Reconstruction of electrons, muons, jets and missing transverse momentum

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The Higgs mechanism

Despite the fermion field Ψ, we can introduce a boson field Φ. From this spin-0 complex field, together with the gauge field Bµ and the covariant derivative Dµ, the Lagrangian has the following form L = (DµΦ†)(DµΦ) − µ2Φ†Φ − λ(Φ†Φ)2 (1.10).
In order to satisfy the SU(2)L × U(1)Y spontaneous symmetry breaking, we need to introduce scalar fields. Since we desire to end up with three heavy vector bosons as-sociated with the weak interactions and a massless vector boson (photon), so we require four independent scalar fields. The simplest choice is a doublet of complex scale fields with one charged and one neutral. ϕ+ ϕ+ + iϕ+ Φ=(ϕ0)=( 1 2 ϕ10 + iϕ20 ) For the vacuum state, we can specify a direction. ( ) µ2 0 Φ0 = √v , v = √ − λ 2 and the fields can be re-expressed as ( ) 0 Φ = v+H(x) √ 2.

Vector boson pair production

A W boson can decay into a lepton and a neutrino. It can also decay to an up-type quark and a down-type quark. The decay width of the W boson to a pair of quark and anti-quark is proportional to the corresponding squared CKM matrix element and the number of quark colours, NC = 3. The unitarity of the CKM matrix implies that: |Vud|2 + |Vus|2 + |Vub|2 = |Vcd|2 + |Vcs|2 + |Vcb|2 = 1. Therefore the leptonic branching ratios of the W boson are approximately Br(e+νe) = Br(µ+νµ) = Br(τ+ντ ) = 19 . The hadronic branching ratio is dominated by the CKM- ¯ favored ud and cs¯ final states. The sum of the hadronic branching ratios has been mea-sured experimentally to be 67.60 ± 0.27%, and the branching ratios of leptonic decays are measured to be Br(lνl) = 10.80 ± 0.09% [1]. Vector boson pair production is one of the most important electroweak processes. Among the massive vector boson pair production reactions, W +W − has larger cross section than W Z and ZZ production. The SM description of electroweak and strong interactions can be tested through precision measurements of the W +W − production cross section at hadron colliders.
At the collider experiment the W boson pairs can be produced in two different processes, via quark-quark annihilation and gluon-gluon fusion. The Standard Model with its gauge symmetry in the electro-weak sector makes precise predictions for the W W γ and W W Z couplings. So the measurement of the W W cross section can offer a good test of the Standard Model. Any deviation from SM expectations in the measured production rates and possible changes in certain kinematic distributions of vector bo-son pairs or their decay products could provide first evidence for effects from physics beyond the SM at high-energy scales. New physics processes that alter the W +W − pro-duction at high mass scales can be described by operators with mass dimension higher than four in an effective field theory (EFT) framework. In addition the pair production of W bosons is one of the most important background processes for the study of the Higgs boson and the search for the new physics beyond the SM, such as the search for super-symmetric particles.
The W bosons can not be observed directly with the detector, since they will decay into other particles very soon. A W boson can decay into two quarks which is recon-structed as jets in the detector, and it may also decay into a lepton plus a neutrino. Other particles produced in pp collisions can lead to similar final states as the W boson pair production. In normal cases, the final states will consist of quarks and since the direct production of quarks happens more than one million times more often than the pair pro-duction of W bosons, it is uneasy to distinguish the W bosons which decay into quarks from direct quark production. After all, the final states with di-electron, di-muons or an electron and a muon, are the ideal choice to analyze the W W production. The details will be stated later.
In ATLAS, Four separate analyses of leptonic WW decay modes have been pub-lished so far. First analysis on the 2010 dataset at 7 TeV (first LHC data) is published as a paper with very limited statistics (34 pb−1) [2]. In the following year two analy-ses have been published, with one on 1.02 fb−1 [3] and the other on the full 2011 data 4.64 fb−1 [4], which gives measured cross section 51.9±2.0(stat)±3.9(syst)±2.0(lumi) compared with the SM prediction 44.7+2−1..19 pb. W W cross section is also measured by the CDF and D0 experiments at the Tevatron collider at 1.96 TeV and compared to the SM prediction 12.0 ± 0.7 pb. CDF shows the measured cross section 12.1 ± 0.9 (stat) +1.6(syst) pb [5]. DO shows the measured cross section 11.5 ± 2.1 (stat+syst) ±0.7 −0.4 (lumi) pb [6].

