experimental signal is made of a high energetic photon with high transverse


77

momentum, and a high missing transverse energy due to the the gravitino which is not detectable. Furthermore, all the quarks produced in the decay chain determine a high multiplicity of high transverse momentum jets. Figure 5.4 shows a view of the neutralino decay into a photon and a gravitino in the transverse plane of CMS.

Figure 5.3: Sketch of a GMSB decay event with two neutralinos in the final states.

Figure 5.4: View of a GMSB decay in the transverse plane of CMS. ˜ In the interesting case of a long-lived neutralino, the photon from the χ˜01 → G+γ decay is produced at the χ˜01 vertex, at some distance from the beam line, hence it results to be displaced relative to the interaction point IP. This means that photons

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coming from long-lived neutralinos are off-time, i.e. they reaches the detector at a later time than photons coming from the bunch crossing, the so-called prompt photons (Figure 5.5). Hence, in order to detect displaced photons, it is necessary to have an excellent energy resolution and a fine granularity to correctly identify the photon direction. It is also essential to have an excellent time resolution in order to distinguish displaced photons from the prompt ones. Then, the time of arrival of the photon at the detector and the missing transverse energy are used to discriminate signal from background.

Figure 5.5: Comparison between prompt photons (left) and displaced photons (right). The analysis is performed on the proton-proton collision data at a center-ofmass-energy of 7 TeV recorded by the CMS detector, corresponding to an integrated luminosity of 4.9±0.1 fb−1 . Signal and background events are generated using Monte Carlo simulations. The χ˜01 mass explored is in the range of 140 to 260 GeV, with proper decay lengths ranging from cτ = 1 mm to 6000 mm. Events with at least one high transverse momentum (pT ) isolated photon in the barrel region and at least three jets not overlap with the photon in the final state are selected in this analysis. The data were recorded using the CMS two-level trigger system. Several trigger selections have been used due to the increasing instantaneous


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luminosity during the data taking. The first 0.20 fb−1 of data were collected with a trigger requiring at least one isolated photon with pT > 75 GeV/c. For the second 3.8 fb−1 , the pT threshold was increased to 90 GeV/c. In the remaining 0.89 fb−1 , the trigger selection required at least one isolated photon with pT > 90 GeV/c in the barrel region and at least three jets with pT greater than 25 GeV/c. All offline selection requirements are chosen to be more restrictive than the trigger selection: Figure 5.6 shows that the trigger becomes 100% efficient with an offline cut of pT > 100 GeV/c for the photon (Figure 5.6(a)) and pT > 35 GeV/c for the third most energetic jet (Figure 5.6(b)). Moreover, the photon has to satisfy the same criteria used in this thesis and listed in Table 1.2.

(a)

(b)

Figure 5.6: Trigger efficiency for photons (a) and jets (b). ˜ + γ events, the time of impact for the photon on the In the search for χ˜01 → G ECAL and the missing transverse energy are used in order to discriminate the GMSB signal from the SM background and then to search for an excess of the events over the expected SM background: the ECAL time is important in order to identified the off-time photon of the event; the gravitino produced by the neutralino decay is not detected and so it provides a high missing transverse energy in the event. Note that the missing transverse energy 6ET is defined as the magnitude of the vector sum of the transverse momentum of all particles identified in the event excluding muons.

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Search for new physics using timing information The time of impact Tsig for the photon on the surface of the ECAL has been

defined previously in equation 2.7. Given that in this analysis we are interested in measuring the displacement of photons with respect to the primary vertex, an event-by-event correction Tprompt is applied to Tsig . This is to have a measurement which is independent of effects like the jitter in the trigger system, and the imperfect knowledge of the time of the interaction within the bunch crossing. This correction is computed with the equation 2.7 using the time of impact of all crystals in the event, excluding those belonging to the two most energetic photon candidates, which are typically due to prompt jets, low-energy prompt photons, and photons from π 0 and η decays. The new calibrated ECAL timing is defined as: Tcalib = Tsig − Tprompt

(5.6)

With this definition, a particle produced at the interaction point has a time of arrival of zero, whereas a delayed photon has a non-zero Tcalib . The distribution in data for Tsig and Tcalib are shown in Figure 5.7.

