This paper presents the electron and photon energy calibration achieved with the ATLAS detector using about 25 fb-1\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s}=7$$\end{document} and 8 TeV. The reconstruction of electron and photon energies is optimised using multivariate algorithms. The response of the calorimeter layers is equalised in data and simulation, and the longitudinal profile of the electromagnetic showers is exploited to estimate the passive material in front of the calorimeter and reoptimise the detector simulation. After all corrections, the Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} resonance is used to set the absolute energy scale. For electrons from Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} decays, the achieved calibration is typically accurate to 0.05 % in most of the detector acceptance, rising to 0.2 % in regions with large amounts of passive material. The remaining inaccuracy is less than 0.2–1 % for electrons with a transverse energy of 10 GeV, and is on average 0.3 % for photons. The detector resolution is determined with a relative inaccuracy of less than 10 % for electrons and photons up to 60 GeV transverse energy, rising to 40 % for transverse energies above 500 GeV.
volume-issue-count12issue-article-count53issue-toc-levels0issue-typeRegularissue-online-date-year2014issue-online-date-month11issue-online-date-day28issue-pricelist-year2014issue-copyright-holderSIF and Springer-Verlag Berlin Heidelbergissue-copyright-year2014article-contains-esmNoarticle-numbering-styleContentOnlyarticle-toc-levels0article-registration-date-year2014article-registration-date-month9article-registration-date-day11article-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessIntroduction
Precise calibration of the energy measurement of electrons and photons is a fundamental input to many physics measurements. In particular, after the discovery of the Higgs boson by the ATLAS and CMS experiments [1, 2], an accurate determination of its properties is of primary importance. A precise measurement of the W\documentclass[12pt]{minimal}
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\begin{document}$$W$$\end{document} boson mass is also a long-term goal of the LHC experiments, and requires an excellent accuracy of the electron energy calibration.
A first electron and photon calibration analysis was performed using 40 pb-1\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s}=7$$\end{document} TeV [3]. The calibration of the ATLAS liquid argon (LAr) calorimeter was primarily based on test-beam measurements; only the absolute energy scale was set using the Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} boson resonance. The uncertainty on the detector material upstream of the LAr calorimeter, which is of primary importance in understanding its response to incident electromagnetic particles, was estimated from engineering drawings and a material survey during construction. The achieved calibration was accurate to 0.5–1 % for electrons, depending on pseudorapidity and energy.
This paper presents the calibration scheme developed for precision measurements involving electrons and photons with |η|<2.47\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |<2.47$$\end{document}1 and mostly derived from collision data. It comprises local corrections to the calorimeter energy measurement, and the intercalibration of its longitudinal layers; a measurement of detector material leading to an improved simulation; an improved simulation-based calibration; and a measurement of the absolute energy scale from Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} boson decays. The universality of the energy scale is verified using J/ψ→ee\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s}=7$$\end{document} TeV.
The paper is organised as follows. After an overview of the energy reconstruction with the ATLAS LAr calorimeter in Sect. 2, the calibration procedure, the data and simulated Monte Carlo (MC) samples used for this purpose are summarised in Sects. 3 and 4. Section 5 describes the simulation-based energy calibration algorithm. Data-driven corrections to the energy measurement and to the detector material budget are presented in Sects. 6 to 8, and the absolute energy scale determination from Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} boson decays is described in Sect. 9. Systematic uncertainties affecting the calibration and cross-checks of the Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document}-based energy scale are given in Sects. 10–13. The results of this calibration procedure applied to the 2011 data sample are summarised in Appendix A. Uncertainties on the energy resolution are discussed in Sect. 14, and the performance of an algorithm combining the calorimeter energy measurement with the momentum measured in the tracking detectors is presented in Sect. 15. Section 16 summarises the achieved results and concludes the paper.
Electron and photon reconstruction and identification in ATLASThe ATLAS detector
The ATLAS experiment [4] is a general-purpose particle physics detector with a forward-backward symmetric cylindrical geometry and near 4π\documentclass[12pt]{minimal}
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Energy reconstruction in the electromagnetic calorimeter
Electrons and photons entering the LAr calorimeter develop EM showers through their interaction with the lead absorbers. The EM showers ionise the LAr in the gaps between the absorbers. The ionisation electrons drift and induce an electrical signal on the electrodes which is proportional to the energy deposited in the active volume of the calorimeter. The signal is brought via cables to the read-out Front End Boards, where it is first amplified by a current-sensitive pre-amplifier. In order to accommodate a large dynamic range, and to optimise the total noise due to electronics and inelastic pp\documentclass[12pt]{minimal}
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The total energy deposited in an EM calorimeter cell is reconstructed asEcell=FμA→MeV×FDAC→μA×1MphysMcali×G×∑j=1Nsamplesaj(sj-p),\documentclass[12pt]{minimal}
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Electron and photon reconstruction
The reconstruction of electrons and photons in the region |η|<2.47\documentclass[12pt]{minimal}
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Clusters matched to a well-reconstructed ID track originating from a vertex found in the beam interaction region are classified as electrons. If the matched track is consistent with originating from a photon conversion and if in addition a conversion vertex is reconstructed, the corresponding candidates are considered as converted photons. They are classified as single-track or double-track conversions depending on the number of assigned electron-tracks. Clusters without matching tracks are classified as unconverted photons [5]. The electron cluster is then rebuilt using an area of calorimeter cells corresponding to 3 ×\documentclass[12pt]{minimal}
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Photons and electrons reconstructed near regions of the calorimeter affected by read-out or HV failures are rejected [11].
The relative energy resolution for these EM objects can be parameterised as follows:σE=aE⊕bE⊕c,\documentclass[12pt]{minimal}
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Electron and photon identification
The clusters associated with electron and photon candidates must satisfy a set of identification criteria, requiring their longitudinal and transverse profiles to be consistent with those expected for EM showers induced by such particles.
