Optimisation of the Clustering Algorithm in the

CMS ECAL Endcaps

Rebecca Falla

11th May 2012

Southampton University,

Southampton,

UK

1

Abstract

The CMS experiment at the Large Hadron Collider in Switzerland isstudying proton-proton interactions at ever increasing energies. It is im-portant for the search of new physics that there are good reconstructionsof electrons and photons, therefore having a good clustering algorithm inthe Electromagnetic Calorimeter (ECAL) is essential. For this reason theclustering algorithm in the ECAL Endcaps of CMS was investigated tocheck the status of it and see if there were any ways in which it could beimproved. This was done initially by looking at reconstructions of elec-trons, and also the resolution of the Z mass peak with respect to positionin the ECAL and Pile-Up. During this research a bug in the algorithm wasdiscovered and �xed, which resulted in an improvement in Monte Carlodata clustering by about 5%. The e�ects of inactive crystals and Pile-Upwere then considered in further detail.

2

Acknowledgments

Firstly I would like to thank my two supervisors - Dave Cockerill and DavidPetyt, as well as the rest of the RAL CMS group for their help and support overthe last year. I would especially like to thank Sam Harper his constant teachingand help with computer programming.

I would also like to thank the ECAL DPG whom I collaborated with duringthis project, particularly Dave Evans.

Special thanks go to Espen and Jack my �atmates, and the rest of the UKLTA PhD students for making me feel extremely welcome at CERN, and alwayshaving new and exciting activities to do.

Finally, I would like to thank Southampton University and Stefano Morettifor giving me the opportunity to come to CERN.

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Contents

1 Introduction 61.1 The LHC and CMS . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Project Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 The Standard Model, The Higgs Boson and it's Detection atthe LHC 92.1 The Standard Model of Particle Physics and the Higgs Boson . . 9

2.1.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.2 Fundamental Forces . . . . . . . . . . . . . . . . . . . . . 92.1.3 The Higgs Mechanism . . . . . . . . . . . . . . . . . . . . 10

2.2 Detection of the Standard Model Higgs Boson at the LHC . . . . 112.2.1 Searches for the SM Higgs Boson . . . . . . . . . . . . . . 112.2.2 The Higgs to diphoton Decay Channel . . . . . . . . . . . 11

3 The CMS ECAL 133.1 The Lead Tungstate Crystals . . . . . . . . . . . . . . . . . . . . 133.2 How Energy is Measured in the ECAL . . . . . . . . . . . . . . . 163.3 The ECAL Endcaps . . . . . . . . . . . . . . . . . . . . . . . . . 163.4 The ECAL Preshower . . . . . . . . . . . . . . . . . . . . . . . . 16

4 ECAL Endcap Clustering 204.1 How Clustering in the ECAL Endcaps Works . . . . . . . . . . . 204.2 The Data Sample and how it was Analysed . . . . . . . . . . . . 214.3 Reconstructions of Electrons . . . . . . . . . . . . . . . . . . . . . 234.4 Resolution of the Reconstructed Z Mass . . . . . . . . . . . . . . 24

5 Changes in Code Due to Unclustered Energy 285.1 Cause of the Problem and Preliminary Fix of the Code . . . . . . 285.2 Results from the Preliminary Fix . . . . . . . . . . . . . . . . . . 315.3 Optimization of Energy Assignment in Basic Clusters . . . . . . 34

5.3.1 Motivation for Optimizing the Energy Assignment in Ba-sic Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3.2 The Proposed Solution - Basic Cluster's Retaining theirown Seeds . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3.3 How the new Clustering Code Works . . . . . . . . . . . . 345.4 Results from the Final Code Change . . . . . . . . . . . . . . . . 36

5.4.1 Basic Cluster Energy . . . . . . . . . . . . . . . . . . . . . 365.4.2 How the New Code A�ects Super Clusters . . . . . . . . . 36

5.5 Outcome of the Code Changes . . . . . . . . . . . . . . . . . . . 37

6 Analysis of Inactive Channels on the EE Resolution 386.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.2 A Cut on Electrons that have seeded near an inactive channel . . 40

6.2.1 How cut works and where it a�ects . . . . . . . . . . . . . 406.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7 Analysis of How Pileup a�ects ECAL Resolution 437.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437.2 A�ect of High Pileup on Mass of Z particles Using Monte Carlo

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

8 Conclusions 47

A High Energy Electron Pair Selection Cuts 48

B An Alternative Clustering Algorithm 49B.1 The Alternate Algorithm . . . . . . . . . . . . . . . . . . . . . . 49B.2 Results of the Alternative Algorithm . . . . . . . . . . . . . . . . 49B.3 The Alternative Algorithm Using 3x3 Sized Basic Clusters . . . . 49B.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

C Comparison Graphs for the Code Changes �This is the onlysection i havnt �nished, i just need to put the graphs in. 51

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1 Introduction

The large Hadron Collider generates proton-proton collisions at high energies.It is currently operating at a centre of mass collision energy of

√s = 8 TeV.

The CMS detector is used to examine the results of these interactions. Inthe search for new physics it is essential to have good electron and photonreconstructions which are detected by the Electromagnetic Calorimeter. TheECAL uses computer algorithms to determine their properties in a process thatis called clustering. This report looks at optimizing the clustering algorithmwithin the ECAL endcaps.

1.1 The LHC and CMS

The Compact Muon Solenoid (CMS) detector is one of the main experimentson the Large Hadron Collider (LHC) at CERN. It is a multipurpose experimentwhich probes particles at the TeV energy scale, by studying the results of proton-proton collisions. The LHC has a design centre of mass collision energy of

√s

= 14 TeV and is currently running at√s = 8 TeV. One of the main purposes

for the LHC being built was to look for the hypothesized Higgs Boson particle.It's properties if it is found, or it not being discovered will play a large rolein helping to �gure out a model of particle physics (eg. the Standard Model,Supersymmetry, extra dimensions or something else). For a low mass Higgs thedecay channel H→ γγ is the most promising channel.

The setup of CMS is shown in Figure 1.1, and the transition of particlesthrough the subdetectors is shown in Figure 1.2. The �rst subdector is thesilicon tracker which records the paths taken by particles close to the beampipe. The vertices that particles came from can be identi�ed from these tracks.After the tracker there is the Electromagnetic Calorimeter (ECAL) and theHadronic Calorimeter (HCAL) which measure energies. The ECAL detectselectrons and photons and the HCAL detects hadrons. Neutral pions, whichinstantaneously decay in two photons, are distinguished from photons in theECAL by the preshower detector which sits in front of the ECAL endcaps.Outside the HCAL is a superconducting solenoid which creates a 3.8T magnetic�eld. This causes charged particles to follow curved paths which makes it easierto determine their momentum and charge. It also spreads the particles outwhich makes them easier to distinguish between within the subdetectors. Theouter part of the detector contains an iron return yoke interspersed with muonchambers. These identify muons and measure their momenta.

This report focuses on the clustering algorithm in the ECAL Endcaps. TheECAL is shown in green in the diagrams.

