Università di Pisa Dipartimento di Fisica "E.Fermi" Corso di Laurea Magistrale in Fisica Hadronic recoil in the W boson production at LHC for a W mass measurement with the CMS experiment CERN-THESIS-2017-157 20/09/2017 Candidato: Relatore: Olmo Cerri prof. Luigi Rolandi ANNO ACCADEMICO 2016/2017 Audentes Fortuna iuvat Alle persone che mi hanno aiutato a completare questo percorso. Che possa restare accanto a voi e ricambiare ciò che ho ricevuto. Contents Introduction 1 1 The Standard Theory of particles 3 1.1 Fields and Symmetries . .3 1.2 Spontaneous symmetry breaking and Brout – Englert – Higgs mechanism7 1.2.1 Gauge boson masses . .7 1.3 Precision test of the ElectroWeak sector . .8 1.3.1 Higher order prediction of W mass . .9 1.3.2 The global electroweak fit . 10 2 The Compact Muon Solenoid experiment 13 2.1 The Large Hadron Collider . 13 2.1.1 Proton-Proton collision physics . 16 2.2 The CMS detector . 18 2.2.1 The layers structure . 20 2.2.2 Trigger . 22 2.3 Physics object reconstruction . 22 2.3.1 Particle Flow algorithm . 23 2.4 Simulation . 24 3 The W boson mass measurement 27 3.1 From discovery to LEP . 28 3.2 W mass measurement in modern hadron collider . 31 3.2.1 Analysis strategy . 31 3.2.2 Main uncertainties . 34 3.2.3 Recent efforts summary . 36 III 4 The hadronic recoil in the W mass measurement 39 4.1 Production Mechanism . 40 4.1.1 Comparison between Z and W .................. 41 4.2 Definition ad characterization of hadronic recoil . 42 4.2.1 Detector effects in measuring the recoil . 43 4.3 Samples definition . 44 4.3.1 Events selection . 45 4.4 Hadronic recoil effect on transverse mass . 48 4.4.1 W mass sensitivity and boson transverse momentum dependence 50 4.5 A precise measurement of the recoil . 52 4.5.1 The recoils as a 2D object . 52 4.5.2 Resolution effects . 55 5 A new recoil definition 59 5.1 Recoil definitions . 60 5.1.1 An improved recoil . 61 5.2 A multivariate semi-parametric regression . 62 5.2.0.1 Neural Networks: a generic function . 62 5.2.0.2 Semi-parametric regression . 64 5.2.1 Application to recoil definition . 65 5.2.2 Details of the trained regression . 68 5.3 Goodness of the definition . 71 5.3.1 Regression - network convergence check . 72 5.3.1.1 Sum of pdfs closure . 73 5.3.2 Goodness event-by-event of recoil estimators . 76 6 Systematic uncertainties 79 6.1 Systematic effects and factorization scheme . 80 6.2 W mass fitting procedure . 81 6.3 Effect of boson kinematic mismodeling . 83 6.3.1 Estimating the systematic uncertainty . 84 6.3.2 Recoil definitions ranking . 88 6.4 Systematic on the recoil mismodeling . 90 6.4.1 Differences between data and simulations . 91 6.5 A multi-dimensional morphing procedure . 92 6.5.1 Procedure for a n-dimensional k-conditional morphing . 94 6.6 Recoil modeling effect and calibration . 96 6.6.1 Procedure check . 98 6.6.2 Systematic assessment before calibration . 99 6.6.3 Systematic assessment after calibration . 100 6.7 Porting the calibration from Z to W . 102 6.7.1 Generated instead of reconstructed boson kinematic variables . 102 6.7.2 Intrinsic MC differences between Z and W . 103 7 Conclusions 105 7.1 Future developments . 107 A DNN training details 111 Bibliography 113 Acknowledgments 127 Introduction After the discovery of the Higgs boson in 2012, the standard model of particle physics (SM) has been further validated and all its free parameters established. Using the full set of SM parameters, it is thus possible to predict with increasing precision rela- tions among observables which can be verified in experiments. The agreement between measurements and theoretical predictions is a severe consistency test for the model: possible deviations of measured values from those predictions would be a clear sign of new physics beyond the standard model. Specifically, precise determination of the W boson mass is of great importance in this testing procedure. From the time of its discovery in 1983, the W boson has been stud- ied and its mass determined in both hadron and lepton colliders. At the state of the art, the W boson mass has a smaller uncertainty in the SM pre- diction of 80:360 0:007 GeV than in the measured value of 80:385 0:015 GeV. A ± ± measurement of the W mass with an uncertainty smaller than 7 MeV might be a break- through and may result in a direct evidence of SM inconsistency. For this reason, such measurement is currently studied at the LHC. The CMS experiment is planning to de- liver a measurement of W mass within the next years. At hadron colliders, production of on-shell W bosons is tagged by the high transverse momentum (pT ) charged lepton from its decay in the leptonic