Electron and photon performance measurements with the ATLAS detector using the
2015–2017 LHC proton–proton collision data This paper describes the
reconstruction of electrons and photons with the ATLAS detector, employed for
measurements and searches exploiting the complete LHC Run 2 dataset. An
improved energy clustering algorithm is introduced, and its implications for
the measurement and identification of prompt electrons and photons are
discussed in detail. Corrections and calibrations that affect performance,
including energy calibration, identification and isolation efficiencies, and
the measurement of the charge of reconstructed electron candidates are
determined using up to 81 fb-1 of proton–proton collision data collected at
$\sqrt{s}=13$ TeV between 2015 and 2017. EGAM-2018-01 JINST CERN-EP-2019-145
JINST 14 (2019) P12006 10.1088/1748-0221/14/12/P12006 Super-cluster
reconstructionhttps://cds.cern.ch/record/2298955 Electron and photon energy
calibrationhttps://cds.cern.ch/record/2651890 Electron
IDhttps://cds.cern.ch/record/2652163 Photon
IDhttps://cds.cern.ch/record/2647979 Electron and photon
isolationhttps://cds.cern.ch/record/2646265 10 July 2019 Maria Josefina
Alconada Verzini, Francisco Alonso, Christos Anastopoulos, Nansi Andari,
Ludovica Aperio Bella, Jean-Francois Arguin, Hicham Atmani, Cyril Becot,
Maarten Boonekamp, Frued Braren, Kurt Brendlinger, Chav Chhiv Chau, Olympia
Dartsi, Jean-Baptiste de Vivie de Régie, David Delgove, Lucia Di Ciaccio,
David Di Valentino, Otilia Anamaria Ducu, Johannes Erdmann, Marc Escalier,
Saskia Falke, Yi Fang, Marcello Fanti, Louis Fayard, Alexandra Fell, Lucas
Macrorie Flores, Gregor Gessner, Dag Ingemar Gillberg, Dominique Godin,
Thibault Guillemin, Sarah Heim, Rachel Hyneman, Lydia Iconomidou-Fayard, Oleh
Kivernyk, Matthew Henry Klein, Thomas Koffas, Kevin Kroeninger, Joe Kroll,
Antoine Laudrain, Yanwen Liu, Kristin Lohwasser, Stefano Manzoni, Julien
Maurer, Jovan Mitrevski, Kazuya Mochizuki, Emmanuel Monnier, Miha Muskinja,
Roger Felipe Naranjo Garcia, Isabel Nitsche, Ioannis Nomidis, Jose Ocariz,
Andreas Petridis, Pavel Podberezko, Thomas Dennis Powell, Pascal Pralavorio,
Nadezda Proklova, Joseph Reichert, Amartya Rej, Elias Michael Ruettinger,
Abhishek Sharma, Nima Sherafati, Philip Sommer, Kerstin Tackmann, Grigore
Tarna, Savannah Jennifer Thais, Evelyn Thomson, Artur Trofymov, Guillaume
Unal, Hanlin Xu, Zhiqing Zhang Olivier Arnaez (chair) Fares Djama Kun Liu
<EMAIL_ADDRESS><EMAIL_ADDRESS>Norman Mccubbin<EMAIL_ADDRESS>
Contents

toc

##  1 Introduction

With an integrated luminosity of about 147 fb-1, the proton–proton ($pp$)
collision dataset collected by the ATLAS detector between 2015 and 2018 at a
centre-of-mass energy of $\sqrt{s}=13$ TeV will allow significant advances in
the exploration of the electroweak scale. Optimal performance in the
measurement of electrons and photons plays a fundamental role in searches for
new particles, in the measurement of Standard Model cross-sections, and in the
precise measurement of the properties of fundamental particles such as the
Higgs and $W$ bosons and the top quark.

The ATLAS Collaboration published three papers describing the performance of
the reconstruction, identification and energy measurement of electrons and
photons with 36 fb-1 of $pp$ collision data collected in 2015 and 2016 [1, 2,
3]. New algorithms for electron and photon reconstruction were introduced in
2017. The present paper describes the performance of these algorithms, and
extends the analysis to the dataset collected between 2015 and 2017, which
corresponds to an integrated luminosity of about 81 fb-1. The discussion is
limited to electrons and photons reconstructed in the central calorimeters,
covering the pseudorapidity range $|\eta|<2.5$.

The transition from the reconstruction of electrons and photons based on
fixed-size clusters of calorimeter cells towards a dynamical, topological cell
clustering algorithm [4] represents the most important modification. The
algorithms used for the identification of the candidates and the estimation of
their energy have been updated accordingly. The performance of these changes
is discussed in detail. In addition, methods allowing an improved rejection of
misreconstructed or non-isolated candidates are presented, and are of
particular importance for measurements of processes with low cross-sections or
high backgrounds, such as the associated production of a Higgs boson with a
top-quark pair, or vector-boson scattering at high energy.

After a summary of the experimental apparatus and the samples used for this
analysis in Sections 2 and 3, Section 4 describes the new reconstruction of
clusters of energy deposits in the electromagnetic (EM) calorimeter, the
estimation of their energy, and the use of information from the inner tracking
detector to distinguish between electrons and photons. Section 5 summarizes
the energy calibration corrections and the associated systematic
uncertainties. Sections 6 and 7 present the re-optimized electron and photon
identification algorithms. Section 8 discusses the discrimination between
prompt electrons and photons and backgrounds from hadron decays. Finally,
studies dedicated to the electron and positron charge identification are
reported in Section 9.

##  2 ATLAS detector

The ATLAS experiment [5, 6, 7] is a general-purpose particle physics detector
with a forward–backward symmetric cylindrical geometry and almost 4$\pi$
coverage in solid angle.111ATLAS uses a right-handed coordinate system with
its origin at the nominal interaction point (IP) in the centre of the detector
and the $z$-axis along the beam pipe. The $x$-axis points from the IP to the
centre of the LHC ring, and the $y$-axis points upward. Cylindrical
coordinates $(r,\phi)$ are used in the transverse plane, $\phi$ being the
azimuthal angle around the $z$-axis. The pseudorapidity is defined in terms of
the polar angle $\theta$ as $\eta=-\ln\tan(\theta/2)$. The angular distance
$\Delta R$ is defined as $\Delta
R\equiv\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}}$. The transverse energy is
$E_{\text{T}}=E/\cosh(\eta)$. The inner tracking detector (ID) covers the
pseudorapidity range $|\eta|<2.5$ and consists of a silicon pixel detector, a
silicon microstrip detector (SCT), and a transition radiation tracker (TRT) in
the range $|\eta|<2.0$. The TRT provides electron identification capability
through the detection of transition radiation photons. It consists of small-
radius drift tubes (‘straws’) interleaved with a polymer material creating
transition radiation for particles with a large Lorentz factor. This radiation
is absorbed by the Xe-based gas mixture filling the straws, discriminating
electrons from hadrons over a wide energy range. Due to gas leaks, some TRT
modules are filled with an Ar-based gas mixture. The ID is surrounded by a
superconducting solenoid producing a 2 T magnetic field and provides accurate
reconstruction of tracks from the primary $pp$ collision region. It also
identifies tracks from secondary vertices, permitting an efficient
reconstruction of photon conversions in the ID up to a radius of about 800 mm.

