Università degli Studi di Perugia Dipartimento di Fisica e ... Solestizi-dottorato.pdf · Dipartimento di Fisica e Geologia Corso di dottorato di ricerca in scienza e tecnologia

Università degli Studi di PerugiaDipartimento di Fisica e Geologia

Corso di dottorato di ricerca in scienza e tecnologiaper la Fisica e la Geologia

XXIX ciclo

PhD thesis

Search for heavy composite Majorana neutrinosin Run II and feasibility study of a track-triggerfor Phase 2 with the CMS detector at the LHC

CandidateLuisa Alunni Solestizi

PhD coordinatorProf. Paola Comodi

SupervisorProf. Livio Fanò

Assistant supervisorsDr. Orlando Panella

Dr. Francesco Romeo

Academic year 2015-2016

A quelli che non amo ...... È merito loro

se vivo in tre dimensioni,in uno spazio non lirico e non retorico,

con un orizzonte vero, perché mobile- Wislawa Szymborska -

Abstract

This thesis intends to present the salient aspects of the research work that wascarried forward, in collaboration with the CMS experiment, during my PhD.

The LHC accelerator and the main features of the CMS detector are illustratedin the first chapter. The second chapter regards the status, performances, and futureperspectives of the CMS tracker subdetector. The crucial role of the tracker in theHigh Luminosity (HL)-LHC era, starting from 2023, is here introduced.

Once clarified the technological context and the working principles of the ma-chines, where the proton collisions take place, and thanks to which the particles canbe detected, a new model, and a specific analysis of the data collected in 2015, bythe CMS experiment, are presented.

First, the Standard Model (SM), its limits and extention possibilities, the currentstate of the searches for new physics, focusing on heavy neutrinos and leptoquarks,are illustrated in chapter 3, where the basis for a new search are provided.

Then, the original model is proposed in chapter 4, that leads a new experimentalanalysis, whose strategy and results are examined in chapter 5. This is a search forphysics beyond the SM in the final state with two same-flavour leptons (electronsor muons) and two quarks. The analysis has been performed using proton-protoncollisions at

√s = 13 TeV , recorded by the CMS experiment, at the LHC; the data

correspond to an integrated luminosity of 2.3 fb−1. The results are interpreted inthe framework of a new model, in which a heavy Majorana neutrino stems from acompositeness scenario.

The CMS collaboration is preparing the field to extend these searches in thefuture, at higher luminosity conditions. The HL LHC will require a totally differenttrigger paradigm, with the inclusion of the tracker at Level 1. After introducing thegeneral needs and upgrade plans towards this new phase (chapter 6), a specific track-trigger proposal is formulated, based on the Principal Component Analysis (PCA)

i

ii ABSTRACT

statistical method, and employing the Field Programmable Gate Array (FPGA)and Associative Memories (AM) devices. The software simulation and the hardwareprototype of this innovative system are finally discussed in chapter 7.

Contents

Abstract ii

List of figures ix

List of tables xi

1 The CMS detector at the LHC 11.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Compact Muon Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Calorimetry system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.1 The ECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4.2 The HCAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Tracker operation 112.1 Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Calibration and timing . . . . . . . . . . . . . . . . . . . . . . 122.1.2 Lorentz-drift correction . . . . . . . . . . . . . . . . . . . . . . 122.1.3 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.1 Track reconstruction . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 Primary vertex . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.3 Energy loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.1 Phase-1 upgrade . . . . . . . . . . . . . . . . . . . . . . . . . 21

iii

iv CONTENTS

2.3.2 Phase-2 upgrade . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Motivations for new physics search at LHC 293.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Shortcomings of the Standard Model . . . . . . . . . . . . . . . . . . 333.3 Principles for a Standard Model extention . . . . . . . . . . . . . . . 343.4 Current state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.5 Some models beyond Standard Model . . . . . . . . . . . . . . . . . . 373.6 Run I CMS searches . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.7 Run II CMS early searches . . . . . . . . . . . . . . . . . . . . . . . . 403.8 A new search for heavy neutrinos . . . . . . . . . . . . . . . . . . . . 43

4 A new model of heavy composite Majorana neutrinos 454.1 Introduction to the model . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Gauge and contact couplings . . . . . . . . . . . . . . . . . . . . . . . 474.3 Heavy neutrino’s production . . . . . . . . . . . . . . . . . . . . . . . 494.4 Heavy neutrino’s decay . . . . . . . . . . . . . . . . . . . . . . . . . . 494.5 Benchmark process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.6 Experimental versatility . . . . . . . . . . . . . . . . . . . . . . . . . 51

5 Experimental search for heavy composite Majorana neutrinos 575.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.2 Preliminary study at generator level . . . . . . . . . . . . . . . . . . . 59

5.2.1 Signal kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 615.2.2 Signal topology . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.3 Object selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.3.1 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.3.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.3.3 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.4 Signal region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.4.1 eeqq channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.4.2 µµqq channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.5 Variable for the signal extraction . . . . . . . . . . . . . . . . . . . . 805.6 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.6.1 DY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

v v

5.6.2 tt and tW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.6.3 QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.7 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 885.8 Statistical interpretation of the results . . . . . . . . . . . . . . . . . 89

5.8.1 The CLs technique . . . . . . . . . . . . . . . . . . . . . . . . 905.8.2 Exclusion limits . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6 CMS track trigger towards the HL-LHC 956.1 LHC status and future plans . . . . . . . . . . . . . . . . . . . . . . . 956.2 CMS trigger upgrade for Phase 2 . . . . . . . . . . . . . . . . . . . . 986.3 Motivations for a Level-1 track trigger . . . . . . . . . . . . . . . . . 98

7 New L1-track-trigger system based on PCA 1017.1 Track-finding process . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.2 A track fitting based on PCA . . . . . . . . . . . . . . . . . . . . . . 103

7.2.1 The PCA fitting simulation . . . . . . . . . . . . . . . . . . . 1047.2.2 Preliminary tests . . . . . . . . . . . . . . . . . . . . . . . . . 1057.2.3 The first results . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.3 Level-1 tracking demostrator . . . . . . . . . . . . . . . . . . . . . . . 1117.4 A pattern recognition mezzanine for L1 track triggers . . . . . . . . . 115

Conclusions 120

Bibliography 121

Acknowledgements 130

List of Figures

1.1 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 CMS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 CMS quadrant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 Muon chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Lorentz angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Parameter resolution VS η . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Parameter resolution VS pT . . . . . . . . . . . . . . . . . . . . . . . 182.4 Primary vertex resolution . . . . . . . . . . . . . . . . . . . . . . . . 202.5 dE/dx simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.6 Phase-1 pixel detector layout compared to the current one . . . . . . 222.7 Tracking efficiency and fake rate of the new pixel detector, compared

to the current one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.8 Working principle of the pT modules for the stub selection . . . . . . 252.9 pT modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1 Standard Model particles . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Leptoquark pair production . . . . . . . . . . . . . . . . . . . . . . . 373.3 Heavy neutrino and WR production . . . . . . . . . . . . . . . . . . . 383.4 Heavy neutrino and leptoquark excess . . . . . . . . . . . . . . . . . . 41

4.1 Production cross section . . . . . . . . . . . . . . . . . . . . . . . . . 504.2 Decay amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Feynman diagram of signal process . . . . . . . . . . . . . . . . . . . 524.4 Resonant and virtual process diagram . . . . . . . . . . . . . . . . . . 524.5 Resonant and virtual cross section . . . . . . . . . . . . . . . . . . . . 52

vii

viii LIST OF FIGURES

4.6 Mass shape consistency . . . . . . . . . . . . . . . . . . . . . . . . . . 544.7 Excess reproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1 Benchmark process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.2 pT distribution of final state objects and heavy neutrino . . . . . . . . 625.3 η distribution of final state objects and heavy neutrino . . . . . . . . 625.4 pT of the final state objects at different Λ . . . . . . . . . . . . . . . . 635.5 ∆R of all the possible pairs of objects . . . . . . . . . . . . . . . . . . 655.6 ∆R between the neutrino and each one of the final state objects . . . 655.7 cos(∆ϕ) of all the possible pairs of objects . . . . . . . . . . . . . . . 665.8 cos(∆ϕ) between the neutrino and each one of the final state objects 665.9 Comparison between decay amplitudes and ∆R between the two partons 675.10 Cumulative efficiency of each request of the "High-pT" muon selection 705.11 Cumulative efficiency of each request of the "HEEP" electron selection 735.12 Cumulative efficiency of each request of the "Tight" jet selection . . . 755.13 Large-radius jet multiplicity . . . . . . . . . . . . . . . . . . . . . . . 775.14 Invariant mass M(µ1, µ2), signal and SM background . . . . . . . . . 785.15 Significance plot for the various jet requests, eeqq channel . . . . . . . 785.16 Significance plot for the various jet requests, µµqq channel . . . . . . 795.17 Cumulative efficiency of the signal region selection . . . . . . . . . . . 805.18 Trigger efficiency VS pT of the leading lepton, in eeqq and µµqq channel 815.19 M(e, e, J) and M(µ, µ, J) distributions in the signal region, back-

ground and overlaid signal . . . . . . . . . . . . . . . . . . . . . . . . 815.20 M(l,l) around the Z mass peak . . . . . . . . . . . . . . . . . . . . . . 835.21 M(e, e, J) in the signal region compared to M(e, µ, J) in the control

region, normalized to 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 845.22 M(µ, µ, J) in the signal region compared to M(µ, e, J) in the control

region, normalized to 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 845.23 M(e, µ, J) for eeqq channel and M(µ, e, J) for µµjj channel, back-

ground compared to data . . . . . . . . . . . . . . . . . . . . . . . . . 855.24 M(e, e, J) (M(µ, µ, J)) in the signal region compared to M(e, µ, J)

(M(µ, e, J)) in the control region, normalized to luminosity . . . . . . 865.25 M(e, e, J) in eeqq channel and M(µ, µ, J) in µµjj channel, data

driven estimation compared to the MC prediction . . . . . . . . . . . 865.26 Resulting invariant mass distribution compared to data . . . . . . . . 93

LIST OF FIGURES ix

5.27 Exclusion limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.28 2-dimension exclusion limit . . . . . . . . . . . . . . . . . . . . . . . . 94

6.1 Extrapolated limit of the heavy neutrino search after phase 2, com-pared to the current one . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.2 LHC luminosity plan . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.1 Outer tracker towers . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.2 Stubs in the 18 tower and in its subtower . . . . . . . . . . . . . . . . 1067.3 Score plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.4 Resolution plots in the r − z plane . . . . . . . . . . . . . . . . . . . 1097.5 Resolution plots in the r − ϕ plane . . . . . . . . . . . . . . . . . . . 1107.6 PRM workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

List of Tables

3.1 CMS results in searches for leptoquarks and heavy neutrinos in RunI and Run II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1 Data samples, used in the analysis corresponding to the 2015 datataking period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Signal MC samples used in the analysis. . . . . . . . . . . . . . . . . 605.3 Background MC samples used in the analysis. . . . . . . . . . . . . . 605.4 SR/CR ratio for tt+Wt extimation . . . . . . . . . . . . . . . . . . . 855.5 Fake selection for electrons . . . . . . . . . . . . . . . . . . . . . . . . 875.6 Fake selection for muons . . . . . . . . . . . . . . . . . . . . . . . . . 875.7 FR for electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.8 FR for muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.9 Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.1 Coordinate covariance matrix eigenvalues . . . . . . . . . . . . . . . . 1077.2 Optimised resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117.3 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

xi

Chapter 1

The CMS detector at the LHC

In this first chapter, after having briefly introduced the Large Hadron Collidermachine (Sec. 1.1), we describe the Compact Muon Solenoid (CMS) particle detector(Sec. 1.2), its subdetecors (Sec. 1.3-1.5), and the trigger working principles (Sec.1.6).

1.1 The Large Hadron Collider

The Large Hadron Collider (LHC) is, currently, the most powerful hadron colliderin the world [1]. It is housed in the already existing, 27-km-long, circular tunnel ofLEP, in the Geneva region, at an average depth of 100 m underground (Fig.1.1). Themachine yields head-on collisions of two proton (or heavy ion) beams, circulating inopposite ways and in two distinct pipes, up to a design energy per beam of 7 TeV

(2.75 TeV for ions) and a design instantaneous luminosity of 1034cm−2s−1.The protons are accelerated by eight superconducting radio-frequency (RF) cav-

ities per beam. This result in a 0.5 GeV/turn energy kick, during the injectionphase. The beam trajectory is steered by 1232 superconducting dipole magnets,each 15-m-long and featuring an 8.3 T field strength. Several thousands, higherorder, magnets (quadrupoles, sextupoles, etc) focus the beam. The LHC is the laststep of a larger acceleretor complex. Linac2 takes the protons extracted from abottle of hydrogen gas, forms the beam, and inject it, at 50 MeV , into the ProtonSynchrotron Booster (PSB). The PSB accelerates the protons up to 1.4 GeV . Thebeam passes to the Proton Synchrotron (PS), and then to the Super Proton Syn-chrotron (SPS). Here, it reaches 450 GeV of energy, enough to be tranferred into the

1

2 1. The CMS detector at the LHC

Figure 1.1: The circunference of the Large Hadron Collider. The four orange dotscorrespond to the four collision points, surrounded by the particle detectors. They are:ATLAS, CMS, ALICE, LHCb, and the smaller TOTEM and LHCf, both using particlesthrown forward by collisions.

LHC. At nominal parameters, the LHC proton beams consist of bunches of O(1011)protons each, spaced by 25 ns. Their tranverse section, near the collision point, hasdimensions of the order of tens of microns.

There are four main experiments, located in underground caverns, in corrispon-dance of the collision points, along the path of the LHC circumference. The ATLAS(A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid) detectors, thepolar opposite of the circumference, are twin experiments. They were designed todiscover the Higgs boson, and to look for signals of new physics beyond the Stan-dard Model (SM), but also to study a wide range of phenomena produced by bothion-ion and proton-proton collisions. The LHCb experiment was designed to carryout precision measurements of the CP-violation and the rare decays of B hadronsin proton-proton (pp) collisions. The ALICE (A Large Ion Collider Experiment)detector is used to study the physics of strongly-interacting matter and the quark-gluon plasma, in heavy-ion collisions. Two more, smaller experiments, TOTEM andLHCf, are interested in the study of the very forward particles from proton-protoncollisions.

The LHC operation began on the 10th of September 2008, when the first beamscirculeted successfully for the first time. After an accident to the dipole circuit,

1.2 Compact Muon Solenoid 3

the machine activity had to be suspended until the autumn 2009, when it restartedaiming to reach half the design energy of 3.5 TeV per beam. The first LHC pp colli-sion at 7 TeV of energy in the centre of mass happened on the 30th of March 2010.The collected integrated luminosity was 45.0 pb−1 in 2010 and 6.1 fb−1 in 2011, at7 TeV of collision energy; while the luminosity delivered in 2012, at 8 TeV , was of23.3 fb−1. Then, the LHC entered a 2-year-long technical stop period, LS1 (LongShutdown 1), in which magnet interconnects have been repaired, in order to collideat design energy and luminosity, in 2015. Last year, the proton beams were back inthe accelerator, and the first beam of Run II, at the record energy of 6.5 TeV , wasrecorded, on the 10th of April 2015. The first collisions at the lower beam energy of450 GeV followed. Since June 2015, new data at 13 TeV have been recorded by thedetectors, reaching an integrated luminosity of 4.2 fb−1 for that year. After a briefwinter shutdown, new data have been collected at the same energy, during 2016.They correspond to an integreted luminosity of 38.27 fb−1.

1.2 Compact Muon Solenoid

The Compact Muon Solenoid (CMS) is a general purpose detector that operatesat the Large Hadron Collider (LHC) at CERN [2]. It is installed, about 100 m

underground, close to the French village of Cessy. CMS has a cilindrical structure(barrel) closed at the basis (endcaps), able to hermetically cover all the solid anglearound a collision, as the schematic view in Fig.1.2 shows. The detector is 21.6 m

long, 14.6 m in diameter, and weighs approximately 14000 t.At its centre, there is the silicon tracker, whose granularity reduces from the

innermost pixel detector to the more external microstrip detector. These are en-compassed by the lead tungstate crystal electromagnetic calorimeter, and the brassand scintillator hadronic calorimeter. A preshower system is located in front of theendcap calorimeter, in order to distinguish pions from prompt photons. A super-conducting solenoid, of 12.5 m of length and 6 m of internal radius, surrounds mostof the calorimeter volume, and provides a magnetic field strength of 3.8 T . Thispowerful magnetic field allows to accurately measure charged particle momenta, upto high energies, using the track curvature. The muon system is all outside of thesolenoid, and consists of three different kind of gas ionization chambers, for identi-


fying muons, and for determining their momenta and charge. These muon stationsare interleaved with iron layers, that behave as return yoke for the magnetic flux.

The purpose of the CMS subdetectors is to measure, the energy, momentum,and position of electrons, muons, photons and hadrons, with high resolution. Theneutrinos can be inferred, thanks to the CMS hermeticity, through the transverseenergy imbalance of all the reconstructed visible particles in the event.

Figure 1.2: Exploded view of the CMS detector.

The coordinate system adopted by CMS has its origin at the nominal collisionpoint, the horizontal x-axis points radially towards the centre of the LHC circun-ference, the y-axis points vertically upwards, and thus the z-axis points along thebeam direction. It is intuitive, for a cilindrical experiment, using cylindrical polarcoordinates; the azimuthal angle ϕ is measured from the positive x-axis in the x-yplane, and the polar angle θ is measured from the positive z-axis in the y-z plane.The pseudorapidity η = −ln(tan θ

2) is often used, instead of the polar angle. Theangular separation of particles in the detector is typically described by the quantity∆R, defined as ∆R =

√(∆ϕ)2 + (∆η)2. Transverse energy ET and momentum pT

are defined as the components of energy and momentum in the x-y plane. The im-balance of the detected energy in the transverse plane, associated with undetectable

1.3 Tracking system 5

particles, such as neutrinos, is defined as the missing-transverse energy, MET.Two levels of trigger systems are used to reduce the event rate from 40 MHz to

the order of 100 Hz for archival storage.

Figure 1.3: View of a CMS quadrant in the R-z plane.

1.3 Tracking system

The tracking system is the part of the detector closest to the beam pipe [3].It measures the trajectories (tracks) of the charge particles travelling through it,thanks to semiconductor detector elements.Consisting in a cilinder of both barrel and endcap components, the system hasan overall length of 5.8 m and a diameter of 2.5 m, and covers a pseudorapidityrange of |η| < 2.5. The heart of the tracker is the Pixel detector. In the outertracker, the barrel part consists of the Tracker Inner Barrel (TIB) and the TrackerOuter Barrel (TOB), whereas the endcap disks are made up of the Tracker InnerDisks (TID) and the Tracker End Caps (TEC). One can refer to Fig.1.4, whereblack lines indicate single-layer modules, whilst each blue line represents a stereomodule. In these modules, each strip is coupled with another one, that is rotatedwith regard to the first one, allowing for the measurement of the missing thirdcoordinate. The innermost components are built using silicon pixel elements, whileall outer components are made up of silicon strip elements. The tracker is equipped


with insulation and a cooling system, ensuring a safe operating temperature.

Figure 1.4: The current CMS tracking system.

The tracks of charged particles are curved, due to the magnetic field of 3.8 T , es-tablished by the solenoid, and a measurement of their curvature allows to determineboth the charge and the momentum of the particles. The momentum resolution inthe tracker is better than 3%, in the central part of the detector (|η| < 1.5), forparticles with transverse momentum up to 100 GeV .The tracker system also provides a robust vertex reconstruction. The spatial res-olution of the tracker permits to distinguish between tracks coming from the hardproton-proton interaction and from the pileup vertices. The transverse impact pa-rameter resolution, for particles with pT > 10 GeV , is better than 35 µm, while thelongitudinal impact parameter resolution is better than 75 µm.Moreover, the tracker performance allows to identify jets containing a bottom quark,using b-tagging algorithms. The identification of b jets is interesting for several stud-ies: top quark decays via the t → bW process with a branching fraction of almost100%, many particles predicted by beyond SM (BSM) theories have final statesinvolving bottom quarks.

1.4 Calorimetry system 7

1.4 Calorimetry system

The main calorimetry system [4] is included inside the solenoid, and consists oftwo subdetectors, both of which enclose the tracking system. The inner subdetectoris the Electromagnetic Calorimeter (ECAL), designed to detect electromagneticallyinteracting particles, like photons and electrons. On the outer side is the HadronCalorimeter (HCAL) that focuses on hadrons, which interact with the detector viathe strong force, and usually are not stopped by the ECAL.

The calorimetry system is important, not only for the direct measurement ofthe energy of the detectable particles, but also for the determination of the overallbalance of the transverse energy in a collision event. This variable gives informa-tion on those particles that cannot be detected, like neutrinos or the various weakinteracting hypothesised particles, in BSM theories.A statistical description of the energy deposit of electrically charged particles travers-ing the detector material is given by:

E(x) = E0e− x

X0 . (1.1)

E(x) is the energy of the particle, after travelling a distance x in the material, E0

is the initial energy, and X0 is the radiation length. This is defined as the distanceafter which the particle energy has been reduced to E0/e. In the case of hadrons,the same formula can be used, but the hadron interaction length λI takes the placeof the radiation length. Because of their direct relation to the physical absorptionprocesses, these two lengths X0 and λI are employed as units for the specificationof the amounts of absorbing material in specific parts of the detector.

1.4.1 The ECAL

The ECAL is made up of lead tungstate (PbWO4) crystals, that work both asabsorbers and as scintillators. Having a single active material allows for a betterenergy resolution than that achieved by adding passive-material layers. The inter-action of an electron or photon, with the scintillating material, results in particleelectromagnetic showers. They consist of electrons, positrons and photons, emittedvia pair production and bremsstrahlung. Precise photo-detectors have the aim toconvert the produced photons in an electrical signal, that is roughly proportional tothe energy of the original particle. The lead tungstate has a density of 8.28 g/cm3,


a radiation length of X0 = 0.89 cm, and is transparent to visible light. It gives anhigh speed of response; about 80% of the light of a given excitation is emitted within25 ns, which corresponds to the design bunch-crossing time.

The ECAL is divided in the Electromagnetic Barrel (EB), consisting of 61200lead tungstate crystals, and in two Electromagnetic Endcaps (EE), located at |z| =314 cm, consisting of 10764 crystals each. The crystals have lengths of 230 mm and220 mm, in the barrel and endcap regions, respectively, comparable to 25 radiationlengths. In the EB, the detection of photons is performed by silicon avalanche pho-todiodes. In the EE, these are replaced by vacuum phototriodes, in order to avoidtoo high leakage currents, due to the higher radiation doses in the endcap region.The endcaps are fitted with preshower detectors, consisting of lead absorbers and sili-con detector layers, which provide a better angular resolution than the lead tungstatecrystals. This allows to improve the discrimination capability between single pho-tons and neutral pions, that decay into two photons with small angular separation.

1.4.2 The HCAL

The HCAL is a sample calorimeter, meaning that it alternates layers of absorberand scintillating material. Brass is used as the main absorber material because isnon magnetic, has an high density of ρ = 8.53 g/cm3 and a short interaction lengthof λI = 16.42 cm. Plastic materials have been chosen as scintillators.