final state, the only one suitable for a precise mass mea- surement. In practice, W mass is extracted from data via a fit to several distributions, which need to be understood and optimized up to an unprecedented level of precision. In the first chapter of this work, an overall picture of the theoretical basis is pre- sented. Starting from the foundations of the Standard Model, Higgs mechanism and electroweak symmetry breaking are introduced, focusing on their role of providing SM gauge boson with masses. The important facts of electroweak precision test are also introduced in the last part of the first chapter. After an overview of the Large Hadron Collider (LHC), which is currently operating at CERN, the second part of this work describes the Compact Muon Solenoid (CMS) experiment, aimed to explore in depth particle physics up to the TeV scale: the main 1 features of the subdetectors are briefly described, together with the reconstruction al- gorithms; focus has been put mostly on those features of interest for W mass physics. The third chapter is devoted to discuss the past and the on going efforts for the W boson mass measurement. The original work developed during the thesis is fully discussed in chapters four, five and six. Two are the main objectives: to deepen the knowledge of the variables used in the W mass measurement, with particular attention on the event-by-event experimental estimator of the boson transverse momentum; to define and calibrate an experimental definition of the recoiling system to the W , suitable for the real measurement process at the CMS experiment. Transverse momentum of the recoil and of the boson are two faces of the same coin: both are crucial in the extraction of the mass value. Events in which the W boson decays into a muon and a neutrino are considered. The W mass is extracted from the distributions of the modulus of the lepton trans- verse momentum (pµ) and of the transverse mass (MT ), a scalar quantity function of the lepton momentum and the recoil, which is the vectorial sum of the momenta of all reconstructed particles excluding the lepton. With the purpose to maximize the performance in terms of systematic uncertainty on the final measurement, a new ex- perimental definition of the recoil, based on machine learning algorithms, is discussed. As support to the remarkable impact of my work, there are reported cross checks and performances of the new definition, in terms of resolution and uncertainty improvement for a W mass measurement. In the last chapter, recoil-related systematic uncertainties on the W mass measurement are presented. Furthermore, it is reported a new method, based on multi-dimensional morphing, used to calibrated the Monte Carlo simulation using collision data. The systematic uncertainties of the W mass measurement before and after this calibration are studied. Finally, conclusions summarize the main results, underlining the importance of the work, and suggesting possible future developments. Document notation Throughout this document the classical notation of high energy physics will be used. In particular, the value of the speed of light and the Plank constant are set to c = 1 and ~ = 1, so that masses, energies and momenta are all expressed in electron volts (eV). All the angles are represented in the space [ π; π]. − Tesi Magistrale - Olmo Cerri 2 Chapter 1 The Standard Theory of particles The “Standard Model” (SM) is the theory that summarizes the knowledge we have about fundamental components of matter and their interactions; it describes a wide range of phenomena and has been tested experimentally with a remarkable accuracy, even if there are some important problems to which it gives no satisfactory answer. The theory has emerged gradually in almost a century of theoretical and experimental investigations and it is now fully established. I will describe it from the logical point of view. Quantum field theory, the framework in which SM is formulated, is a vast subject and even a short but comprehensive resume of it would be too long for this thesis, so I will only introduce the key concepts useful later on. This compilation chapter is thus devoted to describe the SM accurately enough to serve as a theoretical background to the main subject of this thesis. A complete reference can be found in the original papers, such as [1], and in the classic textbooks, such as [2]. Additionally, given the main focus of this thesis, all mathematical details are left over. 1.1 Fields and Symmetries The standard model is based on the existence of 17 different elementary fields which can be grouped into three categories.