The ECAL is made up of a barrel region, which is the cylindrical part alongthe beam direction, and two endcaps which are perpendicular to it; there is alsoa preshower detector which covers most of the endcaps and is used to detectneutral pions. The endcaps are made up of lead tungstate scintillator crystalswhich are attached to vacuum phototriodes (VPTs). The VPTs are used forelectronically reading out how much energy is collected in each crystal.

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Figure 1.1: A diagram of CMS which shows the size of the detector, and itssubdetector composition. (Source ???)

Figure 1.2: An example arrangement of the subdetectors within the CMS barrelwhich shows the transition of particles through the detector.

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The ECAL is used to detect electrons1 and photons which are distinguishedfrom other electromagnetically interacting particles via their shower shape, littleto no energy in the HCAL, and for electrons, the track that they leave in thetracker. Due to di�erences in geometry and also how particles spread out inthese parts of the detector, there are di�erent algorithms for reconstructing theenergy and other variables of particles detected within them which are known asclustering algorithms. This project focuses on the endcaps, which due to theirposition in the ECAL have a large amount of radiation and particles hittingthem.

One of the main decay channels for the low mass Standard Model HiggsBoson is H→ γγ, it's signal would be a resonance peak around the invariantmass of the two photons that would show above the background signal fordiphotons. There is a large background, so a narrow resonance peak is essentialfor observation. This is one of the reasons why it is important to have a goodresolution in the ECAL.

1.2 Project Aims

1. To look at the current clustering algorithm in the endcaps, check the statusof it, and see if there is anything that can be improved.

This study is the focus of Chapter 4. Out of this study additional aims cameabout:

1. To investigate and remove a problem that was found in the clusteringalgorithm where energy was being missed within super clusters.

2. To see the impact that inactive crystals have on the resolution of theECAL endcaps, and see if there is anything that can be done to reducethe a�ect of them.

3. To investigate how having multiple interactions within an event (pileup)a�ects the clustering of particles.

These projects are the subjects of Chapters 5, 6, and 7 respectively.

1For the purpose of this report, 'electrons' will refer to electrons and positrons since thecharge of the particle was not important when looking at how it was clustered.

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2 The Standard Model, The Higgs Boson and it's

Detection at the LHC

2.1 The Standard Model of Particle Physics and the Higgs

Boson

The Standard Model of Particle Physics (SM) is a successful theory which de-scribes the elementary particles and their interactions. It is a quantum �eld the-ory which combines electroweak theory and quantum chromodynamics (QCD);Electroweak theory is the uni�cation of the electromagnetic and weak interac-tions, and QCD describes interactions of the strong force. It contains threemain components:

1. The basic constituents of matter

2. The fundamental forces

3. The Higgs Mechanism

2.1.1 Matter

The basic constituents of matter are fermions and gauge bosons. Fermions arespin- 12 particles which obey Fermi-Dirac statistics and obey the Pauli Exclu-sion Principle. They are split into two subgroups - quarks and leptons, with 6particles in each group which can be split into pairs; the pairs exhibit similarphysical behaviour, to form three increasingly heavy generations. Figure ??illustrates this structure. The �rst generation of quarks is the 'up' and 'down',the second 'charm' and 'strange' and the third 'top' and 'bottom'. Quarks areparticles which carry colour charge, they partake in strong and electroweak in-teractions, and are what make up atomic nuclei. Leptons consist of electrons,muons, taus and their three corresponding neutrinos which are charge neutraland have a small (but non-zero) mass; All leptons are colourless and so onlyhave electroweak interactions; neutrinos only interact with the weak force.

Antiparticles exist for each of these fermions, these are particles with iden-tical mass, spin and lifetime but they have many opposite quantum numberssuch as charge and lepton/baryon number.

Gauge bosons are the force carrying particles, they shall be discussed in thenext subsection.

2.1.2 Fundamental Forces

There are four fundamental forces: electromagnetic, weak, strong and gravita-tional. In the Standard Model the electromagnetic, weak and strong nuclearforces are mediated by force carrying spin-1 gauge bosons - the photon (γ) forthe electromagnetic, the Z, W+, and W− bosons for the weak, and gluons (g)for the strong.

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Figure 2.1: The Elementary Particles: 12 fermions split into 6 quarks and 6leptons, which in turn are paired up to create three generations of matter, aswell as 4 force carrying gauge bosons. The Standard Model also predicts theexistence of the Higgs Boson. [1]

The weak nuclear force is short range (10−18m), it can change the �avourof one quark into another and is therefore responsible for beta decay. TheW±bosons are charged and the Z boson is neutral, the masses of these parti-cles were predicted by the SM and experimentally veri�ed. The strong nuclearforce is responsible for binding quarks into colourless hadrons, it is short range(10−15m). The strength of the strong nuclear force increase with separation.When two quarks separate it becomes energetically favourable to create a newquark-antiquark pair to couple to the original quarks, rather than keep separat-ing them. In the high energy environment within the LHC these quarks keepon separating and then creating new pairs resulting in a hadronic jet, becauseof this gluons cannot be observed directly, but are inferred experimentally fromjets.

Gravity is predicted to have a force-exchanging spin-2 particle called thegraviton (G), which has not been experimentally veri�ed.

2.1.3 The Higgs Mechanism

For the uni�cation of the electromagnetic and weak nuclear forces into the elec-troweak force there has to be spontaneous symmetry breaking, this is becausethe photon is massless but the Z and W± bosons have mass. The mechanismresponsible for this described in the SM is the Higgs Mechanism, it is done byintroducing a spin-0 scalar (since mass is scalar) �eld, the Higgs �eld, whichpermeates all of space to which particles couple to gain mass. The quantum ofthis �eld would be a massive scalar gauge boson, the Higgs Boson.

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2.2 Detection of the Standard Model Higgs Boson at the

LHC

The masses of the W± and Z bosons were predicted by the Higgs Mechanism,and found experimentally at these values [8-ezz], however the Higgs Boson isyet to be discovered, and so the Higgs Mechanism within the SM has not beenexperimentally veri�ed.

2.2.1 Searches for the SM Higgs Boson

The search for the Higgs Boson is done by examining the mass distributions ofit's many decay modes and looking for an excess. For a discovery there needsto be an excess that is at least 5 standard deviations away from the predictedmass of the decay channel without a Higgs Boson - this means that the chancesof the excess being a statistical �uctuation are less than 1 in 3.5 million. [ref]If a signal is not seen in a given mode at a certain mass then that mass regioncan be excluded.

Figure 2.2 shows the latest public results from CMS that shows the ex-cluded mass ranges of the SM Higgs. The mass range looked at was 110 - 600GeV, and the expected excluded mass range at 95% con�dence level was 118-543 GeV. The observed exclusion at 95% con�dence level was 127-600 GeV. [refhttps://twiki.cern.ch/twiki/bin/view/CMSPublic/Hig11032PaperTWiki] An ex-cess was seen at 124 GeV with a local signi�cance of 3.1σ. This corresponds toa global signi�cance level of 1.5σ.

