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Electron and photon energy calibration with the ATLAS detector using LHC Run 1 data
ATLAS Collaboration
TL;DR
Precise electron and photon energy calibration is a fundamental input to physics measurements. ATLAS presents a mostly collision-data-derived calibration scheme using multivariate methods and simulation. The procedure also corrects simulation for a slightly worse energy resolution observed in data.
Problem
Precise calibration of electron and photon energy measurements is a fundamental input to many physics measurements.
Source: §1 · p. 2Method
Results
The energy resolution in data is slightly worse than in simulation, and corrections are derived and applied to simulation to match data.
Source: §3 · p. 6Takeaways & Limitations
The calibration scheme covers electrons and photons with |η| < 2.471 and is mostly derived from collision data.
Source: §1 · p. 2The simulation-based calibration requires accurate descriptions of detector geometry and particle interactions with matter.
Source: §3 · p. 5
Abstract
from arXiv · showhide
This paper presents the electron and photon energy calibration achieved with the ATLAS detector using about 25 fb$^{-1}$ of LHC proton--proton collision data taken at centre-of-mass energies of $\sqrt{s}$ = 7 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 $Z$ resonance is used to set the absolute energy scale. For electrons from $Z$ 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.
1 Introduction
Precise electron and photon energy calibration is a fundamental input to physics measurements, including Higgs-property and W-boson-mass measurements. This paper presents a mostly collision-data-derived calibration scheme and describes its data samples and validation.
1 Introduction
- Accurate electron-energy calibration is needed for Higgs-boson property measurements and is required for precise W-boson-mass measurement.The introduction identifies precise electron and photon energy measurement as a fundamental input to many physics measurements.Source: §1 · p. 2
- The earlier 2010 calibration used 40 pb−1 and achieved 0.5–1% electron calibration accuracy, depending on pseudorapidity and energy.It relied primarily on test-beam measurements, with the absolute scale set using the Z resonance and upstream material estimated from engineering drawings and a construction survey.Source: §1 · p. 2
- The calibration scheme covers electrons and photons with |η| < 2.471 and is mostly derived from collision data.It combines local calorimeter corrections and longitudinal-layer intercalibration, a detector-material measurement and improved simulation, simulation-based calibration, and an absolute scale from Z decays.Source: §1 · p. 2
- The main studies use 20.3 fb−1 of 2012 data at √s = 8 TeV, while the algorithms are tested on 4.5 fb−1 of 2011 data at √s = 7 TeV.The paper also verifies energy-scale universality using J/ψ →ee and Z →ℓℓγ decays.Source: §1 · p. 3
2 Electron and photon reconstruction and identification in ATLAS
ATLAS reconstructs electrons and photons from electromagnetic-calorimeter clusters, using the calorimeter’s longitudinal structure and the inner detector to characterize showers and identify candidates. Identification selections use shower shapes, track information, and calorimeter leakage or isolation.
2.1 The ATLAS detector
- The electromagnetic calorimeter is a longitudinally segmented liquid-argon sampling calorimeter, with a presampler and three shower-depth layers.The transition region has 5 to almost 10 radiation lengths of material before the first active layer; the second layer collects most shower energy, while the third helps correct high-energy leakage.Source: §2.1 · p. 3
2.2 Energy reconstruction in the electromagnetic calorimeter
- Cell signals are amplified, shaped, sampled, digitised, and converted to deposited energy using calibration factors.The optimal filtering coefficients use the predicted ionisation-pulse shape and noise autocorrelation, including electronic and pile-up components.Source: §2.2 · p. 4
2.3 Electron and photon reconstruction
- Electron and photon candidates are built from calorimeter clusters, then classified using track matching and conversion vertices.Cluster sizes vary by particle type and calorimeter region, balancing energy containment against pile-up and noise contributions.Source: §2.3 · p. 4
2.4 Electron and photon identification
- Identification selections combine shower profiles with track criteria for electrons and shower shapes and hadronic leakage for photons.Electron selections become progressively stricter from loose to tight; isolation requirements further suppress hadronic-decay backgrounds.Source: §2.4 · p. 5
3 Overview of the calibration procedure
The calibration procedure combines multivariate simulation-based response calibration with data-driven corrections, material measurement, layer equalisation, and a Z-based absolute scale. It also checks the calibrated scale and adjusts simulated resolution to match data.