Three reference sets of cut-based selections, labelled loose, medium and tight, have been defined for electrons with increasing background rejection power [12, 13]. Shower shape variables in both the first and second layers of the EM calorimeter and the fraction of energy deposited in the hadronic calorimeter are used in the loose selection with additional requirements on the associated track quality and track-cluster matching. Tightened requirements on these discriminating variables are added to the medium criteria together with a loose selection on the transverse impact parameter and on the number of hits in the TRT associated with the track, and a measured hit in the innermost layer of the pixel detector to discriminate against photon conversions.5 The tight selection adds a selection on the ratio of the candidate’s reconstructed energy to its track momentum, E/p\documentclass[12pt]{minimal}
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The identification of photons is performed by applying cuts on shower shapes measured in the first two longitudinal layers of the EM calorimeter and on the leakage into the hadronic calorimeter [14].
To further suppress background from hadronic decays, an isolation requirement is applied. The calorimeter isolation transverse energy ETiso\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^\mathrm{iso}$$\end{document} is also used for electrons and muons. It is built by summing the transverse momenta of the tracks in a cone of size ΔR\documentclass[12pt]{minimal}
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Overview of the calibration procedure
The different steps in the procedure to calibrate the energy response of electrons and photons described in this paper are summarised below, with the item numbers referring to the calibration steps sketched in Fig. 1. The references to their description in the paper is also given.
Schematic overview of the procedure used to calibrate the energy response of electrons and photons in ATLAS
The energy of an electron or photon candidate is built from the energy of a cluster of cells in the EM calorimeter. The calibration proceeds as follows:
The EM cluster properties, including its longitudinal development, and additional information from the ATLAS inner tracking system, are calibrated to the original electron and photon energy in simulated MC samples using multivariate techniques (step 1), which constitutes the core of the MC-based e/γ\documentclass[12pt]{minimal}
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\begin{document}$$e/\gamma $$\end{document} response calibration (step 4). The calibration constants are determined using a multivariate algorithm (MVA) [17]; its optimisation is performed separately for electrons, converted and unconverted photons. The MC samples used in the various analyses presented in this paper are detailed in Sect. 4, while the MC-based MVA calibration is described in Sect. 5. A prerequisite of this MC-based calibration is that the detector geometry and the interactions of particles with matter are accurately described in the simulation. The material distribution is measured in data using the ratio of the first-layer energy to the second-layer energy in the longitudinally segmented EM calorimeter (E1/2\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm{T}$$\end{document} range used in the various analyses (step 2). The procedure to measure the EM calorimeter layer scales is reviewed in Sect. 7.
The MC-based e/γ\documentclass[12pt]{minimal}
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\begin{document}$$e/\gamma $$\end{document} response calibration is applied to the cluster energies reconstructed both from collision data and MC simulated samples (step 3).
A set of corrections are implemented to account for response variations not included in the simulation in specific detector regions (step 4), e.g. non-optimal HV regions, geometric effects such as the inter-module widening (IMW) or biases associated with the LAr calorimeter electronic calibration. These corrections are discussed in Sect. 6, where the stability of the calorimeter response as a function of ϕ\documentclass[12pt]{minimal}
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The overall electron response in data is calibrated so that it agrees with the expectation from simulation, using a large sample of Z→ee\documentclass[12pt]{minimal}
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\begin{document}$$Z \rightarrow ee$$\end{document} events as discussed in Sect. 9. Per-electron scale factors are extracted and applied to electron and photon candidates in data (step 5). Using the same event sample it is found that the resolution in data is slightly worse than that in simulation, and appropriate corrections are derived and applied to simulation to match the data. The electron and photon calibration uncertainties are summarised in Sect. 10.
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\begin{document}$$Z \rightarrow \ell \ell \gamma $$\end{document} events in data, and discussed in Sect. 13.
The determination of the electron and photon energy resolution, and the associated uncertainties, are described in Sect. 14. Finally, the potential for improving the electron energy resolution, by combining the cluster energy with the momentum measured by the ID, is described in Sect. 15.
Collision data and simulated samples
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The measurements are compared to expectations from MC simulation. Comparisons between data and simulation are initially performed using the detector description originally used for most ATLAS analyses (see for instance Ref. [1]), later referred to as the “base” simulation. The detector description resulting from the passive material determination described in Sect. 8 is instead referred to as the “improved” simulation. Large samples of Z→ee\documentclass[12pt]{minimal}
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\begin{document}$$\gamma + X$$\end{document} events were generated with Sherpa [18] and Powheg [19–22] interfaced with Pythia [23]. The generated events are processed through the full ATLAS detector simulation [24] based on Geant4 [25]. The size of the MC samples exceeds the corresponding collision data samples by a factor of up to 10.
For the optimisation of the MC-based e/γ\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document} distribution of such samples is tuned to cover the range from 1 GeV to 3 TeV, while maximising the statistics between 7 and 100 GeV.
For studies of systematic uncertainties related to the detector description in simulation, samples with additional passive material in front of the EM calorimeter are simulated, representing different estimates of the possible amount of material, based on studies using collision data [26–31].
Depending on the signal samples, backgrounds consist of W→ℓν\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} production in association with jets are simulated using Sherpa. Some background contributions are directly determined from data.
The MC events are simulated with additional interactions in the same or neighbouring bunch crossings to match the pile-up conditions during LHC operation, and are weighted to reproduce the distribution of the average number of interactions per bunch crossing in data.
MC-based calibration for electrons and photons
Reconstructed electron and photon clusters are calibrated to correct for the energy lost in the material upstream of the calorimeter, the energy deposited in the cells neighbouring the cluster in η\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}, and the energy lost beyond the LAr calorimeter. Further corrections are applied to correct for the response dependence as a function of the particle impact point within the central cluster cell. The cluster-level calibration constants are extracted from simulated electrons and photons and strongly rely on the assumed amount of passive material in front of the EM calorimeter. The simulation of the detector material uses the improvements described in Sect. 8.
The constants are determined using a multivariate algorithm, applied separately for electrons, converted and unconverted photons in η\documentclass[12pt]{minimal}
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\begin{document}$$1.37\le |\eta |<1.52$$\end{document} where the initial calibration procedure is still used.
