Electron resolution and energy scale correction

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Experimental apparatus : The Tevatron and the DØ detector

This section is dedicated to a presentation of the Tevatron hosted at the Fermi National Accelerator Laboratory (Fermilab) and the DØ detector. Since the search for the WH signal involves, either an electron or a muon, jets originating from b quarks and missing transverse energy from the escaping neutrino, all parts of the detector are used to reconstruct these objects. An attention will be drawn on the production of proton and antiproton beams used in collisions at the Tevatron as well as the whole acceleration chain in Section 2.1. Then, the main components of the DØ detector and data acquisition will be introduced in Section 2.2.

The chain of accelerators and the Tevatron

Located near Chicago (USA), the Fermilab hosts many particle physics experiments and accelera-tors, in particular the Tevatron, a pp¯ collider operating since 1988. Several discoveries have been made in this place such as the Υ meson, demonstrating the existence of the bottom quark from the E288 collaboration led by Leon Lederman in 1977 [19], the top quark by the CDF and DØ experiments in 1995 [20][21] and the tau neutrino in 2000 by the DONUT collaboration [22].
In order to provide high energy collisions, Fermilab benefits from a complex acceleration chain, the most powerful being the Tevatron accelerating beams of protons and antiprotons with an energy of 980 GeV to produce collisions at a center-of-mass energy of 1.96 TeV. The beams are crossing in two interaction points where are located the CDF and DØ detectors. An aerial view is shown in Figure 2.1 along with a diagram depicting the acceleration chain.
Collisions at the Tevatron occurred during two major periods:
• the “RunII”, starting in 2001 after the Tevatron had its center-of-mass energy upgraded to 1.96 TeV. This period is separated is two phases. The RunIIa period corresponds to an integrated luminosity of about 1 fb−1recorded between March 2001 and March 2006. The RunIIb characterized, among others things, by the installation of an additional layer of detector to the Silicon Microstrip Tracker (SMT) at the closest to the beam pipe (more details in Section 2.2.2). The expected delivered luminosity is to be about 12 fb−1by September 2011, when the Tevatron will shut down.

Proton beam production

Hydrogen gas (H2) is first injected into an ionization chamber (also denoted as magnetron ion source). Through electric pulses, a plasma comprised of electrons and protons is created in the chamber. The released protons will be attracted towards the negative electrode of the chamber coated with Cesium. After being trapped by the electrode, they will be hit by the next protons. Since the binding energy of the electrons in Cesium is relatively low, protons will be released after capturing two electrons. Negatively charged H− ions are created. A schematic view of a magnetron is given in Figure 2.2a. H− ions are then focused towards the first step of the acceleration chain, which is the Cockcroft-Walton.
The electric power within the Cockcroft-Walton (see Figure 2.2b) is of 750 kV, therefore ac-celerating hydrogen ions to an energy of 750 keV due to its static electric field.
The next step is a further acceleration of ions through the Linear Accelerator (LINAC) which is 130 meter long. A pulsed beam of 400 MeV is produced by the mean of radio frequency (RF) cavi-ties. By alternating the electric field at a given frequency, the motion of particles is constrained and bunches are formed according to the frequency of the RF cavities. Quadrupole magnets present in drift tubes allows to focus the beam in traverse plane to the direction of the ions.
Before entering the Booster, ions pass through a thin foil of carbon. This will strip off the loosely bound electrons and let protons be accelerated to an energy of 8 GeV. The Booster is a 475 meters long synchrotron, formed by 96 magnets bending the trajectory of the protons and RF cavities operating at 1 GHz to accelerate them. Whereas the time of travel of ions in the LINAC is
20 s, a complete revolution in the Booster takes about 2.2 s. The Booster is typically filled with about 3×1012 protons. This step is the last one before injection to the Main Injector.

The Main Injector and Recycler

After having undergone an acceleration to reach an energy of 8 GeV in the Booster, protons are injected to the Main Injector [23], a synchrotron with a 3.3 km circumference, built between the RunI and RunII. The purpose of the Main Injector has different aspects. It accelerates protons to 120 GeV before sending them to a Nickel target to produce antiprotons through the reaction p + p → p + p + p + p¯. It is interesting to keep in mind that the antiproton production efficiency is at the order of 3×10−6 produced antiprotons per proton on target.
Protons and antiprotons travel in the same beam pipe, surrounded by 344 dipole magnets and 208 quadrupole magnets to focus beams. Before injecting particles in the Tevatron, particles are accelerated up to 150 GeV.
A limiting factor for the Tevatron integrated luminosity is the amount of antiprotons in the accelerator. Since their production efficiency is low, the Recycler [24] can recover antiprotons that are still present after the end of the previous store (period during which protons and antiprotons collide in the Tevatron). The recycler is located in the same tunnel as the Main Injector, as shown in Figure 2.4, and was installed during the Tevatron upgrade before the beginning of the RunII. Since its purpose isn’t to accelerate particles, it is only comprised of permanent magnets.