2.2.2 The Higgs to diphoton Decay Channel

Figure 2.3 shows the branching ratios for the decay modes of the SM Higgs. Atlow mass, 110 < MH < 150 GeV, the most promising decay mode is H→ γγ, despite it's relatively low branching ratio and large background signal. Thisis because this channel has a relatively 'clean' �nal state and would provide amass peak which could be reconstructed to high precision (MH to within ∼ 1GeV). The event display of a H→ γγ candidate is shown in Figure 2.4. It showstwo photons which are almost back to back. Other decay channels at low massare less favourable, despite having larger branching ratios. Figure 2.5 shows aH→ γγ signal, made from Monte Carlo data generated at MH = 130 GeV. Itcan be seen that the signal is small, for this reason it is essential to have a goodresolution in the ECAL.

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Figure 2.2: The Exclusion limit for the mass of the SM Higgs Boson at 95% con-�dence level (below the red line). This is based on 4.7 fb−1 of data collected byCMS between 2010 and 2011 (at

√s= 7TeV). The crossed boxes show the ranges

of mass excluded by LEP, the Tevatron and CMS. The dashed line shows theexpected sensitivity, with the green and yellow bands either side correspondingto 1 and 2 standard deviations away from that. The actual data is the pointsjoined up by a line, where this line goes above the red line, we cannot excludethe Higgs. [ref http://cms.web.cern.ch/news/cms-search-standard-model-higgs-boson-lhc-data-2010-and-2011]

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Figure 2.3: The Branching Ratios of the SM Higgs Decay Modes vs Higgs Mass[2]

3 The CMS ECAL

The overall structure of the CMS electromagnetic calorimeter is shown in Figure3.1. It is made up of three main detectors - the barrel and two endcaps eachwith a preshower detector. The barrel part covers a pseudorapidity range of |η|< 1.479 and contains 61200 Lead Tungstate (PbWO4) crystals, it is parallel tothe beam pipe. The two endcaps cover a pseudorapidity range of 1.479 < |η| <3.0 and contain 7324 crystals each, they are placed perpendicular to the barreland close the detector so it is hermetic. The preshower detector covers 1.653< |η| < 2.6, and is a sampling calorimeter designed to identify neutral pions inthe endcaps, it is placed in front of the endcaps.

3.1 The Lead Tungstate Crystals

Lead Tungstate was chosen for the crystals because it has many useful properties- it's high density (8.28 g/cm3) and short radiation length2 (0.89 cm) allow fora compact detector, and it's small Molière radius3 (2.2 cm) results in a very �negranularity and resolution. The scintillation decay time of the crystals is very

2The mean distance a high energy electron travels within a material before losing all but1/e of it's energy due to Bremsstrahlung radiation.

3When an high energy electron or photon hits a material which causes it to create anelectromagnetic shower, the Molière radius is the radius of a cone around the shower whichcontains 90% of particle's energy.

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Figure 2.4: An Example of an event display of a possible H→ γγ candidate inCMS. The two high energy photons have their energy shown as the red towers.The yellow lines represent the tracks of other particles measured during thecollision.

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Figure 2.5: Two graphs of a H→ γγ signal at MH = 130 GeV. The �rst is withthe background, and the second is after the background has been subtracted.These graphs were made using 100 fb−1 of generated Monte Carlo data.

Figure 3.1: The Layout of the CMS Electromagnetic Calorimeter, showing thearrangement of crystal modules, supermodules and endcaps, with the preshowerin front.

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fast - about 80% of the light is emitted in 25ns, this is useful because the designbunch collision rate at the LHC is 25ns.

3.2 How Energy is Measured in the ECAL

When an electron or photon hits a PbWO4 crystal it starts an electromagneticshower, this is where photons converts into electron-positron pairs, and elec-trons lose energy via Bremsstrahlung Radiation4 These particles then go on toproduce more electrons and photons which carry on the process culminating inan electromagnetic shower which ionizes the crystal. The ionization causes thecrystals to scintillate low energy (~420nm) photons which are detected by thephotodetectors at the end of the crystals (vacuum phototriodes (VPTs) in theendcaps, and avalanche photodiodes in the barrel). Each photodetector sendsan electronic signal, which is proportional to the amount of energy measuredin the crystal, to the system readout. Information from the read-out, such asenergy, pulse shape and timing, is stored in a C++ data structure known as a'recHit' within the CMS software framework (CMSSW). For each event therewill be a collection of rechits, each one corresponding to a di�erent crystal,which go through clustering algorithms to reconstruct the particles.

3.3 The ECAL Endcaps

The crystals are arranged in 5x5 units known as super crystals, which are placedinto a 'Dee'. Figure 3.2 shows examples of a crystal with a VPT, a super crystalmodule, and a Dee. Each Dee makes up half of an endcap and contains 138super crystals, and 18 partial super crystals. The crystals are arranged in arectangular x-y geometry, and angled such that they point 1300mm beyond themain interaction point in order to minimise losses due to energy leakage throughthe cracks between supercrystals and crystals.

3.4 The ECAL Preshower

The preshower detector is located in front of the endcaps between 1.653 < η <2.6, this can be seen in Figure 3.3. It is made of of two layers - lead radiatorsand silicon strip sensors. The dense lead section cause electrons and photonsto create electromagnetic showers. The highly granular silicon strip sensors,which are directly behind the lead section measure the shape of these showersand their energy, from this information it is possible to work out the position ofthe incident particle and infer it's energy. [ref cms tech thing from email aboutplacement]

The main purpose of the preshower is to distinguish neutral pions (π0s) fromsingle photons. When a π0 is created in a p-p collision it quickly decays intotwo closely spaced photons. The resolution of the endcaps is not �ne enough

4The process by which an electron emits a photon to compensate for acceleration due tointeraction and scattering with an electromagnetic �eld (here caused by the Lead Tungstatenuclei).

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(a) A crystal with a VPT attached to it**source**

(b) A supercrystal

(c) A dee

Figure 3.2: Images of a crystal, supercrystal and a dee

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Figure 3.3: A diagram showing the placement of the Preshower Detector on theendcap.

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Figure 3.4: A diagram to show how the preshower is used to detect π0s. EE isthe acronym for the ECAL endcaps, and ES for the ECAL preshower.

to distinguish these two photons from one photon. The preshower detector hasa granularity �ne enough to make this distinction. Figure ?? shows what thepreshower 'sees' in one of these events - Two peaks of overlapping energy.

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4 ECAL Endcap Clustering

4.1 How Clustering in the ECAL Endcaps Works

Clustering in the ECAL is the process of taking all the crystals which have beenrecorded to have energy in them, and from that working out which crystals gotogether to create a particle. This is done using computer algorithms, whichare based on how electrons and photons should look in the ECAL.

The current algorithm used to cluster events in the ECAL Endcaps is called'Multi5x5ClusterAlgo'. An example of diagram of a clustered electron is givenin Figure 4.1 and an event display of a clustered electron is shown in Figure 4.2.The algorithm works in the following way:

1. It takes a collection (vector) of the recorded hits5 in the ECAL, orderedfrom highest transverse energy (ET ) to lowest.