Input variables
The calibration procedure optimises the estimate of the true particle energy at the interaction point (Etrue\documentclass[12pt]{minimal}
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\begin{document}$$E_\mathrm{true}$$\end{document}) from the detector-level observables. The algorithm uses cluster position measurements in the ATLAS and EM calorimeter frames. The ATLAS coordinate system has its origin at the nominal interaction point, with respect to which the calorimeter is displaced by a few millimeters, while all calorimeter cells are in their nominal position in the EM calorimeter frame.
The quantities used for electrons and photons are the total energy measured in the calorimeter, Ecalo\documentclass[12pt]{minimal}
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\begin{document}$$i$$\end{document}; the cluster barycentre pseudorapidity in the ATLAS coordinate system, ηcluster\documentclass[12pt]{minimal}
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\begin{document}$$\eta _\mathrm{cluster}$$\end{document}; and the cluster barycentre in η\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document} within the calorimeter frame. The variable ηcluster\documentclass[12pt]{minimal}
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\begin{document}$$\eta _\mathrm{cluster}$$\end{document} is included to account for the passive-material variations in front of the calorimeter; the inclusion of the barycentre location in the calorimeter frame is important to accurately correct for the increase of lateral energy leakage for particles that hit the cell close to the edge, and for the sampling fraction variation as a function of the particle impact point with respect to the calorimeter absorbers.
Photons are considered converted if the conversion radius Rconv\documentclass[12pt]{minimal}
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\begin{document}$$R_\mathrm{conv}$$\end{document} is used as an additional input to the MVA only if the vectorial sum of the conversion track momenta, pTconv\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^\mathrm{conv}$$\end{document}, is above 3 GeV. In particular for conversions with both tracks containing at least one hit in either the pixel or SCT detector, further quantities are considered: the ratio pTconv/Ecalo\documentclass[12pt]{minimal}
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\begin{document}$$p_{\mathrm {T}}^\mathrm{max}/p_{\mathrm {T}}^\mathrm{conv}$$\end{document}.
Binning and linearity corrections
To help the MVA optimise the energy response in different regions of phase space, the sample is divided into bins of |ηcluster|\documentclass[12pt]{minimal}
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\begin{document}$$2 \times 6$$\end{document} bins are defined in addition for the regions close to the edges of the two half-barrel modules:
An independent optimisation is performed for each bin.
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Performance
The linearity and resolution of the MVA calibration are illustrated in Fig. 2. The linearity is defined as the deviation of the peak position of E/Etrue\documentclass[12pt]{minimal}
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\begin{document}$$E/E_\mathrm{true}$$\end{document} distribution in each bin, normalised to 1.35 standard deviations, its equivalent definition for a normal distribution. These estimators are chosen to reflect the influence of energy tails.
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The obtained MVA calibration non-linearity is everywhere below 0.3 % for ETtrue\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}^\mathrm{true}$$\end{document} above 10 GeV, better than 1 % at lower transverse energies, only reaching 2 % in localised regions for converted photons. An improvement of more than a factor two compared to the initial calibration is achieved, in particular in the high |η|\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |$$\end{document} region. For the resolution, improvements of about 3–10 % in the barrel and 10–15 % in the endcap are obtained for unconverted photons. For converted photons in the same energy range, the resolution is improved by typically 20 %. For electrons, improvements of a few percent are obtained on average, except at 1.52<|η|<1.8\documentclass[12pt]{minimal}
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\begin{document}$$1.52<|\eta |<1.8$$\end{document} where they vary from 10 to 30 % depending on ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document}. While the resolution estimator used here reproduces the expected sampling term resolution for unconverted photons (σ/E∼0.1/E\documentclass[12pt]{minimal}
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\begin{document}$$\sigma /E\sim 0.1/\sqrt{E}$$\end{document} on average), the worse resolution obtained for electrons and converted photons reflects the presence of significant energy tails induced by interactions with the material upstream of the calorimeter.
Figure 3 compares the performance of the MVA calibration with the initial calibration in simulated H→γγ\documentclass[12pt]{minimal}
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\begin{document}$$J/\psi \rightarrow ee $$\end{document} events. The invariant mass resolution of the former improves by 10 % on average, with a maximum improvement of 15 % for converted photons or in the barrel–endcap transition region. The latter reflects the expected linearity improvement; no significant resolution improvement is obtained.
Comparison of the diphoton invariant mass distributions, mγγ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\gamma \gamma }$$\end{document}, for a simulated Standard Model Higgs boson with a mass of 125 GeV, obtained with the initial calibration and with the MVA calibration (left). The same comparison for the dielectron invariant mass distributions, mee\documentclass[12pt]{minimal}
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\begin{document}$$J/\psi \rightarrow ee $$\end{document} decays (right). The vertical dashed lines indicate the simulated masses
Uniformity and stability
Good uniformity of the EM calorimeter energy reconstruction across pseudorapidity and azimuthal angle, and excellent stability of the response as a function of time and pile-up conditions, are necessary to achieve optimal energy resolution in data. They also constitute a prerequisite for the passive material determination and energy scale measurement presented in Sects. 7–9. The present section describes a set of studies, based on the data collected at s=8TeV\documentclass[12pt]{minimal}
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The response uniformity is investigated using E/p\documentclass[12pt]{minimal}
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High-voltage inhomogeneities
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\begin{document}$$\Delta \eta \times \Delta \phi = 0.2 \times 0.2$$\end{document}) of the EM calorimeter, the HV is set to a non-nominal value due to short circuits occurring in specific LAr gaps [11]. The effect of such modifications is first corrected at the reconstruction level using the expected HV dependence of the response. The azimuthal profiles of the electron pair invariant mass in Z→ee\documentclass[12pt]{minimal}
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\begin{document}$$Z \rightarrow ee $$\end{document} events, however, show localised residual effects, affecting less than 2 % of the total number of HV sectors in the EM calorimeter [7]. An empirical correction is derived based on these profiles to restore the azimuthal uniformity in the problematic sectors. The average value of mee\documentclass[12pt]{minimal}
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Average value of mee\documentclass[12pt]{minimal}
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Time dependence of the presampler response
The nominal HV in the EM barrel PS is 2,000 V. To limit the increasing occurrence of sporadic electronics noise [3] with increasing luminosity, the operating HV was reduced to 1,600 V during the 2011 run and until September 2012 (period P1). The HV was later further reduced to 1,200 V, with some sectors brought down to 800 V (period P2). As above, the non-nominal HV is at first compensated at the cell level using a correction defined from the expected HV dependence of the PS response. This correction is of the order of 8 % for P1 and 21 % for P2.