The HCAL consists in the Hadron Barrel (HB), Hadron Outer (HO), HadronEndcap (HE) and Hadron Forward (HF). The HB and HO cover until |η| < 1.3, theendcaps extend from |η| = 1.3 to |η| = 3.0, and the HF has a range of 3.0 < |η| < 5.3.In terms of radiation lenght, it means 5.82 λI for the HB and 10 λI for both HEand HF.The HO is located outside the magnetic coil, for catching the tails of the moreenergetic showers not contained in the HB, it exploits the addictional absorber rep-resented by the solenoid.In the HF a different detection method is used; it employs copper as absorber ma-terial, and relies on quartz fiber calorimetry. The mechanism of interaction hereis the Cerenkov effect: photons are emitted by particles traversing the quarz fibersfaster then light in the means. Dedicated photomultipliers convert photons in elec-trical signals. The advantages of this technique are: higher speed of response, whichlies on a scale much smaller than the design bunch crossing time of 25 ns, and the

1.5 Muon system 9

insensitivity to neutrons’ fluxe, very large in the HF.

1.5 Muon system

The muon chambers [5] are the outermost subdetector of CMS, and alternate tothe magnetic return yokes, thus, they are immersed in a magnetic field of 2 T . Thevast majority of particles able to survive, after passing through all other detectorlayers, are the muons, which, due to their high mass, have comparatively smallenergy losses via bremsstrahlung in the calorimetry systems. Muons occur in manyof the most interesting processes of the SM and of new physics. Their importanceis reflected even in the name that was chosen for CMS as a whole.

The muonic system is divided in three components, see Fig.1.5:

• The Drift Tubes (DT); this system covers |η| < 1.2, and consists in cell of 21mm of lenght, filled with a a gas mixture of 85% Ar and 15% CO2, in whichthe drift time are of the order of 380 ns.

• The Resistive Plate Chambers (RPC); they cover |η| < 1.6, and consistin gas chambers, enclosed between pairs of paralel plate of phenolic resin.They provide high performances in timing, enabling to compensate the slowdetection process in the other muon subsystems, and to trigger the events atonline level.

• The Cathode Strip Chambers (CSC); only in the endcap, extend closerto the beam pipe than the other two subsystems, featuring 0.9 < |η| < 2.4.Consist of multiwire proportional chambers, covering roughly 5 000 m2, andusing about 2.5 million wires.

The individual stations of both the CSC and RPC systems are separated by the irondisks of the flux return yoke.

1.6 Trigger

The high bunch-crossing rate of up to 40 MHz at the LHC, joined to the amountof subdetector readout channels, and to the fact that there are several simultaneouscollitions per crossing, makes impossible to store this amount of data in its entirety.


Figure 1.5: Transverse slices of CMS: the central barrel wheel and representative endcapdisks, indicating the numbering of the DT azimuthal sectors in the barrel and the CSCchambers numbers in the endcaps.

The purpose of the trigger system [6] is precisely to reduce, in a reasonable time,the data to a more manageable subset, while discarding as little useful informationas possible.

The first step of the trigger system is the Level-1 (L1) Trigger, which is performedon custom-designed and programmable electronics, and reduces the data rate toabout 0.1 MHz. It operates on special primitive trigger objects, provided by thecalorimetry and muons systems. A full readout of the detector data can be delayed,until after this trigger has made its decision on the retention of an event. Thereadout systems are activated only for those events passing this first step.

In a second step, the High Level Trigger (HLT) further reduces the rate to under400 Hz. It is implemented in software, using a custom version of the CMS analysissoftware reconstruction algorithms, and runs on a dedicated computing cluster. Thecombination of the electronic devices and computing cluster resources, used for thetrigger system, is referred to as the Data Acquisition (DAQ) system.

Chapter 2

Tracker operation

The scientific programme of the CMS experiment at the LHC covers a verywide spectrum of physics at the TeV scale. The trajectories of charged particles,called tracks, are among the most fundamental objects in the reconstruction of(pp) collisions. Tracks of electrons, muons, taus decays, and hadrons have to bereconstructed.The task of the CMS tracker [3] is to measure the tracks up to high momentum,with high resolution, high reconstruction efficiency, and low fake rate. In addition,tracks may be used to identify b jets, through the displacement of their secondaryvertex, compared to the primary vertex. The tracker has to face a high-densitytracks enviroment, including superimposed pp collisions in the same event (pileup),and a high frequency rate.The achievement of these goals requires a proper modelling of the tracker design,and excellent tracking performances, which depend also on the calibration and thealignment of the tracking devices. In the next-two sections, the commissioning issuesand the performances of the tracker are going to be illustrated.

2.1 Commissioning

Before starting the LHC pp collisions, the CMS experiment was commissioned,using events containing cosmic muons, collected during the Cosmic Run At FourTesla (CRAFT). The detector and the magnetic field conditions during CRAFTwere quite similar to the conditions during pp collisions. Thus, the results obtainedby CRAFT provided good initial operating points for the pixel detector, the strip

11

12 2. Tracker operation

detector, the tracker alignment, and the magnetic field. We focus here on the trackercommissioning [20].

2.1.1 Calibration and timing

In order to apply the bias potential to each of the sensors, calibration procedureswere used to determine the ADC gains and pedestals for all the channels.The tracker readout system uses the 40-MHz LHC clock as input. The signals fromthe CMS trigger system must arrive at the proper time, within the 25 ns clock cycle,to associate the correct bunch crossing with any signal above the readout threshold.An optimally phased clock signal will maximize the number of pixels observed inclusters. Thus, the overall trigger timing was adjusted by varying the clock phase,until the average barrel and endcap cluster sizes, as measured in minimum biastriggers, were maximized.

2.1.2 Lorentz-drift correction

The drift direction of the charge carriers is affected by the Lorentz force, due tothe high magnetic field, in which the tracker is immersed.The Lorentz angle θL, by which charge carriers are deflected in a magnetic fieldperpendicular to the electric field, is defined by

θL = ∆x

d= µHB = rHµB, (2.1)

where d corresponds to the drift distance along the electric field, and ∆x to theshift of the signal position. The drift mobility in a magnetic field, called the Hallmobility, is denoted by µH , the drift mobility without magnetic field by µ. Theyare related by the Hall scattering factor rH = µH/µ. This factor describes the meanfree time between carrier collisions, which depends on the carrier energy.Another important question is the dependence of the Lorentz shift on the irradiationdose. Radiation damage can change the drift properties, which will change theLorentz shift. Such a shift appears as a misalignment of the detector as function ofradiation dose, which itself is a function of the distance from the interaction point.

The Lorentz-drift effects are encoded in the cluster shapes, and the PIXELAVsimulation is used to compute them. The actual Lorentz calibration procedure is to

2.1 Commissioning 13

tune the detailed simulation to agree with data.The 2008 cosmic ray data were calibrated by measuring the cluster x-sizes as func-tions of cot(α), where α is the angle between the x axis and the track projection onthe local x-z plane, see Fig.2.1. In the pixel barrel, -cot(αmin) is equal to tan(θL).The barrel calibration was repeated with collision data in December 2009 using anew technique. This makes use of the two-dimensional pixel segmentation to mea-sure the average transverse displacement of the charge carriers, as a function of thedistance along clusters, produced by highly inclined tracks. Since longitudinal posi-tion in the cluster is completely correlated with depth in the junction, this techniquedetermines the average transverse carrier displacement as a function of depth.The two techniques are affected by different systematic effects. A variation of thefitting procedures suggests that the total systematic uncertainty on the Lorentz an-gle calibration is less than 2%. A consistency better than 1% has been observedbetween the real and simulated measurements.

Figure 2.1: A track in the pixel local coordinate system. The local z axis coincides withthe sensor electric field E. The local x axis is chosen to be parallel to E × B, where B

is the axial magnetic field. The local y axis is defined to make a right-handed coordinatesystem. The angle α is the angle between the x axis and the track projection on the localx-z plane.

2.1.3 Alignment

One of the most important inputs for reconstructing the tracks is the tracker ge-ometry: the set of parameters describing the geometrical properties of all the mod-ules composing the tracker. This has to be determined after an accurate alignment


procedure [22]; any misalignment of the tracker geometry is a potentially limitingfactor for its performance.The statistical accurancy of the alignment should stay below the intrinsic silicon hitresolution of 10 µm in the pixel detector. The other important aspect is the efficientcontrol of the systematic biases: inaccurate treatment of material effects, impreciseestimations of the magnetic field, and a lack of sensitivity of the alignment procedureitself to such degrees of freedom can be source of such systematic distortions.

The magnetic field of the CMS solenoid is to good approximation parallel tothe z-axis. The orientation of the tracker with respect to the magnetic field is ofspecial importance, since the correct parameterisation of the trajectory in the trackreconstruction depends on that. This global orientation is determined by the anglesθx and θy, the rotations of the whole tracker around the x-axis and the y-axis,respectively. These tilt angles are essential to be determined prior to the internalalignment correction, because the latter might be affected by a wrong assumptionon the magnetic field orientation. It is expected that the tilt angles will not changesignificantly with time, hence one measurement should be sufficient for many yearsof operation. The tilt angles have been determined with the 2010 CMS data, andthey have been used as the input for the internal alignment.The CMS silicon tracking subdetector consists of 1440 silicon pixel and 15148 siliconstrip detector modules. To first approximation, the CMS silicon modules are flatplanes and their degrees of freedom are three shifts (u, v, w) and three rotations (α,β, γ). Sensor curvatures can be expected, for instance because of the tensions aftermounting; to take into account such deviations, the vector of alignment parametersis extended to up to nine degrees of freedom.

Track-hit residual distributions are generally broadened if one assumes that thepositions of the silicon modules used in the track reconstruction differ from thetrue positions. Thus, the standard alignment algorithms follow the least squaresapproach, and minimise the sum of squares of normalised residuals from many tracks,

χ2(p, q) =tracks∑

j

hits∑i

(mij − fij(p, q)

σij

)2

, (2.2)

where mij are the hit positions with the uncertainties σij, fij is the trajectory pre-diction of the track, depending on the geometry (p) and track parameters (q).Two independent and complementary alignment algorithms have been used by CMSduring Run II: Millepede-II and HipPy (HIP). Millipede works using a global ap-

2.2 Performances 15

proach, HIP a local one: the first minimises the χ2 function, by taking into accounttrack and alignment parameters simultaneously; whilst HIP does not consider thetrack parameters. Millepede considers the correlations among the modules, thatare ignored by HIP. The latter has the advantage to solve a simpler local problem,with O(101) parameters for every module, compared to Millepede that has to solvea matrix equation of size n, where n is of the order of 106. The HIP’s disadvantageis the need for many iterations to perform the alignment, from 10 to 20, dependingon the element we are aligning, the goodness of the initial geometry, the availabletime, and the computing resources.

2.2 Performances

The physics program aimed by the CMS experiment sets the minimum levelof performance that the tracker has to match [21]. The required efficiency andresolution of the tracking system were evaluated since the early stages of the detectordesign. The tracker should provide:

• a resolution on the transverse momentum, pT , of 1.5% (10%) for 100 GeV

(1000 GeV ) momentum muons

• a correct charge assignment for leptons of energy up to 2 TeV

• a reconstruction efficiency higher than 95% for isolated charged particles ofmomentum above 1-2 GeV , and an efficiency of the order of 90% for particleswith the same momentum threshold, but collimated inside jets

• a measurement of the longitudinal impact parameter with a minimal resolutionof 2 mm, to associate particles to the pp collision vertices they originated from

• a resolution around 20 µm for the transverse impact parameter and around100 µm on the longitudinal one, to implement valuable b-tagging

• a detector occupancy below 1% to facilitate the pattern recognition in thecongested environment of the LHC collisions.

The occupancy is defined as the ratio between the number of detector channelsabove the noise level, and the total number of channels.


Moreover, the amount of material budget is required to be less than 0.15-0.30 ra-diation lengths, at least in the barrel region of the tracker. This requirement isnecessary to avoid that the reconstruction of photons and electrons is spoiled, be-cause of conversions and bremsstrahlung radiation. In the same way, an excessivematerial budget deteriorates the resolution on the trajectory parameters of low en-ergy particles because of multiple scattering.In addition, one has to consider that at the LHC design luminosity of L = 1034 cm−2s−1,about 1000 particles, from more than 20 overlapping interactions, are expected totraverse the tracker volume every 25 ns. The tracking system is required to have asufficiently fast time response in order to associate correctly the detected signals tothe corresponding bunch crossings.Finally, it is imperative that the components of the tracking system are sufficientlyradiation tolerant to maintain, without major interventions, the design performancefor the full extent of the CMS operations at LHC.

2.2.1 Track reconstruction

The track reconstruction algorithms [21] rely on a good estimate of the pp inter-action point, referred to as beamspot.Starting from the location of the beamspot, an initial round of track and vertexreconstruction is performed using only the pixel hits. The standard track recon-struction is performed by the combinatorial track finder (CTF). Tracks are seededfrom either triplets of hits in the tracker or pairs of hits, with an additional con-straint from the beamspot or a pixel vertex. This yields an initial estimate of thetrajectory, including its uncertainty.The seed is then propagated outward in a search for compatible hits. As hits arefound, they are added to the trajectory and the track parameters and uncertain-ties are updated. This search continues until either the boundary of the trackeris reached or no more compatible hits can be found. A second search for hits isperformed starting from the outermost hits and propagating inward.The first two iterations of this procedure use pixel triplets and pixel pairs as seedsto find prompt tracks with pT > 0.9 GeV . The successive iteration uses pixel tripletseeds to reconstruct low-momentum prompt tracks. The following iteration usescombinations of pixel and strip layers as seeds, and is primarily intended to find dis-placed tracks. The two final iterations use seeds of strip pairs to reconstruct tracks

2.2 Performances 17

lacking pixel hits. In the final step, the collection of hits is fitted, to obtain the bestestimate of the track parameters.At the end of each iteration, the reconstructed tracks are filtered to remove tracksthat are likely fakes. The filtering uses information on the number of hits, the nor-malized χ2 of the track, and the compatibility of the track to be originated from apixel vertex. This information is used to enstablish the quality level of the tracks.Tracks that pass the tightest selection are labelled as "highPurity".

In the context of the reconstruction software of CMS, the five parameters usedto describe a track are: d0, z0, ϕ, cotθ, and the pT , defined at the point of closestapproach of the track to the assumed beam axis. This point is called the impactpoint, with global coordinates (x0, y0, z0). Thus, d0 and z0 define the coordinates ofthe impact point in the radial and z directions, being d0 defined as d0 = −y0 ·cosϕ+x0 · sinϕ. The azimuthal and polar angles of the momentum vector of the track aredenoted by ϕ and θ, respectively.The resolution in the parameters is studied using simulated events, and estimatedfrom track residuals, which are defined as the difference between the reconstructedtrack parameters and the corresponding parameters of the generated particles. Foreach one of the five track parameters, the resolution is plotted as a function of theη (pT ) of the simulated charged particle, in different pT (η) ranges, Fig. 2.2, 2.3.


Figure 2.2: Resolution for each track parameter (d0, z0, ϕ, cotθ, pT ) as a function of η

and for different pT values [21].

Figure 2.3: Resolution for each track parameter (d0, z0, ϕ, cotθ, pT ) as a function of pT

and for different η regions [21].

2.2.2 Primary vertex

The goal of primary-vertex reconstruction [21] is to measure the location andthe associated uncertainty of all the pp interaction vertices in each event, includingthe "signal" vertex and any vertices from pileup collisions, using the available recon-structed tracks. It consists of three steps: (1) selection of the tracks, (2) clustering

2.2 Performances 19

of the tracks that appear to originate from the same interaction vertex, and (3)fitting for the position of each vertex using its associated tracks.

1. The track selection involves choosing tracks consistent with being producedpromptly in the primary interaction region, by imposing requirements on themaximum value of significance of the transverse impact parameter (< 5) rela-tive to the centre of the beam spot, the number of strip and pixel hits associ-ated with a track (pixel layers > 1, pixel+strip > 4 ), and the normalized χ2

from a fit to the trajectory (< 20). To ensure high reconstruction efficiency,even for minimum-bias events, there is no requirement on the pT of the tracks.

2. The tracks are clustered according to the z coordinate of the track, at the pointof closest approach to the beamline. This clustering allows for the reconstruc-tion of any number of pp interactions in the same LHC bunch crossing. Theclustering algorithm must balance the efficiency for resolving nearby verticesin cases of high pileup, against the possibility of accidentally splitting a single,genuine interaction vertex, into more than one cluster of tracks.

3. The clusters of tracks are fitted with an adaptive vertex fit, where tracks inthe vertex are assigned a weight between 0 and 1, based on their proximity tothe common vertex. The primary vertex resolution strongly depends on thenumber of tracks used in fitting the vertex and on their pT .

Results from a study of the primary-vertex resolution in x and z as a function ofthe number of tracks associated to the vertex, using both minimum-bias and jet-enriched data samples, are shown in 2.4. The resolution in y is almost identical tothat in x, and is therefore omitted.

2.2.3 Energy loss

Although the primary function of the strip tracker is to provide hit position in-formation for track reconstruction and precise momentum determination, the stripchannel output also provides a measure of the energy loss [21]. The charge col-lected in a hit cluster is directly proportional to the energy lost by a particle, largelythrough ionization, while traversing the silicon.For reconstructed tracks the angle θ between the track direction and the axis normalto module sensor is well defined for each hit on the track. The instantaneous energy


Figure 2.4: Resolution of the primary vertex in x (left) and in z (right), as a function ofthe number of tracks, using a minimum bias or jet-enriched data sample [21].

loss per unit path length dE/dx in the silicon is then approximated by the quantity∆E/(∆L · sec θ), where ∆E is the cluster charge expressed in units of MeV, and∆L is the thickness of the active volume of the silicon sensor.The main point in determining energy loss per unit path length is that, for a givenmedium, dE/dx depends largely on the velocity of the traversing particle. By com-bining dE/dx information with the measured momentum p of a track, one candetermine the mass of the traversing particle.On the scale of charged particle momenta in CMS collisions, there is only a limitedrange, near the low end, where the difference in β values is significant enough todistinguish among long-lived hadrons. To this end, the following relation betweendE/dx, p, and m is assumed for the momenta below the minimum-ionizing region:

dE/dx = Km2

p2 + C. (2.3)

The proton line in is used to extract the parameters K and C.

2.3 Upgrade

The performance of the CMS tracker, which exploits an all-silicon technology,with a pixel and a strip detector, has so far been excellent. Anyway, the foreseenincrease of both the instantaneous and the integrated luminosity by the LHC, duringthe next ten years, will ask for a stepwise upgrade of the CMS tracking detector [23].

2.3 Upgrade 21

Figure 2.5: Simulation of the energy loss dE/dx as a function of p at 900 GeV in thecentre of mass, for some types of particles.

2.3.1 Phase-1 upgrade

During the 2015-2016 data-taking period the peak luminosity has already dou-bled the design one, of 1034 cm−2s−1. Since the pixel detector is the first part ofthe tracker that shows limitations in a high-rate enviroment, this will be replacedduring the extended winter technical stop 2016-2017. This is referred to as the"Phase-1 Pixel Upgrade". The goal of the upgraded Phase-1 pixel detector is tobe fully efficient at a luminosity of 2 × 1034 cm−2s−1, with less material and withfour hit coverage up to |η| < 2.5. For these reasons, a new pixel detector, with afourth barrel layer, an extra disk on each side, and a new ROC (ReadOut Chip) hasbeen proposed. The layout of Phase-1 pixel detector compared to the current oneis shown in Fig. 2.6.

The upgraded front-end electronics is required to enhance the robustness of thesystem at high rate. At the design luminosity 1034 cm−2s−1, the buffer size andthe readout speed of the current pixel ROC will lead to a dynamic inefficiency inthe pixel detector of 4% (16%) with 50 ns (25 ns) bunch spacing. The inefficiencyincreases exponentially with luminosity. The new "PSI46dig" ROC is made in 250-nm CMOS technology, as the present chip (PSI46), and is heavily based on it. Both


Figure 2.6: Pixer detector layout, comparing the different layers and disks in the currentand upgrade pixel detectors. Left: view in the y-z plane, comparing barrel and end-cap layers. Right: transverse-oblique view comparing the pixel barrel layers in the twodetectors [23].

chips feature a column drain architecture. To reduce data losses, the depths of dataand time stamp buffers have been increased. Simulations indicate that data lossesin the first layer will decrease from 16.0% (50%) to 2.4% (4.8%) for a bunch spacingof 50 ns (25 ns) at the instantaneous luminosity of 2 × 1034 cm−2s−1.

The current detector contains also significant passive material, that degrades themeasurements, due to multiple scattering, photon conversions, and nuclear interac-tions. An optimization of the mechanics and services, together with a two-phaseCO2 cooling, will provide a substantial reduction of material in the tracking vol-ume. This reduction in the amount of passive material will have a large impact onthe track reconstruction efficiency, as well as on electron and photon identificationand resolution, thus playing an important role in the reconstruction of the final-statesignatures involving electrons and photons.

All the improvements of the Phase-1 Pixel detector have a net effect on theexpected performances; pattern recognition, track parameter resolution, vertexing,and b-tagging of the upgraded detector are expected to be significantly improvedcompared with current detector.The loss in tracking efficiency, due to the dynamic data loss and to the effect of thehigh pileup expected at 2 × 1034 cm−2s−1 and 25 ns crossing time, would be about10%(16%) for muons in tt samples. For the upgraded detector this is reduced to1.5% (3.7%) for tt (muons). See Fig.2.7 (left) for the tt efficiency as a function ofpileup.The track fake rate rapidly increases with pileup, but is about a factor of two lower

2.3 Upgrade 23

for the upgraded pixel detector, due to the reduced multiple scattering, especiallyfor low momentum tracks, see Fig.2.7 (right) for tt average fake rate. Fake tracksare caused by the incorrect association of hits, and are much more likely in regionswith more passive material.The improvement in tracking efficiency, fake rate, impact parameter resolution, andvertexing all contribute to significantly increase the b-tagging performance of thenew detector. The tagging of b jets is a key ingredient of many physics analyses;indeed, b jets are often produced in association with the Higgs boson or in its decays,and final states involving b jets are also expected in many new physics models.

No tracker upgrades are foreseen for Long Shutdown 2, LS2 (2018-2019), buta replacement of the innermost layer of the pixel detector might be required after250 fb−1 of integrated luminosity, because the radiation hardness of the detectoris not sufficient for operation to the end of Phase 1. The new pixel detector andthe current outer strip tracker will provide optimal tracking performance to CMSthrough 2023.

Figure 2.7: Performance of the current pixel detector (blue squares) and upgraded pixeldetector (red dots) for tt events: average tracking efficiency (left) and fake rate (right) asfunction of the average pileup [23].

2.3.2 Phase-2 upgrade

An upgrade of the accelerator complex is foreseen for the beginning of the nextdecade, during the Long Shutdown 3, LS3 (2023-2025). The LHC is expected toturn into the HL-LHC, that is planned to deliver an instantaneous luminosity of5 × 1034 cm−2s−1. The quoted luminosity corresponds to a number of pileup eventswhich can vary from 100 to 200, according to the operation frequency. This repre-


sents a much more demanding condition for the detectors. In such scenario, CMSwill eventually collect up to 3000 fb−1, after several years of operation.