2. From this collection it �nds local energy maxima using a 'Swiss Cross'(largest out of the hits directly above, below, left and right). These canbe seen in Figure 4.2 by the crosses in the centre of the boxes.

3. For these maxima to be labelled as 'seeds' they must have an ET > 0.18GeV and they cannot be within the 3x3 square of crystals around another(larger) seed.

4. A basic cluster is then made around each seed. This is a 5x5 square ofcrystals with the seed at the centre6.

5. In the case where basic clusters have overlapping hits, the basic clusterwith the largest ET seed retains them.

6. Starting from the largest ET seed, if ET > 1 GeV a super cluster is made,this is where any basic clusters within a φ road of ±0.6 rad and an η roadof ±0.14 from the seed are added together and called a super cluster.

After clustering, the measured preshower energy is added and then this energyis scaled using cluster correction algorithms. This is because the clusteringalgorithm collects about 97% of the electron or photons energy, so the clustercorrections bring this up to 100%. **NEED REFERENCE**

The crystals in the ECAL Endcap have a width of 3cm which is comparableto the Molière radius of Lead Tungstate of 2.2cm **REF**. If an electron orphoton is centred exactly in the middle of a crystal then most of its energyshould be contained within the initial 3x3 square around this crystal, if it hitsslightly to the side of this, then some of the energy will leak into the second ringof crystals around the seed. This is why basic clusters (which represent a singleparticle) are 5x5 squares of crystals, centred on a local maximum.

5'Hits' is another name for crystals which have had energy deposited and recorded in them.6Computationally a basic cluster contains information about the 25 hits as a whole for

example it's relative position in φ and η, and it's (uncorrected) energy.

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Figure 4.1: An example of how overlapping basic clusters distribute their crys-tals. The transverse energy of the seed of cluster 1 is greater than that of cluster2.

Electrons pass through material before reaching the ECAL so they mayconvert some of their energy into photons due to Bremsstrahlung radiation.Likewise, photons may lose energy via e+e- pair production **REF**. Due tothe magnetic �eld of CMS these secondary clusters are often displaced from themain cluster. This is why super clusters (which represent the original photon orelectron) can be made up of multiple basic clusters. Due to the 3.8T solenoidalmagnetic �eld inside CMS, the motion of charged particles is curved and soelectromagnetic showers are spread out in φ, so when adding basic clusters toa super cluster there is a long φ road and small η road. This behaviour can beseen in Figure 4.2 where there are three basic clusters.

4.2 The Data Sample and how it was Analysed

To investigate the status of the clustering algorithm, 2.5 fb−1 of data collectedfrom September - October 2011 at

√s = 7 TeV (run 2011B), was analysed. The

196637 events chosen were Z→ee events where one electron was in the barrel andone was in the endcap, these events passed the standard High Energy ElectronPair (HEEP) cuts7 (Section A). Where the resolution has been calculated, aVoigtian �t has been used on the reconstructed Z mass from the two electrons8.Figure 4.3 shows an example of the Z peak with this �t. A Voigtian �t is aBreit-Wigner resonance (which describes the Z peak) convoluted with a Gaus-sian function (to accommodate for smearing of the peak due to the detectorresolution). The resolution of the peak is the width of the voigtian distribution,

7The HEEP cuts use shower shape properties to rule out 'fake' electrons.8The reconstructed Z mass is calculated from the 4-momenta of the two electrons

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Figure 4.2: An Example of an Electron Reconstruction. The Numbers representthe recorded transverse energy of crystals. The red highlighted hits are theclustered hits. The large boxes represent basic clusters and the small boxesrepresent seeds. The crosses are examples of Swiss Crosses.

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Figure 4.3: The Reconstructed Z Mass with a Voigtian Fit

which is shown in the legend in Figure 4.3 as σv. All the data has been processedusing Root and C++ macros.

To evaluate the clustering algorithm, reconstructions of the clustered andnon clustered hits around electrons were made to give a 'picture' of what theclustered electrons actually looked like. This is the topic of section 4.3. Theresolution of the reconstructed Z mass was studied in di�erent regions of theendcaps and against various variables to see if there were problems which couldbe due to problems with the detector or a bias in the algorithm. This is thesubject of section 4.4.

An alternative clustering algorithm was written and compared alongside theo�cial algorithm. It was shown to give similar results, which are presented inSection B of the appendix.

4.3 Reconstructions of Electrons

To see how the clustering algorithm was actually working, event displays of theclustered electrons were made, as shown in Figure 4.4. The transverse energiesof all the recorded hits are shown on the plot, at their coordinates in eachendcap, with highlighting for the hits which were clustered. A scan of 100 ofthese electrons was done to see what the electrons typically look like. Theresults are presented in Table 1. A 5x5 electron is an electron where the supercluster contains only one basic cluster as shown in Figure 4.4 a). An extended

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electron is an electron where there is more than one basic cluster within thesuper cluster as shown in Figure 4.4 b). A 'gap electron' is an electron that hasa gap of energy larger than 1GeV which should have been clustered but wasn'tas shown in Figure 4.4 c). We will explore why these electrons look like this inChapter 5.

5x5 Electron Extended Electron Gap Electron

40% 54% 6%

Table 1: The Results of a Scan on 100 Electrons. '5x5 Electron' means onebasic cluster, 'Extended Electron' means more than one basic cluster, and 'GapElectron' means a gap in clustered hits greater than 1GeV within the supercluster

The majority of these electrons are extended. This is due to the electronemitting at least one Bremsstrahlung Photon when going through the tracker orpreshower material. The emitted photon(s) hit the ECAL close to the originalelectron, which are clustered as basic clusters and then are picked up within theη-φ box around the super cluster seed. Another example of this can be seen inFigure 4.2.

4.4 Resolution of the Reconstructed Z Mass

Figure 4.3 shows the reconstructed Z mass distribution for all events (points),with a Voigtian �t (blue line). The Z mass peak of the data was at 91.727± 0.011 GeV with a net resolution measured to be 3.102 ± 0.008 GeV. Theactual Z mass is 91.19 GeV, and the systematic error on the energy scale inthe endcaps is 1.5% [reference CMS Detector Performance Summary: CMS-DP2011-008 https://cdsweb.cern.ch/record/1373389/�les/DP2011_008.pdf ].

Figure 4.5 shows the resolution of the reconstructed Z mass vs φ. This wasmade by binning the Z mass according to what region of φ the endcap electronwas in. The results for the two endcaps are shown separately. One can see thatin the positive endcap between -1.2 < φ < 0 there is a signi�cant increase in σ- the width of the peak, this coincides with a known area of inactive crystalsin the ECAL. This prompted a study on the e�ects of inactive crystals on theresolution which is summarized in Chapter 6.

When assessing the performance of the clustering algorithm at the start ofthis project, the resolution and Z mass peak were looked at against the numberof primary vertices in an event - known as pileup. The reason for there beingmore than one interaction per event is due to the way that the LHC works -bunches of protons are �red at each other within the beam, so in an event morethan two protons can interact thus creating multiple primary vertices - which arethe points of interaction. Figure 4.6 shows the resolution and mass against thenumber of primary vertices in an event. When plotting these histograms, binsof roughly equal numbers of events were used (about 20000 events per bin). Onecan see that there is an increase in mass of about 0.6 GeV from 1-37 vertices,

24

(a) An example of a 5x5 Electron (b) An Example of an extended electron

(c) An Example of a Gap Electron.