From SM to the accelerator physics

The SU(2)L ×U(1)Y gauge theory model and the spontaneous symmetry breaking combine the electro-magnetic interactions and explain the weak interactions mediated by massive W ± and Z bosons. Nevertheless, the SM still have problems. We list some problems as follows.
– The SM does not explain why Higgs mass is so much smaller than the Planck mass. It is called the hierarchy problem.
– Gravity is not included in the SM. Unlike the strong or electro-weak interactions which have been described by the SM, it is not described in the SM.
– Neutrinos are massless in the SM, which is not consistent with experimental results.
– The SM cannot explain the observed cold dark matter or dark energy. So as to the universe, the SM is not providing a well-described theory to explain the mass or the energy of the universe.

Silicon microstrip detector

The strips can provide us additional information about the trajectories of charged particles. Like the pixel detectors, precise 3-dimensional position measurement can be derived by the SCT. The SCT is outside the pixel detector and help to measure particle momentum, impact parameter and vertex position. In the barrel, there are 8 layers which help to provide 8 precision measurement per track. Every silicon detector is 6.40 cm long and 6.36 cm wide, with 780 readout strips. The total number of readout channels is about 6.3 million.

Transition radiation tracker

In the larger radius, these are collections of gas-wire drift detectors that consist of 4 mm-diameter straws and 30 µm-diameter wires running through the straw centers. Straws are filled with Xenon gas and high voltage is maintained between center wires and the straw surface. When a particle traverses a straw, we can determine which straw was traversed and how far from the wire the particle passed. Transition radiation is a form of electromagnetic radiation emitted when a charged particle crosses boundary of different dielectric constants. Fields must reorganize and some can be shaken off as transition radiation. The probability intensity of producing transition radiation photons is depending on the gamma factor mE of the particle. The effect starts at the gamma factor above 1000, thus essentially only for electrons in the typical energy range, and it is thus mostly used for identifying electrons. In the TRT, transition radiation photons created between the straws are detected by absorption of the photons in the chamber gas (Xenon mixture, short absorption length for photons) leading to high electronic pluses. There are about 50000 straws in the barrel and 320000 in the end-caps. Readout channels are set up at both ends for barrel and at the outer radius for end-caps. A total number of 420000 readout channels, each with two independent thresholds, give us drift time measurement with a space resolution 170 µm per straw. The beam-test result shows that transition radiation tracker performance meets with the requirements. A drift-time resolution of about 130 µm with an efficiency of 87% is feasible. For an electron efficiency of 90%, the measured pion efficiency is about 1.2%.

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Tracking performance

The track reconstruction efficiency, ϵtrk, is determined from MC and parameterised in bins of pT and η of the generated particle. It is defined as the ratio of reconstructed tracks matched to generated charged primary particles to the number of all generated charged primary particles. Nrecmatched(pT, η) ϵtrk(pT, η) = (2.3) Ngen(pT, η).
The η distribution of the tracking efficiency for tracks with pT > 500 MeV is shown in Figure 2.9 [13]. The shape of the distribution corresponds to the amount of ID mate-rial traversed by charged particles. The systematic uncertainties are dominated by the material uncertainty and are determined using a detector model with +10% additional material in the whole ID.
The resolution of a track parameter X, can be expressed as a function of pT as [12]: σX = σX (inf)(1 pX (2.4) ⊕ pT ).
where σX (inf) represents the resolution when the momentum is infinite and the constant pX is the constant representing the value of pT, for which the intrinsic and multiple-scattering terms are equal for the parameter X under consideration. The detailed studies have been performed for the expected track-parameter resolutions of the electrons and muons as a function of pT and η. For example, in the barrel region if the pT of the muons is infinite, the resolution for 1 is expected to be 0.34 TeV−1. Table 2.1 shows the detailed values of σX (inf) and pX .