3 Overview of the calibration procedure
- Multivariate algorithms calibrate cluster properties, including longitudinal development, and tracking information to the original electron or photon energy in simulation.The optimisation is performed separately for electrons, converted photons, and unconverted photons.Source: §3 · p. 5
- The amount of material before the calorimeter is measured using the first-to-second-layer energy ratio, E1/2, in electron and unconverted-photon samples.The material measurement is a prerequisite for the simulation-based calibration, which requires accurate detector geometry and particle interactions in simulation.Source: §3 · pp. 5–6
- The procedure equalises longitudinal-layer scales in data and simulation before setting the overall energy scale, then applies the simulation-based calibration and regional response corrections.The overall electron response is calibrated against simulation using Z →ee events; scale factors are also validated with J/ψ →ee and Z →ℓℓγ data.Source: §3 · p. 6
- The resolution in data is slightly worse than in simulation, so corrections are derived and applied to simulation to match data.The overview identifies these as step 5 of the calibration sequence.Source: §3 · p. 6
4 Collision data and simulated samples
The paper’s results primarily use 2012 proton–proton collision data at √s = 8 TeV, with a separate 2011 sample at √s = 7 TeV also described.
Appendix A.
The calibration relies on collision and simulated samples spanning multiple electron, photon, and dilepton-plus-photon processes, with simulation tuned to the data-taking conditions.
Appendix A.
- The J/ψ sample used three lepton-trigger thresholds above 4, 9, and 14 GeV, while Z→ℓℓγ selections included separated photons and leptons and a muon-channel collinear-photon sample.The cited selection text also specifies isolation requirements for leptons and photons.Source: Appendix A · p. 7
- MC samples were generated for Z→ee, Z→μμ, J/ψ→ee, W→eν, Z→ℓℓγ, and γ+X, with simulated sample sizes up to ten times those in data.The comparisons used both the original “base” detector simulation and an “improved” simulation incorporating the passive-material determination.Source: Appendix A · p. 7
- The MVA calibration used 20 million simulated single electrons and 40 million single photons, with transverse energies spanning 1 GeV to 3 TeV and denser statistics from 7 to 100 GeV.Source: Appendix A · p. 7
- Simulated events included additional interactions and were weighted to match the data distribution of interactions per bunch crossing.Backgrounds varied by signal sample; some contributions were determined directly from data.Source: Appendix A · p. 7
5 MC-based calibration for electrons and photons
The MC-based calibration uses multivariate algorithms tailored to particle type and detector region, with corrections that improve energy linearity and resolution.
5 MC-based calibration for electrons and photons
- Cluster-level corrections address upstream-material losses, neighbouring-cell leakage, energy lost beyond the calorimeter, and impact-point response variations, using constants extracted from simulated particles.The multivariate calibration is applied separately to electrons, converted photons, and unconverted photons in η and pT bins, except that the earlier procedure remains in 1.37 ≤ |η| < 1.52.Source: §5 · p. 7
5.1 Input variables
- Inputs include calorimeter energy, presampler-energy ratio, shower depth, cluster pseudorapidity, and cluster position within the calorimeter; converted-photon inputs can also use conversion radius and track momentum information.The cluster position captures lateral leakage and sampling-fraction changes near cell edges, while pseudorapidity accounts for passive-material variations.Source: §5.1 · p. 8
5.2 Binning and linearity corrections
- Independent optimisations are performed across particle-type, |ηcluster|, and Ecalo_T bins chosen around detector geometry and response variations.Residual non-linearity is corrected by shifting the peak of EMVA/Etrue to unity; corrections range from +2% to +5% at ET = 10 GeV and rapidly approach zero around 100 GeV.Source: §5.2 · pp. 8–9
5.3 Performance
- MVA non-linearity is below 0.3% above 10 GeV and below 1% at lower energies, reaching 2% only in localised converted-photon regions; H→γγ mass resolution improves by 10% on average, up to 15%.Unconverted-photon resolution improves by 3%–10% in the barrel and 10%–15% in the endcap; converted-photon resolution improves typically by 20%, while electron improvements are a few percent on average, except 10%–30% at 1.52 < |η| < 1.8. J/ψ→ee shows improved linearity but no significant resolution improvement.Source: §5.3 · p. 9
- Energy tails for electrons and converted photons reflect interactions with material upstream of the calorimeter.Source: §5.3 · p. 9
6 Uniformity and stability
Section 6 studies local calorimeter-response non-uniformities and verifies response stability after corrections. These properties support optimal energy resolution and the later passive-material and energy-scale measurements.