Figure 4.4: Examples of Electron Scans

25

Figure 4.5: The resolution of the reconstructed Z mass vs φ in both endcaps.(EE± represents the positive or negative endcap)

26

(a) The Resolution of the reconstructed Z massvs the number of vertices per event, in separateendcaps

(b) The reconstructed Z mass vs the number ofvertices per event, in separate endcaps.

Figure 4.6: The reconstructed Z mass and the resolution of this vs the number ifvertices per event. The number of vertices is the number of primary interactionsin each event.

but the resolution on the Z mass doesn't considerably change. This increasein mass could a�ect physics analyses considerably and so it is the subject ofChapter 7.

27

5 Changes in Code Due to Unclustered Energy

During the analysis in described in Chapter 4 a problem with the clusteringwas observed: some super clusters had areas of unclustered energy, within theη and φ road of the seed, which should have been clustered. A scan of 100electrons showed that about 6% of electrons had an area of crystals (with ET >1GeV) that should have been clustered but wasn't. For some of these electronsup to 10 GeV had been left unclustered. These electrons were not in areas ofinactive crystals so it was ascertained that the problem must lie in the clusteringalgorithm: Multi5x5ClusterAlgo.cc.

After studying a few of these electrons, certain pathologies were noticed,which are presented below with the aid of Figure 5.1, which shows an exampleof a gap electron in detail. The small boxes represent seeds, and large boxes ofthe same colour show the corresponding basic cluster.

• The missed energy is in the shape of a basic cluster.

The primary basic cluster is labelled 'A', it would be the �rst basic cluster tobe made since it's seed of 33.6 GeV is the largest local maxima. The gap inclustering 'B' is in the shape of a basic cluster with a seed of 10.2 GeV. Oncecrystals have been included in a basic cluster they can't be used elsewhere,which is why it's shape is not a square. (See Figure 4.1 for more detail on howhits are spread between basic clusters)

• These basic clusters had their seed contained within a cluster with a largerseed. The remaining hits associated with the basic cluster did not containthe seed.

The seed of B is the 10.2 GeV crystal highlighted in yellow, it is contained withinbasic cluster A.

• Where two basic clusters overlapped, but the larger ET one had beenmissed o� of clustering, the shared hits were not included in the clusteredhit.

It is possible to see this point when looking at basic cluster C: the 4 crystalsto it's bottom right (0.2, 0.2, 0.3, 0 GeV) should have been clustered if basiccluster B was not included in the super cluster.

Basic cluster B looks like a legitimate electromagnetic deposit, and it shouldbe included in the super cluster. B must be within the η-φ search box for thesuper cluster since basic cluster C has also been clustered and it's seed is a localmaxima not within a 3x3 square of another larger seed. This particular electronhas 6.7 GeV of missing energy, this is 7.9% of the total energy that should havebeen clustered.

5.1 Cause of the Problem and Preliminary Fix of the Code

The bug in the code was found to be in a check on whether the sum of a basiccluster's hits without the seed were greater than or equal to zero, this is a check

28

Figure 5.1: An example of a 'Gap Electron' before the code �x. The numbersrepresent the energy (GeV) of recorded hits (crystals) and the red representswhich of these hits have been clustered. The small boxes highlight the seeds,and the larger boxes represent the basic clusters. Basic cluster 'A' has a seed of33.6 GeV. The missed basic cluster 'B' (in white) has a seed of 10.2 GeV. Thebasic cluster 'C' has a seed of 3.6 GeV.

29

on whether the seed is from an actual particle, or just a local maximum gener-ated from noise9. This is a legitimate check, since the addition of noise wouldobscure the energy of the electron or photon that you are trying to reconstruct,however the check was written in the following way:

This meant that basic clusters which did not include their seed were unlikelyto ever pass since the seed should theoretically hold the majority of the energy.Once crystals have been assigned to a basic cluster they are removed from thecollection of hits that are available to be clustered. The way that basic clusterswhich did not pass this check were discarded meant that their associated hitswere not re-entered into this collection. This meant that overlapping basicclusters created after this one could not re-use these hits.

This check was changed to:

9Noise is the term used to describe electronic noise and also event pileup noise which iswhere additional particles cause signals that overlap in time.

30

5.2 Results from the Preliminary Fix

After changing the code, some known 'gap electrons' were scanned and the gapshad been �lled in correctly (Figure 5.2). The new code was then checked onfour Monte Carlo samples10:

• Electron PT 10 GeV 11

• Electron PT 35 GeV

• Photon PT 10 GeV

• Photon PT 35 GeV

Monte Carlo samples were used because one can tell whether the changes fromthe old reconstruction code to the new are improvements because we know thetrue value of the transverse momentum, energy, and transverse energy.

The results of the change in code are presented in Table 2 and in the graphsin Figure 5.3. The improvement on the resolution of the peaks is ~5%, This canbe seen in the graphs, which are of (super cluster ET

12 - trueET )/trueET for thefour samples, where the new codes peak is larger and thinner than the original

10Monte Carlo Samples are computer generated examples of data sets. They are made usingMonte Carlo simulations.

11PT refers to transverse momentum.12This is the energy measured before cluster corrections are applied on top

31

(a) The gap electron before the code �x

(b) The gap electron after the code change

Figure 5.2: An Example of a Gap Electron before and After the code change.

32

(a) Electron PT = 10 GeV (b) Electron PT = 35 GeV

(c) Photon PT = 10 GeV (d) Photon PT = 35 GeV

Figure 5.3: Graphs of (Super cluster ET - trueET )/trueET for the four samples.

code's. 'Super clusterET ' is the recorded ET before adding the standard clustercorrections. 'True ET ' is the ET of the particles in the sample.This shows thatthe code �x works, and has been shown to improve the resolution of the ECALEndcaps. More graphs comparing old to new code can be found in Section C ofthe Appendix.

Sample Old New Improvement

Electron PT 10 GeV 0.103 0.098 4.7%Electron PT 35 GeV 0.055 0.053 4.6%Photon PT 10 GeV 0.085 0.080 5.7%Photon PT 35 GeV 0.044 0.041 7.8%

Table 2: The E�ective Sigma of (super cluster ET - trueET )/trueET . The'E�ective Sigma' is the smallest width on a histogram which contains 68% ofresults.