The accuracy of the correction is verified by comparing the PS response for electrons from Z→ee\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}-dependent variation of up to 1 % is observed. An additional empirical correction is applied to the PS energy at the cluster level, reducing the bias to 0.4 % across η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}. The residual response bias and its corrections are illustrated in Fig. 5.
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Energy loss between the barrel calorimeter modules
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\begin{document}$$\phi <0$$\end{document}, and is interpreted as a gravity-induced widening of the inter-module gaps. The energy loss is adjusted with an empirical function which is then used to correct the calorimeter response. The effect of the inter-module widening and its correction are shown in Fig. 6. This effect is not observed in the EMECs.
Relative energy response of electrons as a function of ϕ\documentclass[12pt]{minimal}
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Energy response in high and medium gain
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Azimuthal non-uniformity and operational stability after corrections
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Intercalibration of the LAr calorimeter layers
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Intercalibration of the first and second calorimeter layers
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\begin{document}$$p_{\mathrm {T}}^\mu >25$$\end{document} GeV. The calorimeter cells crossed by the muon tracks are determined by extrapolating the muon tracks to each layer of the calorimeter, taking into account the geometry of the calorimeter and the residual magnetic field seen by the muon along its path in the calorimeter. In L1, the muon signal is estimated by summing the energies measured in three adjacent cells along η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}, centred around the cell of highest energy among the few cells around the extrapolated track. In L2, due to the accordion geometry, the energy is most often shared between two adjacent cells along ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}; hence the signal is estimated from the sum of the highest energy cell and its most energetic neighbour in ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}.
The observed muon energy distribution in each layer is given by the convolution of a Landau distribution describing the energy deposit, and a Gaussian distribution corresponding to the electronic noise. The MPV of the deposited energy is extracted using an analytical fit with the convolution model, or is alternatively estimated using a truncated mean, by defining the interval as the smallest one containing 90 % of the energy distribution. Denoting ⟨E1/2⟩\documentclass[12pt]{minimal}
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\begin{document}$$\langle E_{1/2} \rangle $$\end{document} the ratio of the MPVs in L1 and L2, the intercalibration result is defined as α1/2=⟨E1/2⟩data/⟨E1/2⟩MC\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _{1/2} =\langle E_{1/2} \rangle ^{\mathrm {data}}/ \langle E_{1/2} \rangle ^{\mathrm {MC}}$$\end{document}. The central value of α1/2\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _{1/2}$$\end{document} is given by the average of the two methods; the difference is used to define its systematic uncertainty. The statistical uncertainty is negligible. The result is illustrated in Fig. 12. All features are observed to be symmetric within uncertainties with respect to η=0\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |$$\end{document}. In the barrel, a negative bias of about 3 % is observed; it shows a falling structure from |η|=0\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |=0.8$$\end{document} to 1.4, with a positive step at the boundary between these regions. In the endcap, α1/2∼1\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _{1/2}\sim 1$$\end{document} on average, but its behaviour across pseudorapidity is not uniform.
Ratio ⟨E1/2⟩data/⟨E1/2⟩MC\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |$$\end{document}, as obtained from the peak position of muon energy deposits in L1 and L2, and from the mean of these energy deposits computed in an interval containing 90 % of the distribution. The error bars represent the total uncertainty specific to the Z→μμ\documentclass[12pt]{minimal}
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\begin{document}$$Z\rightarrow \mu \mu $$\end{document} analysis
The intercalibration of the calorimeter layers with muons relies on the proper modelling in the simulation of the induced ionisation current by muons in each calorimeter layer. The following sources of uncertainty are considered:
uncertainty in the exact path length traversed by muons, related to uncertainty in the geometry of the read-out cells;
uncertainty in the effect of the reduced electric field at the transition between the different calorimeter layers;
uncertainty in the modelling of the conversion of deposited energy to ionisation current due to variations in the electric field following the accordion structure of the absorbers and electrodes;
uncertainty in the cross-talk between different calorimeter cells (between L1 cells, between L1 and L2 cells and between L2 cells) [34] which affects the measured energy for muons (using three cells in L1 and two cells in L2).
These uncertainties are evaluated by implementing the corresponding changes in the simulation. The resulting uncertainty on the relative calibration of L1 and L2 rises from 1 to 1.5 % with the pseudorapidity in the barrel and is 1.5 % in the endcap.
These uncertainties are also propagated to uncertainties on the modelling of E1/2\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}$$\end{document} for electrons and photons, as this variable is used in Sect. 8 for the passive-material determination. For this modelling, the difference between data and simulation in the description of lateral EM shower shape is also taken into account, as it affects L2 more than L1.
In addition, the HG response in L1 is found to be sensitive to the pile-up-dependent optimisation of the OFC, for 1.8<|η|<2.3\documentclass[12pt]{minimal}
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\begin{document}$$1.8<|\eta |<2.3$$\end{document}, with an uncertainty rising from 1 to 5 % in this region. Since in this region most high-ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document} EM showers have their highest energy cell in L1 recorded in MG, this additional uncertainty is accounted for when applying the muon-based calibration to electrons or photons.
The L1/L2 calibration bias α1/2\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _{1/2}$$\end{document} discussed in this section is removed by applying an |η|\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |$$\end{document}-dependent correction to the layer intercalibration in data. The correction can be applied to the energy measured either in L1 (by defining E1corr=E1/α1/2\documentclass[12pt]{minimal}
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\begin{document}$$E_1^\mathrm{corr} = E_1 /\alpha _{1/2}$$\end{document}) or in L2 (E2corr=E2×α1/2\documentclass[12pt]{minimal}
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\begin{document}$$E_2^\mathrm{corr} = E_2 \times \alpha _{1/2}$$\end{document}). The latter option is chosen, as a direct comparison of E2\documentclass[12pt]{minimal}
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\begin{document}$$E_2$$\end{document} in data and simulation shows that the pattern vs |η|\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |$$\end{document} observed in Fig. 12 is localised in L2. After all other corrections discussed in the rest of the paper are applied, and in particular the overall energy scale correction discussed in Sect. 9, the calibrated particle energy is unaffected by this choice.