Figure 5.7: The ECAL timing distribution for data, before and after calibration, overlaid with the results of the Gaussian fits. In order to study if a dependance exists in terms of the mean and resolution of Tcalib , a gaussian fit is performed (Figure 5.7) as a function of the photon energy


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(Figure 5.8). Figure 5.8(a) shows a decrease of Tcalib as energy increases. This is due to the so-called gain switch. As mentioned before, the energy in the ECAL is computed from the ADC count, i.e. a given ADC count corresponds to a given energy. The ADC uses a 12-bit buffer, hence its maximum count is 212 = 4096. The ADC count−energy conversion begins from low energy values, for example 1 ADC counts corresponds to an energy of 1 MeV. This means that the maximum energy which can be measured is about 4 GeV. However, there are more energetic objects: when energy is greater than 4 GeV, 1 ADC count is required to be equal to 10 MeV, and so on as the energy increases. The transition from 1 ADC count → 1 MeV to 1 ADC count → 10 MeV is called gain switch. In this analysis, the gain switch threshold is at 130 GeV: when the most energetic rechit in the Tcalib calculation has energy greater than this threshold, it is removed from the calculation (orange markers in Figure 5.8).

(a)

(b)

Figure 5.8: The energy dependance of the Tcalib offset (a) and resolution (b) before (blue markers) and after (orange markers) gain switch corrections for data. Furthermore, as discussed in section 2.2, there is a difference in time resolution between data and Monte Carlo: Figure 5.9 shows that the resolution in Monte Carlo (blue markers) is lower than that in data (orange markers). Since data and Monte Carlo will be compared (as shown later), a smearing is applied to the ECAL time distribution in Monte Carlo to match what we observe in data. After the smearing,

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the Monte Carlo resolution is that shown by pink markers in Figure 5.9.

Figure 5.9: The Tcalib resolution as a function of the energy E1 for data after applying the gain switch veto (orange markers), for Monte Carlo (blue markers) and for Monte Carlo after applying smearing (pink markers). Figure 5.10 shows the 6ET (Figure (a)) and the ECAL time Tcalib (Figure (b)) distributions for different signal samples with different neutralino lifetimes. The 6ET and Tcalib variables result to be uncorrelated: the 6ET distribution doesn’t change significantly as the neutralino lifetime cτ .

(a)

(b)

Figure 5.10: Missing transverse energy (a) and time of arrival of the photon in the ECAL Tcalib (b) distributions for different signal samples with different neutralino lifetimes. Instead of cutting on these variables, the strategy is to exploit these in order


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to make a 2-dimensional fit from which the neutralino decay cross section can be extracted. The distribution of 6ET and the ECAL time Tcalib are shown in Figure 5.11.

(a)

(b)

Figure 5.11: Missing transverse energy (a) and time of arrival of the photon in the ECAL Tcalib (b) for data and the expected background. Note that in the legend some backgrounds are indicated as “MC”: these background are obtained simply by the Monte Carlo simulation because they are expected to be less than 1%. The other backgrounds, which are indicated as “data” in the legend, are obtained from the control samples. Note that in the legend some backgrounds are indicated as “MC”: these are obtained by the Monte Carlo simulation because they are expected to be less than 1% of the total background. The other backgrounds, which are indicated as “data” in the legend, probably have kinematics and cross sections not well-simulated in Monte Carlo. For this reason, the so-called control samples are created from data in order to estimate the main backgrounds, i.e. QCD and γ+jets. The idea is to build models as representative as possible of the backgrounds by means of a selection orthogonal to the signal selection. The control sample for QCD and γ+jets are created as follows: • QCD − Events which satisfy a selection less restrictive than signal selection