6.1 High-voltage inhomogeneities
- Two non-nominal high-voltage sectors lower the response by about 2% near φ ∼−1 and φ ∼0; an empirical correction restores uniformity.Residual localized effects affect less than 2% of high-voltage sectors.Source: §6.1 · pp. 9–10, Figure 4 · p. 11
6.2 Time dependence of the presampler response
- A residual η-dependent presampler response variation of up to 1% between periods P1 and P2 is reduced to 0.4% by an additional cluster-level correction.The initial cell-level corrections for the presampler response are about 8% in P1 and 21% in P2.Source: §6.2 · p. 11, Figure 5 · p. 11
6.3 Energy loss between the barrel calorimeter modules
- A π/8-periodic response modulation at barrel-module boundaries is about 2% for φ > 0 and 1% for φ < 0; an empirical correction adjusts for the inferred gap widening.The effect is not observed in the EMECs.Source: §6.3 · p. 11, Figure 6 · p. 12
6.4 Energy response in high and medium gain
- Energy calibration is gain-independent within uncertainties across most of the calorimeter, but a percent-level effect appears near |η| ∼0.6 and |η| ∼1.6.A correction based on the data–simulation response difference between high- and medium-gain cells, weighted by the expected medium-gain cluster fraction, removes the observed dependence.Source: §6.4 · p. 12, Figure 7 · p. 12
6.5 Azimuthal non-uniformity and operational stability after corrections
- 0.45% azimuthal non-uniformity is achieved for |η| < 0.8, and 0.75% in the rest of the calorimeter; response versus time and μ is stable at 0.05%.The response versus reconstructed vertex count has a slope because the pile-up compensation becomes imperfect when events are classified by vertex count; simulation describes this effect to 0.05%.Source: §6.5 · pp. 12–13, Figure 8 · p. 13, Figure 9 · p. 13
7 Intercalibration of the LAr calorimeter layers
The layer intercalibration corrects data–simulation differences using muon energy deposits and accounts for passive-material effects when setting the presampler scale. These corrections also support a cross-check of the layer response with electron showers.
7.1 Intercalibration of the first and second calorimeter layers
- Muon deposits, insensitive to upstream passive material, set α1/2 from the L1/L2 deposit ratio in data and simulation, averaging fitted-MPV and truncated-mean estimates.The truncated mean uses the smallest interval containing 90% of the energy distribution; the difference between the two methods defines the systematic uncertainty.Source: §7.1 · p. 14
- A negative bias of about 3% is observed in the barrel, while α1/2 averages near one but varies across the endcap; an η-dependent L2 correction removes the bias.After the paper’s other corrections, including the overall energy-scale correction, the choice to apply the correction to L2 does not affect the calibrated particle energy.Source: §7.1 · pp. 14–15
- The relative L1/L2 calibration uncertainty rises from 1% to 1.5% with pseudorapidity in the barrel and is 1.5% in the endcap.Considered sources include muon path length, reduced electric field at layer transitions, ionisation-current modelling, and cell cross-talk.Source: §7.1 · pp. 14–15
7.2 Presampler energy scale
- Upstream material variations produce a linear correlation between PS activity E0 and E1/2; correlating their data/MC ratios approximately removes local material effects from the PS prediction.Material added between the PS and L1 leaves the correlation slope unchanged but shifts E1/2, since it cannot affect PS activity.Source: §7.2 · p. 15
- After L1/L2 corrections, b1/2 is close to one, but electron data show an average positive bias of about 7% in the endcap; the presampler scale is accurate to 2–3%.The endcap bias indicates a material-description discrepancy; the PS scale analysis applies material corrections to reduce variations in the predicted PS energy.Source: §7.2 · pp. 16–17
7.3 Layer intercalibration cross-check
- For the electron-shower cross-check, material mis-modelling contributes about 0.5% on average to α1/2 uncertainty, rising to 1–2% for 1.37 < |η| < 1.82; cross-talk contributes negligibly.The cross-talk test rescales the L1 response while keeping the sum of L1 and L2 energies constant.Source: §7.3 · p. 17
8 Passive-material determination
The analysis uses electron and unconverted-photon shower profiles to estimate passive material relative to the base simulation. It implements material changes in an improved simulation, reducing several observed discrepancies while leaving some residuals.