Presampler energy scale
The presampler energy scale αPS\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _\mathrm{PS}$$\end{document} is determined from the ratio of PS energies in data and MC simulation and estimated using electrons from W\documentclass[12pt]{minimal}
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\begin{document}$$W$$\end{document} and Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document} decays. Before this ratio can be interpreted in terms of an energy scale, the effects of passive-material mis-modelling must be taken into account, as an inaccurate passive-material description in the detector affects the electron shower development and hence the predicted PS energy distributions with respect to the data, resulting in an apparent energy scale bias. This is addressed by exploiting the expected correlation between E1/2\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} value, under variations of the passive material upstream of the PS.
To study this correlation, a set of detector material variations is implemented in simulation, increasing the passive material in the various detector sub-systems upstream of the PS (ID, services, cryostat) and within the calorimeter volume between the PS and L1. The results are illustrated in Fig. 13. Simulations with additional passive material upstream of the PS result in an earlier shower and simultaneously increase the PS activity and E1/2\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}$$\end{document}; a linear correlation between these observables is observed. Simulations also including passive material between the PS and L1 exhibit the same slope of E0\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}$$\end{document}:E0var(η)E0MC(η)=1+A(η)E1/2var(η)E1/2MC(η)b1/2(η)-1,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \frac{E^\mathrm{var}_0(\eta )}{E^\mathrm{MC}_0(\eta )} = 1 + A(\eta ) \,\,\, \left( \frac{E^\mathrm{var}_{1/2}(\eta )}{E^\mathrm{MC}_{1/2}(\eta ) \,\, b_{1/2}(\eta )} - 1 \right) , \end{aligned}$$\end{document}where E0MC\documentclass[12pt]{minimal}
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\begin{document}$$E^\mathrm{var}_{1/2}$$\end{document} their values in the varied simulations. The simulation samples described above predict A=2.48±0.09\documentclass[12pt]{minimal}
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\begin{document}$$b_{1/2}$$\end{document} parameterises the remaining potential mis-modelling of E1/2\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}$$\end{document} for effects unrelated to the material upstream of the PS (such as an imperfect description of the passive material between the PS and L1 and a possible mis-modelling of the cross-talk between L1 and L2); by definition b1/2≡1\documentclass[12pt]{minimal}
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\begin{document}$$b_{1/2}\equiv 1$$\end{document} in the absence of bias.
Examples of correlation between E0\documentclass[12pt]{minimal}
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\begin{document}$$1.0<|\eta |<1.1$$\end{document} (right). ID material variations refer to additions of up to 15 %X0\documentclass[12pt]{minimal}
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\begin{document}$$Z\rightarrow ee$$\end{document} data, after L1/L2 calibration correction. The errors bars are statistical only
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\begin{document}$$E_{1/2}$$\end{document} thus approximately removes the impact of local material variations on the former, and provides a corrected prediction for this quantity,E0corr(η)E0MC(η)=1+A(η)E1/2data(η)E1/2MC(η)b1/2(η)-1,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \frac{E^\mathrm{corr}_0(\eta )}{E^\mathrm{MC}_0(\eta )} = 1 + A(\eta ) \,\,\, \left( \frac{E^\mathrm{data}_{1/2}(\eta )}{E^\mathrm{MC}_{1/2}(\eta ) \,\, b_{1/2}(\eta )} - 1 \right) , \end{aligned}$$\end{document}where E0corr(η)\documentclass[12pt]{minimal}
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\begin{document}$$E^\mathrm{corr}_0(\eta )$$\end{document} corresponds to the amount of expected PS energy in the simulation, corrected for local material bias via E1/2data(η)\documentclass[12pt]{minimal}
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\begin{document}$$b_{1/2}(\eta )$$\end{document}. Finally, the PS energy scale is defined byαPS(η)=E0data(η)E0corr(η).\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}(\eta )$$\end{document} is intrinsically a measure of the material integral in front of the calorimeter at a given pseudorapidity, the study is performed for different categories of EM showers (electrons, and unconverted photons without PS activity), providing partial information on the distance from the beam axis at which the material is probed.
The detector material categories can be grouped under ID material; cryostat material (“Cryo”), designating material located between the maximal conversion radius and the PS; and calorimeter material (“Calo”), for passive material located between the PS and L1.
Methodology
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\begin{document}$$E_{1/2}$$\end{document} data/MC comparisons repeated. The difference between the material estimate from data and the improved simulation is summarised in Fig. 23. As can be seen, the improved simulation behaves as expected in most of the acceptance: the overall discrepancy in the endcap has disappeared, as well as the strong peak around |η|=1.9\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |=0.6$$\end{document} has been halved. The residual passive-material uncertainties in this improved simulation are presented in Fig. 24. Where no significant excess or deficit remains, the measurement uncertainty is given by the L1/L2 calibration uncertainty, and the sensitivity curves’ systematic uncertainties. When the residual discrepancy is larger than the measurement uncertainty, the size of the discrepancy is taken as the final uncertainty. No measurement was performed for 1.37<|η|<1.52\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}$$\end{document} modelling systematic uncertainties summarised in Sect. 7 are considered correlated across η\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \eta =0.2$$\end{document}, and the corresponding uncertainties are uncorrelated beyond this range.