The CMS tracking system will have to be improved in terms of radiation resis-tance, readout granularity and speed, and capability to contribute to the Level-1trigger. A whole new tracking system, both pixel and outer tracker, is hence needed,which will be installed during LS3. This is referred to as the "Phase2 Upgrade" ofthe CMS tracker [23].The upgraded tracker will have to provide improved tracking performance in a morechallenging enviroment, while producing at the same time fast information for theLevel-1 trigger [71]. The tracking should be robust enough in order to sustain oper-ations with up to 200 collisions per bunch crossing in the worst-case scenario of 20MHz operation, thus, increased granularity is required to maintain the occupancyat the level of a few percent. The detector should provide satisfactory performanceup to an integrated luminosity of about 3000 fb−1, to be compared with the originalfigure of 500 fb−1. This requires the selection of more radiation hard silicon sensormaterial, especially for the innermost regions, as well as more stringent criteria inthe qualification of electronics and mechanical assemblies.The amount of material is the most severe limitation on the performance of thepresent tracker, and it is dominated by electronics and services (notably in the re-gion between barrel and endcap). Thus, to improve the tracking performances atlow transverse momentum, the new tracker should foresee a significant reductionof the material. This fact, together with the request for an increased granularity,drives the choice of technologies for sensors, readout, powering and cooling. IntenseR&D activities are going on to identify the most suitable sensors for the Phase-2tracker. Wafers of different materials, polarities, and thickness, equipped with teststructures and test sensors with different strip lengths, pitches, and strip widths,have been tested, and irradiated with both protons and neutrons.

At HL-LHC, the combinatorial background poses also problems to the Level-1trigger, to the point where it is not possible to keep the trigger rate within thenominal range, mantaining reasonably low cuts on the trigger variables. The CMScollaboration plans to improve the trigger, for example by installing a fourth layerof the Cathode Strip Chambers muon detector, and re-designing the Level-1 triggerhardware. Nevertheless, these improvements will be insufficient for the HL-LHC lu-minosity. A large event-rate reduction factor is currently achieved in the High-Level

2.3 Upgrade 25

software trigger, by using information from the tracker. Including this informa-tion in the Level-1 processing would allow a much better rejection of combinatorialbackground. The collaboration is therefore studying the option of sending trackinginformation in real time to the Level-1 trigger.

In addition, low pT tracks are locally rejected, to reduce the volume of the triggerdata. So-called "pT modules" will perform the discrimination between high and lowpT tracks. Only Level-1 tracks with pT above a certain threshold (e.g. 2 GeV) areformed at the back-end. This could be achieved by performing an on-module pT

selection, exploiting the CMS 3.8-T magnetic field.The basic concept consists of correlating signals in two closely-spaced sensors; thedistance between the hits in the x-y plane is correlated with the particle pT , allowingthe pT discrimination to be made. A pair of hits that fulfils the selection cut is calleda "stub" (Fig. 2.8). For a given pT , the distance between the hits forming the stubis larger at larger radii. Thus, the effective pT cut provided by the modules in thedifferent locations has to be optimized, by tuning both sensor spacing and acceptancewindow. The coordinates of stubs selected by the pT modules are sent to the triggerelectronics at the back-end, where they have to be combined to form Level-1 tracks.

Figure 2.8: Sketch illustrating the stub selection, exploiting the correlation of the twohits signals in two closely-spaced sensors [71].

Two types of pT modules are under development to instrument the radial regionbelow (PS modules) and above 40 cm (2S modules), see Fig.2.9.

• 2S modules; constitute a sandwich of two strip sensors, read out at the edges,by the same set of front-end ASICs that implements the correlation logic, ona high-density substrate. They are two sensors of about 10 × 10 cm2 with5-cm-long strips and a pitch of 90 µm, mounted on a mechanical structurethat provides support and cooling. The sensors are wire-bonded from top and


bottom to the readout hybrids, each of them carries eight CMS Binary Chips(CBCs) plus a Data Concentrator chip. The estimated power consumption forthe readout electronics, including the correlation logic, is below 2 W , compa-rable to the lowest values in the present tracker.The main limitation of this type of module is the lack of segmentation in the zdirection. In order to implement effective isolation cuts on calorimeter clusters,the Level-1 tracks must also have a reasonable precision in the z coordinate.In addition, the relatively long strips limit the use of this module to the radialregion above 40 cm, because of the occupancy.

• PS modules; based on the assembly of one strip and one pixel sensor, theyovercome the limitation of the 2S modules, and can be employed at radiuslower then 40 cm in the tracker. The PS module is half as large as 2S module.The upper sensor carries short strips with dimensions of 2.5 cm × 100 µm,which are wire-bonded to hybrids with readout chips. The lower sensor isstructured with large pixels of dimensions 1.5 mm × 100 µm, and is bump-bonded to dedicated readout chips.Compared to the 2S module, this concept offers a sufficiently precise mea-surement of the z coordinate from the pixellated sensor, while the 2.5-cm-longstrips allow the module to be used down to 20-25 cm radius. On the otherhand, the power consumption is expected to be more than 4 W , dominatedby the pixel ASICs.

Both 2S and PS modules carry a DC-DC converter and a GBTX chip plus opto-electrical converters on service hybrids. R&D on the CBC is well advanced. The 2×127 channel chip is fabricated in 130 nm CMOS technology, and features unsparsifiedbinary readout. The chip receives data from both sensors. After amplification andhit detection, clusters are formed. Following a cluster width discrimination step,clusters from the lower and upper sensor, within a programmable window, and withprogrammable channel offset, are correlated. Stubs are formed and passed to theData Concentrator.

2.3 Upgrade 27

Figure 2.9: Model of a 2S (top) and a PS (bottom) pT module [71].

Chapter 3

Motivations for new physics searchat LHC

In this chapter we briefly recall the Standard Model of particle physics, and wemention its limits and their possible solutions, Sec 3.1, 3.2, and 3.3. We thus reviewthe current state of models beyond the SM, and focus on some specific ones, Sec3.4 and 3.5. Finally, we summarise up the Run I and Run II searches related to thepreviously described models in Sec. 3.6, 3.7, and we introduce a new model dealingwith heavy neutrinos in Sec. 3.8.

3.1 Standard Model

The Standard Model (SM) of the particle physics [7] is a well-tested physicstheory, that explains how the basic building blocks of matter interact, governed byfour fundamental forces. It is currently accepted that the elementary constituents ofmatter are three families of elementary particles, and their fundamental interactionsare the electromagnetic, the weak, the strong, and the gravitational force. TheSM includes all these forces except gravity, as fitting gravity comfortably into thisframework has been unsuccessful so far.

The elementary particles are leptons, and quarks, they carry spin 1/2, thusbelonging to the category of fermion, and are grouped into three "families", or "gen-erations" (Fig. 3.1). Each fermion has an associated antifermion, featuring thesame mass of the fermion, but opposite electric charge, colour charge, and thirdcomponent of weak isospin.

29

30 3. Motivations for new physics search at LHC

The forces acting between quarks and leptons are mediated by particles calledgauge bosons (Fig. 3.1). The strong and the electroweak forces are mediated viathe exchange of 12 vector bosons: eight massless gluons (g) for the strong force,one massless photon (γ) for the electromagnetic force, and three massive bosons forthe weak force (W ± and Z0). Although not yet found, the graviton should be thecorresponding force-carrying particle of gravity.These forces work over different ranges, and have different strengths. Gravity is theweakest, but it has an infinite range. The electromagnetic force also has infiniterange, but it is many times stronger than gravity. The weak and strong forces areeffective only over a very short range, and dominate only at the level of subatomicparticles. Despite its name, the weak force is much stronger than gravity, but it isindeed the weakest of the other three. The strong force, as the name suggests, isthe strongest of all four fundamental interactions.

Figure 3.1: Overview table of the known SM particles with their basic properties: charge,mass, spin.

The concept of symmetry plays an important role in particle physics; its im-

3.1 Standard Model 31

portance in nature was first emphasised by Emma Noether, who showed in 1918,that there is a symmetry associated with every conservation law [8]. The invarianceunder spacetime transformations such as space translation, time displacement androtation leads to the conservation of momentum, energy and angular momentum,respectively. Similarly, the requirement of charge conservation (electron charge orcolor charge) follows from invariance under a global phase (gauge) transformation.In the SM, energy (E), momentum (p), angular momentum (L), charge (Q), colour(c), baryon number (B) and lepton number (L) are conserved in all the three inter-actions. Parity (P), charge (C), and time (T) are conserved in the strong and in theelectromagnetic interaction, but not in the weak interaction. For the charged cur-rent of the weak interaction, parity violation is maximal; the charged current onlycouples to left-handed fermions and right-handed antifermions. The neutral weakcurrent is partly parity violating, since it couples to left-handed and right-handedfermions and antifermions, but with different strengths. The charged current of theweak interaction is the only one able to transforms one type of quark into anotherquark of different flavour, and one kind of lepton into another. Thus, the quantumnumbers determining the quark flavour, third component of isospin (I3), strangeness(S), charm (C) are conserved in all the other interactions. The magnitude of theisospin (I) is conserved in strong interactions.The symmetry underlying the SM is assumed to be spontaneously broken at somescale, in order for the elementary particles to acquire mass. The existence of theHiggs boson, a neutral particle introduced to break the symmetry, has been experi-mentally confirmed in 2012 by the CMS and Atlas experiments.

The gauge symmetry group of the SM [7] is SU(3) × SU(2) × U(1). There areno particular reasons for this choice, except that it successfully describes the ex-perimental data, and it is the simplest group that reproduces the currently knownfeatures of particles interactions. The SU(2) × U(1) group was chosen, in the six-ties, by Glashow to unify electromagnetic and weak interactions. It predicted theexistence of four massless gauge fields. Later, Weinberg and Salam showed that theweak bosons can acquire mass via spontaneous breaking of the SU(2) × U(1) gaugesymmetry. This theory is known as the Glashow-Weinberg-Salam model. The SU(3)symmetry group, on the other hand, is associated with the local color symmetry ofquarks. It underlies the theory of Quantum Chromo Dynamics (QCD), establishedin sixties and seventies, which describes the interaction of quarks inside hadrons.


Hereafter, we focus on the electroweak part of the theory. The electroweakLagrangian can be written as a sum of three contributions.

• LG, the gauge part, describing kinetic energy of fermions, their interactionswith the gauge fields, gauge fields themselves and their self interactions, reads

LG =∑

f

i{fLγµ(DL)µfL + fRγµ(DR)µfR} − 14

BµνBµν − 14

W iµνW µν

i . (3.1)

The sum is over all left- and right-handed fermion fields, denoted by fL andfR respectively. The covariant derivatives for the left- and the right-handedfields are:

(DL)µ = ∂µ + igIiWiµ + ig′ Y

2Bµ, (DR)µ = ∂µ + ig′ Y

2Bµ. (3.2)

W iµ, i=1,2,3 and Bµ are respectively the SU(2) and U(1) gauge fields.

• LH , the part describing the Higgs potential and the Higgs interactions withgauge bosons, has this shape:

LH = ((DL)µH)†((DL)µH) − V (H, H†). (3.3)

The self-interaction term of the Higgs fields, which has the famous "mexicanhat" shape, V(H), is given by:

V (H) = −µ2H†H + λ2(H†H)2, λ2 > 0. (3.4)

• LG is the part describing Higgs-fermion (Yukawa) interactions:

LY = −∑

f

gf (ΨfLH)Ψf

R + h.c.. (3.5)

The SM symmetry group SU(3)C × SU(2)L × U(1)Y is spontaneously broken viathe Higgs mechanism, and the remaining symmetry is SU(3)c × U(1)em. The Higgsmechanism gives rise to the masses of the gauge fields, W ±

µ and Zµ, and leaves thephoton field, Aµ, massless. The physical gauge fields are defined as:

W ±µ =

W 1µ ∓ W 2

µ√2

, Zµ =gW 3

µ − g′Bµ√g′2 + g2 , Aµ =

g′W 3µ + gBµ√

g′2 + g2 . (3.6)

The first two ones acquire mass:

M2W = g2v2

4, M2

Z = M2W (g2 + g′2)

g2 = M2W

cos2θW

. (3.7)

The value of sen2θW is 0.23, the masses of W and Z are 80.4 and 91.2 GeV , respec-tively. The coupling value v is 246 GeV .

3.2 Shortcomings of the Standard Model 33

3.2 Shortcomings of the Standard Model

The SM has been continuously confirmed by the experiments, revealing itself asa very successful theory. However, many clues suggest it is not the ultimate theoryof nature, but rather a low-energy remnant of some more fundamental theory. Thereasons for that are twofold: both theoretical and experimental [9], [10].

Theoretical reasons for a SM extention:

• Unification. Each of the gauge groups within the SM, SU(3)C , SU(2)L

and U(1)Y , can be associated with its coupling running constant. Precisionmeasurement have shown that they do not converge at high scale within theSM, as it was supposed to be.

• Gravity. The fourth type of interaction, gravity, is not included in the SM.At the electroweak scale, gravity is so weak as to be negligible. The scale atwhich effects of quantum gravity are expected to become important is of theorder of 1019 GeV , referred to as the Planck scale, Mp.

• Baryogenesis. The origin of the baryon-antibaryon asymmetry observed inthe universe is not completely explained by the SM.

• The mass hierarchy of fermions. The SM does not explain why there areexactly three generations of quarks and leptons, the last two being heavierversions of the first one. Furthermore, the masses of the fermions span overmany orders of magnitude. The reason for that is unknown.

• The Higgs fine tuning. The question is why the Higgs boson is so muchlighter than the Planck mass. One would expect that the large quantumcontributions to the square of the Higgs boson mass would inevitably makethe mass huge, comparable to the scale at which new physics appears, unlessthere is an incredible fine-tuning cancellation between the quadratic radiativecorrections and the bare mass. This precise adjustment of the SM parameters,to fix the hierarchy problem, is not very satisfying.

Experimental reasons for a SM extention:

• Mass of neutrinos. The experimental observation of the flavour oscillationsof atmospheric and solar neutrinos has provided evidence for neutrino non-zeromasses and mixing. The SM assumes the neutrinos to be massless particles.


• Dark matter and dark energy. The measurement of the rotation velocityof galaxies and the effect of the gravitational lenses are just some of the proofsof the gravitational contribution of a not visible matter, referred to as darkmatter. The measure of the accelerating expansion of the current universesuggests the existence of an unknown form of energy, called dark energy. Theseand other cosmological observations, such as the cosmic microwave backgroundand the matter structure of galaxies, show that the energy content of theuniverse consists of roughly 5% of baryonic matter, 25% of dark matter and70% of dark energy. The SM describes only the baryonic matter.

3.3 Principles for a Standard Model extention

Several possible extentions of the SM have been formulated to address the justexplained limits of the current theory. In this section, some of the general principlesthis new models are based on will be breafly illustrated [9], [10].

• In Grand Unified Theories (GUTs), the symmetry of the SM, SU(3)C ×SU(2)L × U(1)Y , is supposed to originate from a larger symmetry group re-lating quarks and leptons. This symmetry is preserved at some higher energyscale, where all the interactions are described by a local gauge theory, withonly one running coupling constant.

• The basic idea of the extra-dimensions theories is that the four-dimensionalworld we live in is embedded in a higher dimensional space. The reason whythese extra-dimensions have not been observed so far is that they are com-pactified, as in the N.Arkani-Hamed, S.Dimopoulos, and G.Dvali (ADD), andUniversal Extra Dimension (UED) models, or have a strong curvature, whichmakes it hard to escape from them, as in the Randall- Sundrum (RS) model.Since these models assume that only gravity can propagate in the extra dimen-sions, the gravity intensity is diluited with respect to the other forces, and theSM particles experience only a small fraction of the total gravitational force,so solving the hierarchy problem. In scenarios where SM particles are allowedto propagate in extra dimensions (such as in the UED model), for every SMparticle there is a series of particles, the so-called Kaluza-Klein (KK) excita-tions. The lightest of these KK modes is stable, and it is a good candidate for

3.4 Current state 35

dark matter.

• The dynamical symmetry breaking of the electroweak symmetry is mo-tivated by the premise that every fundamental energy scale should have adynamical origin, and has been developed in order to eliminate the elemen-tary Higgs boson. The electroweak symmetry is dynamically broken through anew strong interaction, called technicolour. Technicolour (TC) and ExtendedTechnicolour (ETC) models are asymptotically free gauge theories of fermionswith no elementary scalars.

• Supersymmetry (SUSY) provides a solution to the hierarchy problem, whichrefers to divergent corrections to the Higgs mass squared parameter, due toloop diagrams of couplings between the Higgs and massive SM particles. Asymmetry relating fermions to bosons is proposed, resulting in a supersymmet-ric partner for each SM particle, with spin differing by 1/2. All SM fermionswill have a SUSY boson partner, and all SM bosons will have a SUSY fermionpartner. These SUSY partners are at a displaced mass scale, due to the break-ing of supersymmetry, the exact nature of which is not fixed, except the factthat the added terms must be gauge invariant.

• Compositeness assumes the composite nature of SM quarks and leptons. If itexists, will manifest itself, above a characteristic energy scale Λ, as a spectrumof excited states. Such excited fermions, f ∗, may couple to SM leptons andquarks via a four-fermion contact interaction (CI), that can be described by aneffective Lagrangian. In addition to the coupling via CI, excited fermions canalso interact with SM fermions via gauge interactions. Models of quark andlepton compositeness may explain the number of fermion generations, charges,and masses, which are not predicted in the SM.

3.4 Current state

The discovery of the Higgs boson at the LHC was announced together by theCMS and ATLAS collaborations in 2012, and has opened a new exciting era forthe high-energy physics. Albeit the huge efforts put in by these experiments, thehunting for new particles has been unsuccessful so far, and the robustness of the SMhas been continuously confirmed.


However, the already mentioned unexplained phenomena and problems, such as theevidence for dark matter, the difficulty of incorporating gravity in the theoreticalframework, and the hierarchy problem, suggest that BSM physics is required toaccurately describe the universe we observe. Many such new physics models exist,conventionally separated into supersymmetry models and all the other BSM models,referred to as exotica. This provides a rich terrain to probe experimentally, and bothATLAS and CMS experiments at the LHC have run extensive physics programs tocover as many scenarios as possible.The current Run II of the LHC started in June 2015; the machine reached an energyof 13 TeV in the center-of-mass frame, and collected an integrated luminosity ot4.2 fb−1 and 37.82 fb−1 in 2015 and 2016 respectively, marking new records forthe hadron colliders. These new experimental conditions are providing a greaterstatistics and cross section, for the discovery of new particles or for the extensionof the exclusion limits in their search. The main aims of the ongoing Run II is adetailed characterization of the Higgs boson and the continuance of the search fornew physics.In principle, all the new physics searches are based on similar methods: definingregions in which to compare the number of expected and observed events. Thereare also some new physics particles, whose signal can be distinguished from thebackground in quite specific and novel ways, for example the long-lived particles.Background estimation methods tend to vary from analysis to analysis, with somenormalising MC simulations, and some employing more sophisticated data-drivenor semi-data-driven techniques. Due to the number and diversity of the consideredmodels, and the similarity of the signatures many would give at the LHC, thesesearches can be better categorised by the search methods and final states, ratherthan by the models.The dilepton plus dijet final state is one of the more promising channels, in the newphysics search; it is sensitive to many theoretical models beyond the SM. They caninclude scalar leptoquarks of the three generations and heavy Majorana neutrinos,e.g. arising from the seesaw mechanism, in the context of a LR-symmetry extensionor in a compositeness scenario, as we will discuss in the following sections.

3.5 Some models beyond Standard Model 37

3.5 Some models beyond Standard Model

In this section, an incomplete theoretical introduction is presented about modelsthat foresee the existence of leptoquarks and heavy neutrinos, and that can produce,in some benchmark process, a final state of two same flavour leptons plus two jets,considered in various analyses of CMS: [11], [12], [13], [14], [15], [16], [17].

Several BSM theories, like Grand Unification, compositness, superstrings andtechnicolor include leptoquarks (LQ) of the three generations. These new particlesare scalar or vector bosons which carry non-zero leptonic and baryonic number, colorcharge and fractional electric charge.Experimental limits suggest that their research should be mainly focused on LQpair production, via gluon fusion or quark annihilation, and on the dominant decayprocess in a lepton and a quark of the same generation of the LQ. In these theories,the free parameters are the LQ mass (MLQ) and the decay branching ratio in acharge lepton plus a quark, usually denoted as β. Since the production is in pairs,the final state of this kind of processes presents two same flavour leptons plus twojets.

Figure 3.2: Feynman diagrams for the pair production and decay of leptoquarks.

The SM assumes that the neutrinos of the three generations are massless, how-ever, the observation of neutrino oscillations implies a non-zero mass, and definitelypoints to new physics models.The leading model that naturally generates light neutrino masses is the "seesaw"mechanism that, in its simplest implementation, justifies the smallness ot the ob-served neutrino masses, introducing a heavy neutrino state N. The SM neutrino


mass is given by mν ∼ y2νv2/mN , where yν is a Yukawa coupling of the neutrino

ν to the Higgs field, v is the Higgs vacuum expectation value in the SM, and mN

is the mass of a new heavy neutrino state, N. If the seesaw mechanism was theright way to explain the masses of the known neutrinos, both the light and heavyneutrinos would have to be Majorana particles, so processes that violate the leptonnumber conservation by two units would be possible. Therefore, searches for heavyMajorana neutrinos at the colliders are very important in resolving the nature ofneutrinos and the origin of masses.A natural way to confer mass to neutrinos is provided by the Left-Right Symmetryextension, LRSM, in which the SM group SUL(2) has a right-handed counterpart andthe symmetry group is SUC(3) ⊗ SUL(2) ⊗ SUR(2) ⊗ U(1). This symmetry grouphas been originally introduced to explain the reason of parity non conservation inweak interactions; by introducing a new symmetry group, parity violation in weakinteractions is explained as the result of a spontaneously broken symmetry. Thenew SUR(2) group, similar to the SUL(2), predicts the existence of three new gaugebosons, W ±

R and Z’, and three heavy right-handed neutrino states Nℓ (ℓ = e, µ, τ),partners of the light neutrinos states νℓ, and can explain the neutrinos’ mass hier-archy in the context of the seesaw mechanism.A refererence process allowed by this model is the production of a heavy neutrinothrough a WR boson and its decay into a same flavour lepton plus another WR whichdecays hadronically: qq → WR → ℓ+Nℓ → ℓ+(WR +ℓ) → ℓ+(qq′)+ ℓ, this processgives two jets and two same flavour leptons in the final state.

Figure 3.3: Feynman diagram of the heavy neutrino production through a WR boson.

3.6 Run I CMS searches 39

3.6 Run I CMS searches

Using an integrated luminosity of 19.7 fb−1, collected by CMS, during the Run I,at a centre-of-mass energy of 8 TeV , several searches for heavy Majorana neutrinosand leptoquark has been conducted, that have in common the dilepton plus dijetfinal state.

