Photon energy calibration uncertainties from shower leakage mismodeling

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The ATLAS detector 

The largest general-purpose particle detector ever constructed, the ATLAS (A Toroidal LHC ApparatuS) detector, is installed in its experimental cavern at point 1at CERN, as shown in 2.1. With the unprecedented energy and luminosity achieved by the LHC, the ATLAS detector was designed to search for new phenomena that involve highly massive particles which were not observed before with the former accelerators, and to measure the known physics processes with higher precision. Among which, the most strong physical motivation is to search for the Higgs boson. In July 2012, the discovery of the Higgs boson was made by the ATLAS. The CMS collaboration has independently discovered the particle and announced the discovery at the same time. The overall ATLAS detector layout is illustrated in Fig. 2.6. The detector is 44 meters long, 25 meters high, 25 meters in diameter and has a total weight of about 7,000 tons. The ATLAS detector is composed of three subsystems. From the inside out, there are the Inner Detector (ID), the Calorimeters, and the Muon Spectrometer (MS).
The detector is forward-backward symmetric, each subsystem has multiple layers, and consists of a series of concentric cylinders (barrel) around the interaction point. For the purpose of a larger coverage, there are also disc-shaped components (end-cap) set along the beam direction. Functions of each detector complement each other: the Inner Detector provides a precise measurement of the trajectories and vertices of the charged particles, the Calorimeters provide the energy and position information of the stopped particles, and additional measurements of muons are given by the Muon Spectrometer.  For charged particles, their tracks are bent by the magnet system and left in the ID  and the MS. Considering the huge event rates coming from the pp collisions, a trigger  system is installed in order to select the events of interest. The main performance goals are listed in Tab. 2.1.

The Semiconductor Tracker (SCT)

The Semiconductor Tracker[29] is designed to provide high-resolution pattern recognition capabilities using discrete space-points. It consists of four concentric cylinders, and nine disks at each end-cap region with silicon microstrip. There are 2,122 modules on the cylinders, and 1,976 modules on the disks, embedded with 6.2 million read out channels in total. The total measurable area is 61 m2. For each track, the SCT can give precisely at least four additional space points, resulting in a resolution of 17 μm (R−)× 580 μm(z).

 The Transition Radiation Tracker (TRT)

 The TRT[30] is the outmost part of the Inner Detector. It is a transition radiation  detector that uses gas ionization to track the charged particles. The TRT is composed  of straw-tubes with a diameter of 4 mm and length of 144(37) cm in the cylindrical(end624 ) layer. The straw-tubes are filled with a mixture of Xenon gas, which is operated at a voltage of -1500 V. When charged particles pass by and ionize the gas, the anions move towards the wire located in the centre of the straw, generating a current pulse signal. The precision of the measurements performed by the TRT is merely 170 mm per straw-tube, however this lack of precision can be compensated by large number of hits. In addition, transition radiation is emitted when charged particles with moving speed close to the speed of light pass the interface of material with different refractive indices (polyethylene fibres and air). For a given momentum, the energy of the photons generated by electrons will be much higher for electrons than for pions and muons, as it is proportional to the relativistic factor ( = E/m) of the incident particle. This difference can be used to distinguish electrons from pions.

Energy reconstruction

The readout electronics of the ATLAS calorimetry is designed to measure the energy in each calorimeter cell, and provide the L1 trigger system with the deposited energy. The signal readout begins when the electromagnetic showers ionize the LAr in the EM calorimeter, resulting in drifting electrons which induce a triangular current pulse on the copper electrodes. The amplitude of the triangular signal is proportional to the deposited energy. The signal is then amplified, shaped and digitalized to optimise the signal-to-noise ratio. The triangular input current pulse and the shaped output pulse from the FEB are shown in Fig. 3.1.
The signals are then sampled at the LHC bunch crossing frequency of 40 MHz, and temporarily stored here during the L1 trigger latency. Once the events are accepted, the samples are read out and digitized by a 12-bit Analog to Digital Converter (ADC). A Gain Selector chips (GSEL) is used to choose the most suitable gain for each channel in each event, in order to optimize the precision of the energy measurement. In the end, The digitized samples with the chosen gain are transmitted to the corresponding readout drivers (ROD). Equation 3.1 shows the conversion of the reconstructed pulse amplitude A to the deposited energy (E) in MeV. E = FμA!MeV ×FDAC!μA× 1 Mphys Mcali ×G× NsaXmples j=1 aj(sj −p).