33

5.3 Optimization of Energy Assignment in Basic Clusters

5.3.1 Motivation for Optimizing the Energy Assignment in BasicClusters

A side e�ect of the preliminary code change is that the additional basic clustersonly have partial energy, this can be seen in Figure 5.2 where the extra basiccluster has a small energy and an unphysical shape. Due to the way that thesebasic clusters are constructed, the shape recorded energy and position, of thisbasic cluster is quite di�erent to the intrinsic shower shape that would have beencreated around the seed crystal of 10.2 GeV. Whilst this does not a�ect particlesrepresented by the super cluster, some physics analyses look at separate basicclusters, and so the inclusion of these missed basic clusters has highlighted aproblem with the energy sharing between basic clusters. One such variable isEele/Pout, which is the ratio of the reconstructed energy of an electron to themomentum of the track associated with that electron. This variable is usedin Higgs analyses. Figure 5.4 is a graph of the Eele/Pout distribution in theendcaps. The blue line represents the old code, and the red points representthe values after the preliminary code change. One can see that for values ofEele/Pout < 1 there is a peak in the data for the newer code, this is due to theextra basic clusters for which the energy of the basic cluster is much less thanthe corresponding energy of the shower. Before the code changes, the missedbasic clusters did not get matched to a track so this problem was masked.

5.3.2 The Proposed Solution - Basic Cluster's Retaining their ownSeeds

A proposed solution to this problem was the inclusion of seeds in their ownbasic cluster. This does not solve the energy sharing problem completely, sincethe higher seeded basic clusters still retain some of the smaller seeded basiccluster's energy, but due to the close proximity of these basic clusters, it isthe best approximation for a basic cluster's actual energy that can be founde�ciently13. This solution should not a�ect the super cluster, just the basicclusters within it.

5.3.3 How the new Clustering Code Works

The new clustering code is the same as the old (4.1) with the preliminarychanges, except for some minor changes (which have been written in bold):

1. It takes a vector of the recorded hits in the ECAL, ordered from highesttransverse energy (ET ) to lowest.

2. From this list it �nds local maxima using a 'Swiss Cross' (largest out ofthe hits directly above, below, left and right).

13Other methods of �nding the basic clusters actual energy are using iterative methods withgaussian curves to try to �nd the best way of sharing the energy. This method takes a longtime, and is not guaranteed to ever converge.

34

Figure 5.4: Eele/Pout for each individual basic cluster within a super clusterin the ECAL Endcaps on Monte Carlo sample, after the �rst code change. Theblue line represents the the original values, and the red points shows Eele/Poutafter the �rst code change.

35

3. For these maxima to be labelled as 'seeds' they must have an ET > 0.18GeV and they cannot be within the 3x3 square of crystals around another(larger) seed.

4. A 'proto basic cluster'14 is then made around each seed. This is a 5x5square of crystals with the seed at the centre.

5. In the case where proto basic clusters have overlapping hits, the protobasic cluster with the largest ET seed retains them.

6. Once all proto basic clusters have been made (the collection(vector) of possible seeds has been run through) any seeds thatare not included in their own proto basic cluster are moved tothe one that they seed.

7. Once all seeds have been moved to their correct proto basiccluster, they are turned into basic clusters.

8. Starting from the largest ET seed, if ET > 1GeV a super cluster is made,this is where any basic clusters within a φ road of 0.6 rad and an η roadof 0.14 are added together and called a super cluster.

5.4 Results from the Final Code Change

5.4.1 Basic Cluster Energy

Figure 5.5 shows the Eele/Pout graph for the seed swapping algorithm (redpoints) against the old code with the preliminary code �x15 (blue line). Onecan see that the low tail is essentially removed with the latest algorithm. Thisimproved value of Eele/Pout will improve Higgs analyses since basic clustershave closer energies to the electromagnetic deposits that make them, and alsothe missed basic clusters from before the �rst change in code can be attributedto their momentum tracks, thus improving the overall data resolution.

5.4.2 How the New Code A�ects Super Clusters

On testing the new code over the same Monte Carlo samples that were tested inSection 5.2 a di�erence in results between the two code changes was seen at the0.1% level, in both position and energy. This could arise for the basic clusterson the outside of a super cluster's φ-η box. If the seed was originally containedwithin a neighboring basic cluster within the φ-η box. The latest code changewould remove the outside basic cluster's seed from the super cluster; This wouldhappen very rarely and so could explain the small di�erence. The position ofsuper clusters/basic clusters can also change due to the relative position of the

14a proto basic cluster is the same as a basic cluster except that it contains a vector of thehits included, and also it has information on whether or not it contains it's own seed.

15Note that the 1st code change has swapped from red points in Figure 5.4 to the blue linein Figure 5.5.

36

Figure 5.5: Eele/Pout for each individual basic cluster within a super clusterin the ECAL Endcaps on a Monte Carlo sample, after the �nal code change.The blue line is the values after the �rst code change and the red points are theresults after the second code change.

cluster changing due to one extra or less crystal (the position of clusters isweighted via their energy).

5.5 Outcome of the Code Changes

Since the �nal code change was shown to �x the problem in the clustering algo-rithm, improve the resolution of the ECAL endcaps by about 5%, and improvehow energy is shared between basic clusters it was implemented into the CMSsoftware framework (CMSSW)16 and is now used in physics analyses. (The codecan be found here).

16CMSSW is the o�cial CMS code.

37

(a) The Resolution in the positive endcap vs φ in bandsof η

(b) A map of the inactive channels in the positive end-cap

Figure 6.1: A comparison of the resolution and the inactive crystals in thepositive endcap. The circled regions correspond to the same area

6 Analysis of Inactive Channels on the EE Res-

olution

Inactive channels are channels which are broken or noisy and therefore recordenergy that isn't there, or dead which is where they don't record any energy.These channels are �agged as bad and are not used in the event reconstruction.This means that the measurement associated with these channels will print out0 GeV, and the basic clusters cannot seed on them. There were 244 inactivechannels at the time of this study, 66 in the negative endcap and 178 in thepositive.

6.1 Motivation

In chapter 4, the resolution of the reconstructed Z mass peak vs phi was studied(Figure 4.5) and it was noted that in the positive endcap there was a degradationin data near a large area of inactive channels.

Figure 6.1 shows the resolution in the positive endcap vs φ in bands of ηand also the inactive channels in the positive endcap. The circled areas on thetwo graphs correspond to the same place. One can see that this area has a largedead region and corresponds to degradation in the data, which is shown as aworsening in the resolution. This degradation is due to the electrons not havingall of their energy clustered due to the missing channels. Figure 6.2 shows anexample of an electron with a dead channel within the primary basic cluster.It can be inferred from the other crystals within a Swiss Cross of the seed thatthis electron is missing a signi�cant amount of energy.

Due to the amount of energy that electrons near these areas could be missing,

38

Figure 6.2: An Example of an electron a�ected by a bad channel. The zerosuppressed channel is at (48, 23)

39

(a) Positive endcap (b) Negative endcap

Figure 6.3: Graphs of the areas where super clusters cannot seed using the badchannel cuts. Blue = bad crystals, green + blue = 3x3 area around bad crystals,red + green + blue = 5x5 area around bad crystals.

it can be argued that they should not actually be included in data and so a studyon the resolution of the endcaps when these electrons are not included was done.