The EM calorimeter is a lead/liquid-argon (LAr) sampling calorimeter with an
accordion geometry. It is divided into a barrel section (EMB) covering the
pseudorapidity region $|\eta|<1.475$,222The EMB is split into two half-barrel
modules, which cover the positive and negative $\eta$ regions. and two endcap
sections (EMEC) covering $1.375<|\eta|<3.2$. The barrel and endcap
calorimeters are immersed in three LAr-filled cryostats, and are segmented
into three layers for $|\eta|<2.5$. The first layer, covering $|\eta|<1.4$ and
$1.5<|\eta|<2.4$, has a thickness of about 4.4 radiation lengths ($X_{0}$) and
is finely segmented in the $\eta$ direction, typically $0.003\times 0.1$ in
$\Delta\eta\times\Delta\phi$ in the EMB, to provide an event-by-event
discrimination between single-photon showers and overlapping showers from the
decays of neutral hadrons. The second layer (L2), which collects most of the
energy deposited in the calorimeter by photon and electron showers, has a
thickness of about $17X_{0}$ and a granularity of $0.025\times 0.025$ in
$\Delta\eta\times\Delta\phi$. A third layer, which has a granularity of
$0.05\times 0.025$ in $\Delta\eta\times\Delta\phi$ and a depth of about
2$X_{0}$, is used to correct for leakage beyond the EM calorimeter for high-
energy showers. In front of the accordion calorimeter, a thin presampler layer
(PS), covering the pseudorapidity interval $|\eta|<1.8$, is used to correct
for energy loss upstream of the calorimeter. The PS consists of an active LAr
layer with a thickness of 1.1 cm (0.5 cm) in the barrel (endcap) and has a
granularity of $\Delta\eta\times\Delta\phi=0.025\times 0.1$. The transition
region between the EMB and the EMEC, $1.37<|\eta|<1.52$, has a large amount of
material in front of the first active calorimeter layer ranging from 5 to
almost $10X_{0}$. This section is instrumented with scintillators located
between the barrel and endcap cryostats, and extending up to $|\eta|=1.6$.

The hadronic calorimeter, surrounding the EM calorimeter, consists of an
iron/scintillator tile calorimeter in the range $|\eta|<1.7$ and two
copper/LAr calorimeters spanning $1.5<|\eta|<3.2$. The acceptance is extended
by two copper/LAr and tungsten/LAr forward calorimeters extending up to
$|\eta|=$ 4.9, and hosted in the same cryostats as the EMEC. Electron
reconstruction in the forward calorimeters is not discussed in this paper.

The muon spectrometer, located beyond the calorimeters, consists of three
large air-core superconducting toroid systems with eight coils each, with
precision tracking chambers providing accurate muon tracking for $|\eta|<2.7$
and fast-triggering detectors up to $|\eta|=2.4$.

A two-level trigger system [8] is used to select events. The first-level
trigger is implemented in hardware and uses a subset of the detector
information to reduce the accepted rate to a maximum of about
$100\text{\,}\mathrm{kHz}$. This is followed by a software-based trigger that
reduces the accepted event rate to $1\text{\,}\mathrm{kHz}$ on average,
depending on the data-taking conditions.

##  3 Collision data and simulation samples

###  3.1 Dataset

The analyses described in this paper use the full $pp$ collision dataset
recorded by ATLAS between 2015 and 2017 with the LHC operating at a centre-of-
mass energy of $\sqrt{s}$ = 13 TeV and a bunch spacing of 25 ns. The dataset
is divided into two subsamples according to the typical mean number of
interactions per bunch crossing, $\left\langle\mu\right\rangle$, with which it
was recorded :

  * •

The ‘low-$\mu$’ sample was recorded in 2017 with
$\left\langle\mu\right\rangle\sim 2$; after application of data-quality
requirements, the integrated luminosity amounts to 147 pb-1.

  * •

The ‘high-$\mu$’ sample corresponds to an integrated luminosity of 80.5 fb-1;
for this sample, $\left\langle\mu\right\rangle$ was on average 13, 25 and 38
for 2015, 2016 and 2017 data, respectively. The corresponding integrated
luminosities are 3.2 fb-1, 33.0 fb-1 and 44.3 fb-1. In 2016, a small sample
corresponding to 0.7 fb-1 of data was recorded without magnetic field in the
muon system; it is added to the ‘high-$\mu$’ sample for electron
reconstruction and identification studies.

Two different LHC filling schemes were used in 2017. The nominal filling
scheme, labelled 48b in the following, corresponding to an integrated
luminosity of 17.9 fb-1 and $\left\langle\mu\right\rangle\sim 32$, was built
from ‘sub-trains’ of 48 filled bunches followed by seven empty bunches.
Simulated event samples use this configuration,333The simulation used in
conjunction with 2015 and 2016 data has a similar bunch configuration,
consisting of 72 filled bunches followed by eight empty bunches. as it
represents about 70% of the collected data; the implications of this
approximation for the energy calibration are discussed in Section 5. The
second scheme, labelled 8b4e, corresponding to an integrated luminosity of
26.4 fb-1 and $\left\langle\mu\right\rangle\sim 42$, was made of sub-trains of
eight filled bunches followed by four empty bunches. To sustain these
conditions, a levelling of the instantaneous luminosity at $2\times 10^{34}$
cm-2s-1 was necessary at the beginning of the fill, resulting in a peak
$\left\langle\mu\right\rangle$ around 60. The noise induced by pile-up, or
multiple $pp$ interactions occurring in the same bunch crossing as the event
of interest or in nearby crossings, is 10% smaller than for the standard
configuration for a given $\mu$. The LHC filling scheme for the ‘low-$\mu$’
data sample was 8b4e.

Several levels of object identification and isolation criteria are employed to
select the event samples used in the analyses described in this paper.
Electrons are identified using a likelihood-based method combining information
from the EM calorimeter and the ID. Different identification working points,
Loose, Medium and Tight are defined [2]. Similar levels are used at trigger
level (online), with slightly different inputs. A Very Loose working point is
also defined for the online selection. Photons are selected using a set of
cuts on calorimeter variables [1] in the pseudorapidity range $|\eta|<2.37$,
with the transition region between the barrel and endcap calorimeters,
$1.37<|\eta|<1.52$, excluded. Two levels of identification, Loose and Tight,
are considered. A Loose identification is used at trigger level to select a
sample of inclusive photons.

The measurements of the electromagnetic energy response and of the electron
identification efficiency use a large sample of $Z\to ee$ events selected with
single-electron and dielectron triggers. The dielectron high-level triggers
use a transverse energy ($E_{\text{T}}$) threshold ranging from 12 GeV (2015)
to 17 or 24 GeV (2016 and 2017) and a Loose (2015) or Very Loose (2016 and
2017) identification criterion. The single-electron high-level trigger has an
$E_{\text{T}}$ threshold ranging from 24 GeV in 2015 and most of 2016 to 26
GeV at the end of 2016 and during 2017; it requires a Tight identification and
loose tracking-based isolation criteria. The offline selection for the energy
calibration measurement requires two electrons with Medium identification and
loose isolation [2] with $E_{\text{T}}>27$ GeV, resulting in $\sim$ 36 million
$Z\to ee$ candidate events.