8.1 Methodology
- For |η| < 1.82, electrons and unconverted photons separate material before the PS from material between the PS and L1; above that, only total material up to L1 is measured.At small η, a 1% relative change in E1/2 corresponds to about 2.5%X0 for upstream material in electrons and 1.5%X0 for between-PS-and-L1 material probed with unconverted photons.Source: §8 · p. 17, §8.1 · pp. 19–20
8.3 Improvements to the ATLAS material simulation
- The improved simulation removes the overall endcap discrepancy and the peak near |η| = 1.9, halves the barrel excess at |η| = 0.6, but leaves the deficit at 1.5 < |η| < 1.6.Material modifications were added upstream of the PS, primarily in regions with substantial services between the ID active area and calorimeter cryostat; the revised simulation was used for energy calibration.Source: §8.3 · pp. 20, 22, Figure 23 · p. 22
- No material measurement was performed for 1.37 < |η| < 1.52, where upstream-of-L1 material uncertainty is estimated at ∼0.4X0; reported uncertainties are uncorrelated beyond Δη = 0.2.Where a residual discrepancy exceeds the measurement uncertainty, its size is taken as the final uncertainty.Source: §8.3 · pp. 20, 22
8.2 Material determination
- The material estimate integrated up to L1 shows endcap excesses up to 0.6–0.7X0 and a 0.5X0 deficit near 1.55 < |η| < 1.6; integrated estimates are accurate to about 0.04–0.06X0.The excess reaches 0.2X0 at |η| = 0.6 in the barrel, while material features up to the PS resemble those up to L1, indicating biases upstream of the PS.Source: §8.2 · p. 20, Figure 20 · p. 21
9 Energy scale and resolution determination with electrons from Z →ee decays
The Z→ee template method determines energy-scale and resolution corrections by pseudorapidity, after which the corrected data and simulation agree closely across the Z mass window. The scale and resolution corrections are quantified with regional uncertainties and tested against alternative fits and selections.
9.1 Methodology
- The fit uses simulation templates on a two-dimensional grid of energy-scale α and resolution c perturbations, with optimal values and correlations obtained by χ2 minimisation.Templates are built separately for electron pseudorapidity configurations and compared with categorised data.Source: §9.1 · pp. 23–24, Figure 25 · p. 23
9.2 Results and uncertainties
- 0.3 × 10−3, 2 × 10−3, and 0.5 × 10−3 are the energy-scale determination accuracies for |η| < 1.37, 1.37 < |η| < 1.82, and |η| > 1.82, respectively.The corresponding scale uncertainty is larger in the transition region.Source: §9.2 · p. 24, Figure 26 · p. 24
- 0.8% in the barrel and about 1% in the endcap are the average resolution corrections, determined accurate to 0.3% and 0.5%, respectively.The constant-term values at positive and negative η are statistically compatible and symmetrised.Source: §9.2 · p. 24, Figure 27 · p. 24
- 3.8 × 10−4 is the average scale difference between template and likelihood methods over the full η range, falling to 1.3 × 10−4 when the transition region is excluded.Their fitted constant terms agree within δc = 1.2 × 10−3.Source: §9.2 · pp. 24–25
- No bias beyond statistical accuracy is found in injected-distortion tests, while selection changes and modeling uncertainties contribute additional scale and resolution uncertainties.The assigned test uncertainties are δα = 0.5 × 10−4 and δc = 1.1 × 10−3; selection variations and background or signal modeling also affect the fitted corrections.Source: §9.2 · p. 25
9.3 Data/MC comparison after corrections
- 1% agreement between data and simulation is achieved for 80 < mee < 100 GeV, rising to 2% toward the interval’s low end.A slight low-mass excess remains because the data’s energy tails are not fully modelled, but it lies within the passive-material uncertainty.Source: §9.3 · p. 25
10 Summary of uncertainties common to electrons and photons
The common electron and photon uncertainty model accounts for energy-, pseudorapidity-, and particle-dependent effects, including layer response, gain transitions, and passive material. It is expected to apply up to about 500 GeV in transverse energy.