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\begin{document}$$|\eta |$$\end{document}. The integrated material estimate up to L1 is obtained from data/MC comparisons for electrons, after L1/L2 calibration corrections; the integrated estimate up to the PS is obtained by comparing electron and unconverted photon data. The error bars include statistical and systematic uncertainties
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\begin{document}$$E_{1/2}$$\end{document} modelling, Geant4 and L1 gain systematic uncertainties are assumed correlated across η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}. The remaining part of the uncertainty is data driven and considered uncorrelated
The MC-based energy calibration described in Sect. 5 is applied using the new detector description, to reoptimise the energy response in the endcap, where significant amounts of passive material were added in the simulation. The resulting MC calibration constitutes, together with the energy corrections described in Sects. 6 and 7, the basis of the absolute scale determination presented in the next section.
Energy scale and resolution determination with electrons from <inline-formula id="IEq557"><alternatives><mml:math><mml:mrow><mml:mi>Z</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:math><tex-math id="IEq557_TeX">\documentclass[12pt]{minimal}
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\begin{document}$$Z\rightarrow ee$$\end{document}</tex-math><inline-graphic xlink:href="10052_2014_3071_Article_IEq557.gif"/></alternatives></inline-formula> decays
As shown in Sect. 6, no significant mis-calibration is observed as a function of ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}, in a given η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} region. The residual non-uniformity is at the level of 0.75 % or better as illustrated in Fig. 8, matching the design constant term of 0.7 %. Furthermore, the energy response is shown in Figs. 9 and 10 to be stable with time at the level of 0.05 %. Consequently, the absolute scale determination is carried out as a function of η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} only, and independently of time and azimuth.
Methodology
The energy mis-calibration is defined as the difference in response between data and simulation, and is parameterised as follows:Edata=EMC(1+αi)\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} E^\mathrm{data}=E^\mathrm{MC}(1+\alpha _i) \end{aligned}$$\end{document}where Edata\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \begin{aligned} m_{ij}^\mathrm{data}&= m_{ij}^\mathrm{MC} (1+\alpha _{ij}), \\ \alpha _{ij}&\sim \frac{(\alpha _{i} + \alpha _{j})}{2}, \end{aligned} \end{aligned}$$\end{document}neglecting second-order terms and assuming that the angle between the two electrons is perfectly known; mijdata\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \left( \frac{\sigma _E}{E}\right) ^\mathrm{data} = \left( \frac{\sigma _E}{E}\right) ^\mathrm{MC} \quad \oplus \, c. \end{aligned}$$\end{document}The sampling term is assumed to be known to 10%\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \left( \frac{\sigma _m}{m}\right) _{ij}^\mathrm{data}&= \left( \frac{\sigma _m}{m}\right) _{ij}^\mathrm{MC} \oplus c_{ij} \nonumber \\&= \frac{1}{2} \left[ \left( \frac{\sigma _E}{E}\right) _{i}^\mathrm{MC} \oplus c_{i} \oplus \left( \frac{\sigma _E}{E}\right) _{j}^\mathrm{MC} \oplus c_{j} \right] , \nonumber \\ c_{ij}&= \frac{(c_{i} \oplus c_{j})}{2}, \end{aligned}$$\end{document}where cij\documentclass[12pt]{minimal}
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\begin{document}$$c$$\end{document} parameters, histograms of the invariant mass are created from the simulation, including energy scale and resolution perturbations to the reconstruction-level quantities, in a range covering the expected uncertainty in narrow steps. The templates are built separately for the electron pseudorapidity configurations (ηi,ηj)\documentclass[12pt]{minimal}
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An alternative method relies on the same kinematical relations, but replaces the templates by a parameterisation of the Monte Carlo distributions, and performs a likelihood fit to the energy scales. The parameterisation is based on the convolution of a Breit–Wigner function and a Gaussian distribution; the energy scales are determined by minimising with respect to αij\documentclass[12pt]{minimal}
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Results and uncertainties
The methods described above are applied to a sample of Z→ee\documentclass[12pt]{minimal}
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Top energy scale corrections α\documentclass[12pt]{minimal}
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Top effective constant term corrections c\documentclass[12pt]{minimal}
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The uncertainties quoted above are averages; the values depend on pseudorapidity, with larger values in regions with a large amount of material upstream of the calorimeter and in the transition region between the barrel and endcap. The stability of the corrections with the energy is discussed in Sect. 11.
Data/MC comparison after corrections
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\begin{document}$$m_{ee}=100$$\end{document} GeV. Figure 28 shows the dielectron mass distribution for the data corrected with the energy scale factors and for the MC simulation with and without the resolution corrections. In addition the ratios of the corrected data and uncorrected MC distributions to the corrected MC distribution are illustrated together with the final calibration uncertainty.
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Summary of uncertainties common to electrons and photons
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\begin{document}$$E_{\mathrm {T}}\sim 10$$\end{document} GeV and is counted as a separate systematic uncertainty.
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\begin{document}$$E_{\mathrm {T}}$$\end{document}, as discussed above. For electrons, the layer calibration uncertainties reach about 0.15 % at low ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}\sim 40$$\end{document} GeV, and rise to about 0.05 % towards high energy. For unconverted photons, the layer uncertainties are largest at high energy, reaching about 0.1 %. The uncertainty related to the HG/MG transition contributes above ET∼50\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document}-based calibration, the same material deficit induces an overestimate of the energy response for unconverted photons by about 0.05 %, regardless of the passive material type. The energy dependence of this effect is negligible for unconverted photons and the corresponding uncertainties are considered independent of ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document}.
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\begin{document}$$|\eta |<0.6$$\end{document}, for electrons and unconverted photons. The curves show the effect on the energy scale of upward variations of the listed sources of uncertainty; depending on source and particle type, the effect can change sign as a function of ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document}. Left uncertainties from the relative response of L1 and L2 (data-driven uncertainties of the PS and L1/L2 response measurements; uncertainty in the application of the muon-based measurement to electrons; L2 HG/MG uncertainty). Right passive-material uncertainties (ID, cryostat and calorimeter material)
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\begin{document}$$\eta $$\end{document}. Tables 2, 3, 4, 5 and 6, show the uncertainty contributions discussed above as a function of pseudorapidity, and fixed values of ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}=$$\end{document} 11 and 40 GeV are typical of J/ψ→ee\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}\sim 500$$\end{document} GeV. At these energies, the contribution of the third calorimeter layer to the energy measurement is enhanced, and a significant fraction of electrons and photons are recorded in low gain. These aspects are not addressed in this paper.