A search for heavy, right-handed, neutrinos Nℓ(ℓ = e, µ) and right-handed WR

bosons, which arise in the left-right symmetry extension of the SM, has been per-formed [11]. The search was based on a sample of two same-flavour lepton plustwo jet events. For models with strict left-right symmetry and assuming only oneNℓ flavor contributes significantly to the WR decay width, the region in the two-dimensional (M(WR), M(Nℓ)) mass plane excluded at a 95% of confidence level(CL), has been significantely extended compared to the previous searches. Theµµjj and eejj channels have been investigated, and a broad excess, corrispondingto 2.8 σ, around the neutrino’s mass MN = 2.2 TeV , has been measured with respectto the cross section of the SM background. This cannot be explained consideringthe LR (left-right) model parametrization of the analysis. Fig. 3.4 (top) showsthe excess of events measured in the distribution of the invariant mass of the twoelectrons and the two jets on the left, and the correspondent exclusion limit on theright.For completness, we mention two other search for heavy neutrinos.The first search [13] considers a Type-1 seesaw model with at least one heavy neu-trino, that mixes with the SM neutrinos. The neutrino’s mass and VNℓ, the elementdescribing the mixing of the heavy neutrino with the SM neutrino, are the freeparameters of the model. The heavy Majorana neutrinos (N), produced togheterwith a lepton, decays into a W boson, featuring hadronic decay, and another lepton.This gives a final signature of two jets and either two same sign electrons or a samesign electron-muon pair. The data are found to be consistent with the expectedSM background, and limits are set on the cross section times branching fraction ofthe production of heavy Majorana neutrinos in the mass range between 40 and 500GeV .A similar search [12] is performed for heavy Majorana neutrinos (N), using an eventsignature defined by two same-sign muons and two jets, adopting a more phenomeno-logical approach, in the same range of neutrino’s mass. No excess of events is ob-


served beyond the expected SM background, and new limits are set.

Concerning the LQ scenario, with the LQ produced in pairs, it has been possibleto exclude, at the 95% of CL, for the first generation (LQ1) MLQ1 < 950(845) GeV

with β = 1(0.5), for the second generation (LQ2) MLQ2 < 1070(785) GeV , withβ = 1(0.5) [15], and for the third one (LQ3) MLQ3 < 740 GeV [16], with β = 1.An excess of 2.4 (2.8) σ with respect to the predicted contribution from the SMbackground has been observed at around 650 GeV in the eejj (eνjj) final state. Thisexcess cannot be explained within the LQ1 model considered in the analysis [15].On the left bottom side of Fig. 3.4, the distribution ST , which is the pT sum of theparticle in the final state (two electrons and two jets), is reported, and an excess ofdata compared to the SM background is visible. The exclusion plot on right bottomside of the same figure shows the deviation of the observed upper limit compared tothe expected one.

To summarise, the CMS measurements of Run I, looking for first generationleptoquarks and heavy neutrinos, have shown two significant excesses, in the finalstate with two electrons and two jets, in analyses performed at the center-of-massenergy of 8 TeV , using 19.7 fb−1. No excess has been observed in the dimuonplus dijet channel. The ditau plus dijet signature has not yet been explored forthe heavy neutrinos specific search, but only for searches motivated by leptoquarksmodels, in the final state where the tau pair is produced with two b or two t quarks,giving results in agreement with the SM expectation, in Tab. 3.1 these results aresummarised togheter with the early results of Run II that are going to be brieflydiscussed in the next section.

3.7 Run II CMS early searches

Using the first 13 TeV data collected by CMS, during the Run II of LHC, newanalyses have been published, referring to heavy neutrinos and leptoquark searches.A search for heavy, right-handed neutrinos, Nℓ , and right-handed WR bosons, whicharise in the left-right symmetric extensions of the SM, has been performed [14]. Thesearch focuses on the scenario where the WR and Nℓ decay chains result in a pair ofhigh-pT τ leptons, which decay hadronically, besides two high-pT jets. The analysishas used 2.1 fb−1 of data, collected by the CMS experiment, in 2015. For models

3.7 Run II CMS early searches 41

Figure 3.4: Above, the results of the heavy neutrino and WR search of Run I; on theleft the distribution of the invariant mass of the system, on the right the exclusion plotshowing the deviation of the observed upper limit compared to the expected one [11].Below, the results of the first generation leptoquark search of Run I; on the left thedistribution of the ST , that is the pT sum of the four objects in the final state, on theright the exclusion plot showing the deviation of the observed upper limit compared tothe expected one [15].


with strict left-right symmetry and assuming that only the Nτ flavor contributessignificantly to the WR decay width, WR masses below 2.35 (1.63) TeV have beenexcluded at 95% of CL, assuming the Nτ mass to be 0.8 (0.2) times the mass ofWR boson. Limits have been also set on pair production of third generation scalarleptoquarks.A second search has been presented for pair-produced second generation scalar lep-toquarks, using 2.7 fb−1 of data collected by CMS during the 2015 [17] . A final statesignature, containing two high pT muons and at least two jets, has been taken intoaccount. Second generation scalar leptoquarks with masses less than 1165 (960)GeV have been excluded, when assuming the leptoquark branching fraction to acharged lepton and a quark β = 1 (β = 0.5).Both these searches of the Run II have not found any excess with respect to the SMbackground (Tab. 3.1).

For completness, we mention that direct searches for heavy neutrinos have beenperformed by the ATLAS experiment as well: a search for heavy neutrinos and right-handed W bosons in events with two leptons and jets in pp collisions at

√s = 7 TeV

[18]; and a search for heavy Majorana neutrinos with the ATLAS detector in pp

collisions at√

s = 8 TeV [19], in the context of a Type-I seesaw mechanism. Boththe analtses have not reported any excesses, and limits on the production cross-section times branching ratio are set with respect to the masses of heavy Majorananeutrinos and heavy gauge bosons WR and Z’. These previous searches have beenperformed in the ℓℓqq (ℓ = e, µ, τ) channels, which are the same final states we willanalyse in the measurement presented in Chapter 4.

Search Exclusion ExcessLeptoquarks (8 TeV) M1st−gen < 1010(850) Gev 2.4 σ in eejj, 2.6 σ in eνjj

[15] M2nd−gen < 1080(760) GeVfor β = 1 (β = 0.5) No

Leptoquarks (13 TeV) M2nd−gen < 1165(960) GeV[17] for β = 1(β = 0.5) No

Leptoquarks and M3rd−gen < 740 GeV Noheavy neutrinos (13 TeV) MWR

< 2.35(1.63) TeV[14] with M(N) = 0.8(0.2)MWR

NoWR and heavy neutrinos (8 TeV) MWR

< 3 TeV 2.8σ in eejj, no in µµjj

[13]heavy Majorana neutrinos on |VµN |2, |VeN |2

type-1 seesaw (8 TeV) |VeN V ∗µN |2/(|VeN |2 + |VµN |2)

[12] mass range 40-500 GeV No

Table 3.1: CMS results in searches for leptoquarks and heavy neutrinos in Run I andRun II

3.8 A new search for heavy neutrinos 43

3.8 A new search for heavy neutrinos

Several theoretical attempts have been made to reproduce the excess in theelectron channel, observed in a search for heavy neutrinos within the LR-symmetryextension and in a search for leptoquarks of first generation, during Run I. Some ofthem are: a LR-symmetry extention with gL = gR, production and decay of W’ andZ’ that are hypothetical gauge bosons arising from extensions of the electroweaksymmetry, R-parity violating processes via the resonant production of a slepton,and models which connect leptoquarks to dark matter.

Besides the extensions of the SM that has been already considered, we havestudied a model in which the heavy Majorana neutrino arises assuming the com-positeness of fermions [26], in order to clarify the nature of these deviations of thedata from the SM expectations. Within a composite model for heavy Majorananeutrinos, a benchmark process with a same flavour dilepton plus diquark signatureis taken into consideration, to provide a possible explanation of the excess, and toextend the limits on the parameters of the heavy neutrino search, exploiting theRun II data. The new model and its experimental search will be described in thetwo following chapters.

Chapter 4

A new model of heavy compositeMajorana neutrinos

In this chapter we investigate the fenomenlogoy of a new model of heavy neutrinosto be searched for at the upcoming LHC Run II at a center-of-mass energy of 13TeV . This new model, of which I am among the main contributors: embeds heavycomposite Majorana neutrinos (Sec. 4.2-4.5), complements the composite heavyneutrinos with the contact interaction for the first time at LHC (Sec. 4.2), is able toreproduce the eeqq final state and other observed experimental features (Sec. 4.6).

4.1 Introduction to the model

As discussed in Chapter 3, the CMS collaboration reported two excesses over theSM background expectations [11], [15] in Run I. The first excess was measured ina search for right-handed gauge boson, WR, in the eejj and eνejj final states. Thesecond excess was observed in a search for first generation leptoquarks, exploringthe signature eejj. Both the analyses used 19.7 fb−1 of integrated luminosity.Several attempts have been made to explain these excesses in the context of variousmodels [27], [28], [29], [30], [31], [32], [33]:

• considering the WR decay, by embedding the conventional (Left-Right-Symmetryextension) LRSM (gL = gR)

• in the pair production of vector-like leptons

• in R-parity violating processes via the resonant production of a slepton

45

46 4. A new model of heavy composite Majorana neutrinos

• in superstring inspired E6 models, which can also accomodate for the baryonasymmetry of the universe via leptogenesis.

Anyway, it is well known that the same-sign dilepton plus diquark (eeqq) final state,violating the lepton number of two units (∆L = 2), is a proper signature to lookfor heavy Majorana neutrinos at high energy hadron collisions. Thus, we propose toexplain the observed CMS excess(es), assuming the existence of a heavy Majorananeutrino, arising from the scenario of compositeness of quarks and leptons [26].

Compositeness [26] is a possible extention of the SM. In this approach, quarks andleptons are expected to have an internal substructure, which should become manifestat some sufficiently high energy scale, the compositeness scale Λ. Ordinary fermionsare thought to be bound states of some, as yet unobserved, fundamental constituentsgenerically referred to as "preons". Quite natural and model-independent propertiesof this picture are:

• the prediction of heavier excited states of the SM fermions, such as q∗, ℓ∗, ν∗,with masses m∗ ≤ Λ

• the existence of a contact interaction, a residual force of the internal dynam-ics, acting between ordinary fermions and also between ordinary and excitedfermions.

The SM fermions are expected to interact with the heavier excited states, such asthe heavy neutrinos of the three generations (Ne, Nµ, Nτ ), by means of both contactand gauge couplings.

Current bounds on excited lepton masses have been recently strengthened bythe LHC Run-I analyses, in the scenario where these excited heavy states couple,through gauge interactions, with the ordinary SM fermions. In particular, the Atlascollaboration performed an analysis at

√s = 8 TeV , using an integrated luminosity

of 13 fb−1, and gave a lower bound on the mass of both excited muons and electrons,up to 2.2 TeV (derived within the hypothesis m∗ = Λ) [35]. Similarly, the CMScollaboration reported some results, after collecting 19.7 fb−1 at

√s = 8 TeV , and

(always assuming m∗ = Λ) excluded excited electron (muon) masses up to 2.45(2.48) TeV [36], [37].Our aim is to complement the composite Majorana neutrino model with the contactinteractions, a generic expectation of a composite fermion scenario, never included

4.2 Gauge and contact couplings 47

so far in the LHC searches. Based on previous studies related to the productionat LHC of exotic doubly charged leptons [34] , we expect these contact interactionsto be the dominant mechanism for the resonant production of the heavy Majorananeutral particles N in the process pp → ℓN .

One possible composite models, with respect to the idea of introducing leptonnumber violation (LNV), via a composite Majorana neutrino is Mirror type Model.For simplicity’s sake, we are going to show explicitly the singlets and doublets onlyfor the first generation. The model contains a right handed doublet and left handedsinglet:

e∗L, [ν∗

L], L∗R =

ν∗R

e∗R

.

We may suppose that there is no left handed excited neutrino (ν∗L), associate to

ν∗R a Majorana mass term, and treat ν∗ as a Majorana particle. The above mirror

type model is the one to which we will refer our detailed simulation in the resultspresented below.One could also consider extended isospin composite models, where the excited statesare grouped in triplets (IW = 1) or quadruplets (IW = 3/2) instead of doublets(IW = 1/2) as considered above. Such extensions of the composite scenario containexotic charge states like doubly charged leptons and quarks of charge Q = (5/3)e.Some phenomenology of these extensions involving the doubly charged leptons hasbeen addressed. Such extended weak isospin composite models could also be consid-ered with the additional hypothesis that the excited neutrino is a Majorana particle.

4.2 Gauge and contact couplings

The new model we have studied [26] is described by a magnetic type couplingbetween the left-handed SM doublet and the right-handed excited doublet throughthe SU(2)L × U(1)Y gauge fields:

L = 12Λ

L∗Rσµν(gf

τ

2· Wµν + g′f ′Y Bµν)LL + h.c.. (4.1)

LT = (νℓL, ℓL) is the ordinary SU(2)L lepton doublet, g and g’ are the SU(2)L

and U(1)Y gauge couplings, Wµν and Bµν are the field strengths of the SU(2)L andU(1)Y gauge fields, f and f’ are dimensionless couplings typically assumed to be ofthe order of unity.


For an excited Majorana neutrino N = ν∗, arising from this model, the relevantcharged current of the gauge interaction is:

LG = gf√2Λ

NσµνℓL∂νW µ + h.c.. (4.2)

The interaction in the equation above describes the charge current interaction ofa heavy Majorana neutrino both in the (IW = 1/2) mirror type model and in acomposite model with extended weak isospin (IW = 3/2), always of the mirror type,provided that we make the correspondence

√2f3/2/

√3 = f .

Contact interactions between ordinary fermions and between ordinary and ex-cited fermions may arise by constituent exchange and/or by exchange of the bindingquanta of the new unknown interaction. The dominant effect is expected to be givenby the dimension-6-four-fermion interaction, which scales with the inverse square ofthe compositeness scale Λ:

LC = g2∗

2Λ2 jµjµ, (4.3)

jµ = ηLfLγµfL + η′Lf ∗

Lγµf ∗L + η′′

Lf ∗L + h.c. (4.4)

where g2∗ = 4π and the η factors are usually set equal to unity. In this work

the right-handed currents will be neglected for simplicity. The single productionqq′ → ℓN proceeds through flavour conserving but non-diagonal terms, in particularwith currents like the third term in Eq. (4.4), which couples excited states withordinary fermions:

LC = g2∗

Λ2 qLγµq′LNLγµℓL. (4.5)

The gauge interactions and the contact interactions have been both implemented inthe process generation.

In this work the assumption for the dimensionless couplings is that f , f ′, f1,f3/2 are O(1). The production cross sections and all simulations presented in thefollowing are obtained assuming f = f ′ = f1 = f3/2 = 1. This should be takenin mind when quoting the resulting bounds on the other parameters of the model,namely (m∗, Λ). In this regard, we point out that the cross section yield in theeeqq final state cannot easily be rescaled if f = f ′, f3/2 = 1 because, although theproduction mechanism is dominated by contact interactions (which do not dependon these constants) the decay of the heavy Majorana neutrino is affected by bothcontact and gauge interactions, and hence by the factors f , f ′, f1, f3/2. A directcomparison with other studies, which derived bounds on the mixing parameters for

4.3 Heavy neutrino’s production 49

the electron flavour of the heavy neutrinos, would require to change these factors inthe simulations.

4.3 Heavy neutrino’s production

A heavy Majorana neutrino N can be produced, in association with a lepton ℓ inp-p collisions. The production qq′ → ℓN proceeds through flavour conserving butnon-diagonal terms, which couples excited states with ordinary fermions. The pro-duction cross section of the heavy neutrino is dominated by the contact interaction,greater than the gauge one of 3-4 orders of size, depending on the heavy neutrino’smass hypothesis (Fig. 4.1).We are going to present the production cross section for the heavy Majorana neu-trino N in pp collisions, stemming from the partonic collisions. Owing to the QCDfactorisation theorem, the hadronic cross section are given in terms of convolution ofthe partonic cross sections σ(τ s, m∗), evaluated at the partons centre of mass energy√

s =√

τs, and the universal parton distribution function, which depends on theparton longitudinal momentum fractions, x, and on the factorisation scale Q:

σ =∑ij

∫ 1

m∗2s

dτ∫ 1

τ

dx

xfi(x, Q2)fi

(τ

x, Q2

)σ(τs, m∗). (4.6)

For the calculations, the CTEQ6 [47] parton distribution functions have been em-ployed, while the factorisation and renormalisation scale has been set to Q = m∗.In Fig. 4.1 we present the cross section against the heavy neutrino mass for Λ =10 TeV for the LHC centre of mass energy

√s = 13 TeV . It is clear that the contact

interaction dominates the production of the heavy composite Majorana neutrino bya factor that ranges between two and three orders of magnitude, varying the heavyneutrino mass between 1 and 5 TeV , and for the given choice of the compositenessscale of Λ = 10 TeV . This is valid for all the points in the parameter space that weare going to consider in our analysis.

4.4 Heavy neutrino’s decay

The heavy composite Majorana neutrino can decay through both gauge andcontact interactions, and in this case the dominant interaction changes depending


Figure 4.1: Contribution of gauge (blue line) and contact (red line) interaction to thecross section of production of the heavy neutrino, in the process pp → Nℓℓ

+ with ℓ = e, µ,as a function of its mass m∗, setting Λ = 10 TeV .

on Λ and neutrino’s mass. The possible decays are:

N → ℓqq′, N → ℓ+ℓ−ν(ν), N → ν(ν)qq′.

• In the first one we can have a positive lepton, a down-type quark and anup-type antiquark or a negative lepton an up-type quark and a down-typeantiquark

• In the second decay, due to the Majorana character of N we can have eithera neutrino or an antineutrino of the same flavour of the heavy neutrino Nand accordingly two opposite sign leptons belonging to a family that can bethe same or different from the other one, or alternatively a positive (negative)lepton of the same family of the heavy neutrino and a negative (positive)lepton and an antineutrino (neutrino) belonging to a family that can be thesame or different from the other one.

• In the third one, we can have a neutrino or an antineutrino and a quark andan antiquark of up-type or of down-type.

The decay channel with the highest branching ratio (BR) is N → ℓqq′. For that rea-son, we chose as our benchmark process: pp → ℓN → ℓ(ℓqq′). The decay vertex canbe dominated by gauge or contact interaction, according to the chosen parametri-sation (Λ, m∗) (Fig. 4.2).

4.5 Benchmark process 51

Figure 4.2: Contribution of gauge (blue line) and contact (red line) interaction to thedecay amplitude of the heavy neutrino, in the process N → ℓ+qq′, where ℓ = e, µ, as afunction of its mass m∗, considering the three different values of Λ of 5, 15 and 25 TeV .

4.5 Benchmark process

In our benchmark process the heavy composite Majorana neutrino is produced inassociation with a lepton featuring the same flavour, and decays into a same-flavourlepton plus two quarks. The correspondent Feynman diagram in Fig.4.3 representsthe vertices as grey blobs, including both contact and gauge interactions.Although the dilepton plus dijet final state can occur via a virtual (t-channel) ora resonant (s-channel) neutrino (Fig. 4.4), the production of a virtual neutrino isnegligible (Fig. 4.5). Thus, the final cross section is calculated considering only thes-channel, see the Feynman diagram in Fig.4.3. In this analysis the final state ℓℓqq

will be considered, particularly the cases in which ℓ is either an electron or a muon,giving rise to the eeqq or µµqq channel.Anyway, we decided to do not ask for any charge requirement for the final stateleptons in the analysis, because we would like to be experimentally sensitive to boththe following hypoteses: same sign leptons, obtainable only via a Majorana neutrinoand a leptonic number violation ∆L = ±2, and opposite sign leptons, possible viaboth Majorana and Dirac neutrino, with the leptonic number conservation.

4.6 Experimental versatility

In this section, the experimental potentialities of this composite model of heavyMajorana neutrinos will be explained. We show that the excess observed by theCMS collaboration in the eejj invariant mass distribution in the interval 1.8 <

Meejj < 2.2 TeV [11], and some other experimental properties, can be justified or


Figure 4.3: Feynman diagram of the benchmark process in which a composite Majorananeutrino is produced in association with a lepton, and decay in a same-flavour lepton anda pair of quarks.

Figure 4.4: On the left the process with the virtual heavy composite Majorana neutrino(N), on the right the process with resonant production of N and its subsequent decay. Thegrey blobs include both gauge and contact interactions.

Figure 4.5: Cross section of the process that produces the heavy composite Majorananeutrino, pp → e+e+jj, via virtual (dashed line) and resonant production (continuousline).

4.6 Experimental versatility 53

qualitatively reproduced by the model:

• The excess shape of the invariant mass of the two electrons and the twojets in the final state, obsevred by the CMS experiment in Run I, has beenreproduced using the simulations. Fig.4.7 shows that the eejj invariant massdistribution can qualitatively accommodate an excess in the interval whereit has been measured by CMS, assuming the point of the parameter spaceΛ = 10 TeV and m∗ = 1 TeV . The processes

pp → tt → ℓ+ℓ+νν + jets, pp → W +W +W − → ℓ+νℓ+νjj

have been considered as possible sources of background, because they canreproduce the dilepton plus dijet signature. In general, we expect an invariantmass distribution characterised by a peak for Mℓℓjj ≥ MN . Such picture is notaltered by the relative importance that contact and gauge interactions mayhave in the decay process; furthermore, the production cross section is alwaysdominated by contact interactions. The consistency of the invariant mass hasbeen proved for different values of the compositeness scale Λ = 5, 15, 25 TeV ,and for a given value of the excited mass m∗ = 1500 GeV (Fig.4.6).

• The excess has been observed in the electron channel but not in themuon channel. This could be explained by our model by invoking a rathernatural mass splitting between the excited electron (e∗) and muon (µ∗) insteadof assuming full degeneracy between the families, i.e. that me ∼ mµ ∼ m∗.

• The observed eejj excess consists indeed of 14 events of which 13 areopposite sign (OS) and only one is same sign (SS). It must be saidthat our Mirror type composite model with one Majorana neutrino producesthe same yield of OS and SS events. Anyway, such feature could be explainedwithin our composite model assuming the existence of an additional Majoranaν∗ state with a slightly different mass. In that case, the interference betweenthe contributions of two different Majorana states could depress the SS yieldrelative to the OS.

• In a search for high-mass diboson resonances with boson-tagged jets at√

s = 8 TeV the Atlas collaboration has reported an excess at around 2 TeV

with a global significance of 2.5 standard deviations [38], the same search per-formed by CMS has not observed a similar excess [39]. Our model contains


fermion resonances (excited quarks and leptons) which do not couple directlyto a pair of gauge bosons. On general grounds, our fermion resonances couldproduce final states with a pair of gauge bosons, provided that these are ac-companied by other objects such as leptons and jets. As an example, one mightthink to pair produce the excited neutrinos pp → Z∗ → ν∗ν∗, decaying leptoni-cally ν∗ → W ±e∓. These processes give a final signature of W +W −e+e− whichis different from the one considered in the Atlas search for high-mass dibosonresonances, consisting of only gauge boson pairs (WW,WZ or ZZ). However,one might imagine as well to pair produce the charged excited fermions, forinstance e∗ and/or q∗, almost at threshold (if they are very massive). Suchpair of heavy fermions could in principle form a 1S bound state (via the knownCoulomb and/or color interaction) which in turn could decay to a pair of inter-mediate vector boson given the high mass of the hypothetical heavy fermions.Therefore, our model has in principle the potential to reproduce an excess inthe diboson signal.