6.2 A Cut on Electrons that have seeded near an inactive

channel

6.2.1 How cut works and where it a�ects

At the time of this study there were a total of 244 dead channels in the ECALendcaps, this is 1.7% of the crystals. Two cuts on electrons were investigated:

1. Electrons that had a bad channel within the 3x3 square of crystals aroundthe super cluster seed (inner 9 crystals of the primary basic cluster)

2. Electrons that had a bad channel within the 5x5 square of crystals aroundthe super cluster seed (the primary basic cluster)

If an electron had one of these conditions then it did not pass that cut andwas removed from the dataset. These reduced the acceptance of the electronsamples by 4.1% and 11.5% respectively. Figure 6.3 shows the areas within theECAL endcaps where a super cluster cannot seed due to these cuts, the greyarea is the position of the crystals in the endcap and the blue areas are the badchannels. The cut on having a bad channel within a 3x3 square around the seedwould disallow seeding within the blue and green areas on the graphs, likewisea cut on bad channels within a 5x5 of the seed would exclude seeding in the red,green or blue areas.

6.2.2 Results

Figure 6.4 shows the results of the cut in the positive endcap vs. φ for η < 1.8.This was the highlighted region in Figure 6.1 a) which was a�ected most by the

40

Figure 6.4: Resolution vs. φ for η < 1.8 in the Positive Endcap without cuts (justcan't seed on dead channels), a cut on electrons with inactive channels within3x3 of the super cluster seed, and a cut on electrons with inactive channelswithin 5x5 of the super cluster seed

inactive channels. It can be seen that there is a dramatic improvement between-0.6 < φ < 1.4 which is where there are a large number of these bad channels,particularly at φ = -0.6 for which there is an improvement on the resolutionof ~0.8 GeV between the original sample and cutting any electrons with a badchannel within a 5x5 square of crystals around the seed. This corresponds toan improvement in that bin of ~19%.

Table 3 shows the overall results of these cuts on the resolution. The overallimprovement in the resolution is 1.6% for the 3x3 cut, and 1.9% for the 5x5 cut inthe positive endcap, and 0.6%, 1.0% respectively in the negative endcap. Thesevalues re�ect what resolution the endcaps could be if there where no inactivechannels. Electrons which have a bad channel within their super cluster, butnot within the primary cluster, can still pass the cuts. From Table 1 it wasshown that 54% of electrons, the 'Extended electrons', had more than one basiccluster. The resolution for these could be even better if the missing channelswere recovered.

41

Endcap: Positive Negative

Resolution (GeV) % of Zs that pass Resolution (GeV) % of Zs that passNo cut 3.09 100 3.12 100No bad

channels within3x3 of seed

3.04 (1.6%) 95.5 3.10 (0.6%) 96.4

No badchannels within5x5 of seed

3.03 (1.9%) 87.5 3.09 (1.0%) 89.4

Table 3: The results from using the bad channel cuts on the Z→ee sample. Allthe resolution results have an error of 0.01 GeV

6.3 Conclusions

The inactive channels are a detector problem that has an a�ect on physics. Ithas been shown that there is an issue which is non-negligible. The probabilitythat the primary basic cluster of an electron will be a�ected by an inactivechannel is re�ected in the acceptance levels of the 5x5 cut which reduces thesample by 11.5 %. My recommendations for future work are to encourage CMSto �x these problems. For the single channels an energy recovery algorithmshould be looked into. For larger areas of dead channels, �xing or replacingthem should be a priority in the scheduled 2013 Long Shutdown.

42

Figure 7.1: An event display of a high pileup event, showing the interactionsalong the z axis. This event had 29 primary vertices, each one shown in adi�erent colour.

7 Analysis of How Pileup a�ects ECAL Resolu-

tion

Pileup is the term used to describe how many interactions there are in an event.The proton beams in the LHC consist of bunches of protons. When the beamscross there is often more than one proton pair that interacts. Larger amountsof initial collisions create many �nal particles which increases the chance ofparticles overlapping in the detector. Figure 7.1 shows an event with 29 primaryvertices. From this it is easy to see the complexity of measuring particles athigh pileup, since there is a huge amount of additional particles that reach thedetector.

7.1 Motivation

In the original analysis of the clustering algorithm it was noted that there wasan increase in the reconstructed mass of the Z with an increase in the number ofvertices (see Figure 4.6). The dataset from which these graphs were made had amean number of vertices per event of 9, with a range of 1-37; it's distribution canbe seen in Figure 7.2 . In 2012, the projected instantaneous luminosity of theLHC will be 7 x 1033cm−2s−1, thus increasing the estimated average number ofvertices per event to 35***need to �nd proper references for these 2 numbers***.This increase in pileup could signi�cantly increase the apparent recorded mass ofobjects in the ECAL which could a�ect physics analyses greatly, so an analysison the a�ect of pileup was made.

43

Figure 7.2: A Graph of the Number of Vertices per Event against Frequency for2011 data

Dataset Number of Events Mass Mean Sigma

A 5034 91.93 ± 0.07 3.23 ± 0.05B 5118 92.39 ± 0.07 3.49 ± 0.05

Table 4: The Results of the Z mass and it's resolution on two datasets using aVoigtian �t, where A is 9<vertices < 20 vertices, and B is 25 < vertices < 32

7.2 A�ect of High Pileup on Mass of Z particles Using

Monte Carlo Data

To assess the a�ect of pileup at higher luminosities, high pileup Monte Carlodata were used (since high pileup data had not been created at the time of theanalysis). The MC data sample used was 'Drell-Yan to two leptons' which wasskimmed for Z→ee events, of which there were 23192. The range of primaryvertices in this set can be seen in Figure 7.3. The mean is 23 and the range on thenumber of vertices in an event is from 9-45. Figure 7.4 shows the reconstructedmass of the Z particle against the number of primary vertices with a line ofbest �t (which is calculated from 10-40 vertices since other bins did not containenough data). This clearly shows an increase in apparent mass, which is about1 GeV. This is a larger a�ect then was seen previously.

Another way of assessing the e�ect of pileup on the reconstructed Z masswas to look at two large bins of data: 9 < vertices < 20 and 25 < vertices < 32.This was to decrease the chance of results being skewed by particularly large orsmall events, and to have a quantitative way of interpreting the data. Table 4shows the results of this study. One can see that there is an increase in apparentmass of 0.46 GeV between the two sets, whilst the resolution is only degradedby 0.26 GeV.

7.3 Conclusions

This analysis has shown that there is an increase in apparent mass with pileupwhich is consistent with what was seen in Chapter 4. The luminosity of the LHC

44

Figure 7.3: The Distribution of the Number of Primary Vertices in an Event forthe Monte Carlo Sample 'Drell-Yan to two leptons'.

will continue to increase until it gets to the design performance of 1034cm−2s−1,which in turn will increase the pileup. Therefore it is important to �nd a wayto correctly reconstruct the mass, otherwise the problem will get worse. Dueto this the ECAL Detector Performance Group is trying to reduce the e�ectof pileup, and is looking to improve ways of dealing with the increased pileupexpected in 2012.

The increase in mass is probably due to event pileup noise which is whereadditional particles cause signals that overlap in time. The increased pileupwould increase the amount of overlapping particles, causing more energy to berecorded than there should be. This needs to be looked into further to con�rm.

45

Figure 7.4: The Reconstructed Z mass Against Number of Primary Vertices,with a line of best �t.