A sample of $J/\psi\to ee$ events with at least two electron candidates with
$E_{\text{T}}>4.5\ \text{Ge\kern-1.00006ptV}$ and $|\eta|<2.47$ was collected
for studies with low-$E_{\text{T}}$ electrons using dedicated prescaled
dielectron triggers with electron $E_{\text{T}}$ thresholds ranging from 4 to
14 GeV. Each of these triggers requires Tight trigger identification and
$E_{\text{T}}$ above a certain threshold for one trigger object, while only
demanding the electromagnetic cluster $E_{\text{T}}$ to be higher than some
other (lower) threshold for the second object.

Samples of $Z\to\ell\ell\gamma$ events, used to validate the photon energy
scale and measure photon identification and isolation efficiencies at low
$E_{\text{T}}$, were selected with the same triggers as for the $Z\to ee$
sample for the electron channel and single-muon or dimuon triggers in the muon
channel. The dimuon (single-muon) trigger transverse momentum ($p_{\text{T}}$)
threshold was 14 (26) GeV at the high-level trigger; a loose tracking-based
isolation criterion was applied at the high-level trigger for the single-muon
trigger. The $\mu\mu\gamma$ ($ee\gamma$) samples, after requiring two muons
(electrons) with Medium identification [9], $p_{\text{T}}>15$ GeV (18 GeV) and
one tightly identified and loosely isolated photon with $E_{\text{T}}>15$ GeV,
contain $\sim$ 110000 ($\sim$ 54000) events.

Single-photon triggers with Loose identification and large prescale factors
are used for measurements of the photon identification and isolation
efficiencies. The lowest transverse energy threshold of these triggers is 10
GeV.

###  3.2 Simulation samples

Large Monte Carlo (MC) samples of $Z\to\ell\ell$ events ($\ell=e,\mu$) were
simulated at next-to-leading order (NLO) in QCD using Powheg [10] interfaced
to the Pythia8 [11] parton shower model. The CT10 [12] parton distribution
function (PDF) set was used in the matrix element. The AZNLO set of tuned
parameters [13] was used, with PDF set CTEQ6L1 [14], for the modelling of non-
perturbative effects. Photos++ 3.52 [15] was used for QED emissions from
electroweak vertices and charged leptons. To model the background in photon
identification and isolation measurements using radiative $Z$ decays, samples
of $Z\to\ell\ell$ events with up to two additional partons at NLO in QCD and
four additional partons at leading order (LO) in QCD were simulated with
Sherpa [16] version 2.2.1, using the NNPDF30NNLO [17] PDF in conjunction with
the dedicated parton shower tuning developed by the Sherpa authors.

Both non-prompt (originating from $b$-hadron decays) and prompt (not
originating from $b$-hadron decays) $J/\psi\to ee$ samples were generated
using Pythia8. The A14 set of tuned parameters [18] was used together with the
CTEQ6L1 PDF set.

Samples of $Z\to\ell\ell\gamma$ events with transverse energy of the photon
above 10 GeV were generated with Sherpa version 2.1.1 using QCD leading-order
matrix elements with up to three additional partons in the final state. The
CT10 PDF set was used.

Samples of inclusive photon production were generated using Pythia8. The
signal includes LO photon-plus-jet events from the hard subprocesses $qg\to
q\gamma$ and $q\bar{q}\to g\gamma$, and photon production from quark
fragmentation in LO QCD dijet events. The fragmentation component was modelled
by QED radiation arising from calculations of all 2 $\to$ 2 QCD processes
involving light partons (gluons and up, down and strange quarks).

A large sample of backgrounds to prompt photon and electron production was
generated with Pythia8, including all tree-level 2 $\to$ 2 QCD processes as
well as top-quark pair and weak vector-boson production, filtered at particle
level to mimic a first-level EM trigger requirement. For this sample and the
inclusive-photon samples, the A14 set of tuned parameters was used together
with the NNPDF23LO PDF set [19].

The Pythia8 sample production used the EvtGen 1.2.0 program [20] to model
$b$\- and $c$-hadron decays.

The generated events were processed through the full ATLAS detector simulation
[21] based on Geant4 [22]. The MC events were simulated with additional
interactions in the same or neighbouring bunch crossings to match the pile-up
conditions during LHC operations. The overlaid $pp$ collisions were generated
with the soft QCD processes of Pythia8 using the A3 set of tuned parameters
[23] and the NNPDF23LO PDF. Although this set of tuned parameters improves the
modelling of minimum-bias data relative to the set used previously (A2 [24]),
it overestimates by roughly 3% the hadronic activity as measured using
charged-particle tracks. Simulated events were weighted to reproduce the
distribution of the average number of interactions per bunch crossing in data,
scaled down by a factor 1.03.

Many analyses rely on MC samples generated with the ATLAS fast simulation,
which uses a parameterized response of the calorimeters [21]. Dedicated
corrections to the reconstructed energy and identification efficiencies of
electrons and photons were determined for these samples to match the
performance observed in the samples using the full simulation of the ATLAS
detector.

The response of the new reconstruction algorithm was optimized using samples
of 40 million single-electron and single-photon events simulated without pile-
up. Their transverse energy distribution covers the range from 1 GeV to 3 TeV.
Smaller samples with a flat $\left\langle\mu\right\rangle$ spectrum between 0
and 60 were also simulated to assess the performance as a function of
$\left\langle\mu\right\rangle$.

Studies presented throughout this paper using MC simulation select electrons
originating from $Z\to ee$ or $J/\psi\rightarrow ee$ decays using generator-
level information. The matching of reconstructed and generated electron is
based on the ID track [25] which can be reconstructed from the primary
electron or from secondary particles produced in a material interaction of the
primary electron or of final state radiation emitted collinearly. Similarly,
reconstructed and generator-level photons are matched based on their distance
in $\eta$–$\phi$ space.

##  4 Electron and photon reconstruction

In replacement of the sliding-window algorithm previously exploited in ATLAS
for the reconstruction of fixed-size clusters of calorimeter cells [26, 2, 1],
the offline electron and photon reconstruction has been improved to use
dynamic, variable-size clusters, called superclusters. While fixed-size
clusters naturally provide a linear energy response and good stability as a
function of pile-up, dynamic clusters change in size as needed to recover
energy from bremsstrahlung photons or from electrons from photon conversions.
The calibration techniques described in Ref. [3] exploit this advantage of the
dynamic clustering algorithm, while achieving similar linearity and stability
as for fixed-size clusters.

An electron is defined as an object consisting of a cluster built from energy
deposits in the calorimeter (supercluster) and a matched track (or tracks). A
converted photon is a cluster matched to a conversion vertex (or vertices),
and an unconverted photon is a cluster matched to neither an electron track
nor a conversion vertex. About $20\%$ of photons at low $|\eta|$ convert in
the ID, and up to about $65\%$ convert at $|\eta|\approx 2.3$.