Electron calibration cross-checks
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\begin{document}$$E_{\mathrm {T}}$$\end{document} regimes using additional probes.
The results presented here are based on the J/ψ→ee\documentclass[12pt]{minimal}
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\begin{document}$$J/\psi \rightarrow ee $$\end{document} sample described together with the selection criteria in Table 1, and consisting of about 185K events. After selections [12], the average electron transverse energy is ET=11\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}=11$$\end{document} GeV, making this sample a useful test of the energy response in the low energy range where electrons from Z\documentclass[12pt]{minimal}
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The invariant mass distribution of the events selected in the data sample shows a sizeable background contribution and a hint of the ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$J/\psi $$\end{document} signal is parameterised by an empirical function taking into account the Gaussian core of the peak and the non-Gaussian tails. The parameterised signal is used as input for a fit to the data to extract the combinatorial background, parameterised as a second-order polynomial, and the ψ(2S)\documentclass[12pt]{minimal}
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\begin{document}$$J/\psi $$\end{document} signal, up to a scaling of the mass and the corresponding expected change in resolution.
The events are categorised as a function of electron pseudorapidity as in Sect. 9. For each (ηi,ηj\documentclass[12pt]{minimal}
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\begin{document}$$\eta _i , \eta _j$$\end{document}) category, the electron pair invariant mass PDF, Lij(mee)\documentclass[12pt]{minimal}
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\begin{document}$$L_{ij}(m_{ee})$$\end{document}, is built from the fitted signal and background components. The electron energy scale factors αi\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _i$$\end{document} are extracted using a simultaneous fit using the likelihood function given in Eq. (11).
The statistical uncertainty on the electron energy scale extraction amounts to 0.1–0.2 %, depending on pseudorapidity. The main source of systematic uncertainty is induced by the imperfect modelling of the electron isolation. The J/ψ\documentclass[12pt]{minimal}
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\begin{document}$$m_{ee}$$\end{document} after energy corrections. The corrected data and the simulation agree within uncertainties across the mass window used in the analysis.
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\begin{document}$$J/\psi $$\end{document} selection in data and simulation, after the energy corrections described in the text are applied to the electron candidates in data. A background component is determined from data and added to the simulated J/ψ\documentclass[12pt]{minimal}
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Energy linearity in <inline-formula id="IEq773"><alternatives><mml:math><mml:mi>Z</mml:mi></mml:math><tex-math id="IEq773_TeX">\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document}</tex-math><inline-graphic xlink:href="10052_2014_3071_Article_IEq773.gif"/></alternatives></inline-formula> events and overall electron calibration accuracy
Finally, a study of the energy dependence of the calibration is performed. The Z→ee\documentclass[12pt]{minimal}
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\begin{document}$$J/\psi \rightarrow ee$$\end{document} analyses of Sects. 9, 11.1 are repeated, now categorising the electrons in broad intervals of |η|\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |$$\end{document}, with the following boundaries:
The analysis is performed after applying all corrections derived above, so that the energy scale corrections derived here are expected to be close to zero and constant. The results are shown in Fig. 32. In all cases, the resulting energy scales lie within the calibration systematic uncertainty envelopes.
Energy scale factors Δα\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document} in different pseudorapidity bins. The band represents the calibration systematic uncertainty. The error bars on the data points represent the total uncertainty specific to the cross-checking analyses
Photon-specific uncertainties Conversion reconstruction inefficiency and fake conversions
The fraction of photons that convert to electron–positron pairs before reaching the calorimeter is directly connected to the amount of material upstream. The efficiency to reconstruct the corresponding tracks and match them to clusters is close to unity for conversions in the innermost layers of the detector and drops at larger radii, in the region instrumented by the TRT. The energy of true converted photons reconstructed as unconverted is typically underestimated by about 2 %, depending on pT\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} and the radius of the conversion. On the other hand, wrong associations between tracks induced by pile-up interactions or fake tracks and clusters lead to “fake conversions” that induce around 2% overestimation of the energy. This effect is also more frequent for tracks reconstructed in the TRT due to the imprecise measurement of η\documentclass[12pt]{minimal}
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Both effects impact the absolute photon energy scale if the efficiency and fake rates are imperfectly described by the simulation. Systematic uncertainties associated with these quantities were estimated by comparing the conversion rates in data and MC simulation, and using a template method based on the ratio E1/2\documentclass[12pt]{minimal}
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\begin{document}$$E_{1/2}$$\end{document}. The latter exhibits a different behaviour for photons that do or do not convert before the calorimeter and therefore is sensitive to the “true” conversion status of the photon. By combining the true and reconstructed conversion status, one can determine the reconstruction efficiency and fake rate in data. The method can also provide an estimate of the material upstream and could be used in the future to constrain this quantity.
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Impact on the energy scale of unconverted (converted) photons from the additional inefficiency (fake rate) in four pseudorapidity bins, in %
Electrons and photons deposit about 6 % of their energy outside of the cluster used in the reconstruction, depending on pseudorapidity and particle type. Although this effect is to first order taken into account by the MC calibration, a calibration bias could appear in the case of imperfect modelling of lateral shower development, as the energy loss would be different in data and simulation.
The energy scale factors obtained from the Z\documentclass[12pt]{minimal}
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\begin{document}$$Z$$\end{document}-based effective calibration described in Sect. 9 absorb such discrepancies. The energy dependence of the difference between data and simulation for electron lateral leakage was investigated and found to be negligible. Therefore the only component yet to be determined is the mis-modelling difference between electrons and photons.
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\begin{document}$$\begin{aligned} \Delta (\gamma -e)&= \left( \frac{E_{7\times 11} - E_\mathrm{nom}}{E_\mathrm{nom}}\right) ^\mathrm{data} \nonumber \\&\quad - \left( \frac{E_{7\times 11} - E_\mathrm{nom}}{E_\mathrm{nom}}\right) ^\mathrm{MC}, \end{aligned}$$\end{document}is estimated for three pseudorapidity intervals, separating unconverted and converted photons.