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Search for new physics using timing information and fail at least one of the isolation requirement listed in Table 1.2. This is because in QCD events photons are in general not isolated. • γ+jets − Less than 3 jets events with: – a well-identified photon (i.e. a photon which satisfy all the requirements listed in Table 1.2); – the most energetic jet being back-to-back with the photon with the same transverse momentum; – the second most energetic jet having a little fraction of the photon momentum; In Figure 5.11 the observed event yield in data is consistent with the SM back-

ground prediction, and so upper limits are obtained on the production cross section of a long-lived neutralino in the context of the GMSB model, assuming B(χ˜01 → ˜ + γ) = 100%. Figure 5.12 shows the observed and expected 95% confidence level G (CL) upper limits on the cross section for GMSB production in terms of χ˜01 mass (a), and proper decay length (b). The one-dimensional limits are combined to provide exclusion limits in the mass and proper decay length plane of the χ˜01 in Figure 5.13. In this scheme, we obtain an exclusion region as a function of both the neutralino mass and its proper decay length. The mass of the lightest neutralino is then restricted to values m(χ˜01 ) > 220 GeV (for neutralino proper decay length cτ < 500 mm) at 95% CL, and the neutralino decay length cτ must be greater than 6000 mm (for m(χ˜01 ) < 150 GeV). These limits are the most stringest for long-lived neutralinos.


(a)

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(b)

Figure 5.12: Upper limits at the 95% CL on the cross section as a function of the χ˜01 mass for cτ = 1 mm (a), and for the χ˜01 proper decay length for Mχ˜01 = 170 GeV (b) in the SPS8 model of GMSB supersymmetry.

Figure 5.13: The observed exclusion region for the mass and proper decay length of the χ˜01 in the SPS8 model of GMSB supersymmetry.

Conclusions In this thesis the performance of the timing reconstruction with the CMS electromagnetic calorimeter (ECAL) has been studied. The ECAL is a hermetic calorimeter made of lead tungstate (PbWO4 ) crystals and the combination of the scintillation timescale of the PbWO4 , the electronic pulse shaping and the sampling rate provide an excellent time resolution. High momentum photons and electrons events from pp √ collisions at s = 7 TeV have been used for this purpose. The first part of the study was devoted to validate the time resolution measurements obtained prior to LHC collisions. Using samples of reconstructed photons the energy dependence of the resolution has been extracted. The noise term, proportional to 1/E, came out similar to previous studies on data, although there is a small difference which is probably due to a different hardware confirguration. The constant term is confirmed to be of the order of 200 ps. The second part was about the study of the time development of the electromagnetic showers. This is possible since for large photon energies (> 20 GeV) the time can be measured with better than 1 ns resolution in many crystals involved by the shower. Given that the size of the crystals is about 20 cm × 3 cm × 3 cm, delays of a fraction of ns are expected in outlying crystals. A clear dependence of the measured time as a function of the distance from the impact position has been observed. This time dependance has been also exploited to implement a discriminant variable for photon identification purposes. Results are encouraging and this new variable could be used to further improve the photon-jet separation in physics analyses. In the third part, a novel method to determine the position of the primary

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Conclusions

vertex using timing information has been also developed. This method is completely independent of the tracking, and may offer an important alternative to reject noise from pileup and to handle in events where there is a small track activity, such as H → γγ events. A resolution on the vertex position along z axis of about 10 cm and about 5 cm has been obtained in data and Monte Carlo, respectively. The method is not yet usable but if an improved time calibration (< 50 ps) will be reached, O(1cm) resolutions may be obtained. Such a result, if achieved, would give an important additional ingredient for the H → γγ analysis to better determine the vertex position. These studies can also guide some of the ongoing feasibility studies aimed to design the upgrade of the ECAL detector. Finally, the search for long-lived particles has been presented. It is the first publication of CMS which makes use of the ECAL timing information [14]. This analysis has been focused on the SUSY theories with GMSB, where the neutralino is the Next to Lightest Supersymmetric Particle (NLSP) decaying into a photon ˜ In this model, G ˜ play the role of the Lightest Supersymmetric and a gravitino G. Particle (LSP) and behaves as a massive neutrino, since it is stable, neutral and weakly interacting. The analysis has used the missing transverse energy and the ECAL timing to search for an excess of events over the SM background prediction. A fit to the 2-dimensional distribution in these variables yields no significant excess of events beyond the SM contributions, and upper limits at 95% are obtained on the GMSB production cross section in the SPS8 model of GMSB supersymmetry. Moreover, we obtain an exclusion region as a function of both the neutralino mass and its proper decay length. The mass of the lightest neutralino is then restricted to values m(χ˜01 ) > 220 GeV (for neutralino proper decay length cτ < 500 mm) at 95% CL, and the neutralino decay length cτ must be greater than 6000 mm (for m(χ˜01 ) < 150 GeV). These limits are the most stringest for long-lived neutralinos.