The reconstruction of electrons and photons with $|\eta|<2.5$ proceeds as
shown in Figure 1. The algorithm first prepares the tracks and clusters it
will use. It selects clusters of energy deposits measured in topologically
connected EM and hadronic calorimeter cells [4], denoted topo-clusters,
reconstructed as described in Section 4.1. These clusters are matched to ID
tracks, which are re-fitted accounting for bremsstrahlung. The algorithm also
builds conversion vertices and matches them to the selected topo-clusters. The
electron and photon supercluster-building steps then run separately using the
matched clusters as input. After applying initial position corrections and
energy calibrations to the resulting superclusters, the supercluster-building
algorithm matches tracks to the electron superclusters and conversion vertices
to the photon superclusters. The electron and photon objects to be used for
analyses are then built, their energies are calibrated, and discriminating
variables used to separate electrons or photons from background are added.

Figure 1: Algorithm flow diagram for the electron and photon reconstruction.

The steps are described in more detail below.

###  4.1 Topo-cluster reconstruction

The topo-cluster reconstruction algorithm [26, 4] begins by forming proto-
clusters in the EM and hadronic calorimeters using a set of noise thresholds
in which the cell initiating the cluster is required to have significance
$\left|\varsigma_{\text{cell}}^{\text{EM}}\right|\geq 4$, where

$\varsigma_{\text{cell}}^{\text{EM}}=\frac{E_{\text{cell}}^{\text{EM}}}{\sigma_{\text{noise,cell}}^{\text{EM}}},$

$E_{\text{cell}}^{\text{EM}}$ is the cell energy at the EM scale444The EM
scale is the basic signal scale accounting correctly for the energy deposited
in the calorimeter by electromagnetic showers. and
$\sigma_{\text{noise,cell}}^{\text{EM}}$ is the expected cell noise. The
expected cell noise includes the known electronic noise and an estimate of the
pile-up noise corresponding to the average instantaneous luminosity expected
for Run 2. In this initial stage, cells from the presampler and the first LAr
EM calorimeter layer are excluded from initiating proto-clusters, to suppress
the formation of noise clusters. The proto-clusters then collect neighbouring
cells with significance $\left|\varsigma_{\text{cell}}^{\text{EM}}\right|\geq
2$. Each neighbour cell passing the threshold of
$\left|\varsigma_{\text{cell}}^{\text{EM}}\right|\geq 2$ becomes a seed cell
in the next iteration, collecting each of its neighbours in the proto-cluster.
If two proto-clusters contain the same cell with
$\left|\varsigma_{\text{cell}}^{\text{EM}}\right|\geq 2$ above the noise
threshold, these proto-clusters are merged. A crown of nearest-neighbour cells
is added to the cluster independently on their energy. In the presence of
negative-energy cells induced by the calorimeter noise, the algorithm uses
$\left|\varsigma_{\text{cell}}^{\text{EM}}\right|$ instead of
$\varsigma_{\text{cell}}^{\text{EM}}$ to avoid biasing the cluster energy
upwards, which would happen if only positive-energy cells were used. This set
of thresholds is commonly known as ‘4-2-0’ topo-cluster reconstruction. Proto-
clusters with two or more local maxima are split into separate clusters; a
cell is considered a local maximum when it has
$E_{\text{cell}}^{\text{EM}}>500\,\text{Me\kern-1.00006ptV}$, at least four
neighbours, and when none of the neighbours has a larger signal.

Electron and photon reconstruction starts from the topo-clusters but only uses
the energy from cells in the EM calorimeter, except in the transition region
of $1.37<|\eta|<1.63$, where the energy measured in the presampler and the
scintillator between the calorimeter cryostats is also added. This is referred
to as the EM energy of the cluster, and the EM fraction ($f_{\text{EM}}$) is
the ratio of the EM energy to the total cluster energy. Only clusters with EM
energy greater than $400\,\text{Me\kern-1.00006ptV}$ are considered. The
distribution of $f_{\text{EM}}$ is shown in Figure 2(a) and the electron
reconstruction efficiency for various cuts on $f_{\text{EM}}$ is shown in
Figure 2(b), for electron clusters which have been simulated with
$\left\langle\mu\right\rangle=0$, and for pile-up clusters. A preselection
requirement of $f_{\text{EM}}>0.5$ was chosen for the initial topo-clusters,
as it rejects $\sim 60\%$ of pile-up clusters without affecting the efficiency
for selecting true electron topo-clusters.555In the transition region, some
topo-clusters are also selected as EM clusters, even if they fail the
requirement on $f_{\text{EM}}$, when they satisfy
$E_{\text{T}}>1\,\text{Ge\kern-1.00006ptV}$, in order to increase the
reconstruction efficiency in that region. These clusters are referred to as EM
topo-clusters in the rest of this paper.

((a))

((b))

Figure 2: (a) Distribution of $f_{\text{EM}}$ and (b) reconstruction
efficiency as a function of the $f_{\text{EM}}$ selection cut for simulated
true electron (black) and pile-up (red) clusters.

###  4.2 Track reconstruction, track–cluster matching, and photon conversion
reconstruction

Track reconstruction for electrons is unchanged with respect to Ref. [2, 1]. A
summary of the changes applied for photons is given below.

Standard track-pattern reconstruction [27] is first performed everywhere in
the inner detector. However, fixed-size clusters in the calorimeter that have
a longitudinal and lateral shower profile compatible with that of an EM shower
are used to create regions-of-interest (ROIs). If the standard pattern
recognition fails for a silicon track seed (a set of silicon detector hits
used to start a track) within an ROI, a modified pattern recognition algorithm
based on a Kalman filter formalism [28] is used, allowing for up to 30% energy
loss at each material intersection. Track candidates are then fitted with the
global $\chi^{2}$ fitter [29], allowing for additional energy loss when the
standard track fit fails. Additionally, tracks with silicon hits loosely
matched666The match must be within $|\Delta\eta|<0.05$ and
$-0.20<q\cdot(\phi_{\mathrm{track}}-\phi_{\mathrm{clus}})<0.05$ when using the
track energy to extrapolate from the last inner detector hit, or
$|\Delta\eta|<0.05$ and
$-0.10<q\cdot(\phi_{\mathrm{track}}-\phi_{\mathrm{clus}})<0.05$ when using the
cluster energy to extrapolate from the track perigee; $q$ refers to the
reconstructed charge of the track. to fixed-size clusters are re-fitted using
a Gaussian sum filter (GSF) algorithm [30], a non-linear generalization of the
Kalman filter, for improved track parameter estimation.

The loosely matched, re-fitted tracks are then matched to the EM topo-clusters
described above, extrapolating the track from the perigee to the second layer
of the calorimeter, and using either the measured track momentum or rescaling
the magnitude of the momentum to match the cluster energy. The momentum
rescaling is performed to improve track–cluster matching for electron
candidates with significant energy loss due to bremsstrahlung radiation in the
tracker. A track is considered matched if, with either momentum magnitude,
$|\Delta\eta|<0.05$ and
$-0.10<q\cdot(\phi_{\mathrm{track}}-\phi_{\mathrm{clus}})<0.05$, where $q$
refers to the reconstructed charge of the track. The requirement on
$q\cdot(\phi_{\mathrm{track}}-\phi_{\mathrm{clus}})$ is asymmetric because
tracks sometimes miss some energy from radiated photons that clusters measure.