In summary, the results presented are quite encouraging and certainly endorse theinterest and feasibility of a full fledged analysis of the experimental data of the LHCRun II for a search for heavy composite Majorana neutrinos, within a Mirror typemodel, in proton-proton collisions.

Figure 4.6: Invariant mass M(eejj) plotted for different values of the compositenessscale Λ = 5, 15, 25 TeV , and for a given value of the excited mass m∗ = 1500 GeV . Theconsistency of the three distribution is shown.

4.6 Experimental versatility 55

Figure 4.7: Shape reproduction in simulations (right) of the excess observed by CMS(left). The parameters employed for the signal are Λ = 10 TeV and m∗ = 1 TeV . Theconsiedered backgrounds are pp → tt → ℓ+ℓ+νν + jets, pp → W +W +W − → ℓ+νℓ+νjj.

The simulation has been performed with CalcHEP [44].

Chapter 5

Experimental search for heavycomposite Majorana neutrinos

In this chapter a search for heavy composite Majorana neutrinos will be pre-sented. The analysis has been performed on 2.3 fb−1 of data collected by the CMSexperiment during 2015, with pp collisions at

√s = 13 TeV. This work, of which I

am among the primary authors, is summarised in the conference note [40], whichsupports the ongoing paper publication.

In the following sections, the data and Montecarlo (MC) simulations samples,that have been used, will be described (Sec. 5.1); after analysing the topology andkinematics of our signal, using the information of the MC generator (Sec. 5.2),the trigger selection, the reconstruction and identification of the particles we areinterested in will be discussed (Sec. 5.3); the signal region and the variable for thesignal extraction will be then defined (Sec. 5.4); an estimation of the backgroundsthat contaminate the signal region will be detailed (Sec. 5.5); finally, we will discussthe systematic uncertainty of the measurement, and the statistical treatment of theresults (Sec. 5.6).

5.1 Datasets

The data used in this analysis were collected during the 2015 pp collision run,and have been reconstructed using the release 7_6_3 of CMSSW (CMS Software),a dedicated software developed by the CMS community. The recorded data havebeen preselected considering only events in which all the CMS subdetectors have

57

58 5. Experimental search for heavy composite Majorana neutrinos

performed correctly, the good events are listed in a JSON file. In particular, in ouranalysis, we have relied on the fileCert_13TeV _16Dec2015ReReco_Collisions1525nsJSON.txt.The dataset names considered for the eeqq and µµqq channels, each correspondingto an integrated luminosity of 2.3 fb−1, are reported in Table 5.1.

The MC samples for the signal are generated at the leading order for the values ofthe parameter Λ of 1, 5, 9, 13, 15, 25 TeV , and for six values of the heavy compositeMajorana neutrino mass, MN , of 0.5, 1.5, 2.5, 3.5, 4.5, and 6.5 TeV , for the casesin which MN is lower than Λ. The signal samples produced with Λ = 5 TeV havebeen used as reference samples in the analysis, while the samples generated withother values of Λ are used to study how the signal efficiency changes, as discussed inSec. 5.5. The signal generation uses CalcHEP 3.6 [44] and NNPDF3.0 [46] partondistribution functions (PDF). The list of the simulated signal samples, together withtheir cross section at 13 TeV is shown in Table 5.2.

The list of the background samples, with their cross sections at 13 TeV, is re-ported in Table 5.3. The tt, tW , tW , WW , inclusive DY (Drell Yan), and inclusiveW + jets backgrounds are calculated at the NNLO, the WZ and ZZ backgroundsare calculated at the NLO; whilst the binned DY and W + Jets are calculated atthe LO, and their cross sections are multiplied for a K-factor. The binned DY andW + jets samples are produced to guarantee high statistic in specific regions of genHT, which is the hadronic activity, defined as the sum of the pT of the partons,taken considering the information of the generator. The simulation for the tt, tW ,and tW (the latter two simply referred as tW below) processes is performed withPOWHEG 2.0 [43], while the DY and the W + jets are generated with MAD-GRAPH 5 [42]. These background samples are interfaced with PYTHIA 8 [41],for the simulation of the parton shower and hadronisation, and use the NNPDF3.0PDF [46]. The WW , WZ, and ZZ processes are produced with PYTHIA 8 and theCTEQ5 PDF [48]. The pile-up is taken into account, by superimposing simulatedminimum bias interactions onto the hard scattering process, matching the pile-upprofile in data. MC-generated events are propagated through the full GEANT-basedsimulation [49] of the CMS detector.

In order to make the MC samples comparable with the data, the following cor-rections are applied to the simulations:

• For DY JetsToLL_M -50_TuneCUETP8M1_13TeV -madgraphMLM -pythia8

5.2 Preliminary study at generator level 59

and WJetsToLNu_TuneCUETP8M1_13TeV -madgraphMLM -pythia8, onlythe events with gen HT< 100 GeV are considered.

• The events are normalised to the integrated luminosity of data.

• The events are reweighted, in order to account for differences between thedistributions of the number of pile-up interaction, compared to data. Thegenerated pile-up conditions in MC samples are meant to cover the expectedpile-up scenario of 2015. Nevertheless, the pile-up profile of the data is notexactly matched by simulations. Therefore, the measured distribution of dataHdata is divided by the MC one, Hsim, to calculate the distribution of weightsw, as a function of the number of interactions per bunch crossing, i:

w(i) = Hdata(i)Hsim(i)

. (5.1)

• The events are weighted considering the lepton scale factor correction. As willbe mentioned in Sec. 5.2, these factors account for possible differences betweendata and simulation, related to the particle reconstruction and identificationalgorithms.

Data samples Luminosity (fb−1)/SingleElectron/Run2015(C,D)-16Dec2015-v1/MINIAOD 2.3

/SingleMuon/Run2015(C,D)-16Dec2015-v1/MINIAOD 2.3

Table 5.1: Data samples, used in the analysis corresponding to the 2015 data takingperiod.

5.2 Preliminary study at generator level

A kinematical and topological study has been performed at generator level onsignal samples at Λ = 5, 15, 25 TeV , and for three values of the heavy neutrino’smass: 500, 1500, and 2500 GeV , at the energy of 13 TeV in the centre-of-mass frame.We show this study only for the µµqq channel, even though all the considerationscan be extended to the eeqq channel as well. The considered objects are the muonproduced in association with the heavy neutrino and originated directly from the


Signal samples Cross section (pb)ExtendedW eakIsospinModel_ℓℓjj_L1000_M500_CalcHEP 429.4

ExtendedW eakIsospinModel_ℓℓjj_L1000_M1500_CalcHEP 169.6ExtendedW eakIsospinModel_ℓℓjj_L5000_M500_CalcHEP 331.7e-03

ExtendedW eakIsospinModel_ℓℓjj_L5000_M1500_CalcHEP 114.4e-03ExtendedW eakIsospinModel_ℓℓjj_L5000_M2500_CalcHEP 22.36e-03ExtendedW eakIsospinModel_ℓℓjj_L5000_M3500_CalcHEP 5.029e-03ExtendedW eakIsospinModel_ℓℓjj_L5000_M4500_CalcHEP 1.282e-03ExtendedW eakIsospinModel_ℓℓjj_L9000_M500_CalcHEP 26.05e-03

ExtendedW eakIsospinModel_ℓℓjj_L9000_M1500_CalcHEP 8.731e-03ExtendedW eakIsospinModel_ℓℓjj_L9000_M2500_CalcHEP 2.131e-03ExtendedW eakIsospinModel_ℓℓjj_L9000_M3500_CalcHEP 0.4793e-03ExtendedW eakIsospinModel_ℓℓjj_L9000_M4500_CalcHEP 0.1223e-03ExtendedW eakIsospinModel_ℓℓjj_L9000_M6500_CalcHEP 0.006608e-03ExtendedW eakIsospinModel_ℓℓjj_L13000_M500_CalcHEP 5.714e-03

ExtendedW eakIsospinModel_ℓℓjj_L13000_M1500_CalcHEP 1.488e-03ExtendedW eakIsospinModel_ℓℓjj_L13000_M2500_CalcHEP 0.4659e-03ExtendedW eakIsospinModel_ℓℓjj_L13000_M3500_CalcHEP 0.4659e-03ExtendedW eakIsospinModel_ℓℓjj_L13000_M4500_CalcHEP 0.1101e-03ExtendedW eakIsospinModel_ℓℓjj_L13000_M6500_CalcHEP 0.02809e-03ExtendedW eakIsospinModel_ℓℓjj_L15000_M500_CalcHEP 3.197e-03

ExtendedW eakIsospinModel_ℓℓjj_L15000_M1500_CalcHEP 0.7725e-03ExtendedW eakIsospinModel_ℓℓjj_L15000_M2500_CalcHEP 0.226e-03ExtendedW eakIsospinModel_ℓℓjj_L15000_M3500_CalcHEP 0.06214e-03ExtendedW eakIsospinModel_ℓℓjj_L15000_M4500_CalcHEP 0.415e-03ExtendedW eakIsospinModel_ℓℓjj_L25000_M500_CalcHEP 0.415e-03

ExtendedW eakIsospinModel_ℓℓjj_L25000_M1500_CalcHEP 0.08383e-03ExtendedW eakIsospinModel_ℓℓjj_L25000_M2500_CalcHEP 0.02008e-03ExtendedW eakIsospinModel_ℓℓjj_L25000_M3500_CalcHEP 0.005687e-03ExtendedW eakIsospinModel_ℓℓjj_L25000_M4500_CalcHEP 0.001841e-03

Table 5.2: Signal MC samples used in the analysis.

Background samples Cross section (pb)T T _T uneCUET P 8M1_13T eV − powheg − pythia8 831.76

ST _tW _top_5f_inclusiveDecays_13T eV − powheg − pythia8_T uneCUET P 8M1 35.6ST _tW _antitop_5f_inclusiveDecays_13T eV − powheg − pythia8_T uneCUET P 8M1 35.6

DY JetsT oLL_M − 50_T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 6025.2DY JetsT oLL_M − 50_HT − 100to200T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 147.40*1.23DY JetsT oLL_M − 50_HT − 200to400T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 40.99*1.23DY JetsT oLL_M − 50_HT − 400to600T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 5.678*1.23DY JetsT oLL_M − 50_HT − 600toInfT uneCUET P 8M1_13T eV − madgraphMLM − pythia8 2.198*1.23

W JetsT oLNu_T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 61526.7W JetsT oLNu_HT − 100T o200T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 1345*1.21W JetsT oLNu_HT − 200T o400T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 359.7*1.21W JetsT oLNu_HT − 400T o600T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 48.91*1.21W JetsT oLNu_HT − 600T o800T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 12.05*1.21

W JetsT oLNu_HT − 800T o1200T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 5.501*1.21W JetsT oLNu_HT − 1200T o2500T uneCUET P 8M1_13T eV − madgraphMLM − pythia8 1.329*1.21W JetsT oLNu_HT − 2500T oInfT uneCUET P 8M1_13T eV − madgraphMLM − pythia8 0.03216*1.21

W W _T uneCUET P 8M1_13T eV − pythia8 118.70838W Z_T uneCUET P 8M1_13T eV − pythia8 47.13ZZ_T uneCUET P 8M1_13T eV − pythia8 16.523

Table 5.3: Background MC samples used in the analysis.


parton interaction (Mupart) and the products of the heavy neutrino’s decay: theother muon (Muhn), the leading quark (q1), and the subleading quark (q2), where"leading" ("subleading") means the first (second) in pT . Only if we have a decayvertex through gauge interaction, the two quarks originate from a W SM boson.Finally we take into account the heavy neutrino itself (N).

Figure 5.1: Feynman diagram of the benchmark process. The nomenclature is explainedin the text.

5.2.1 Signal kinematics

The kinematical behaviour in terms of pT and η is shown for all the final stateobjects and for the heavy neutrino (Fig.5.2,5.3). The particles are produced withhigh pT and centrally in η. As expected, increasing the neutrino’s mass, the pT

distributions of its decay products tend to populate higher values. A minor shiftcan be observed for pT distributions of the heavy neutrino and of the muon producedin association, due to the fact that part of the energy is used to produce the heavyneutrino’s mass. In Fig. 5.4 the pT distributions of the four final state objects, atdifferent Λ, introducing Λ = 15 and 25 TeV , are compared. One can conclude thatthe behaviour in pT varies with the heavy neutrino’s mass, but is not affected bythe value of Λ.


Figure 5.2: The pT distribution of the final state objects and of the heavy neutrino atgenerator level, at Λ = 5 TeV and masses of 500,1500 and 2500 GeV .

Figure 5.3: η distribution of the final state objects and of the heavy neutrino at generatorlevel, at Λ = 5 TeV and masses of 500,1500 and 2500 GeV .


Figure 5.4: pT of the final state objects at generator level, at different values of Λ(Λ = 5, 15, 25 TeV from the first to the third column) and mass (500,1500,2500,3500 and4500 GeV ).


5.2.2 Signal topology

The topology of the signal has been explored by considering the angular openingbetween each pair of objects in the final state, and between each one of them andthe heavy neutrino. We show the distributions for the variable ∆R (Fig.5.5,5.6),defined as ∆R =

√(∆η)2 + (∆ϕ)2, and for the cos(∆ϕ) (Fig.5.7,5.8).

The two muons tend to have a back-to-back configuration in all the cases ofmass. The products of the heavy neutrino’s decay show a more collinear topologyat a mass of 500 GeV , with respect to the other two cases of 1500 and 2500 GeV ,where we observe a greater angular opening. This is more evident for the pair ofquarks that are angularly very close at 500 GeV , see Fig.5.5 and Fig.5.7.The explanation of this behavior is that the curves of gauge and contact amplitudeat the decay vertex, setting Λ = 5 TeV , intersect in corrispondence of a mass valueof about 1000 TeV (Fig.4.2). Thus, at a mass of 500 GeV we are dominated by thegauge contribution, that implies a forward decay due to the boost of the heavy neu-trino (MN >> MW ) and the mediation of a W boson that correlates the two quarks.From 1 000 GeV forward, the greater is the mass, the stronger is the contributionof the contact contribution. A decay vertex where there is contact interaction im-plicates a decay of the heavy neutrinos in three objects, without any W mediation.This results in a more randomized topology for the decay products and in a clearseparation in the ∆R distribution of the two partons.A direct comparison between the gauge and contact contribution to the decay am-plitude and the ∆R of the pair of partons is shown in Fig. 5.9 .The ∆R plotsshows the peak at low values due to the gauge decay and a bump at higher valuesascribable to the contact decay.

In addition, from the topological study, we learn that there is always a non-negligible probability, greater than 10%, to produce events with two very collinearquarks (∆R < 0.4), which end up in merged jets at reconstruction level. It will benecessary to apply specific techniques and algorithms, to deal with such overlappedjets.


Figure 5.5: The ∆R distribution of all the possible couples of objects in the final stateat generator level, setting Λ = 5 TeV and MN = 500, 1500, 2500 GeV .

Figure 5.6: The ∆R distribution between the neutrino and each one of the final stateobjects at generator level, setting Λ = 5 TeV and MN = 500, 1500, 2500 GeV .


Figure 5.7: The cos(∆ϕ) distribution of all the possible couples of objects in the finalstate at generator level, setting Λ = 5 TeV and MN = 500, 1500, 2500 GeV .

Figure 5.8: The cos(∆ϕ) distribution between the neutrino and each one of the finalstate objects at generator level, setting Λ = 5 TeV and MN = 500, 1500, 2500 GeV .

5.3 Object selection 67

Figure 5.9: Comparison between the decay amplitude curves (above) and the ∆R atgenerator level between the two partons (below) at three different values of Λ, which areΛ = 5 TeV (first column), Λ = 15 TeV (second column), Λ = 25 TeV (third column).

5.3 Object selection

In this section we introduce the algorithms for the reconstruction and identifica-tion of the objects used in the analysis: muons, electron, and jets. These algorithmsare developed by dedicated groups in CMS, the Physics Object Groups (POG), andassure the highest efficiency, toghether with the lowest possible misidentificationrate, in the object reconstruction and identification.The POG also provide the scale factors used in the analysis to improve the data-to-simulation comparison. These factors correct for slight differences in the electronand muon trigger, identification and isolation efficiencies between data and simula-tions. Each MC event is assigned a weight

SF = ϵdata(pT (lead), η(lead))ϵMC(pT (lead), η(lead))

· ϵdata(pT (sublead), η(sublead))ϵMC(pT (sublead), η(sublead))

, (5.2)

where

• ϵdata(pT (lead), η(lead)) is the (pT , η)-depending efficency of the leading leptonmeasured in data


• ϵMC(pT (lead), η(lead)) is the (pT , η)-depending efficency of the leading leptondetermined in MC

• ϵdata(pT (sublead), η(sublead)) is the (pT , η)-depending efficency of the sublead-ing lepton measured in data

• ϵMC(pT (sublead), η(sublead)) is the (pT , η)-depending efficency of the sublead-ing lepton determined in MC.

The scale factor is the product of two efficiency ratios, because two are the leptonsexpected in the final state, with the exception of the trigger scale factor, that isconsidered only for the leading lepton, being a single-electron (muon) stream. Thecorrection will be applied for the trigger, identification, and isolation efficiency, thusit will result in a product of three scale factors for each event, for both muon andelectron channel.

5.3.1 Muons

In the µµqq channel, we start the selection of events considering only those thatpass the online data taking where at least a muon candidate is found with minimumpT of 50 GeV , adopting the stream of trigger HLT_Mu50. This trigger selection isalso applied to the MC samples. The minimum pT of the leading muon is requiredto be 53 GeV , slightly higher than the trigger threshold, whilst that of the sub-leading muon is 30 GeV . The muon candidates are required to be within |η| < 2.4.Different definitions, in order of increasing purity, are provided by the POG forthe muon selection, which are labelled as "Loose", "Soft", "Tight" and "High-pT".Among them, we choose the "High-pT" selection for the signal muons, because inour search we look for a high-mass resonance decaying into high-pT particles. TheHigh-pT selection consists of the following requests:

• IsGlobalMuon; a muon is called global when it has been reconstructed withboth the tracker and muon chambers subdetectors.

• Number of valid hits > 0; at least one muon chamber hit included in theglobal-muon track fit is required, to suppress hadronic punch-through andmuons from decays in flight.


• Number of matched stations > 1; muon segments in at least two muonstations are demanded, to suppress punch-through and accidental track-to-segment matches.

• |dxy| < 0.2 cm; this is a request on the transverse impact parameter of themuon track, referred to the primary vertex, which suppresses cosmic muonsand muons from decays in flight.

• |dz| < 0.5 cm; this is a request on the longitudinal impact parameter of themuon track, referred to the primary vertex, which further suppresses cosmicmuons, muons from decays in flight and tracks from pile-up.

• Number of valid inner hits > 0; at least one pixel hit in the track of theglobal muon, to further suppress muons from decays in flight.

• Number of tracker layers > 5; at least six layers are passed trough thetracker, to guarantee a good pT measurement and to suppress muons fromdecays in flight.

• ∆pT /pT < 0.3; requirement on the relative error on pT to suppress grosslymis-reconstructed muons.

In Fig. 5.10 we show the efficiency of the High-pT muon selection with respect tothe initial number of events (cumulative efficiencies). The plot shows that we have ahigh efficiency for almost all the requests on the leading muon (Mu1) and subleadingmuon (Mu2) for the signal, for a mass of 0.5 TeV and Λ = 5 TeV , where we expecttwo real muons; for the background instead we see the requirements for a secondmuon candidate cause a loss in efficiency, since in this case we do not expect themuon candidate to correspond to a real muon and thus to be selected. We obtain ahigh efficiency for the signal selection of about 85%, while most of the backgroundsare rejected.The "High-pT" muon selection is complemented with the requirement of an isolationcriterion. The choosen criterion is an isolation based on tracker information. Thisis defined as follows

TrackerIso =∑

pT (track within ∆R < 0.3)/pT (µ), (5.3)

where pT (track within ∆R < 0.3) indicates the sum of pT of the tracks in a cone ofradius 0.3 around the muon direction, and pT (µ) is the transverse momentum of the


muon candidate. TrakerIso is required to be lower than 0.10. The efficiency relatedto the isolation is close to 100% of all signal events.

Figure 5.10: Cumulative efficiency of each request of the "High-pT" selection, sequen-tially applied to the leading muon, Mu1, and to the subleading muon, Mu2, "M500" is thesignal sample featuring Λ = 5 TeV and MN = 500 GeV .

5.3.2 Electrons

In the eeqq channel, we consider the events that pass the online data taking ac-cording to the presence of an electron candidate with minimum pT of 105 GeV (ac-cording to stream of trigger HLT_Ele105_CaloIdV T_GsfTrkIdT ). This triggerselection is also applied to the MC samples. The electrons are identified accordingto the "HEEP" selection [51], described below. The minimum pT of the leadingelectron has to be 110 GeV , to comply with trigger pT threshold, whilst that ofthe subleading one is 35 GeV . The electron candidates are required to be within|η| < 2.4. The "HEEP" selection for the electrons contains the following requests:

• |ηsc| < 1.4442 for the electron crossing the barrel part of the detector and1.566 < |ηsc| < 2.5 for the electrons traversing the endcap part, where ηsc isthe supercluster pseudorapidity. A supercluster indicates energy deposit inthe ECAL constructed by grouping hot cells found inside a window that is


centred around the cell with the maximal energy (seed) and extends over ±0.3radians in ϕ and by 0.09 units of η.

• isEcalDriven = 1; the electron is reconstructed using the energy deposit inthe ECAL.

• ∆ηseedin < 0.004 for a barrel electron and ∆ηseed

in < 0.006 for an endcap electron.This is the difference in η of the track, as measured in the inner layers, extrap-olated to the interaction vertex and then extrapolated to the calorimeter, andthe η of the supercluster. Instead of the supercluster pseudorapidity, it usesthe one of the seed of the supercluster, which is a more accurate indication ofthe η of the original electron before bremsstrahlung.

• ∆ϕin < 0.06; the difference in ϕ between the track position as measured inthe inner layer, extrapolated to the interaction vertex and then extrapolatedto the calorimeter, and the ϕ of the supercluster.

• H/E < 2/E+0.05 for a barrel electron and H/E < 12.5/E+0.05 for an endcapelectron, where H/E is the ratio of the hadronic energy of the CaloTowers, in acone of radius 0.15 centred on the electron’s position, in the calorimeter, overthe electromagnetic energy of the electron’s supercluster.

• Full 5 × 5 σiηiη < 0.03 for the endcap electrons; a condition on the spread ineta in units of crystals of the electron’s energy in the 5 × 5 block centred onthe seed crystal.

• E2×5/E5×5 > 0.94 || E1×5/E5×5 > 0.83 (referred to as e/ShowerShape).These variables are defined in the (η, ϕ) plane as the ratio of the energy ofthe most energetic 2 × 5 (1 × 5) band of ECAL crystals centred in ϕ to thehottest crystals to the energy collected in the 5 × 5 matrix of ECAL crys-tals. The two variables are complementary; while E1×5/E5×5 is well designedfor electrons hitting the centre of a crystal, E2×5/E5×5 allows the recovery ofelectrons that hit the crystal close to its edge. Combining the two variables,instead of using just one of them, allows us to set strong cut values on both andthus better reject background while keeping a high efficiency on real electrons.