10 Summary of uncertainties common to electrons and photons
- Gain dependence is measured by comparing Z-peak positions for clusters with all L2 cells in high gain versus at least one cell in medium gain, then corrected in data.A pile-up-only comparison finds an average pedestal offset of about 15 MeV, with non-linearity reaching 0.1% at ET ∼10 GeV.Source: §10 · p. 26
- Material-response uncertainties are obtained by comparing nominal and modified-material simulations and scaling response differences to the measured material uncertainties.Source: §10 · p. 26
- For |η| < 0.6, layer-calibration uncertainties reach about 0.15% for low-ET electrons and 0.1% for high-ET unconverted photons; the HG/MG transition reaches 0.3% at high ET.The cryostat-material deficit produces a −0.3% scale drop at ET = 5 GeV; after Z-based calibration, the material deficit shifts unconverted photons by about 0.05%.Source: §10 · p. 26, Figure 29 · p. 27
- The uncertainty model is expected to be valid up to ET ∼500 GeV; enhanced third-layer contributions and frequent low-gain recording at those energies are not addressed.Source: §10 · p. 27
11 Electron calibration cross-checks
J/ψ→ee events provide a low-energy cross-check of the electron calibration, while energy-binned Z→ee and J/ψ→ee analyses test linearity. The measured scales are consistent with the expected calibration uncertainties.
11.1 Energy scale from J/ψ →ee
- The J/ψ sample has average ET = 11 GeV, providing a low-energy check where electrons from Z decays are unavailable.It contains about 185K selected events.Source: §11.1 · p. 27
- 0.1% to 0.2% is the statistical uncertainty on the J/ψ electron energy-scale extraction, depending on pseudorapidity.Imperfect isolation modeling contributes a 0.2% systematic uncertainty through uncertainty in direct and b→J/ψ fractions and jet contributions to cluster energy.Source: §11.1 · p. 29
- The J/ψ-derived scales agree satisfactorily with expected uncertainties, though they tend to sit about one standard deviation above the Z results.Residual differences are associated with read-out pedestal settings centrally and material-description uncertainties in 1 < |η| < 1.82.Source: §11.1 · p. 29, Figure 30 · p. 29
11.2 Energy linearity in Z events and overall electron calibration accuracy
- The energy scales from the ET-binned Z and J/ψ analyses lie within the calibration systematic uncertainty envelopes.The analyses apply the preceding corrections and use broad pseudorapidity and transverse-energy intervals.Source: §11.2 · p. 29
12 Photon-specific uncertainties
Photon-specific uncertainties include conversion reconstruction inefficiency and fake conversions, as well as differences between electron and photon lateral leakage. These effects are evaluated using conversion-sensitive information and electron–photon comparisons.
12.1 Conversion reconstruction inefficiency and fake conversions
- True converted photons reconstructed as unconverted are typically underestimated by about 2%, while fake conversions overestimate energy by around 2%.Track reconstruction and cluster matching efficiency falls at larger radii in the TRT region.Source: §12.1 · pp. 29–30
- The conversion-rate and E1/2 template method combines true and reconstructed conversion status to estimate conversion efficiency and fake rate in data.The study uses leading photons in selected diphoton events and subtracts jet background in each E1/2 bin.Source: §12.1 · pp. 30–31
- A few 10−4 is the typical energy-scale impact from additional conversion inefficiency or fake rate, reaching 10−3 for 1.52 < |η| < 1.81 around ET = 60 GeV.The measured inefficiencies and fake rates exceed simulation predictions by up to a few percent.Source: §12.1 · p. 31, Table 7 · p. 31
12.2 Lateral leakage mis-modelling
- The Z-based effective calibration absorbs electron lateral-leakage discrepancies, whose energy dependence was found negligible; the remaining term is the electron–photon difference.That difference is estimated by comparing nominal-cluster and larger-window energies in Z→ℓℓγ and Z→ee samples.Source: §12.2 · pp. 31–32
- (0.46 ± 0.10)% for converted photons and (0.10 ± 0.06)% for unconverted photons are the largest electron–photon lateral-leakage differences, both in 0.8 < |η| < 1.37.The assigned photon-scale uncertainty per bin is the larger of the difference and its uncertainty, and is assumed independent of ET.Source: Table 8 · p. 31, §12.2 · p. 32
13 Photon calibration cross-checks
Photon scale universality is tested with radiative Z decays across electron and muon channels and photon conversion types. The measured scales agree with expectations within uncertainties.