If multiple tracks are matched to a cluster, they are ranked as follows.
Tracks with hits in the pixel detector are preferred, then tracks with hits in
the SCT but not in the pixel detector. Within each category, tracks with a
better $\Delta R$ match to the cluster in the second layer of the calorimeter
are preferred, unless the differences are small (less than 0.01). The
extrapolation of the track through the calorimeter is done first with the
track momentum rescaled to the cluster energy and successively without
rescaling. If both the first and the second extrapolation result in small
$\Delta R$ differences, the track with more pixel hits is preferred, giving an
extra weight to a hit in the innermost layer. The highest-ranked track is used
to define the reconstructed electron properties.

The photon conversion reconstruction is largely unchanged from the method
described in Ref. [1]. Tracks loosely matched to fixed-size clusters serve as
input to the reconstruction of the conversion vertex. Both tracks with silicon
hits (denoted Si tracks) and tracks reconstructed only in the TRT (denoted TRT
tracks) are used for the conversion reconstruction. Two-track conversion
vertices are reconstructed from two opposite-charge tracks forming a vertex
consistent with that of a massless particle, while single-track vertices are
essentially tracks without hits in the innermost sensitive layers. To increase
the converted-photon purity, the tracks used to build conversion vertices must
have a high probability to be electron tracks as determined by the TRT [31].
The requirement is loose for Si tracks but tight for TRT tracks used to build
double-track conversions, and even tighter for tracks used to build single-
track conversions.

Changes were made with respect to the reconstruction software described in
Ref. [1], both to improve the reconstruction efficiency of double-track Si
conversions (conversions reconstructed with two Si tracks), and to reduce the
fraction of unconverted photons mistakenly reconstructed as single- or double-
track TRT conversions (conversions reconstructed with one or two TRT tracks).
The efficiency for double-track Si conversions was improved by modifying the
tracking ambiguity processor, which determines which track seeds are retained
to reconstruct tracks. For double-track conversion topologies, the two tracks
are expected to be close to each other, parallel, and potentially to have
shared hits, so that frequently only one track is reconstructed. The
optimization in the ambiguity processor results in the recovery of the second
track that was previously discarded. Overall, these modifications result in a
$2$–$4\%$ improvement in efficiency for double-track Si conversions, with
larger improvements of up to $9\%$ for photons with conversion radii larger
than 200 mm. In addition to reconstructing the second track of what would
otherwise have been single-track Si conversions, the overall conversion
reconstruction efficiency is improved by about $1\%$ by reducing the fraction
of low-radius converted photons that are only reconstructed as electrons.

To reduce the fraction of unconverted photons reconstructed as double- or
single-track TRT conversions, requirements on the TRT tracks were tightened.
The tracks are required to have at least $30\%$ precision hits, where a
precision hit is defined as a hit with a track-to-wire distance within 2.5
times its uncertainty [32]. In addition, the requirement on the probability of
a track to correspond to an electron, as determined by the TRT, was tightened
to 0.75 for tracks used in double-track TRT conversions and to 0.85 for tracks
used in single-track TRT conversions, compared with the previous requirement
of 0.7 for tracks used in both conversion types. The fraction of unconverted
photons erroneously reconstructed as converted photons is below $5\%$ for
events with $\left\langle\mu\right\rangle<60$, improving by a factor of two
compared to the previous algorithm.

The conversion vertices are then matched to the EM topo-clusters.777If the
conversion vertex has tracks with silicon hits, a conversion vertex is
considered matched if, after extrapolation, the tracks match the cluster to
within $|\Delta\eta|<0.05$ and $|\Delta\phi|<0.05$. If the conversion vertex
is made of only TRT tracks, then if the first track is in the TRT barrel, a
match requires $|\Delta\eta|<0.35$ and $|\Delta\phi|<0.02$, and if the first
track is in the TRT endcap, a match requires $|\Delta\eta|<0.2$ and
$|\Delta\phi|<0.02$. If there are multiple conversion vertices matched to a
cluster, double-track conversions with two silicon tracks are preferred over
other double-track conversions, followed by single-track conversions. Within
each category, the vertex with the smallest conversion radius is preferred.

###  4.3 Supercluster reconstruction

The reconstruction of electron and photon superclusters proceeds
independently, each in two stages: in the first stage, EM topo-clusters are
tested for use as seed cluster candidates, which form the basis of
superclusters; in the second stage, EM topo-clusters near the seed candidates
are identified as satellite cluster candidates, which may emerge from
bremsstrahlung radiation or topo-cluster splitting. Satellite clusters are
added to the seed candidates to form the final superclusters if they satisfy
the necessary selection criteria.

The steps to build superclusters proceed as follows. The initial list of EM
topo-clusters is sorted according to descending $E_{\text{T}}$, calculated
using the EM energy.888An exception to the $E_{\text{T}}$ ordering is made for
clusters in the transition region that fail the standard selection but pass a
looser selection; these are added at the end. The clusters are tested one by
one in the sort order for use as seed clusters. For a cluster to become an
electron supercluster seed, it is required to have a minimum $E_{\text{T}}$ of
1 GeV and must be matched to a track with at least four hits in the silicon
tracking detectors. For photon reconstruction, a cluster must have
$E_{\text{T}}$ greater than 1.5 GeV to qualify as a supercluster seed, with no
requirement made on any track or conversion vertex matching. A cluster cannot
be used as a seed cluster if it has already been added as a satellite cluster
to another seed cluster.

If a cluster meets the seed cluster requirements, the algorithm attempts to
find satellite clusters, using the process summarized in Figure 3.

Figure 3: Diagram of the superclustering algorithm for electrons and photons.
Seed clusters are shown in red, satellite clusters in blue.

For both electrons and photons, a cluster is considered a satellite if it
falls within a window of $\Delta\eta\times\Delta\phi=0.075\times 0.125$ around
the seed cluster barycentre, as these cases tend to represent secondary EM
showers originating from the same initial electron or photon. For electrons, a
cluster is also considered a satellite if it is within a window of
$\Delta\eta\times\Delta\phi=0.125\times 0.300$ around the seed cluster
barycentre, and its ‘best-matched’ track is also the best-matched track for
the seed cluster. For photons with conversion vertices made up only of tracks
containing silicon hits, a cluster is added as a satellite if its best-matched
(electron) track belongs to the conversion vertex matched to the seed cluster.
These steps rely on tracking information to discriminate distant radiative
photons or conversion electrons from pile-up noise or other unrelated
clusters.

The seed clusters with their associated satellite clusters are called
superclusters. The final step in the supercluster-building algorithm is to
assign calorimeter cells to a given supercluster. Only cells from the
presampler and the first three LAr calorimeter layers are considered, except
in the transition region of $1.4<|\eta|<1.6$, where the energy measured in the
scintillator between the calorimeter cryostats is also added. To limit the
superclusters’ sensitivity to pile-up noise, the size of each constituent
topo-cluster is restricted to a maximal width of 0.075 or 0.125 in the $\eta$
direction in the barrel or endcap region, respectively. Because the magnetic
field in the ID is parallel to the beam-line, interactions between the
electron or photon and detector material generally cause the EM shower to
spread in the $\phi$ direction, so the restriction in $\eta$ still generally
allows the electron or photon energy to be captured. No restriction is applied
in the $\phi$-direction.