• EcalIso+HadDepth1Iso < 2+0.03·ET +0.28ρ (< 2.5+0.03·(ET −50)+0.28ρ),with ET < 50 GeV (ET > 50 GeV ). EcalIso is the transverse energy of all the


rec-hits with ET > 80 MeV in the Barrel and ET > 100 MeV in the Endcaps,in a cone of 0.3 radius centred on the electron’s position in the calorimeter.HadDepth1Iso is the transverse energy of all the towers of the first layer ofthe HCAL in a cone of 0.3 radius centred on the electron’s position in thecalorimeter. ρ is a variable introduced to correct for energy contaminationdue to pile-up.

• Track pT isolation < 5 GeV ;this variable is defined as the sum of the pT ofall the CFT tracks in a double ∆R cone of 0.04-0.3 centred on the electrondirection. Only tracks having pT > 700 MeV and ∆z with the electron track< 0.2 cm are considered, where z is the minimum distance of the track to(0,0,0). This variable presents the advantage of being much less sensitive tothe pile-up (a vertex-matching is performed) and does not show dependencywith the electron ET .

• Num Lost Hits < 2; electron tracks must not have more than one missing hitsin the inner layers of the pixel detector, in order to remove electrons comingfrom conversions.

• dxy < 0.02 and dxy < 0.05, respectively for a barrel and endcap electron.

We use the data/MC scale factors for the electrons according to the measurementreported in [54].The cumulative efficiency of each one of the mentioned request is plotted in Fig.5.11, for the leading and subleading electron, setting a Λ = 5 TeV and a mass of500 GeV for the signal, and shows the major inefficiency on the backgrounds withrespect to the signal.

5.3.3 Jets

Jets are collections of particles, originating from a common parton, as a resultof the hadronization process. They are emitted within a relative small cone, thehigher is the momentum magnitude of the original parton, the smaller is the coneamplitude. The aim of the jet clustering algorithms (JCAs) is to properly identify,and cluster the final state particles of the same jet, ignoring potential fakes.Two main difficulties arise in identifying jets. The first, known as collinearity, ariseswhen two close particles are not resolved; the JCA interprets them as one single


Figure 5.11: Cumulative efficiency of each request of the "HEEP" selection, sequentiallyapplied to the leading electron, Ele1, and to the subleading electron, Ele2, "M500" is thesignal sample featuring Λ = 5 TeV and MN = 500 GeV .

energetic particle, which leads to an incorrect jet seed. The second problem, theinfrared sensitivity, involves soft radiation between two seeds from different jets; theJCA produces a single merged jet.

Building infrared and collinear-safe (IRC) algorithms is non-trivial. The so-called kt JCAs, currently among the most frequently used jet algorithm in CMS,are IRC-safe by construction, but computationally demanding. They are built uponan iterative process using abstract distances d between protojets or preclusters.Initially, each particle is labelled as a protojet. The distance dij is computed forevery possible pair of protojets, as well as the distance diB for each individualprotojet, as defined by the following equations:

dij = min(k2pti , k2p

tj ) ·∆2

ij

R2 , ∆2ij = (yi − yj)2 + (ϕi − ϕj)2 (5.4)

diB = k2pti . (5.5)

kt, y and ϕ refer respectively to the protojet’s transverse momentum, rapidity, andϕ-coordinate; while p and R are algorithm parameters controlling the relative powerof the momentum versus geometrical energy scales, and the characteristic peripheral


size, respectively. The minimum distance, dmin among all dij and diB is determined.If dmin is found within the set of dij, which naturally occurs at least in the firstiteration, since a minimum of two particles is needed to form a jet, the two protojets

in question are replaced by a protojet built from the merger of their four-momenta.The protojet in question is upgraded to the category of jet, only when dmin is notan element of the dij set. The process is repeated, starting with the updated listof protojets, until no protojets remain. The anti − kt JCA, used in parts of theCMS trigger and almost all the offline analyses, is a particular instance of kt JCAs,in which p = -1. Under this construction, the distance dij is dominated by themomentum of a high-pT particle and the distance to other particles. This results ina tendency for soft, close particles to group themselves with hard particles, actingindirectly as jet seeds. Perfectly conical jets are hence produced if no hard particlesare found within a radius of 2R; and, in this case, the hard particle seeding the jetsimply accumulates soft particles. Conversely, two distinct jets are created if twohard particles exist such that R < ∆ < 2R. Given jets 1 and 2 with kt1 ≫ kt2,jet 1 will be conical and jet 2 will be partly conical. Neither jet will be conical ifkt1 = kt2. In conclusion, the anti − kt JCA prevents soft particles from altering theshape of the jet, while allowing hard particles to seed new jets and redefine otherjets’ boundaries when necessary. Two predefined R values have been validated, 0.4and 0.8, although the former is the most commonly used in CMS, the latter will beused for the purpose of this analysis, as we will better clarified in Sec. 5.4. Thejets we consider are identified according to the recommended "Tight" working point,in [53], whose cuts are briefly described below.The kinematic and geometric acceptance requirements are:

• pT > 30 GeV (pT > 190) for the jets reconstructed in a 0.4 (0.8) radius

• |η| < 2.4 GeV for both.

The requests to apply vary according to η.For |η| < 3:

• Neutral hadronic energy fraction < 0.9

• Neutral electromagnetic energy fraction < 0.9

• Number of constituents > 1


• Charged hadronic energy fraction > 0

• Charged multiplicity > 0

• Charged electromagnetic energy fraction < 0.99.

For |η| ≥ 3:

• Neutral electromagnetic energy fraction < 0.9

• Number of neutral particles > 10.

The cumulative efficiency request by request on the leading large-radius jet is plottedin Fig. 5.12, considernig for the signal the parameters Λ = 5 TeV and MN =500 GeV .

Figure 5.12: Cumulative efficiency of each request of the "Tight" selection, applied tothe leading fat jet, "M500" is the signal sample featuring Λ = 5 TeV and MN = 500 GeV .

We further perform a cleaning against electrons and muons, requiring jets to beangularly separeted from them by ∆R > 0.4 and (∆R > 0.8). The energy scaleand resolution of the jet candidates are corrected in the simulation, in order toreproduce better the data, according to the most updated recommendations [56]. Inthe following text, we will call "jet" the jet reconstructed in a 0.4-radius cone, and


"large-radius-jets" the 0.8-radius jets.We finally mention about the algorithm for identifying jets originating from b-quarkdecays. This is done done in CMS relying on the combined secondary vertex tagger[57]. This algorithm is based on the reconstruction of secondary vertices, togetherwith track-based lifetime information. For b quark jets with pT > 30 GeV and|η| < 2.4, the identification efficiency is approximately 85%, while the probabilityfor a light-quark or gluon (charm quark) jet to be misidentified as a b quark jetis approximately 10%(20%). Despite we will not use this algorithm in the mainanalysis, it has been considered during the optimisation of the signal region.

5.4 Signal region

The final state that we consider is characterised by the presence of two sameflavour leptons and two quarks. Because of the topology of our signal, we expectthat the two quarks may be generated spatially close to each other, ending up in asingle reconstructed large-radius jet.

As we have discussed in Sec. 5.2, this possibility can be realised when the heavycomposite Majorana neutrino decays through gauge interaction, which is mediatedby a W gauge boson. In particular, when the W boson is boosted, it constraints thetwo quarks to be produced in the same direction with a small angular separation,and in this case only one large-radius jet is reconstructed. When it is not enoughboosted the two quarks are more angularly separated, and two resolved jets can bereconstructed.Nevertheless, we have found that in more than 90% of signal events in which thecontact interaction dominates (without being W-mediated) we can still reconstructat least one large-radius jet. The multiplicity of the large-radius jets per event isreported for different mass points in Fig. 5.13, for a Λ value of 15 TeV , but thisresult is found to be valid for any Λ point we have considered. This can be justifiedby considering the final state radiation of these high-energy jets, which enlarges theirreconstruction cone.Based on the above considerations, it appears that our signature can have either 2leptons plus 2 jets or 2 leptons plus at least 1 large-radius jet.

In order to understand which jet selection would be the most suitable for theexperimental search, we have compared two selections, 2 jets and at least 1 large-

5.4 Signal region 77

Figure 5.13: Multiplicity of the large-radius jets, setting Λ = 15 TeV , and consideringthe mass values of 500, 1500, 2500, 3500 and 4500 GeV .

radius jet in the final state, in addition to the two leptons. In this study we havefurther included the possibility of adding a veto on the presence of jets tagged as b-quark jets, which could be useful to reduce the tt background (Fig. 5.15, 5.16). Theb-quark jets have been identified using three different criteria of increasing purity:"loose", "medium","tight". This optimisation study has been performed consideringtwo leptons selected as described in Sec. 5.3 and restricting the selection to the high-mass region given by M(ℓ, ℓ) > 300 GeV , where we expect our signal to competeagainst the background, as you can observe in Fig. 5.14 for the muon channel.As it is shown in Fig. 5.15 and 5.16, we see that the selection with two leptonsand at least one large-radius jet has the highest significance, defined as S = s√

s+b,

where s is the expected number of signal events and b of background events, fromMC samples normalised to 2.3 fb−1. The conditions on the multiplicity of b-quarkjets are found to be not relevant, and are then not considered anymore.Although the plots have been shown only for Λ = 5 TeV and MN = 1500 GeV , thisconclusion has been demonstrated to be valid for any mass and Λ point considered.The final signal region selection for the eeqq and µµqq final states is summarised inthe following two subsections.


Figure 5.14: Distribution of the invariant mass M(µ1, µ2) for backgrounds (stackplot)with overlaid signal featuring MN = 500 GeV and Λ = 5 TeV (red dotted line).

Figure 5.15: Significance plot for the various jet requests, for the eeqq channel, atΛ = 5 TeV and for a neutrino’s mass of 500 GeV (left) or 1500 GeV (right). The labelsstay for: FJ=fat (large-radius) jets, j=jets, Lbj=loose b-tag jets, Mbj=medium b-tag jets,Tbj=tight b-tag jets.

5.4 Signal region 79

Figure 5.16: Significance plot for the various jet requests, for the µµqq channel, atΛ = 5 TeV and for a neutrino’s mass of 500 GeV (left) or 1500 GeV (right). The labelsstay for: FJ=fat (large-radius) jets, j=jets, Lbj=loose b-tag jets, Mbj=medium b-tag jets,Tbj=tight b-tag jets.

5.4.1 eeqq channel

The signal region (SR) for the eeqq channel is defined by:

• HLT_Ele105_CaloIdV T_GsfTrkIdT

• 2 electrons, with pT (e1) > 110 GeV and pT (e2) > 35 GeV and |η| < 2.4

• at least 1 large-radius jet, with pT > 190 GeV and |η| < 2.4

• M(e1, e2) > 300 GeV.

e1 and e2 indicate the leading and subleading electron, respectively.

5.4.2 µµqq channel

The signal region (SR) for the µµqq channel is defined by:

• HLT_Mu50

• 2 muons, with pT (µ1) > 53 GeV and pT (µ2) > 30 GeV and |η| < 2.4

• at least 1 large-radius jet, with pT > 190 GeV and |η| < 2.4


• M(µ1, µ2) > 300 GeV.

µ1 and µ2 indicate the leading and subleading electron, respectively.In Fig. 5.17 we show the cumulative efficiency in the signal region for both

channels and at different Λ points. We found that the signal efficiency changeswithin a small percentage for signal samples generated with Λ between 3 and 13TeV . For completeness, in Fig. 5.18 we also show the expected trigger efficiency forboth channels, measured from the signal region, considering a signal MC sample ofΛ = 5 TeV and MN = 500 GeV , the results are comparable for the other parameterpoints.

Figure 5.17: The cumulative efficiency of the signal region selection for the electronchannel and the muon channel at different Λ points, as a function of neutrino’s mass.

5.5 Variable for the signal extraction

We want to perform a shape analysis, the variable we use for extracting the signalis M(ℓ, ℓ, J), the invariant mass of the two leptons and the leading large-radius jet.In Fig. 5.19 we plot the distribution of M(ℓ, ℓ, J) in the signa region (SR) andreport the number of events of signal expected by simulation and of backgroundas estimated in Sec. 5.6. The considered backgrounds are DY , tt, tW , W + Jets,WW , WZ, ZZ, and QCD multijet. From these plots we can see that DY , tt, andtW are more relevant, while the other backgrounds are expected to contribute lessand will be referred alltogether as "Other". The results in Fig.5.19 also show thatthe observable M(ℓ, ℓ, J) can effectively separate the signal from the backgrounds.

5.5 Variable for the signal extraction 81

Figure 5.18: Trigger efficiency as a function of pT of the leading lepton, in eeqq (left) andµµqq (right) channel, considering a signal MC sample of Λ = 5 TeV and MN = 500 GeV

Figure 5.19: Invariant mass of the system eeJ (left) and µµJ (right) in the signal region,for background (stackplot) and overlaid signal (green lines).


5.6 Background estimation

In this section, we describe the evaluation of the backgrounds that may con-taminate our SR. We use semi-data-driven techniques for the DY , tt and tW pro-cesses, while we evaluate the QCD multijet contribution with a complete data-drivenmethod. They main backgrounds are tt and tW , that can mimic the signal signatureif two W are produced and dacay leptonically and a large-radiusjet is reconstructedin the final state. The DY process represents another source of background whentwo leptons are produced together with initial state radiation that results in a jet.QCD multijet events, with at least three jets, may enter the signal region or thecontrol region if two of them are misidentified as leptons.

5.6.1 DY

The DY contribution to the signal region (SR) is estimated normalizing the MCsimulation to the data in a control region (CR), defined with the same requirementsof the signal region selection, but using as observable the dilepton invariant mass,taken around the Z peak, 80 < M(ℓ, ℓ) < 100 GeV (Fig. 5.20). A scale factor (SF)is evaluated in this control region as

SF = NdataDY

NMCDY

, (5.6)

where NdataDY is the number of DY data events, after substracting the MC minority

contribution of the other backgrounds, NdataDY = Ndata −NMC

notDY . NMCDY is the number

of DY events expected by the MC. The scale factor for eeqq channel is 1.08 ± 0.02,while for µµqq it is 1.16 ± 0.02.This SF is assumed to be the same in the signal region of our analysis. In orderto check the validity of this assumption, we have extended the region of mass upto 300 GeV , to remain out from the signal region, and we have evaluated the sameratio. We have found a constant value comparable with the one taken between 80and 100 GeV , the 2% difference is used to quote a systematic uncertainty.

5.6.2 tt and tW

For the estimation of the tt and tW backgrounds, we first take the shape of tt

plus tW in an eµ control region (CR) from data, subtracting the other backgrounds,

5.6 Background estimation 83

Figure 5.20: M(ℓ, ℓ) distribution for data (black dots) and backgrounds (stack plot)around the Z mass peak, for electron (left) and muon channel (right), the bottom plotreports the Data/MC ratio bin by bin.

using the MC simulations. Then, we use the tt and tW MC samples to estimate theratio of events of the signal region over the control region, RSR/CR.This eµ control region is defined exactly as the signal region, but substituting thesubleading lepton with a lepton of the other flavor. This will be a High-pt muon,selected with loose tracker isolation and the same kinematic requirements of thesubleading electron, in the eeqq channel, and a HEEPv6.0 electron, with the samekinematic requirements of the subleading muon, in the µµqq channel.Finally, we estimate the tt plus tW contribution to the signal region as

NSRtt+tW = (NCR

data − NCRNot tt,tW MC) × RSR/CR.

Since we perform a shape analysis, the previous formula has to be read consideringit for all the bins of the M(ℓ, ℓ, J) distribution. In particular both the variablesNCR

data − NCRNon tt,tW MC and RSR/CR are bin dependent.

In order to validate this method we check the following two points:

• The consistency of the shape of M(ℓ, ℓ, J) distribution between the signal andthe control region for the tt and the tW processes, using the MC samples.This is proved by the plots in Fig. 5.21 and 5.22, where the two distributions,normalized to 1 are overlapped, both muon and electron channel are presented.

• The eµqq or µeqq control region has a high purity in tt, and tW , and the MCsimulation is well modelled for these processes. These two facts are shown to


be valid by the plots in Fig. 5.23, for eeqq and for µµqq channel.

Figure 5.21: Distributions of M(e, e, J) and M(e, µ, J) for the MC backgrounds tt (left)and tW (right), respectively in the signal region (red dots) and in the control region (blackdots). The distributions are normalized to 1 for shape comparison.

Figure 5.22: Distributions of M(µ, µ, J) and M(µ, e, J) for the MC backgrounds tt (left)and tW (right), respectively in the signal region (red dots) and in the control region (blackdots). The distributions are normalized to 1 for shape comparison.

Finally, we need to estract the bin per bin ratio RSR/CR, using the MC samples.The distribution of M(ℓℓJ) and the resulting ratios are reported in Fig.5.24. Theexplicit values of the ratios are also illustrated in the Table 5.4.The final estimation of tt and tW backgrounds is shown in Fig. 5.25, where we alsooverlap, for comparison, the nominal MC expectation of the tt and tW processes inthe SR. The agreement between the data-driven estimation and the MC expectation


Figure 5.23: Stack plot of the backgrounds with overlaid data for the distributionM(e, µ, J) for the eeqq channel (left) and M(µ, e, J) for the µµqq channel (right), inthe control region.

is found to be good, thus validating the method itself and avoiding introducing asystematic uncertainty on it.

Bin 400-600 600-800 800-1000 1000-1400 1400-2000 2000-3500tt + tW e-channel 0.56 ± 0.09 0.64 ± 0.05 0.55 ± 0.05 0.59 ± 0.06 0.63 ± 0.10 0.62 ± 0.24tt + tW µ-channel 0.67 ± 0.07 0.69 ± 0.04 0.72 ± 0.04 0.74 ± 0.05 0.83 ± 0.10 0.92 ± 0.28

Table 5.4: Ratio, bin by bin, between the number of events in the SR and in the CR, forthe tt + tW MC samples.

5.6.3 QCD

We evaluate the QCD multijet background from poorly identified, non-isolatedlepton canditates selected from data and weighted by a correction factor, whichallows to extrapolate the final contribution to the signal region.We rely on the method developed in searches of high-mass dilepton resonances, bythe Z ′ → ℓℓ group [59]. The used formula is:

QCDSR = QCDCR × W iSR/CR × W j

SR/CR, (5.7)


Figure 5.24: Distributions of M(e, e, J) and M(e, µ, J) (M(µ, µ, J) and M(µ, e, J)) forthe MC backgrounds tt + tW, respectively in the signal region (red dots) and in thecontrol region (black dots), for e-channel (µ-channel). On the left the electron channel, onthe right the muon channel. The distributions are normalised to the integrated luminosity.The bottom plot shows the ratio for each bin, between the number of events in signal andcontrol region.

Figure 5.25: M(e, e, J) in eeqq channel and M(µµJ) in µµqq channel, the data-drivenestimation for tt and tW (black dots) is compared to the nominal MC prediction.


where QCDSR is the multijet contribution estimated in the signal region; QCDCR

is taken from the data, applying the signal region requests, but on leptons takenwith a looser selection, referred below as fake-rate preselection. W i,j

SR/CR is the pT

and η-dependent weight, used to correct QCDCR, in order to estimate QCDSR, andi, j refer to the two lepton candidates. For W i,j

SR/CR, we rely on the measurementcarried on by the Z ′ → ℓℓ group [59].The fake rate preselections for electrons and muons, in µµqq and eeqq channel re-spectively, are defined in Table 5.5 and 5.6. The weight WSR/CR is defined asWSR/CR = FR(1 − FR) and the FR functional form, depending on the lepton kine-matic variables, is reported in Table 5.7 and 5.9 for electrons and muons, respectively.

Variable Barrel Endcapσiηiη < 0.13 < 0.34H/E < 0.15 < 0.10

# missing hits < 2 < 2|dxy| < 0.02 < 0.05

Table 5.5: Fake selection for electrons, in the eeqq channel.

Variable Cut value|dz| < 1.0

# of tracker layer with measurement > 5# valid pixel hits > 0

Table 5.6: Fake selection for muons, in the µµqq channel.

In the electron channel, we find out that QCDSR is ∼ 0.3. As it is lower thanthe other backgrounds, we decided to neglect it. In the muon channel, we calculatethat QCDSR is 1.5 ± 1.2. As it is low, but not negligible, we decided to considerit in the analysis. It will be included in the final distribution of M(µ, µ, J), amongthe minor backgrounds that are labelled as "Other". It is worth commenting aboutthe fact that the QCD contribution is higher in the µµqq channel, compared to theeeqq one, due to the lower lepton pT threshold requested in this channel.


η region ET range functional form35 ≤ ET ≤ 76.1 0.0524 − 0.000589 × ET

Barrel 76.1≤ ET ≤ 145.6 0.0124 − 6.38 × 10−5 × ET

ET ≤ 145.6 0.0031535 ≤ ET ≤ 75.8 0.0953 − 0.000815 × ET

Endcap |η| < 2.0 75.8 ≤ ET ≤ 186.9 0.0377 − 0.000558 × ET

ET ≤ 186.9 0.027335 ≤ ET ≤ 88.6 0.0824 − 0.000492 × ET

Endcap |η| > 2.0 88.6 ≤ ET ≤ 145.7 0.0321 + 7.52 × 10−5 × ET

ET ≤ 145.7 0.0506

Table 5.7: Funcional form of FR for electrons, in the eeqq channel.

η region pT range functional formBarrel pT > 50 2.22 × 10−2 + exp(−3.16 + 2.80 × 10−2 × pT )

Endcap 50 < pT < 110 8.83 × 10−3 + exp(5.93 − 1.33 × 10 × pT )Endcap pT > 110 −2.91 + exp(1.08 + 1.32 × 10−4 × pT )

Table 5.8: Funcional form of FR for muons, in the µµqq channel.

5.7 Systematic uncertainties

Systematic effects on the background estimations and the simulated MC signalshave to be considered, before dealing with the interpretatiton of the results. Forthe uncertainty on the luminosity we consider a value of 2.7% on the normalisationof both backgrounds and MC signals [60]. For the uncertainties related to thecorrections, which we apply to the MC samples, we proceed as follows:

1. We take the central value of our measurement given by the distribution M(ℓ, ℓ, J),which contains the backgrounds estimated according to the methods describedin Section 5.6.

2. For every systematic effect we repeat the whole analysis twice, considering thedeviations up and down due to the systematic, and producing two distributionsaccordingly: M(ℓ, ℓ, J)Up and M(ℓ, ℓ, J)Down.

3. We perform the subtractions |M(ℓ, ℓ, J)Up−M(ℓ, ℓ, J)| and |M(ℓ, ℓ, J)Down−M(ℓ, ℓ, J)|, and take the maximum difference in every bin. This new dis-tribution of the maximum difference, M(ℓ, ℓ, J)Sys, shows the shape of thesystematic errors.