Ringraziamenti La lista delle persone da ringraziare è davvero lunga e sono costretta a sfoltirla. Spero, tuttavia, che ognuna delle persone incontrate in questi miei sei anni di studi sappia che ha contribuito a farmi giungere a questo traguardo. Tra le persone che hanno avuto pi` u peso in questo passo finale, ringrazio in primis il Dr. Daniele Del Re, ottimo relatore, sempre disponibile e soprattutto paziente. Ho apprezzato molto quando, insieme al Prof. Luciano M. Barone, mi ha offerto comprensione in un momento difficile della mia vita e per avermi risollevato permettendomi di realizzare un lavoro di tesi davvero bello ed interessante. Ringrazio tutta la ciurma di CMS Roma, dai ricercatori e professori, che mi hanno ascoltato nelle riunioni e mi hanno offerto critiche costruttive e consigli per migliorare, agli abitanti della baita, che hanno reso le giornate di duro lavoro piacevoli e divertenti e mi hanno affiancato nell’eterna battaglia contro Root (consolandomi quando quest’ultimo mi derideva con qualche “Break violation”). Ed un grazie speciale va a Livia, capa, mentore ed amica: senza il suo aiuto questa tesi non sarebbe stata semplice, sia a livello tecnico che emotivo. L’amicizia nata tra noi durante questo periodo ha impreziosito notevolmente questa esperienza ed io ne ho fatto tesoro. Ringrazio i miei amici delle pause pranzo e delle pause Simone trascorse sul pratino davanti al VEF e sul balcone del primo piano: quei momenti di relax fatti di risate e non-sense mi rimettevano al mondo. Ed un grazie particolare va ad Andrea, che grazie allo scambio via Skype di spezzoni tratti dai film di Bud Spencer e Terence Hill, ha dato una marcia in pi` u al mio lavoro.

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Ringraziamenti Un grazie davvero speciale è per i miei amici pi` u stretti, Nicolò, Alex e le Ninja

girls: spero siano consapevoli di quanto sia stato fondamentale per me averli avuti vicino nell’ultimo anno. Un po’ pi` u di striscio in questa tesi, ma pur sempre fondamentali nel fortificare la mia autostima, sono stati i mitici Arnulf Boys, di cui gelosamente conservo la maglietta di appartenenza. Quelle due settimane insieme a loro sono state un sogno che mi ha dato un’ulteriore conferma del piacere di essere un fisico. Ringrazio, poi, la mia famiglia: il Babbo per il suo affetto sconfinato; i miei nonni per le perle di saggezza e gli aneddoti divertenti; Maurizio per il suo chiamarmi Sette facendomi sentire un genietto; la Mommo per i suoi consigli e la pazienza in risposta ai miei scatti di nervi; i bimbi della casa, ossia Pepo, Stella e Luna, per la serenità e la tenerezza che portano nel mio cuore. Infine, per ultimi ma non ultimi, ringrazio il mio fratellone Mattia, mio eroe e modello da imitare, che non ha mai smesso di aver fiducia nella sua sorellina tutta pepe; ed il mio ragazzo Andrea, dolce e premuroso che, nonostante la nostra sia una relazione a distanza, mi è sempre stato vicino.

E con questa tesi chiudo il mio capitolo di vita romana. Una nuova avventura in qualche altro posto mi attende. Allons-y! (cit. The Tenth Doctor)

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