###  4.4 Creation of electrons and photons for analysis

After the electron and photon superclusters are built, an initial energy
calibration and position correction is applied to them, and tracks are matched
to electron superclusters and conversion vertices to photon superclusters. The
matching is performed the same way that the matching to EM topo-clusters was
performed, but using the superclusters instead. Creating the analysis-level
electrons and photons follows. Because electron and photon superclusters are
built independently, a given seed cluster can produce both an electron and a
photon. In such cases, the procedure presented in Figure 4 is applied. The
purpose is that if a particular object can be easily identified only as a
photon (a cluster with no good track attached) or only as an electron (a
cluster with a good track attached and no good photon conversion vertex), then
only a photon or an electron object is created for analysis; otherwise, both
an electron and a photon object are created. Furthermore, these cases are
marked explicitly as ambiguous, allowing the final classification of these
objects to be determined based upon the specific requirements of each
analysis.

Figure 4: Flowchart showing the logic of the ambiguity resolution for
particles initially reconstructed both as electrons and photons. An ‘innermost
hit’ is a hit in the functioning pixel nearest to the beam-line along the
track trajectory, $E/p$ is the ratio of the supercluster energy to the
measured momentum of the matched track, $R_{\mathrm{conv}}$ is the radial
position of the conversion vertex, and $R_{\mathrm{firstHit}}$ is the smallest
radial position of a hit in the track or tracks that make a conversion vertex.

Because the energy calibration depends on matched tracks and conversion
vertices, and the initial supercluster calibration is performed before the
final track and conversion matching, the energies of the electrons and photons
are recalibrated, following the procedure described in Ref. [3].

Subsequently, shower shape and other discriminating variables [2, 1] are
calculated for electron and photon identification. A list is given in Table 1,
along with an indication if they are used for electron or photon
identification. The lateral shower shapes are based on the position of the
most energetic cell, so they are independent of the clustering used, provided
the same most energetic cell is included in the clusters. More information
about the variables and the identification methods are given in Sections 6 and
7 for electrons and photons, respectively.

Table 1: Discriminating variables used for electron and photon identification. The usage column indicates if the variables are used for the identification of electrons, photons, or both. For variables calculated in the first EM layer, if the cluster has more than one cell in the $\phi$ direction at a given $\eta$, the two cells closest in $\phi$ to the cluster barycentre are merged and the definitions below are given in terms of this merged cell. The sign of $d_{0}$ is conventionally chosen such that the coordinates of the perigee in the transverse plane are $(x_{0},y_{0})=(-d_{0}\sin\phi,d_{0}\cos\phi)$, where $\phi$ is the azimuthal angle of the track momentum at the perigee.  Category |  Description | Name | Usage
---|---|---|---
Hadronic leakage |  Ratio of $E_{\mathrm{T}}$ in the first layer of the hadronic calorimeter to $E_{\mathrm{T}}$ of the EM cluster (used over the ranges $|\eta|<0.8$ and $|\eta|>1.37$) | $R_{\mathrm{had_{1}}}$ | $e/\gamma$
|  Ratio of $E_{\mathrm{T}}$ in the hadronic calorimeter to $E_{\mathrm{T}}$ of the EM cluster (used over the range $0.8<|\eta|<1.37$) | $R_{\mathrm{had}}$ | $e/\gamma$
EM third layer |  Ratio of the energy in the third layer to the total energy in the EM calorimeter | $f_{3}$ | $e$
EM second layer |  Ratio of the sum of the energies of the cells contained in a $3\times 7$ $\eta\times\phi$ rectangle (measured in cell units) to the sum of the cell energies in a $7\times 7$ rectangle, both centred around the most energetic cell | $R_{\eta}$ | $e/\gamma$
|  Lateral shower width, $\sqrt{(\Sigma E_{i}\eta_{i}^{2})/(\Sigma E_{i})-((\Sigma E_{i}\eta_{i})/(\Sigma E_{i}))^{2}}$, where $E_{i}$ is the energy and $\eta_{i}$ is the pseudorapidity of cell $i$ and the sum is calculated within a window of $3\times 5$ cells | $w_{\eta_{2}}$ | $e/\gamma$
|  Ratio of the sum of the energies of the cells contained in a $3\times 3$ $\eta\times\phi$ rectangle (measured in cell units) to the sum of the cell energies in a $3\times 7$ rectangle, both centred around the most energetic cell | $R_{\phi}$ | $e/\gamma$
EM first layer |  Total lateral shower width, $\sqrt{(\Sigma E_{i}(i-i_{\mathrm{max}})^{2})/(\Sigma E_{i})}$, where $i$ runs over all cells in a window of $\Delta\eta\approx 0.0625$ and $i_{\textrm{max}}$ is the index of the highest-energy cell | $w_{s\,\mathrm{tot}}$ | $e/\gamma$
|  Lateral shower width, $\sqrt{(\Sigma E_{i}(i-i_{\textrm{max}})^{2})/(\Sigma E_{i})}$, where $i$ runs over all cells in a window of 3 cells around the highest-energy cell | $w_{s\,3}$ | $\gamma$
|  Energy fraction outside core of three central cells, within seven cells | $f_{\mathrm{side}}$ | $\gamma$
|  Difference between the energy of the cell associated with the second maximum, and the energy reconstructed in the cell with the smallest value found between the first and second maxima | $\Delta{}E_{s}$ | $\gamma$
|  Ratio of the energy difference between the maximum energy deposit and the energy deposit in a secondary maximum in the cluster to the sum of these energies | $E_{\mathrm{ratio}}$ | $e/\gamma$
|  Ratio of the energy measured in the first layer of the electromagnetic calorimeter to the total energy of the EM cluster | $f_{1}$ | $e/\gamma$
Track conditions |  Number of hits in the innermost pixel layer | $n_{\mathrm{innermost}}$ | $e$
|  Number of hits in the pixel detector | $n_{\mathrm{Pixel}}$ | $e$
|  Total number of hits in the pixel and SCT detectors | $n_{\mathrm{Si}}$ | $e$
|  Transverse impact parameter relative to the beam-line | $d_{0}$ | $e$
|  Significance of transverse impact parameter defined as the ratio of $d_{0}$ to its uncertainty |  |$d_{0}/\sigma(d_{0})$| | $e$
|  Momentum lost by the track between the perigee and the last measurement point divided by the momentum at perigee | $\Delta p/p$ | $e$
|  Likelihood probability based on transition radiation in the TRT | eProbabilityHT | $e$
Track–cluster matching |  $\Delta\eta$ between the cluster position in the first layer of the EM calorimeter and the extrapolated track | $\Delta\eta_{1}$ | $e$
|  $\Delta\phi$ between the cluster position in the second layer of the EM calorimeter and the momentum-rescaled track, extrapolated from the perigee, times the charge $q$ | $\Delta\phi_{\text{res}}$ | $e$
|  Ratio of the cluster energy to the measured track momentum | $E/p$ | $e$

###  4.5 Performance

Figure 5 shows the reconstruction efficiencies for electrons. The
reconstruction efficiency at high $p_{\text{T}}$ approaches the tracking
efficiency, as expected. One interesting feature, however, is the difference
between the efficiency to reconstruct the cluster and track (green triangles)
and the efficiency to reconstruct an electron (purple inverted triangles) at
lower $p_{\text{T}}$. The reason for this is that tracks with silicon hits are
considered for matching to superclusters only if they have had a GSF re-fit
performed. The fixed-size clusters used for choosing the tracks on which the
GSF re-fit is performed introduce an $E_{\text{T}}$ threshold, which is the
source of this inefficiency. To alleviate this feature, the EM topo-clusters
as defined in Section 4.1 could be used to seed the GSF fit.