5.8 Statistical interpretation of the results 89

This procedure is used for all the backgrounds and the MC signal samples, and forboth eeqq and µµqq. The approach is used for the following systematic uncertainties.The systematic uncertainty on the lepton energy scale and resolution are found tobe of the order of 5%(6%) for the background and 3%(4%) for the signal, for theelectron (muon) channel, according to the indications in [62] and [61]. Uncertaintiesrelated to jet energy scale amount to 3%(4%) for the background of the eeqq (µµqq)channel, while it is found to be around 1% for the signal regardless of the channel,they are evaluated according to the prescriptions in [63]. Uncertainties related tojet energy resolution correspond to 2% and 4% for the background and the signal inboth channels, applying the prescriptions in [63]. The imperfect modelling of pileupinteraction leads to a systematic uncertainty of about 4% for background and 2%for signal. The uncertainty on the total integrated luminosity amounts to 2.7% forthe 2015 data.We further consider a systematic associated to the methods used for estimating thebackgrounds. In this analysis all the backgrounds are estimated with a formulathat can be generalised as BkgSR = BkgCR × w. BkgSR represents the backgroundcontribution extrapolated to the signal region, BkgCR the background in a givenCR, and w a weight used to normalise BkgCR to the signal region. The systematicerror, on the estimation of BkgSR, is given by

δBkgSR =√

(δBkgCR × w)2 + (BkgCR × δw)2. (5.8)

This formula is used for every bin of the distributions of the estimated backgrounds,in both eeqq and µµqq channel.Moreover, to account for the theoretical uncertainty that may affect the M(ℓ, ℓ, J)distribution of the Drell-Yan and signal processes, we also consider the variation onthe Drell-Yan mass shape, which is estimated relying on the PDF4LHC prescription[65].The average uncertainty for each systematic effect is reported in Table 5.9.

5.8 Statistical interpretation of the results

In this section we conclude our analysis with the statistical interpretation of theresults. First, we briefly recall the concept of upper limit extraction (Subsec. 5.8.1),then we set the upper limit on the existence of a heavy Majorana neutrino as afunction of its mass, at different scales of energy Λ (Subsec. 5.8.2).


Systematic % Bkg (eeqq) Sig (eeqq) Bkg (µµqq) Sig (µµqq)Luminosity 2.7 2.7 2.7 2.7

Pile-up 4 2 4 1Electron SFs 1 2 1 (TT+tW only) -

Electron en. scale 5 3 - -Muon SFs 2 (TT+tW only) - 6 10

Muon pT scale - - 6 4JER 2 0.4 2 0.4JES 3 1 4 1

Background 15 - 15 -Drell-Yan/Sig theory 10 2 10 2

Table 5.9: Systematic errors for signal and background in eeqq and µµqq channels.

5.8.1 The CLs technique

The CLs technique [67], [68] is used to extract the upper limits on the productof the cross section and branching fraction of the signal process. This gives a quan-titative assessment of the incompatibility of the signal + background model and thebackground only hypotheses, provided no excess of observed events relative to thebackground only expectation has been observed. The probability P to observe kevents under a model that predicts λ events is computed by means of the Poissonstatistic as

P (k|λ) = λke−λ

k!. (5.9)

In this analysis, λ is the sum of expected background yields. Since not only eventyields are considered, but also the shapes of visible mass distribution (or any otherobservable), P must be promoted to the Poisson likelihood, L, which reads

L =Nbins∏i=1

P (ki|λi) =Nbins∏i=1

λkii e−λi

ki!, (5.10)

where Nbins is the total number of bins, while i is the bin iterator. As shown in 5.11equation, in which S and B are the signal and background estimates respectively,the systematic uncertainties in the measurement of λ are taken into account by in-troducing n nuisance parameters, θ = θ1, θ2, ..., θn. Furthermore, a floating signalstrength parameter, µ, effectively allows for the determination of the most com-patible product of signal cross section and branching ratio provided the measureddata:

λ = µ · S(θ) + B(θ). (5.11)

The Poisson likelihood thus reads

L(k|µ, θ) =Nbins∏i=1

[µ · S(θ)i + B(θ)i]kie[µS(θ)i+B(θ)i ]ki!

.. (5.12)


A test statistic, tµ , is defined as the ratio of likelihoods so that θ and µ maximisethe numerator and denominator respectively,

Iµ = −2ln

L(s|µ, θµ)L(s|µ, θ)

, (5.13)

where the numerator represents the best agreement to the observed data for a fixed-size signal, while the denominator is the configuration of signal-plus-backgroundmodels that best fits the observed data. An array of tµ is produced by generating alarge number of pseudo-experiments, in which tµ are determined by considering thepseudo-data as k. Pseudo-experiments are randomly drawn from a pool based onthe average expectations derived from the analysis, which are then shifted up anddown as a function of the uncertainties. The resulting distribution is compared tothe observed value, tobs, which is calculated from the observed data. The CLs is theratio of p-values for the signal-plus-background (ps+b) and the background-only (pb)hypothesis,

CLs = ps+b

pb

, (5.14)

whereps+b = P [tµ > tobs

µ |µ · S(θobsµ ) + B(θobs

µ )], (5.15)

pb = P [tµ > tobs0 |B(θobs

0 )]. (5.16)

The confidence level (CL) is given by (1 − CLs). Consequently, this procedure isreiterated for varying µ until CLs = 0.05, in order to obtain a limit at the 95% CL.

5.8.2 Exclusion limits

In this section we illustrate the results of our search.In Fig.5.26 we show the distribution of the variable M(ℓ, ℓ, J) for the estimatedSM backgrounds (stackplots), the signal (lines), having considered the parametersΛ = 5 TeV and the masses M(N) = 2500 GeV and M(N) = 3500 GeV , and thedata (black points), for the eeqq (top) and the µµqq (bottom) channels. The errorbars stand for the statistical plus systematic uncertainty. The observations are inagreement with the SM expectations.Since there is no evidence of new physics decaying to two leptons and a fat jet,we set corresponding upper limits on the existence of heavy composite Majorananeutrinos. The upper limits have been evaluated using the CMS tool "Combine", in


which the CLs criterion is implemented [66], providing as inputs the mass shape ofestimated backgrounds, the expected signal, and the data. We further include thesystematic uncertainties described in 5.7, which are treated as uncorrelated nuissanceparameters among the bins of the M(ℓ, ℓ, J) distributions, for systematic related tothe background, and as correlated nuissance parameters for the other systematics.

We use a CLs criterion to set an upper limit at 95% on the cross section of theheavy composite Majorana neutrino produced in association with a lepton timesits branching fraction to two same-flavour leptons and two quarks, σ(pp → ℓN) ×B(N → ℓqq), and on the compositeness scale Λ.The observed and expected upper limits on σ(pp → ℓN)×B(N → ℓqq) as a functionof the mass of the heavy composite Majorana neutrino are shown in Fig. 5.27. Thecoloured bands represent the expected variation of the limit to one (green) and two(orange) standard deviations. The blue curve indicates the theoretical prediction ofσ(pp → ℓN) × B(N → ℓqq) for MN = Λ, while the cyan curves the same theoreticalprediction for seven Λ values ranging from 6 to 12 TeV , in step of 1 TeV .

The corresponding exclusion limits on the compositeness scale Λ are displayedin Fig.5.28. At low MN masses, the compositeness scale Λ can be excluded up to11.5 and 10 TeV in the eeqq and µµqq channels. The sensitivity to Λ decreases athigher masses of MN . For the case of MN = Λ, the resulting exclusion limits are upto 4.60 TeV in the eeqq channel and 4.70 TeV in the µµqq channel.When deriving these limits, we assume that the signal efficiency is independent ofΛ. This hypothesis has been validated for signal samples produced with Λ between5 and 13 TeV , while for samples with Λ lower than 5 TeV the difference can beup to 25%. Despite this difference, the whole region in Fig. 5.28 remains excludedbecause of the much higher cross section for lower Λ points. We further verify thatthe upper limits on MN for a given Λ value vary at most by 5%, comparing to thecases in which the MC signal M(ℓ, ℓ, J) distributions featuring Λ equal to 5 and 13TeV are used as input in the limit calculation.


Figure 5.26: Distribution of the variable M(ℓ, ℓ, J) for the estimated SM backgrounds(stackplots),the signal (lines) having considered the parameters Λ = 5 TeV and two massesof N equal to 2500 and 3500 GeV , and the data (black dots) for the eeqq (left) and theµµqq (right) channels. The error bars stand for the statistical plus systematic uncertainty.

Figure 5.27: The observed 95% CL upper limits (solid black lines) on σ(pp → ℓN) ×B(N → ℓqq), obtained in the analysis of the eeqq (a) and the µµqq (b) final states, as afunction of the mass of the heavy composite Majorana neutrino, Nℓ. The correspondingexpected limits are shown by the dotted lines, and the coloured bands represent theexpected variation of the limit to one (green) and two (orange) standard deviations. Theblue curve indicates the theoretical prediction of σ(pp → ℓN)×B(N → ℓqq), for MN = Λ,while the light cyan curves represent the same theoretical prediction for seven Λ valuesranging from 6 to 12 TeV in step of 1 TeV and different values of the mass of N.


Figure 5.28: The observed 95% CL upper limits (solid blue lines) on the compositenessscale Λ, obtained in the analysis of the eeqq (a) and the µµqq (b) final states, as a functionof the mass of the heavy composite Majorana neutrino, Nℓ. The dotted lines representthe corresponding expected limits and the coloured bands the expected variation to one(green) and two (orange) standard deviations. The grey zone represents the phase spaceof Λ < MN , which is not allowed by the model.

Chapter 6

CMS track trigger towards theHL-LHC

The original design of the LHC was to operate at 1034 cm−2s−1 of instantaneousluminosity, with 25 ns of bunch spacing and approximately 25 simultaneous inelasticcollisions per crossing (pileup), already reached in Run II. After the upgrades to theLHC, the luminosity and the pileup will more than double, during the Phase 2.We are going to present: the advanteges in the new physiscs searches using ourheavy neutrino analysis as a reference, and the serious efforts needed to improve theperformances of the Level-1 trigger system of the CMS detector [69], [70], [71].

6.1 LHC status and future plans

The central mission of the CMS HL-LHC physics program will include precisemeasurements of the properties of the recently discovered Higgs boson and furthersearches for new physics beyond the Standard Model. The higher luminosity willextend the discovery mass reach, allow more sensitive searches for signatures for newphysics, and enable studies of any newly found particles and their interactions.

Specifically, the so far discussed search for heavy composite Majorana neutrinoswill substancially benefit of new data-taken conditions. We extrapolate the exclusionlimit of this analysis in the mass and Λ parameter space for three stages of greaterluminosity (30, 300, 3000 fb−1), thanks to the Delphes fast simulator [45]. In firstapproximation, the significance curves S=5 have been considered as exclusion limits,so that the region below each curve is the excluded one (right plot in Fig. 6.1).

95

96 6. CMS track trigger towards the HL-LHC

This plot is compared with the already shown exclusion limit plot, resulting afteranalysing 2.3 fb−1 of Run-2 data, taken during 2015. The extrapolation is verypreliminar and has to be evaluated with caution, but it gives an idea of the exclusionpotential gained in Phase 2, when the expected collected luminosity is of 3000 fb−1.

Figure 6.1: Comparison between the extrapolated (left) and current (right) limit ofexclusion of the heavy composite Majorana neutrino search in (Λ, MN ) parameter space.On the right plot the significance (S) curves at S=5, calculated by Delphes [45], are shownfor three stages of integrated luminosity. On the right plot the measured exclusion limitof the analysis is plotted (below the blue curve); the SM expectation is represented bythe green plus orange band (one and two σ of uncertainty), while the gray region is notallowed by the model.

We briefly remind the current LHC plan, before introducing the Phase-2 triggerupgrade. This plan calls for a series of long periods of data-taking, referred to asRun I, Run II, Run III, etc. interleaved with long shutdowns, indicated as LS1, LS2,LS3, etc., the whole schedule is in Fig.(6.2)Run I is the name given to the completed data-taking period in 2011 and 2012. Dur-ing the first long shutdown, LS1, which started in 2013, and ended at the beginningof 2015, some modifications were made to the LHC, to enable it to run at the centerof mass energy of 13 TeV .Run II began in 2015, and is still ongoing. The bunch spacing has been reducedto 25 ns, from 50 ns. The original performance goal for the LHC, to operate atan instantaneous luminosity of 1034 cm−2s−1, with 25 ns bunch spacing, has beenachieved relatively soon after the startup. Under these conditions, early in Run

6.1 LHC status and future plans 97

II, CMS experienced an average of about 25 inelastic interactions per bunch cross-ing, referred to as pileup. This is the operating scenario the CMS experiment wasdesigned for. A new scheme to form the bunch trains in the Proton Synchrotron(PS) will allow the luminosity to overtake the original design before the second longshutdown, LS2, planned for 2018-2019. In LS2, the injector chain will be furtherimproved and upgraded to deliver very bright bunches. The peak luminosity shoudreach 2 × 1034 cm−2s−1 in this first phase of the LHC program, providing an inte-grated luminosity of over 300 fb−1, by 2023. To maintain its present performancein this period, the CMS detector will undergo an upgrade program, called "CMSPhase-1 Upgrade".By 2023, the quadrupoles that focus the beams at the ATLAS and CMS collisionregions will be replaced, and crab cavities will be added to optimize the bunch over-lap at the interaction region. These modifications will produce a significant increasein the LHC luminosity. The high luminosity period that follows LS3, with the up-graded LHC, is referred to as HL-LHC or Phase 2. The proposed operating scenariois to level the instantaneous luminosity at 5 × 1034 cm−2s−1 and to deliver 250 fb−1

per year for a further ten years of operation. Under these conditions, the eventpileup will rise substantially to become a major challenge for the experiments, andthe performance degradation, due to the integrated radiation dose, will need to beaddressed.

Figure 6.2: LHC luminosity plan [69].

98 6. CMS track trigger towards the HL-LHC

6.2 CMS trigger upgrade for Phase 2

The tricky goal of the Phase-2 upgrade [69] will be to maintain the overall physicsacceptance under the challenging HL-LHC conditions. CMS must mantain its capa-bility to efficiently trigger events originating from low mass physics processes (e.g.Higgs production at 125 GeV ), and to perform precision measurements of low tomedium pT physics objects, leptons (e, µ, τ), photons, jets (including b tagging),and missing transverse energy (MET).

To achieve this, a number of major trigger upgrades are foreseen during the thirdLong Shutdown (LS3) [71]. The main one is the addition of a tracker trigger at L1(Level 1), which is an integral part of the design of the new silicon tracker. CMSalso plans an upgrade to the detector readout, L1 trigger and HLT systems. Thiswould allow up to 750 kHz of Level-1 readout, compared to the current 100 kHz; upto 12.5 µs Level-1 latency, compared to the current 4 µs; up to 7.5 kHz permanentevent storage rate, compared to the current 1 kHz.These upgrades are motivated by dedicated L1 menu studies. They show that, usingL1-trigger algorithms designed for the Phase-1 detector, for beam conditions of 140events of pileup, at least 1 500 kHz of L1 acceptance rate would be required tomaintain the same physics acceptance of the Phase 1. For an environment of 200pileup events, the same L1 menu would require almost 4 000 kHz. Such bandwidthis beyond the technical feasibility of the CMS upgrades.However, the same studies also demonstrate that, adding tracking information to L1trigger, substantially, reduces these rates to about 260(500) kHz for the same beamconditions of 140 (200) pileup. These estimates do not include any uncertainty,such as simulation imperfections, limitation in releasing the L1 track based triggersin hardware and other ones. If we consider that, accounting for these uncertaintiesrequires a margin of 50% in the total L1 acceptance rate, we expect that the inclusionof a track trigger at L1, in conjunction with a L1 bandwidth increased up to 750kHz, will enable CMS to retain its Phase-I physics acceptance up to 200 pileup [70].

6.3 Motivations for a Level-1 track trigger

The tracker will provide L1 tracks, built from the outer tracker information, foreach bunch crossing. These tracks, parameterized by five helix track parameters,

6.3 Motivations for a Level-1 track trigger 99

will be used in the L1 trigger to form the trigger decision, by combining the trackswith the information delivered by the muon and calorimeter trigger system.

The inclusion of the tracker in the trigger decision should allow to:

• better identify charged leptons (e, µ, τ)

• improve the pT determination of charged leptons

• determine the isolation of leptons and photons with respect to the neighboringtracks

• determine the provenance vertex of charged leptons and jets

• determine an event primary vertex and the transverse missing energy carriedby L1 tracks that come from this vertex.

With the L1 tracks, the global trigger will have several new handles to increase itsselectivity.It will be possible to improve the selection of isolated leptons and photons, byimposing a tracker based isolation requirement, that is more robust, with respect topileup, than isolation criteria which rely solely on calorimeter information.Multi-object triggers can also be made more robust, by imposing that the objectscome from the same interaction, exploiting their z-vertex.Hadronic triggers, that require that the scalar or vector sum of the transverse energyof jets be above a given threshold, will also be improved, by restricting these sumsto the jets that come from a common vertex.

Chapter 7

New L1-track-trigger systembased on PCA

After introducing the track-finding problem in CMS for the Phase 2 (Sec. 7.1),a solution for a track-fitting algorithm based on the Principal Component Analysis(PCA) is proposed, showing its working principles, preliminary tests, and perfor-mances in simulations (Sec. 7.2). The goal of the CMS collaboration is to builda demostrator able to measure the relevant observable in the track-trigger process,and to compare the performances of the different solutions, in order to choose themost suitable one for the HL-LHC period (Sec. 7.3). Finally, a pattern recogni-tion and fitting mezzanine, combining the power of both Associative Memory (AM)and Field Programmable Gate Array (FPGA) devices, developed by the INFN ispresented (Sec. 7.4).

7.1 Track-finding process

A tracking algorithm has the aim to reconstruct the trajectory of a chargedparticle, using the hits left in each component of the tracker detector. Given thetrajectories of each event, one can know the pT of the tracks, thanks to the curvaturedue to the magnetic field, and the coordinates of the primary and secondary verticesof the event.The CMS challange is now to develope an online tracking algorithm with a decisiontime compatible with the L1 trigger latency time, of 12.5 µs, and high-quality re-construction performances. Specially in higher rate conditions and raised number

101

102 7. New L1-track-trigger system based on PCA

of pileup events, the tracking algorithm has the challanging task of solving the com-binatorial problem to associate the N hits of an event to a set of track candidates,distinguishing whose track is each group of hits, and throwing out the fake tracks.To be more precise, the information left in the CMS tracker goes through differentsteps.First, a preselection of hits is enstabilished according to the cluster width, that isproportional to the radial distance of the sensor from the collision point and in-versely proportional to the pT .Secondly, according to the correlation between preselected hits in nearby sensors,track stubs are selected, only above a given pT threshold of 2-3 GeV, thanks to thetrack direction of flight measurement.We end up with a set of stubs for each event, to be associated to tracks featuringa pT greater than 2-3 GeV. The track-finding problem will be solved in two levels,here presented:

1. Pattern recognition; a certain number of patterns, that reproduce physicallyinteresting events is stored in bank files. The pattern recognition is the compar-ison, in parallel, between the stubs of the data event and each stored pattern.Each pattern contains a set of low resolution tracks: the roads. The Asso-ciative Memory (AM) chip receives the event stubs, and looks for compatibleroads. The output of this process are the addresses of all the patterns withmatched roads. Then, the interesting roads are extracted by each pattern, andassociated to the high resolution stubs which will be used to perform the fit.

2. Track fitting; this is the second step of the track-finding process, it takes asinput the coordinates of the selected stubs, and gives as output the parametersof each track. In principle, it can be performed with various algorithms, ex-ploiting the hardware device of the Field Programmable Gate Array (FPGA).

The Phase-2 tracker will be involved in the L1 Trigger and, taking advantage ofboth the Associative Memories and the FPGA device, will ensure a trigger decisionin proper time and with satisfactory performances.

7.2 A track fitting based on PCA 103

7.2 A track fitting based on PCA

The "trick" to improve the quality in the events selection, and gain a reductionfactor is to anticipate at L1 the reconstruction process, that now is performed onlyin the High Level Trigger (HLT). At each bunch crossing, the stubs on data areprocessed to form L1 tracks, that are the tracker primitives to combine to the othersubdetectors information to perform the L1 trigger.The track finding process has to be very fast, and can benefit from the employmentboth of the Associative Memories (AM), a custom chip already used in the CDFexperiment, and of the programmable device FPGA. The junction of these twotecnologies provides a faster pattern recognition function, thanks to the parallelismof the AM chips, and the extraction of high quality tracks, implementing the trackfitting algorithm in the FPGA device.

One of the proposed algorithms for the fitting is based on the Principal Compo-nent Analysis method, and will be presented in the following text.The Principal Component Analysis (PCA) [74] is probably the oldest and best knownof the techniques of multivariate analysis. The central idea of the PCA is to reducethe dimensionality of a dataset, in which there is a large number of interrelatedvariables, while retaining as much as possible of the variation present in the dataset.This reduction is achieved by transforming the initial set of variables to a new setof variables, called principal components, which are ordered, so that the first fewretain most of the variation present in all of the original variables, and are not cor-related. The computation of the principal components reduces to the solution of aneigenvalue-eigenvector problem for a positive semidefinite symmetric matrix.

In the fitting case, the transformation takes as input the coordinates of the stubs,and gives as output the track fitting parameters. In the simplest and ideal scenario,a track crossing all the barrel outer layers of the tracker, one stub per layer, leaves3 × 6 = 18 stub coordinates. However, a track has 5 degree of freedom, so only 5parameters are needed to define that.Thus, five locally linear functions should exist, that link the track parameters to thestub coordinates:

pi ∼∑

j

Aijxj + qi, i = 1, ..., 5 j = 1, ..., 18 (7.1)

The validity of the linearity of the functions p(x) improves, diminishing the starting


variability of the coordinates, for instance, if one restricts the geometry amplitudeof the tracker sector where the tracks are taken from.

The PCA method studies the coordinates and parameters correlation, in orderto find the transformation constants (Aij and qi). The PCA constant calculationuses proper simulated samples of prompt muons, and is the most computing labo-rious step of the fitting procedure. A different set of constant is needed for eachgeometrical sector of the tracker, that can be only barrel, only endcap or hybrid.Milion of muon tracks per sample are needed, and they are expected to uniformlycover all the geometrical acceptance of each sector of the tracker.The starting requirement is to minimize the mean difference in absolute modulebetween the fitted and the true (with hat) track parameters:

min < pi − pi >, i = 1, ..., 5. (7.2)

This leads to the PCA constant resulting formulas:

Ali =∑m

V −1lm (< xmpi > − < xm >< pi >), (7.3)

qi = pi −∑

j

Aijxj. (7.4)

• Ail are the element of the rotation matrix of the PCA transformation

• qi are the elements of the translation vector of the PCA transformation

• xm are the stub coordinates

• pi are the true track parameters

• Vlm is the coordinates covariance matrix.

Once one have stored the PCA constant in dedicated files, the PCA fitting simplytakes as input the stub coordinates, and gives as output the track fitted parameters,through a simple scalar product, using the known constants, Eq. 7.1.

7.2.1 The PCA fitting simulation

Using the framework inhttp : //sviret.web.cern.ch/sviret/Welcome.php?n = CMS.HLLHCTuto620,


we are able to simulate the expected geometry for the Phase 2, to generate simulateddata of PGUN muons, and to perform the pattern recognition.