Antiproton beam production

The main motivation for building a pp¯ collider was to initiate reactions from opposite charge parti-cles in order to search for a top quark pair production. This allows as well to make use of a single magnet system where both proton and antiproton beams circulate. However, the creation of an antiproton beam requires three devices: a fixed Nickel target from which antiprotons are created and two synchrotrons to accumulate and cool them.
As previously emphasized, antiprotons are produced from the collisions between 120 GeV protons and the Nickel target, with a rate close to one antiprotons created for one million protons on target.
The outgoing antiprotons are created with an average energy of 8 GeV and with a large angular spread. Both Debuncher and Accumulator which will be described here are operating at 8 GeV. First, produced particles are focused with a magnetic lens and then are passing through a mass spectrometer in order to separate antiprotons from other type of particles that can be created at the same time. This process is depicted on Figure 2.5.
(a) Representation of antiprotons creation and (b) Scheme representing the antiproton beam ocusing. trajectory after production.
Figure 2.5: After protons hitting the Nickel target, produced antiprotons are focused and filtered from other particles (a). Antiprotons have then their energy spread reduced in the Debuncher.
As the protons hit the target by bunches, outgoing antiprotons do have the same structure. The Debuncher is a triangular 505 meters circumference synchrotron. Lower energy particles will travel closer to the inner part of the cavity whereas higher energy particles will tend to have an outward trajectory. By traveling at a different radial distance from the beam center, beams will travel in a different RF field intensity , thus bringing them to the desired trajectory and speed, in a 100 ms process. This setup will destroy the bunch structure of the beam, hence the name of this part of the acceleration chain.
The beam being stable, the process of stochastic cooling [25] can be initiated. This allows to reduce the transverse oscillation of the beam and consequently the energy spread. This process is achieved by detecting fluctuations in the momentum and slightly correcting the trajectory each time a particle travels at the vicinity of an electrode called pickup. By measuring its position relative to the nominal beam trajectory, this measurement is converted in an electric signal through the electric field created in the pickup. This signal is then sent to the kicker which will modify its electric field to bend the particle according to the received signal. Figure 2.6 shows a brief description of the Debuncher and how the stochastic cooling is performed.
After 2.4 seconds, antiprotons are then sent to the Accumulator, located in the same tunnel. Here, the bunch structure of the antiproton beam will be formed again and antiprotons are cooled further by interacting with a low emittance electron beam until thermal equilibrium. The process of antiproton accumulation is called stacking and lasts about 8 hours. Potentially the life time of the p¯ beam can be extended to several days without major losses as a result of the beam stability. Once the Tevatron has dumped the beam from the previous store, antiprotons stored in the Accumulator

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The Tevatron

The last accelerator in the chain is the Tevatron, where physics collisions take place in two points, CDF and DØ , where the p and p¯ beams cross. The circular synchrotron has a 1 km radius. It is comprised of 8 accelerating cavities, 816 dipole superconducting magnets and 204 quadrupole mag-nets. Dipole magnets are made of Niobium-Titanium alloy wire. The superconducting behaviour is reached when cooled to liquid Helium temperatures (4.3 K). Beams from the Main Injector are accelerated from 150 GeV to 980 GeV by the RF cavities operating at a frequency of 53 MHz. Dipole magnets are generating then a 4.2 T magnetic field, a full revolution of particles in the Tevatron is achieved in 21 s.
Optimization studies from the Accelerator Division yielded the most efficient way to produce collisions at the highest rate is to fill the Tevatron with 36 bunches of approximately 3×1011 protons and about 1010 antiprotons at the beginning of a store. The bunch structure of the proton and antiproton beams, as shown in Figure 2.7, is formed by 3 “super bunches” separated by 2.64 s, each of them containing 12 bunches separated by 396 ns. After p and p¯ beams, traveling in the same beam pipe in an helical motion (see Figure 2.8), reached 980 GeV, collisions can start after beam focusing and halo removal. 1.96 TeV pp¯ interactions take place in the interaction region, located around the center of the CDF and DØ detectors. The distribution of the luminous region along the beam axis corresponds to a gaussian distribution with a spread σz=18 cm.
Major changes have been made for continually improving the Tevatron performance, see Ta-ble 2.1. The instantaneous luminosity has been increasing also during the RunII as shown in Figure 2.9.