Figure 5: The cluster, track, cluster and track, and electron reconstruction
efficiencies as a function of the generated electron $E_{\text{T}}$.

The top plot in Figure 6 shows the reconstruction efficiency for converted
photons as a function of the true $E_{\text{T}}$ of the simulated photon for
the previous version of the reconstruction software, described in Ref. [1],
and the current version, described in Section 4.2, along with the
contributions of the different conversion types. For a photon to be classified
as a true converted photon, the true radius of the conversion must be smaller
than $800\,\mathrm{mm}$. Only simulated photons with transverse energy greater
than 20 GeV are considered. The simulated photons are distributed uniformly in
$\left|\eta\right|$, with most of the photons having a transverse momentum
smaller than 200 GeV. The bottom left plot of Figure 6 shows the
reconstruction efficiency for converted photons along with the contributions
of the different conversion types as a function of
$\left\langle\mu\right\rangle$. The improvement (see Section 4.2) in the
reconstruction efficiency for double-track Si conversions and the
corresponding reduction of single-track Si conversions is clearly visible in
those two plots. A slight reduction in double- and single-track TRT conversion
efficiency is also visible, with the purpose of significantly reducing the
probability for true unconverted photons to be reconstructed as TRT
conversions, as can be seen in the bottom right plot of Figure 6. The
probability for true unconverted photons to be reconstructed as Si conversions
is negligible in comparison.

Figure 6: The top plot shows the converted photon reconstruction efficiency
and contributions of the different conversion types as a function of
$E_{\text{T}}^{\text{true}}$, averaged over $\left\langle\mu\right\rangle$ for
a uniform $\left\langle\mu\right\rangle$ distribution between 0 and 60. On the
bottom, efficiency of the reconstruction of converted photons and
contributions of the different conversion types (left), and the probability of
an unconverted photon to be mistakenly reconstructed as a converted photon and
contributions of the different conversions types (right), both as a function
of $\left\langle\mu\right\rangle$.

An important reason for using superclusters is the improved energy resolution
that superclusters provide by collecting more of the deposited energy. The
peaks of the energy response, $E_{\text{calib}}/E_{\text{true}}$, where
$E_{\text{true}}$ is the true energy of the simulated particle prior to any
detector simulation, and $E_{\text{calib}}$ is the calibrated reconstructed
energy, do not deviate from one by more than $0.5\%$ for the different
particles. To quantify the width (resolution) of the energy response, the
_effective interquartile range_ is used, defined as

$\text{IQE}=\frac{Q_{3}-Q_{1}}{1.349},$

where $Q_{1}$ and $Q_{3}$ are the first and third quartiles of the
distribution of $E_{\text{calib}}/E_{\text{true}}$, and the normalization
factor is chosen such that the IQE of a Gaussian distribution would equal its
standard deviation.

Comparisons of the resolutions of the calibrated energy response of simulated
single electrons, converted photons, and unconverted photons, built using
fixed-size clusters and superclusters, are given in Figure 7. In particular,
Figure 7 shows the IQE of the two approaches in different regions of
$|\eta_{\text{true}}|$ and $E_{\text{T}}^{\text{true}}$. The reconstructed
electrons and photons in these distributions are required to correspond to
true primary electrons and photons and to satisfy loose identification
requirements. After calibration, the supercluster algorithm shows a
significant improvement in resolution compared with the sliding-window
algorithm for electrons. In absence of pile-up, an improvement in resolution
of up to $20$–$30\%$ is found in some bins in the endcap region of the
detector, as well as in the central region for low-$E_{\text{T}}$ electrons.

Figure 7: Calibrated energy response resolution, expressed in terms of IQE,
for electrons (top), converted photons (middle), and unconverted photons
(bottom) simulated with $\left\langle\mu\right\rangle=0$. Two representative
pseudorapidity ranges are shown. The response resolution for fixed-size
clusters based on the sliding window method is shown in dashed red, while the
supercluster-based response resolution is shown in full blue. For all plots,
the bottom panel shows the ratios between the IQE obtained using the
supercluster reconstruction and using the sliding window method.

Similarly, a large improvement in the resolution is seen for converted
photons, over $30\%$ in a few bins. For unconverted photons, the overall
change in performance is small, due to the generally narrower shower width.
However, some improvement is observed for high $E_{\text{T}}$ bins in the
endcap region. In presence of pile-up, the improvement in resolution still
reaches 15 to 20%, depending on $\eta$ and $E_{\text{T}}$.

An important consideration is the performance of the supercluster
reconstruction at different pile-up levels. Figure 8 shows the calibrated
energy response resolution at different $\left\langle\mu\right\rangle$ levels
for electrons, converted photons, and unconverted photons, in two $|\eta|$
regions.

Figure 8: Calibrated energy response resolution, expressed in terms of IQE,
for simulated single electrons (top), converted photons (middle), and
unconverted photons (bottom) at different $\left\langle\mu\right\rangle$
levels. The plots on the left are for the central calorimeter, while the plots
on the right are for the endcaps. The response for fixed-size clusters based
on the sliding-window algorithm is shown in dashed red, while the
supercluster-based response is shown in full blue. The supercluster-based
energy response resolution for $\left\langle\mu\right\rangle=0$ is also given
as a black dashed line for comparison.

The topo-cluster noise thresholds for the ‘high-$\mu$’ data sample were tuned
for $\left\langle\mu\right\rangle\sim 40$. For electrons and converted
photons, the IQE of the supercluster reconstruction generally remains better,
although the supercluster-based response is more sensitive to pile-up, as seen
by its larger slope as a function of $\left\langle\mu\right\rangle$. Part of
the reason is that the topo-cluster noise thresholds remain fixed even though
$\left\langle\mu\right\rangle$ changes. For unconverted photons, however, the
supercluster reconstruction shows worse IQE for
$\left\langle\mu\right\rangle>15$. This degradation could be mitigated in
particular by limiting the growth of the size of the clusters.

##  5 Electron and photon energy calibration

The energy calibration of electrons and photons closely follows the procedure
used in Ref. [3], updated for the new energy reconstruction described in
Section 4. The energy resolution of the electron or photon is optimized using
a multivariate regression algorithm based on the properties of the shower
development in the EM calorimeter. The adjustment of the absolute energy scale
using $Z\to ee$ decays is updated, together with systematic uncertainties
related to pile-up and material effects. The universality of the energy scale
is verified using radiative $Z$-boson decays.

###  5.1 Energy scale and resolution measurements with $Z\to ee$ decays

The difference in energy scale between data and simulation is defined as
$\alpha_{i}$, where $i$ corresponds to different regions in $\eta$. Similarly,
the mismodelling of the energy resolution is parameterised as an
$\eta$-dependent additional constant term, $c_{i}$. The corresponding energy
scale correction is applied to the data, and the resolution correction is
applied to the simulation as follows:

$E^{\text{data,corr}}=E^{\text{data}}/\left(1+\alpha_{i}\right),\qquad\left(\frac{\sigma_{E}}{E}\right)^{\text{MC,corr}}=\left(\frac{\sigma_{E}}{E}\right)^{\text{MC}}\oplus
c_{i}\,,$

where the symbol $\oplus$ denotes a sum in quadrature.