13 Photon calibration cross-checks
- The universality test uses radiative Z decays in electron and muon channels for unconverted, one-track, and two-track converted photons, with photon purity estimated at 97%–99%.Collinear Z → µµγ events are included only for unconverted photons.Source: §13 · p. 32
- A double ratio compares radiative and non-radiative dilepton mass ratios in data and simulation, suppressing lepton-scale uncertainty and differences in lepton kinematics.The αi giving R(αi) = 1 defines the photon scale; scales from the event topologies are then combined.Source: §13 · p. 32
- The measured photon energy scales agree with expectations within uncertainties; total systematic uncertainty is about 0.1%, while statistical uncertainty ranges from 0.2% to 1.5%.Statistical uncertainty varies with pseudorapidity and photon conversion type.Source: §13 · p. 32
14 Resolution accuracy
The paper quantifies resolution uncertainty, improves low-energy electron resolution by combining track momentum and calorimeter energy, and reports Run 1 calibration results and cross-checks. The results include energy- and region-dependent scale uncertainties and a limitation on the expected validity range of the scale model.
14 Resolution accuracy
- At ET = 40 GeV, resolution uncertainty is 5% for electrons and about 10% for unconverted photons; pile-up dominates at low energy, while sampling and material contributions matter at high energy.The electron and photon resolution curves and uncertainty contributions are shown in Figs. 35 and 36.Source: §14 · p. 34, Figure 35 · p. 35, Figure 36 · p. 35
15 Energy–momentum combination
- Combining track momentum with cluster energy improves low-energy electron resolution by about 20% in J/ψ events and helps in the 1.37 < |η| < 1.52 transition region.The method is not applied for |η| > 1.52.Source: §15 · p. 36
16 Summary
- Energy resolution improves over the previous calibration by about 10% for unconverted photons and 20% for converted photons, and by a few percent to 30% for electrons depending on acceptance.The largest electron improvement is in 1.52 < |η| < 1.82, where upstream material is greatest.Source: §16 · p. 36
- Calorimeter energy response is stable to 0.05% over time and pile-up; layer calibration corrects a ∼3% barrel bias, and upstream material is measured to 3–10% X0.The material accuracy depends on pseudorapidity; the simulation and MVA calibration are adjusted using these measurements.Source: §16 · p. 36
- At ET ∼ 40 GeV, average electron scale uncertainty is 0.04% for |η| < 1.37, 0.2% for 1.37 < |η| < 1.82, and 0.05% for |η| > 1.82.At ET ∼ 11 GeV, electron response uncertainty ranges from 0.4% to 1% for |η| < 1.37, is about 1.1% for 1.37 < |η| < 1.82, and is 0.4% for |η| > 1.82.Source: §16 · pp. 36–37
- Relative resolution uncertainty is better than 10% for ET < 50 GeV, rising asymptotically to about 40% at high energy; combination improves cluster resolution by about 20% for ET < 30 GeV and |η| < 1.52.The paper identifies this combination for measurements involving low-ET electrons.Source: §16 · p. 37
A Calibration results using 2011 data
- In 2011 cross-checks, the energy scale shows about 1% dependence in 1.37 < |η| < 1.52, while results outside that transition region agree with Z-based calibration across ET and η.For radiative photons, unconverted results agree with expectations; converted-photon differences from Z-based calibration are within two standard deviations.Source: A Calibration results using 2011 data · p. 38