In addition, we have developed a new track fitter class that, taking as in-put the stubs matched in the pattern recognition process, gives as outputs theL1 fitted tracks. The PCA constants to perform the fitting are stored in .txtfiles for each tower, where "tower" is the neomeclature used by CMS to indicatea geometrical sector of the outer tracker 7.1. The developed code is in https ://github.com/lstorchi/pca_fit. The interested reader can set up our software envi-ronment on lxplus following the instructions in https : //github.com/lstorchi/pca_fit/wiki.

Figure 7.1: The tracker is divided into 48 trigger towers, 8 divisions in ϕ and 6 in η (hereshown). This repartition ensures an optimal data sharing; a stub cannot belong to morethan 4 towers.

7.2.2 Preliminary tests

As a pleriminar test, to get in touch with this statistical method, we used twoelements of the PCA analysis: the covariance matrix eigenvalues and the scores.We perform the tests, first using all the tracks in the 18 barrel tower, then takingthe tracks from a more restricted geometrical sector, a subtower included in the 18tower see Fig. 7.2. The 18 barrel tower is defined in the range of η from -0.6 to 0.4and ϕ from 1.1 to 2.9. The sample of muons, generated in the pT range (2, 200)GeV , contains 10 milions of events.

To perform the calculations we use the Armadillo library [73] , that is a highquality C++ linear algebra library, aiming towards a good balance between speedand ease of use, has API syntax similar to Matlab (Octave), and can work with


Figure 7.2: Representation of the stubs in the 18 barrel tower of the outer tower (reddots) and within one of its subtowers (green dots), in a xyz reference frame with the zaxis parallel to the beam line. The blue line represents a track crossing this tower.

external libraries. As input we use the 18 stub coordinates and the 5 track trueparameters per track extracted from the muon training sample. The elements of the18×18 covariance matrix of the stub coordinates are Vij =< xixj > − < xi >< xj >.In principle, we expect as eigenvalues of the covariance matrix: 5 greater eigenvaluescorrispondent to the 5 degrees of freedom of the tracks and 13 negligible eigenvalues.These 13 eigenvalues contribute to the calculation of χ2, a quality parameter thatcan discriminate between tracks and random combinations of stubs.

The score matrix T is the projection of the initial coordinates xi in the newPrincipal Component frame of reference, it is defined as:

T = XL, (7.5)

where X is the xi coordinate matrix and L is the eigenvector matrix, each columnof which is an eigenvector of the covariance matrix. The score plots are the repre-sentation of this projections in the Principal Component frame (e.g. on the first 3PC axes, because we can depict up to three dimensions), and show the behaviour ofthe object analised (the tracks). It is possible to point out: groups of similar objects(clusters), particular objects (outliers), and new variables correlation. The expec-tation is that the more the PCA method works, the more compact the resultingcluster are, and the lower is the number of outliers.

The results of this preliminar and qualitative test show that the first 5 eigenvec-tor, expeted to be the Principal Component, assume greater values for a subtower,


compared to a tower, and the variance they cover increases from 98.89% to 99.61%,restricting the geometry. The 18 eigenvalues for the two cases are reported in Table7.1.In addition, the scores plot, in Fig. 7.3, gives encouraging results as well; If wetake all the tracks within the tower 18 we see a main cluster and some outliers.Restricting to the tracks of a subtower the outlier fraction is reduced and 7 clusterscan be clearly observed, which reveal the geometrical substructure of the subtoweritself.

Tower eigenvalues Subtower eigenvalues56.686 1565.2916.272 57.8787.091 21.4951.836 7.0261.149 1.8140.528 1.3930.206 1.2330.094 1.0690.041 0.9590.028 0.6290.021 0.5420.005 0.3750.003 0.0910.002 0.0450.002 0.026

0 0.0210 0.0140 0.003

Table 7.1: Coordinate coovariance matrix eigenvalues for the 18 tower and for a subtowerwithin the 18 tower. The first 5 lines correspond to the 5 degrees of freedom of a track.

7.2.3 The first results

Now we are more confident about the statistical operation of the PCA method,and decide to perform the fitting procedure using the muon simulated samples withinthe same 18 tower. The aim is to compare the resulting fitting parameters of thetracks with the true parameters.For the choice of the fitting parameters are important: the linearity, between thevariables measured by the tracker and the fitting parameters, and the flatness of the


Figure 7.3: Score plot for the 18 tower (left) and for a subtower within the 18 tower(right).

fitting parameter distributions in the training muon samples. Taking this in mind,we choose as 5 independent parameters of the track: the longitudinal impact pa-rameter z0, the transverse impact parameter d0, the pseudorapidity η, the azimuthalangle ϕ and the curvature c/pT .First, the fitting problem has been divided in two sub-problems:

• in plane r − z, from the coordinates (ri, zi), where i is referred to the stub,we find the two parameters of the track: z0 and η. There are 2 × 6 = 12 stubcoordinates for each track.

• In plane r −ϕ, from the coordinates (ri, ϕi), where i is referred to the stub, wefind the two parameters of the track: c/pT and ϕ, where c is the charge. Hereit is possible to use only the three more internal layers to perform the fitting,so we have as input 2 × 3 = 6 stub coordinates for each track.

One can notice that the parameter d0 is non extracted via this fitting procedure, butit is left to a second step. This is possible if one assumes that the beam spot of thecollisions is perfectly centered, this means that you do not have any systematicaldiplacement of the beam spot and neither of the prompt tracks in the transverseplane. In other words, we have one parameter already set, because is d0 = 0 in anyevent featuring a not displaced beam spot. Thus, we start here showing the plotsreferred to a 4-parameter fit.

We plot for each of the four parameter the resolution, defined as the module ofthe difference between the fitted and the true (hat notation) track parameter:

∆p = |pfit − p|, (7.6)


and we consider the RMS (Root Mean Square) parameter as a first estimate of theresolution value. The results are shown in Fig.7.4 and Fig.7.5 for three differentintervals for η in the r − z plane and for pT in the r − ϕ plane. It is possibleto observe that, resctricting the intervals, the fitting resolution tends to improve,as expected. Anyway, increasing the number of subintervals, means to increase thenumber of set of constant to be stored, so increasing the needed resources of memoryin the FPGA.An optimization procedure has to be followed, in order to obtain a compromisebetween the resolution quality and the number of set of PCA constants to be stored.

Figure 7.4: Resolution distributions for the two parameters extracted in the r − z plane:η (above) and z0 (below). Three different intervals in η have been considered.


Figure 7.5: Resolution distributions for the two parameters extracted in the r − ϕ plane:ϕ (above) and c/pT (below). Three different intervals in pT have been considered.

We repeated the fitting procedure chosing different binnings in η for the r − z

plane and different binnings in pT for the r − ϕ, and for all the barrel towers. Herewe present the final configuration, that ensures a good resolution and a feasibleimplementation in the FPGA:

• In r − z plane we have 20 bins in η, so 20 sets of constants per barrel tower.

• In r − ϕ plane we have 7 bins in pT and separate positive and negative muons,this gives 7 × 2 = 14 sets of constants per barrel tower.

The resulting values of the resolutions are reported in Table 7.2, mediated for thevarious barrel towers.

These results are in line with the requirements of the CMS detector for theresolution of the L1 tracks, the study has been extended to the hybrid and endcaptowers and to the case of missing stub in one layer. The whole code has beentransferred in the CMSSW framework, an integer version has been coded to makethe input parameter readable by the FPGA.The final aim is the full integration of a demostrator that will evaluate these results,compare them to the simulation/emulation ones, and provide a final estimate of

7.3 Level-1 tracking demostrator 111

∆η 0.0024∆z0 0.089 cm∆ϕ 0.0002-0.0017

∆c/pT (0.8 - 4.1) %

Table 7.2: The values of the mean parameter resolutions, adopting a 20-binning in η anda 7-binning in pT , respectively in r − z and r − ϕ plane. We report only one value for η

and z0 because the resolution is stable versus η, whilst we indicate a range for ϕ and c/pT

because the resolution varies with pT .

the time of the L1-track reconstruction, which has to be lower than the L1 triggerlatency time of the Phase 2, of 12.5 µs.

7.3 Level-1 tracking demostrator

The goal of the CMS Level-1 tracking demonstrator is to establish the feasi-bility of the online tracking, within few µs, for particles with pT down to 3 GeV .The different CMS Level-1 tracking approaches are studying the performances oftheir proposed systems in software, and implement them in small-scale prototypehardware devices. The three main approaches evaluated by CMS are:

1. AM + FPGA, based on Associative Memories (AM) for pattern recognitionand FPGA for track fitting (such as the PCA aproach described so far).

2. Geometry-Based Time-Multiplexed Trigger (TMT), uses hough transform +track fit algorithm, both implemented in the FPGA.

3. Tracklet-Based, algorithmic approach, entirely based on FPGA.

The demonstration studies will utilise information obtained from several sources:

• Simulation will be used to evaluate the tracking performance (e.g. tracking effi-ciency, parameter resolution, track rates) and its impact on tracking-associatedtrigger quantities (e.g. track isolation, tracks within jets), specially in non-nominal conditions.


• Hardware emulation, means to understand how simulated tracking perfor-mances translate to hardware. Emulation software will directly correspondto the algorithms studied in the simulation and implemented in the hardwaredemonstrator.

• Hardware demonstration is needed for the bitwise validation of the emulations,and for providing measurements of the overall latency associated with L1 trackfinding.

• Scaling/Projection will be required to extrapolate from demonstration resultsin terms of performance, scale and cost of the final system.

The baseline geometry to be used for the demonstrators is the standard TP2014[72] available in CMSSW_SLHC_6_2_X_SLHC. Hardware demonstrators andemulators should proceed with this standard geometry.

The simulated tracking performances will be shown using the entire tracker de-tector. To reduce reconfiguration and operational overhead, the hardware demon-strators may instead target a subset of tracker modules.The hardware systems have to demonstrate the L1 track finding in a representativeη slice of the detector, then the results should be easily scaled to a full system. Thisregion should be commonly defined, so that per-track comparisons between the dif-ferent approaches can be performed at the hardware level. For these reasons, eachof the Level-1 tracker hardware demonstrators will explore a ϕ range between 1.346and 1.122, spanning positive η values.

The demonstrators will evaluate the tracking performances using the data sam-ples listed in Table 7.3. These datasets, which range from simple single particleevents to more complex physics topologies (e.g. tt + PU), will provide an un-derstanding of the intrinsic performance of L1 tracking, and of its dependence onpileup and physics conditions. Average pileup conditions of 0, 140 and 200 will beexplored. Semileptonic top decays will be used to investigate the tracking perfor-mance for high-pT leptons in a busy physics enviroment. Hadronic W decays andb-jets in the top sample will also be used to explore the performance of trackingwithin jets.

The L1-tracking groups will analyze their results using the tools developed byfor the Technical Proposal [69] and Scope Document [70]. These tools expect inputfiles with trees containing TrackingParticles, which represent Monte Carlo truth,

7.3 Level-1 tracking demostrator 113

Single µ samples:/RelV alSingleMuP t1 ∗ /CMSSW _6_2_0_SLHC17 − DES23_62_V 1_UP G2023Muon − v1/GEN − SIM − DIGI − RAW

/RelV alSingleMuP t10 ∗ /CMSSW _6_2_0_SLHC17 − DES23_62_V 1_UP G2023Muon − v1/GEN − SIM − DIGI − RAW



/RelV alSingleMuP t1/CMSSW _6_2_0_SLHC26 − DES23_62_V 1_LHCCRefP U140 − v1/GEN − SIM − DIGI − RAW



/RelV alSingleMuP t1/CMSSW _6_2_0_SLHC26 − P U_DES23_62_V 1_LHCCRefP U200 − v1/GEN − SIM − DIGI − RAW



Single e samples:/RelV alSingleElectronP t10 ∗ /CMSSW _6_2_0_SLHC17 − DES23_62_V 1_UP G2023Muon − v1/GEN − SIM − DIGI − RAW

/RelV alSingleElectronP t35 ∗ /CMSSW _6_2_0_SLHC17 − DES23_62_V 1_UP G2023Muon − v1/GEN − SIM − DIGI − RAW

/RelV alSingleElectronP t1000 ∗ /CMSSW _6_2_0_SLHC17 − DES23_62_V 1_UP G2023Muon − v1/GEN − SIM − DIGI − RAW

/RelV alSingleElectronP t10/CMSSW _6_2_0_SLHC26 − DES23_62_V 1_LHCCRefP U140 − v1/GEN − SIM − DIGI − RAW




Single π:/RelV alSingleP iE50HCAL/CMSSW _6_2_0_SLHC17 − DES23_62_V 1_UP G2023Muon − v1/GEN − SIM − DIGI − RAW

Single tt:/RelV alT T bar14T eV/CMSSW _6_2_0_SLHC26 − DES23_62_V 1_LHCCRefP U140 − v1/GEN − SIM − DIGI − RAW

/RelV alT T bar14T eV/CMSSW _6_2_0_SLHC26 − P U_DES23_62_V 1_LHCCRefP U200 − v1/GEN − SIM − DIGI − RAW

Table 7.3: Single µ, Single e, Single π and tt samples used for the simulations. Thestrings PU140 and PU200 indicate the number of pileup events, whilst the samples notcontaining this string do not simulate the pileup.

and TTTracks, that are the tracks after fitting. To use these tools, the simulationframeworks of the different L1-tracking approaches must produce compatible outputtrees. The trees used by the groups to produce simulation results will be madepublicly available, so that the groups can easy compare relative performance. Thetrack objects used for L1-tracking performance measurements are:

• Truth, TrackingParticles in the low and high-pT regimes, with |ηT P | ≤ 2.4,with |zT P

0 | ≤ 30 cm, with pT > 3 GeV , with dxy < 1 cm.

• GoodTracks, TTTracks corresponding to fit tracks from simulation, with|ηfit| ≤2.4 with |zfit

0 | ≤ 30 cm that satisfy all other L1-tracking selections/constraints(e.g. χ2).

• MatchedTracks, GoodTracks output from simulation, matched to Truth us-ing the trackToTrackingParticleMap.

The L1-tracking teams should characterize tracking performance separately inlow-pT (3 - 8 GeV ) and high-pT (8 - 100 GeV ) ranges. The motivation here is todelineate performance in pT regimes in which multiple scattering is more/less rele-vant.


The primary quantities of interest with regard to L1-tracking performances are effi-ciency, parameter resolutions and the total rate of tracks output from the L1-trackingsystem. The definitions of these quantities are given below:

• Efficiency;ϵ = Nmatched

Ntruth

. (7.7)

• Resolution;σ = RMS(pmatched − ptruth). (7.8)

• Rate;f = Nfit/BX, (7.9)

defined as the average number of fit tracks per bunch-crossing. The rate shouldbe examined in the low pT range (starting from 3 GeV threshold) and at highermomentum (pT > 10 GeV ). The rate at low momentum drives the total ratethat the L1 trigger has to deal with, and the rate at higher range gives anestimate of the purity and fake rate of the tracks.

The efficiency and resolution metrics should be assessed for single electrons,muons and pions from the particle gun samples, and for electrons and muons in thett samples. Tracking efficiency and resolutions should also be evaluated inclusivelyfor the tt samples. As mentioned, efficiencies and resolutions should be producedseparately for the low and high pT ranges.Track isolation and vertex-based pileup rejection will become important handles forthe rate reduction in the HL-LHC CMS trigger. The ability to perform trackingwithin jets could also lead to the development of new classes of L1 triggers that usejet properties or substructure.

• To define the track isolation the variable is:

Isotrk =∑

i pT (i)pT (trk)

, (7.10)

where the sum extends over the i particles in a ∆R cone centered on a track(trk) of interest. Demonstrator studies will investigate the efficiency of a Isotrk

selection for truth-matched muon tracks with pT ≥ 20 GeV in the single muon0, 140, 200 pileup datasets. These studies will use a ∆R cone of 0.3 and includeall particles with pT > 3 GeV and with |zmuon − zi| < 0.5 cm.

7.4 A pattern recognition mezzanine for L1 track triggers 115

• Pileup rejection:the performance of pileup rejection will be assessed with a selection on the z0

parameter of fit tracks. The TrackingParticles in the tt + pileup samples willbe associated with the primary vertex using the algorithm described in theTechnical Proposal [69], which is implemented in the tools.

• Tracking within jets:a basic performance evaluation of L1 tracking within jets will be performedusing the hadronic decays of W bosons in tt samples. Track parameter res-olutions and relative track multiplicities with respect to charged final-stateTrackingParticles within the jets will be plotted against jet pT , η, and pileup.

In conclusion, the performance of the L1 track finding must be shown to be robustunder non-nominal conditions for the Tracker TDR. The L1-tracking demonstrationsshould pursue additional simulation and hardware studies to help to establish thisrequirement. The aim of these studies will be to demonstrate performance stabilitywith respect to: module loss, higher pileup, and beamspot displacement.

7.4 A pattern recognition mezzanine for L1 tracktriggers

One prososed prototype for the pattern recognition and fitting of the Level-1tracks is a Pattern Recognition Mezzanine (PRM), that combines the power of bothAssociative Memory custom ASIC and modern Field Programmable Gate Array(FPGA) devices [75].

To deal with the HL-LHC rate, the key is the usage of the precise tracker informa-tion for the reconstruction of the largest number of particle tracks in each individualevent, in the required latency of few microseconds. A dedicated hardware processoris hence needed to select interesting signatures at the 40 MHz, and currently suchclass of processors is provided by the Associative Memory (AM) technology, alreadyadopted in the CDF experiment, and recently in the ATLAS Level-2 trigger, theFast Tracker processor, at the High Level Trigger stage, where a longer latency isallowed. CMS is pursuing a vigorous R&D to demonstrate the feasibility of such anapproach with the state of the art of the AM technology.


The block diagram of the tracker algorithm implemented in the Pattern Recog-nition Mezzanine (PRM) board consists of two sequential steps (Fig.7.6):

1. In the first step, the pattern recognition algorithm is carried out, by using theAM chip, which finds track candidates in a coarse resolution, called roads.

2. In the second step, the FPGA device performs the fitting algorithm, in whichthe full resolution stubs are used to fit the matched roads and to determinethe track helix parameters and the goodness of the fit.

Figure 7.6: A schematic view of the Pattern Recognition Mezzanina workflow.

The full resolution stubs are received from the tracker by a Data Organizer (DO)module, that consists in a Smart Data Base where the stubs are stored in a formatthat allows rapid access. In addition to storing stubs at full resolution, the DOalso converts them to coarser resolution hits, the Super Strip IDentification (SSID),appropriate for pattern recognition in the AM.

The generated SSIDs are sent at the same clock cycle to all the AM devices, thatwork similarly to a Content-Addressable Memory (CAM). Each pattern is stored in8 independent 16-bit words, in which the coordinates, where the particle hits thesilicon detector, are stored. Data are sent on 8 parallel buses, one for each wordof the pattern. The feature of this device consists that all words in the AM are

7.4 A pattern recognition mezzanine for L1 track triggers 117

independent and simultaneous compared with the data presented on its own bus.Every time a match is found, the match flip-flop is set and remains set until the endof the event processing, when a reset signal is propagated.

The results of the pattern matching stage are collected inside the FPGA, andall the possible combinations are produced to form track candidates, by using thestub information stored in the DO. The so-called Track Fitting (TF) algorithm canprovide high-resolution track parameters, using the values for the center of the road,and applying corrections that are linear in the actual stub position in each layer.

For each combination a fast linear fit is performed computing the χ2 value andthe track parameters. Those tracks with a χ2 value below a predetermined thresh-old are considered to be good quality fits. The fit is using the same method as inFTK , based on the Principal Component Analysis (PCA), implemented by usingthe Digital Signal Processing (DSP) logic block inside the FPGA.The FPGA implements, in addition, the auxiliary functions to control the AM de-vices (configuring and programming the bank) and also several tools for monitoringand debugging the internal data flow.

Conclusions

In this dissertation we have detailed the work carried out during my PhD withinthe CMS collaboration.The original anspects of this thesis are: a search for heavy Majorana neutrinos basedon a compositeness model including contact interactions, and a feasibility study ofa new Level-1 track trigger expected to be ready for the Phase 2 of the LHC, forthe CMS detector.

The new analysis has been carried on data collected by the CMS detector in2015, corresponding to an integrated luminosity of 2.3 fb−1, and at the energy of13 TeV in the centre of mass. The observed data are in good agreement with theSM predictions. An upper limit at 95% CL on the product of the cross sectiontimes branching ratio, σ(pp → ℓN) × B(N → ℓqq), of the heavy composite Majo-rana neutrino has been calculated as a function of its mass, and for different valuesof the energy scale Λ, being ℓ an electron or a muon. For the representative caseMN = Λ, the exclusion limits are up to 4.60 (4.55) TeV in the eeqq channel and4.70 (4.75) TeV in the µµqq channel, considering the observation (SM expectation).This measurement represents the first search for heavy Majorana neutrinos at LHCthat complements the compositness scenario with the contact interactions [26], andexplores the signature of two same-sign leptons plus a large-radius jet. Some pre-liminar simulations have indicated that this analysis will significantly benefit of theincoming High-Luminoity era of the LHC, and the exclusion limit can be furtherextended.

The ongoing efforts to build a solution for this High-Luminosity perspective, alsoreferred to as Phase 2, have been discussed, focusing on the L1 track trigger. Thesimulations of a new track trigger, whose fitting algorithm is based on the PrincipalComponent Analysis (PCA) method have given encouraging results. The proposedprocessor for the hardware implementation will provide high computation power, by

119

120 CONCLUSIONS

combining the Associative Memory (AM) and the Field Programmable Gate Array(FPGA) technologies. The integration of firmware and hardware is going to bringto a L1-tracker demostrator planned to be ready by the end of this year, that hasthe aim to establish the feasibility of this track trigger project.

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Acknowledgements

Many people have contributed to the completion of this thesis.Firstly, I would like to thank my supervisor Livio for the continuous support onmy PhD study and research, toghether with the two assistant supervisors, Orlandoand Francesco for their leading and facilitating role in the work development andunderstanding.I would like to express my gratitude to my external thesis assessors, Prof. PaoloBartalini and Dr. Jonathan Jason Hollar, who have accepted to dedicate their time,expertise and knowledge to read my thesis, and to help me to improve this workpresentation and contents.My sincere thanks also go to the team I joined to conduct the seach for heavyMajorana neutrinos, that is the main topic of this thesis; again to Livio, Francescoand Orlando for their deep competence and supprot from both experimental andtheoretical side, and to my colleague Roberto for his hard work, cooperation andavaliability. The heterogeneity of the group allowed me to approach to the workfrom different points of view and to reflect about each related physical question asa whole. Thank you all again for giving me very good advice and guidance!Further, Loriano and Aniello have my gratitude for what concern the track-triggerproposal study for the HL-LHC. Loriano provided me the opportunity to access frominside the code developing, and Aniello has been supporting me on the simulations.More generic but not less important thanks can be extended to all the people ofthe INFN and CMS group of Perugia, who have been helping me and going alongme during my thesis work and all PhD years. Finally, I am grateful and honoredto have collaborated for the CERN institution, and with the CERN people comingfrom all around the world, and sharing the same dedication to Physics and Science.I feel lucky to have experienced this intense period of personal and professionaldevelopement, thanks to such challenging enviroments and brilliant people.

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130 ACKNOWLEDGEMENTS

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