Hadronic calorimeter

The hadronic calorimeter surrounds the electromagnetic calorimeters. It is de-signed to measure the energy of hadrons (typically protons, neutrons, pions and kaons). When high energy hadrons traverse the absorbing materials, they produce a hadronic shower in which the initial particle energy is partially transformed into the rest masses of lower energy hadrons and partially used to knock out protons and neutrons from the Figure 2.13 Top: electron pair invariant mass distribution for Z → ee decays in data and im-proved simulation. Energy scale corrections are applied to the data. The improved simulation is shown before and after energy resolution corrections, and is normalised to the number of events in data. Bottom: ratio of the data and uncorrected MC distri-butions to the corrected MC distribution with the calibration uncertainty band.
nuclei of some of the atoms of the absorber material, which will be detected by in the active material readout by sensing devices.
The hadronic calorimeter is based of three parts as follows. For small angle relative to the beam pipe or high η, 3.1 < |η| < 4.9, jets are detected by the Forward Calorimeter (FCAL) made of copper/tungsten for the absorber part and LAr for the active material. For angles between 5 and 25 degrees or |η| = 1.5 up to |η| = 3.1, the detector is the Liquid Argon Hadronic end-cap Calorimeter (HEC) made of copper plates for the absorbers and LAr for the active material. For angles greater than 25 degrees, or |η| < 1.7, jets are detected in the Tile Calorimeter placed around the LAr electromagnetic calorimeter.
The hadronic calorimeter provides accurate hadronic energy measurements. It measure the energies and directions of jets, which correspond to the energy and direc-tion of a quark or a gluon produced in the proton-proton collision. For neutrinos, which are weakly interacting with matters and thus not directly detectable, it participates to their energy measurements. Using the principle of conservation of the transverse com-ponents of momentum, it contributes to the measurement of the total missing transverse.

Table of contents :

Chapter 1 Introduction
1.1 Particles and forces
1.2 QCD and strong nuclear force
1.3 Electro-weak model and the Higgs mechanism
1.3.1 SU(2)L × U(1)Y gauge theory
1.3.2 The Higgs mechanism
1.3.3 Vector boson pair production
1.4 From SM to the accelerator physics
Chapter 2 The framework of LHC and ATLAS experiment
2.1 LHC and ATLAS overview
2.2 Inner detector
2.2.1 Solenoid magnet
2.2.2 Pixel detectors
2.2.3 Silicon microstrip detector
2.2.4 Transition radiation tracker
2.2.5 Tracking performance
2.3 Calorimeter
2.3.1 Electromagnetic calorimeter
2.3.2 Hadronic calorimeter
2.4 Muon spectrometer
2.4.1 Monitored drift tubes
2.4.2 Cathode strip chambers
2.4.3 Resistive plate chambers and thin gap chambers
2.5 Reconstruction of electrons, muons, jets and missing transverse momentum
2.6 Trigger and data acquisition system
2.6.1 Level 1 trigger
2.6.2 Level 2 trigger
2.6.3 Level 3 trigger and data acquisition
Chapter 3 W+W􀀀 → ℓ+νℓℓ􀀀 ¯ νℓ analysis
3.1 Physics overview
3.2 Dataset and MC samples
3.2.1 Dataset
3.2.2 Theoretical calculation for W+W􀀀 production cross section
3.2.3 Signal MC
3.2.4 MC modelling for backgrounds
3.3 Object selection
3.3.1 Electron
3.3.2 Muon
3.3.3 Jet
3.3.4 Overlap removal
3.4 Event selection
3.4.1 W+W􀀀 event selection criteria
3.5 Background estimation
3.5.1 W+jets background
3.5.2 Top background
3.5.3 Di-boson
3.5.4 Z+jets background
3.5.5 Summary of the observed WW candidates and background expectations
3.6 Systematics
3.6.1 Experimental systematics
3.6.2 Theoretical systematics
3.6.3 PDF uncertainty
3.7 Cross section
3.8 The differential WW cross section measurement
3.9 Limits on anomalous gauge couplings
3.9.1 Theoretical models
3.9.2 ATGC study and results
3.10 Conclusions


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