Energy calibration 

After summing up the energy of all the cells of the three layers of the EM calorime882 ter and the pre-sampler, the photon energy is corrected by a dedicated calibration procedure. In general, the cluster energy is calibrated to the original electron or photon energy, and an absolute energy scale is obtained using data-driven method to correct for the data-MC difference using Z !ee samples. Photon specific uncertainties are applied due to the difference of the shower shape between electrons and photons. As shown in Fig. 3.5, the calibration proceeds as follows:
The first step is the training of MC-based e/ calibration. A multivariate (MVA) regression algorithm is trained based on Monte-Carlo (MC) simulation of the detector, in order to calibrate the EM cluster properties to the original electron and photon energy. The calibration constants are determined using the MVA, and its optimization is performed separately for electrons, converted and unconverted photons. The following variables are used as an input to the MVA algorithm:
• total energy in the accordion, Eacc = Eraw 1 +Eraw 2 +Eraw 3 , where Eraw x is the uncalibrated energy of each layer.
• ratio of the energy in the pre-sampler to the energy in the accordion, E0/Eacc896 , only used for the clusters within the geometric range of the pre-sampler || < 1.8.
• ratio of the energy in the first layer to the energy in the second layer, Eraw 1 /Eraw 898 2 , which provides the information of the longitudinal shower depth.
• pseudorapidity cluster 900 in the ATLAS frame.
• cell index, an integer number defined as the integer part of calo/, where calo is the pseudorapidity of the cluster in the calorimeter frame, and = 0.025 is the size of one cell in the middle layer. This variable is sensitive to the non-uniformities of the calorimeter.
• with respect to the cell edge.
• with respect to the lead absorbers.

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Data and simulated samples

Radiative Z decaying to a lepton pair and one photon provides a photon sample of high purity, although it is limited in statistics and the available kinematic range. In this study, the lateral leakage for electrons is extracted from a sample of Z !ee events. To avoid the electron to photon ambiguity, the Z !ee channel is not used, while a Z !μμ event selection is applied to provide low-pT photon samples. Photons with higher pT coming from QCD production of photon pairs are also studied as a
cross-check and an extension. By the time the study was done, the data taking of Run 2 was not finished and  only a dataset of 33 fb−1 collected in 2016 is used in the analysis (the results may still  be referred as “Run 2 results” when they are compared with Run 1 results). For both  Z !μμ and Z !ee processes, the simulated samples are generated and showered  with Powheg, Pythia8, EvtGen and Photospp generators. The diphoton events are  generated with the Sherpa generator. The simulation is performed in slices of the diphoton invariant mass M , therefore the samples for all slices are then merged with the proper normalization to match the luminosity corresponding to the one in the data.

Table of contents :

Introduction
1 Theory 
1.1 The Standard Model of particle physics
1.1.1 The gauge theory
1.1.2 The Standard Model Lagrangian
1.1.3 Spontaneous symmetry breaking and the Higgs mechanism
1.1.4 The production and decay of Higgs boson
1.1.5 Non-resonant diphoton production
1.2 Beyond the Standard Model
1.2.1 The Two-Higgs-Doublet Models
1.2.2 The Randall-Sundrum model
2 The Large Hadron Collider and the ATLAS detector 
2.1 The Large Hadron Collider
2.1.1 The LHC injection chain
2.1.2 Luminosity and performance
2.2 The ATLAS detector
2.2.1 Inner detector
2.2.2 Calorimetry
2.2.3 Muon spectrometer
2.2.4 Magnet system
2.2.5 Forward detectors
2.2.6 Trigger system
3 Photon reconstruction and performance 
3.1 Photon reconstruction
3.1.1 Energy reconstruction
3.1.2 Track matching
3.2 Energy calibration
3.3 Photon identification
3.4 Photon isolation
4 Photon energy calibration uncertainties from shower leakage mismodeling
4.1 Method
4.1.1 Definition of leakage variables
4.1.2 Data and simulated samples
4.1.3 Background subtraction in the diphoton sample
4.2 Measurement of the lateral leakage and double difference
4.2.1 Measurement of the lateral leakage
4.2.2 Measurement of the double difference
4.3 Studies on the double difference
4.3.1 pT and dependence
4.3.2 Leakage along and directions
4.3.3 Pile-up dependence
4.3.4 Impact of additional material
4.3.5 Other effects
4.3.6 Conclusion
4.4 Refined double difference measurement and final results
4.4.1 Corrections on the double difference
4.4.2 Systematic uncertainty of background subtraction method for diphoton sample
4.4.3 Final results
5 Search for diphoton resonances 
5.1 Data and Monte Carlo samples
5.1.1 Low-mass samples
5.1.2 High-mass samples
5.2 Event selection
5.3 Signal modeling
5.3.1 Narrow-width signal modeling
5.3.2 Large-width signal modeling
5.4 Background modeling
5.4.1 Non-resonant background
5.4.2 Resonant background
5.4.3 Background modeling results
5.5 Fiducial and total acceptance corrections
5.5.1 Fiducial volume and correction factor
5.5.2 Acceptance factor
5.6 Systematic uncertainties
5.6.1 Signal modeling uncertainties
5.6.2 Signal yield uncertainties
5.6.3 Background modeling
5.6.4 Migration between categories
5.6.5 Systematics uncertainties summary
5.7 Statistical method
5.7.1 Profile log-likelihood ratio method
5.7.2 Discovery p-value
5.7.3 Look-elsewhere effect
5.7.4 Upper limits
5.7.5 Statistical models
5.8 Results
5.8.1 Low-mass search results
5.8.2 High-mass search results
5.9 Conclusion
5.9.1 Low-mass analysis
5.9.2 High-mass analysis
Conclusion
Appendices
A Stitching of the sliced MC background samples 
B Functional Decomposition smoothing 

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