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The most significant effects found are (0.46±0.10)%\documentclass[12pt]{minimal}
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Photon calibration cross-checks
The energy scale factors extracted in Sect. 9 are expected to be valid for electrons and photons. Their universality is tested using photons from radiative Z\documentclass[12pt]{minimal}
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\begin{document}$$Z \rightarrow ee $$\end{document} channel. The total systematic uncertainty is of the order of 0.1 % while the statistical uncertainty ranges between 0.2 and 1.5 % depending on the pseudorapidity and on the photon conversion type.
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The main way to probe the resolution in data is provided by the study of the Z\documentclass[12pt]{minimal}
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\begin{document}$$\Delta _\mathrm {int}$$\end{document} on the squared resolution induced by a 10 % relative increase in the intrinsic resolution is:Δint(E,η)=(1.12-1)×[σint2(E,η)-σint2(⟨ETe(Z→ee)⟩×coshη,η)]\documentclass[12pt]{minimal}
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\begin{document}$$\pm 200$$\end{document} MeV is appropriate. Its impact isΔnoise(E,η)ET2=δnoise(η)ET2-δnoise(η)⟨ETe(Z→ee)⟩2.\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \frac{\Delta _\mathrm{noise}(E,\eta )}{{E_{\mathrm {T}}}^2} = \left( \frac{\delta _\mathrm{noise}(\eta )}{E_{\mathrm {T}}}\right) ^2 - \left( \frac{\delta _\mathrm {noise}(\eta )}{\langle E_{\mathrm {T}}^{e (Z\rightarrow ee)}\rangle }\right) ^2. \end{aligned}$$\end{document}The impact of detector material uncertainty on the resolution is treated as follows. Assuming the ID, cryostat and calorimeter material uncertainties discussed in Sect. 8, Z→ee\documentclass[12pt]{minimal}
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The results are illustrated in Fig. 37. In the low ET\documentclass[12pt]{minimal}
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The electron pair invariant mass distribution, as reconstructed from data using either the calibrated cluster energies, or the combination of the cluster energy and the track momentum. LeftJ/ψ→ee\documentclass[12pt]{minimal}
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Energy–momentum combination is applied in measurements involving final states with low-ET\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document} electrons, such as Higgs boson decays to four leptons [36]. The systematic uncertainty on the combined momentum is given by the cluster energy scale uncertainty summarised in Sect. 10, and by the momentum scale uncertainty. The latter is assessed using J/ψ→ee\documentclass[12pt]{minimal}
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\begin{document}$$\eta =0$$\end{document} to about 1 % in the barrel–endcap transition region. The cluster energy and track momentum systematic uncertainties are combined in quadrature to obtain the total uncertainty on the combined energy–momentum scale.
Summary
The calibration procedure for electron and photon energy measurement with the ATLAS detector is presented using LHC Run 1 proton–proton collision data corresponding to a total integrated luminosity of about 25 fb-1\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s}=8$$\end{document} TeV. The calorimeter energy measurement is optimised on simulation using MVA techniques, improving the energy resolution with respect to the previous calibration approach [3] by about 10 % (20 %) for unconverted (converted) photons; for electrons, the improvement ranges from a few percent in most of the acceptance up to 30 % in the region with the largest amount of material upstream of the active calorimeter, 1.52<|η|<1.82\documentclass[12pt]{minimal}
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The calorimeter energy response in data is stable at the level of 0.05 % as a function of time and pile-up. After corrections for local mechanical and high-voltage defects, the azimuthal non-uniformity is less than 0.5 % in the barrel, and less than 0.75 % in the endcap, meeting the original design goals. The relative response of the calorimeter layers is analysed, notably correcting a bias of about 3 % in the barrel. After calibration corrections, the shower depth is used to probe the amount of material upstream of the calorimeter with a typical accuracy of 3–10 %X0\documentclass[12pt]{minimal}
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This procedure yields definite predictions for the energy dependence of the electron and photon calibration and its uncertainty. The uncertainty for electrons at ET∼40\documentclass[12pt]{minimal}
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\begin{document}$$1.52<|\eta |<1.82$$\end{document}, the uncertainty is 0.9 and 0.4 % for unconverted and converted photons, respectively. Outside of this range, similar accuracy is achieved for converted and unconverted photons, and the energy dependence is weak. The electron and photon calibration is confirmed using independent resonances provided by J/ψ\documentclass[12pt]{minimal}
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Finally, the relative uncertainty on the energy resolution is better than 10 % for ET<50\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}<50$$\end{document} GeV, and asymptotically rises to about 40 % at high energy. For analyses involving low-ET\documentclass[12pt]{minimal}
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\begin{document}$$E_\mathrm{T}$$\end{document} electrons, an energy–momentum combination algorithm is defined, which improves the electron energy resolution obtained from the calorimeter cluster by about 20 % for ET<30\documentclass[12pt]{minimal}
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The present results form the basis of ATLAS precision measurements using electrons and photons in LHC Run-1 data.
Acknowledgments
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWF and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET, ERC and NSRF, European Union; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany; GSRT and NSRF, Greece; ISF, MINERVA, GIF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, The Netherlands; BRF and RCN, Norway; MNiSW and NCN, Poland; GRICES and FCT, Portugal; MNE/IFA, Romania; MES of Russia and ROSATOM, Russian Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, UK; DOE and NSF, USA. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (The Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.
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The calibration procedure described in this paper was applied to 4.7 fb-1\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document}-dependent Z→ee\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {T}}$$\end{document}, in different pseudorapidity bins and using 2011 data. The band represents the calibration systematic uncertainty. The error bars on the data points represent the total uncertainty specific to the cross-check analyses
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\begin{document}$$Z$$\end{document}-based calibration is within two standard deviations.
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ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document} regions.
The delay between the event trigger and the time slices is optimised to ensure that the third sample is on average at the signal maximum in each read-out channel.
Only in L2 does the cell granularity correspond exactly to this tower size: the number of cells selected by the clustering algorithm in the other layers varies according to the position of the cluster barycentre in L2 [10].
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