The DØ detector

After the production of pp¯ collisions at 1.96 TeV being introduced, the detector used to record and study their outcome is described in this section. The DØ detector [26] [27] is a multi-purpose detector with a cylindric geometry. It is comprised of different parts, listed here from the innermost to the outermost of the beam pipe, that will be described in more details in this section:
• the Silicon Microstrip Tracker (SMT)
• the Central Fiber Tracker (CFT)
• the superconducting solenoid magnet
• preshower detectors
• the electromagnetic and hadronic calorimeter
• the muon spectrometer

Table of contents :

1 The Standard Model and the Higgs boson 
1.1 The Standard Model
1.1.1 The elementary constituents of matter
1.1.2 The fundamental forces
1.2 The Quantum Electrodynamics Field Theory
1.3 The Quantum Chromodynamics Field Theory
1.4 The electroweak sector
1.5 The Higgs mechanism
1.5.1 The scalar Higgs field
1.5.2 Mass generation for the Standard Model particles
1.6 Higgs searches
1.6.1 Theoretical constraints
1.6.2 Experimental constraints
1.7 Conclusion
2 Experimental apparatus : The Tevatron and the DØ detector 
2.1 The chain of accelerators and the Tevatron
2.1.1 Proton beam production
2.1.2 The Main Injector and Recycler
2.1.3 Antiproton beam production
2.1.4 The Tevatron
2.2 The DØ detector
2.2.1 Coordinate system
2.2.2 Tracking and vertexing system
2.2.3 Preshower detectors
2.2.4 Calorimeter
2.2.5 Muon system
2.2.6 Luminosity monitor
2.2.7 Trigger and data acquisition system
2.2.8 Data format and detector simulation
3 Objects reconstruction and identification 
3.1 Tracks
3.2 Primary Vertices
3.3 Electrons
3.3.1 Reconstruction and identification criteria
3.3.2 Electron resolution and energy scale correction
3.3.3 Identification efficiency between data and simulation
3.4 Muons
3.4.1 Reconstruction and identification criteria
3.4.2 Muon energy resolution
3.4.3 Reconstruction efficiency in data and simulation
3.5 Jets
3.5.1 Jet reconstruction
3.5.2 Jet identification and vertex confirmation
3.5.3 Jet Energy Scale
3.5.4 Jet Shifting, Smearing and Removal
3.6 Missing transverse energy
3.7 b-jet identification
3.7.1 b-jets properties
3.7.2 b jet taggability
3.7.3 Individual b-jet identification algorithms
3.7.4 The NN b-tagger
4 Selection and physics processes modeling in the WH analysis 
4.1 Overview
4.2 Foreword on the analysis work flow
4.3 Data and Monte Carlo used in the WH analysis
4.3.1 Data samples
4.3.2 Monte Carlo samples and generators
4.3.3 Trigger selection
4.4 Event selection
4.4.1 Primary vertex selection
4.4.2 Lepton selection
4.4.3 Missing ET selection
4.4.4 Jet selection
4.4.5 Triangular cut
4.4.6 Vetoes
4.5 Reweighting of W+jets and Z+jets samples
4.6 Multijet background estimation
4.6.1 Multijet background modeling strategy
4.6.2 Lepton fake rates
4.7 Simulation normalization scheme
4.7.1 Multijet sample normalization
4.7.2 Experimental K factors for the W+jet background
4.7.3 Heavy flavor scale factor
4.8 Pre-tag summary
4.9 b-tagging applied in the WH analysis
4.9.1 Taggability scale factors
4.9.2 b-tagging efficiency scale factors
4.9.3 Post b-tagging results
5 Multivariate classification, limit derivation and results for the WH analysis 
5.1 Improving sensitivity using a Random Forest
5.1.1 Principle of a Random Forest
5.1.2 Input variables and training parameters
5.1.3 Rebinning of the Random Forest output
5.1.4 Random Forest distributions
5.2 The CLs method
5.2.1 Principle of the method
5.2.2 Systematic uncertainties : sources and treatment
5.3 Limits obtained in the WH analysis
6 Future improvements and prospects 
6.1 Improvements in the WH analysis
6.1.1 Jet Energy Resolution
6.1.2 Changes in the analysis
6.1.3 Summary of potential improvements
6.2 Prospects at the Tevatron and LHC
6.2.1 Prospects at the Tevatron
6.2.2 Prospects at the LHC
6.2.3 Conclusion


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