46

8 Conclusions

The ECAL Endcap clustering algorithm was scrutinised analysed to check itsstatus and see if there were any areas in which it could be improved to ensure thebest possible resolution. As well as aiding other physics analyses, this wouldhelp in the search for the Standard Model Higgs Boson. Certain pathologieswere found and some were resolved.

From initial studies where electrons were reconstructed, an issue within theclustering algorithm was highlighted and �xed. This lead to the issue of ba-sic cluster energy sharing being highlighted, and �xed with a seed swappingalgorithm. Testing these �xes on Monte Carlo data showed that there was animprovement of about 5%.

Studies on the resolution of reconstructed Z→ee events also hinted that in-active channels were worsening the resolution in the Endcaps. Further investi-gation showed that if all electrons did not contain an inactive channel within theprimary basic cluster, then the overall resolution in the positive endcap (whichhas the majority of bad channels) would improve by 1.9%, and in certain areasthere could be an improvement of up to 19%. Due to this it would be bene�cialto work on energy recovery algorithms for single inactive channels, and repairthe larger areas of bad channels if possible during the next long shutdown ofthe LHC.

A study on the a�ect of pileup on mass has shown that there is a correlationbetween the two. It is important for CMS to look into this issue because theincreased luminosity in 2012 will increase the pileup signi�cantly.

47

References

[1] http://www.fnal.gov/pub/inquiring/matter/madeof/index.html StandardModel image credit

[2] http://twiki.cern.ch/twiki/bin/view/LHCPhysics/CERNYellowReportPageBRStandard Model Higgs Branching Ratio Plot credit

A High Energy Electron Pair Selection Cuts

The HEEP selection cuts are presented in the table below.Cut Barrel Endcap

ET > 25 GeV > 25 GeV|∆ηin| < 0.005 < 0.007|∆φin| < 0.09 < 0.009

isEcalDriven True TrueH/E < 0.05 < 0.05σiηiη NA < 0.03

E2x5/E5x5 > 0.94 NAEM + hadDepth 1 (for ET < 50) < 2 + 0.3*ET GeV < 2.5 GeVEM + hadDepth 1 (for ET < 50) < 2 + 0.3*ET GeV < 2.5 + 0.03*(ET - 50) GeV

hadDepth 2 NA < 0.5 GeVTrack PT < 7.5 GeV < 15 GeV

Variable De�nitions:

ET the transverse energy of the electron

|∆ηin| the modulus of the di�erence between the electron and it's associatedtrack in η

|∆φin| the modulus of the di�erence between the electron and it's associatedtrack in φ

isEcalDriven this means that a super cluster is found �rst and then there isa check to look for a track, rather then the other way around.

H/E the ratio of the energy deposited in the Hadronic Calorimeter (HCAL) tothe energy deposited in the ECAL.

σiηiη the spatial covariance of the electromagnetic shower.

E2x5/E5x5 the ratio of the energy in a strip of 2x5 crystals around the seed bythe 5x5 square around the seed in the barrel.

EM the transverse electromagnetic energy of all the recHits.

hadDepth the transverse depth of energy measured in the HCAL in a cone of0.3 radius around the electron's position in the calorimeter. The di�erencebetween 1 and 2 is which caloTowers are used.

48

Track PT the transverse momentum of the associated track.

B An Alternative Clustering Algorithm

B.1 The Alternate Algorithm

The alternative algorithm was a special algorithm, created for comparison withthe original clustering algorithm. It is the same as the original code (Section4.1) except:

1. There was no limit on how close two seeds can be.

2. The minimum seed ET = 0 GeV.

3. ∆η = 2.0, ∆φ = 0.3665 rad. (These values were optimized).

4. There was no check on the energy of a basic cluster before it was includedin a super cluster.

B.2 Results of the Alternative Algorithm

Figure B.1 shows the same scans as in Figure 4.4, it can be seen that thealternative algorithm performs the same as the original in most cases, but is nota�ected by the 'energy gap' bug.

Figure B.2 shows the reconstructed Z mass against the number of primaryvertices for the two algorithms. Both algorithms show an increase with pileupand the alternative algorithm performs worse with an increase of 0.7% againstthe originals 0.6%, this is probably due to the alternative algorithms larger ηand φ limits for basic clusters to be added to a super cluster - more basic clustersare added, so more noise is added.

B.3 The Alternative Algorithm Using 3x3 Sized Basic Clus-

ters

This was analysis was repeated using the same alternative algorithm, but chang-ing the size of basic clusters to 3x3 instead of 5x5, the results are presented here.

Figure B.3 shows some reconstructions of electrons using both the algo-rithms. It can be seen that the 3x3 algorithm misses a lot of energy due toshowers not producing local maxima close enough together to create basic clus-ters.

Figure B.4 shows the ratio of the resolution of the reconstructed Z massagainst the reconstructed Z mass against φ in the two endcaps, for both algo-rithms. It can be seen that the 3x3 algorithm performs worse. Cluster cor-rections couldn't improve on the actual value of the ratio much because theyrequire super clusters to contain a constant amount of the actual energy of aparticle, the 3x3 algorithm does not do that otherwise the line would be muchmore stable.

49

(a) (b)

(c)

Figure B.1: The Same Scans as in Figure 4.4 but comparing the two algorithms.Green = both algorithms clustered, red = only the new algorithm clustered.These studies were made before the code �xes of Chapter 5.

50

(a) Reconstructed Z Mass against Pileup for theoriginal algorithm

(b) Reconstructed Z Mass against pileup for theAlternative Algorithm

Figure B.2: Comparison Graphs of the Reconstructed Z Mass against pileup forthe original and alternative algorithms

B.4 Conclusions

The alternative algorithm showed similar results to the original algorithm beforethe code changes due to the 'energy gap' bug and basic cluster energy sharingissue. It showed that the 'energy gap' bug could be �xed, and was not dueto detector problems. It performed worse than the original algorithm whenlooking at the mass resolution against pileup, and due to the cluster correctionsimproving the original code by about 5% it was predicted that the currentalgorithm will perform better than the alternative algorithm.

An algorithm using basic clusters of size 3x3 instead of 5x5 showed signi�-cantly worse results.

C Comparison Graphs for the Code Changes �

This is the only section i havnt �nished, i just

need to put the graphs in.

graphs to show that position is not a�ectedgraphs to show #SC not a�ectgraphs to show #BC/SC goes upgraphs of Et

51

(a) (b)

(c)

Figure B.3: The Same Scans as in Figure 4.4, using the 3x3 Algorithm. Green= both clustered, Red = only the alternative algorithm clustered, Blue = onlythe original algorithm clustered.

52

(a) The Ratio of Resolution/Reconstructed ZMass against φ for the original (old) and the al-ternative (new) algorithms in the positive end-cap.

(b) The Ratio of Resolution/Reconstructed ZMass against φ for the original (old) and thealternative (new) algorithms, in the negativeendcap.

Figure B.4: The Ratio of Resolution/Reconstructed Z Mass against φ for theoriginal (old) and the alternative (new) algorithms.

53