For samples of $Z\to ee$ decays, with electrons reconstructed in $\eta$
regions $i$ and $j$, the effect of the energy scale correction on the
dielectron invariant mass is given in first order by
$m_{ij}^{\mathrm{data,corr}}=m_{ij}^{\mathrm{data}}/(1+\alpha_{ij})$, with
$\alpha_{ij}=(\alpha_{i}+\alpha_{j})/2$. Similarly, the difference in the
simulated mass resolution is given by
$({\sigma_{m}}/m)_{ij}^{\mathrm{MC,corr}}=({\sigma_{m}}/m)_{ij}^{\mathrm{MC}}\oplus
c_{ij}$, with $c_{ij}=(c_{i}\oplus c_{j})/2$. The values of $\alpha_{ij}$ and
$c_{ij}$ are determined by optimizing the agreement between the invariant mass
distributions in data and simulation, separately for each $(i,j)$ category.
The $\alpha_{i}$ and $c_{i}$ parameters are then extracted from a simultaneous
fit of all categories.

Two methods are used for this comparison and the difference is taken as a
systematic uncertainty. In the first method, the best estimates of
$\alpha_{ij}$ and $c_{ij}$ are found by minimizing the $\chi^{2}$ of the
difference between data and simulation templates. The templates are created by
shifting the mass scale in simulation by $\alpha_{ij}$ and by applying an
extra resolution contribution of $c_{ij}$. In the second method, used as a
cross-check, a sum of three Gaussian functions is fitted to the data and
simulated invariant mass distributions in each $(i,j)$ region; the
$\alpha_{i}$ and $c_{i}$ are extracted from the differences, between data and
simulation, of the means and widths of the fitted distributions.

Figures 9 (a) and (b) show the results of $\alpha_{i}$ and $c_{i}$ derived in
68 and 24 $\eta$ intervals, respectively, separately for 2015, 2016 and 2017.
The difference in $\alpha_{i}$ for the different years is mainly due to two
effects: variations of the LAr temperature, and the increase of the
instantaneous luminosity. The former effect induces a variation in the
charge/energy collection, affecting the energy response by about –2%/K [33].
The latter implies an increased amount of deposited energy in the liquid-argon
gap that creates a current in the high-voltage lines, reducing the high
voltage effectively applied to the gap and introducing a variation of the
response of up to 0.1$\%$ in the endcap region. A prediction of the different
effects that can impact the results is presented in Ref. [3]. Given the small
size of the observed dependence, well within 0.3%, dedicated energy scale
corrections for each data taking year provide an adequate stability of the
energy measurement.

For the constant term corrections $c_{i}$, a dependence on the pile-up level
is observed through the different values obtained for 2015 to 2017 data; this
is addressed in Section 5.2. A weighted average of the $c_{i}$ values for the
different years is applied in the analyses of the complete dataset. The
additional constant term of the energy resolution is typically less than 1$\%$
in most of the barrel and between 1$\%$ and 2$\%$ in the endcap.

((a))

((b))

Figure 9: (a) Energy scale factors $\alpha_{i}$ and (b) additional constant
term $c_{i}$, as a function of $\eta$. The shaded areas correspond to the
statistical uncertainties. The bottom panels show the differences between (a)
$\alpha_{i}$ and (b) $c_{i}$ measured in a given data-taking period and the
measurements using 2017 data.

Figure 10(a) shows the invariant mass distribution for $Z\to ee$ candidates
for data and simulation after the energy scale correction has been applied to
the data and the resolution correction to the simulation. No background
contamination is taken into account in this comparison, but it is expected to
be at the level of 1$\%$ over the full shown mass range. The uncertainty band
corresponds to the propagation of the uncertainties in the $\alpha_{i}$ and
$c_{i}$ factors, as discussed in Ref. [3]. Within these uncertainties, the
data and simulation are in fair agreement. Figure 10(b) shows the stability of
the reconstructed peak position of the dielectron mass distribution as a
function of the average number of interactions per bunch crossing for the data
collected in 2015, 2016 and 2017. The variation of the energy scale with
$\left\langle\mu\right\rangle$ is well below the 0.1$\%$ level in the data.
The small increase of energy with $\left\langle\mu\right\rangle$ observed in
data is consistent with the MC expectation and is related to the new dynamical
clustering used for the energy measurement, as introduced in Section 4.

((a))

((b))

Figure 10: (a) Comparison between data and simulation of the invariant mass
distribution of the two electrons in the selected $Z\to ee$ candidates, after
the calibration and resolution corrections are applied. The total number of
events in the simulation is normalized to the data. The uncertainty band of
the bottom plot represents the impact of the uncertainties in the calibration
and resolution correction factors. (b) Relative variation of the peak position
of the reconstructed dielectron mass distribution in $Z\to ee$ events as a
function of the average number of interactions per bunch crossing. The error
bars represent the statistical uncertainties.

###  5.2 Systematic uncertainties

Several systematic uncertainties impact the measurement of the energy of
electrons or photons in a way that depends on their transverse energy and
pseudorapidity. These uncertainties were evaluated in Ref. [3]. The amount of
passive material located between the interaction point and the EM calorimeter
is measured using the ratio of the energies deposited by electrons from
$Z$-boson decays in the first and second layer of the EM calorimeter
($E_{1/2}$). The sensitivity of the calibrated energy to the detector material
was re-evaluated to reflect the changes in the reconstruction described above.
The systematic uncertainty due to the material description of the innermost
pixel detector layer and the services of the pixel detector were updated with
regards to Ref. [3] using a more accurate description of these systems in the
simulation [34].

The dependence of the constant term on the amount of pile-up, observed in
Figure 9(b), is explained by the larger pile-up noise predicted by the
simulation, compared with that observed in the data. Figure 11 shows an
example of the evolution of the second central moment of the cell energy
deposit in data and simulation as a function of $\mu$ for the second layer and
$1.0<|\eta|<1.1$ assuming $\phi$ symmetry. The contribution of the pile-up
noise varies linearly with $\sqrt{\mu}$, while the electronic noise remains
constant. An average difference of 10$\%$ between the pile-up noise in data
and simulation is observed. This mismodelling is absorbed in the $c_{i}$
parameters for electrons of $E_{\text{T}}$ $\sim 40$ GeV, the average
$E_{\text{T}}$ value for electrons from $Z\to ee$ decays used to derive the
energy corrections. The two methods used for the extraction of the energy
resolution corrections, described in Section 5.1, are compared and the full
difference is taken as an uncertainty in the energy resolution. This
uncertainty amounts to up to $0.2\%$ in the barrel and is due to the different
sensitivities of the two methods to the pile-up. The impact of a 10$\%$
difference in pile-up noise at a different energy is propagated to the energy
resolution uncertainty relying on the predicted dependence of the pile-up
noise effect as a function of the energy. For electrons and photons in the
transverse energy range 30–60 GeV, the uncertainty in the energy resolution is
of the order of $5\%$ to $10\%$. In order to mimic the pile-up noise
estimation in the simulation, the pile-up rescaling factor, described in
Section 3, is changed from 1.03 to 1.2 for the 48b filling scheme and to 1.3
for the 8b4e filling scheme. A systematic uncertainty in the energy scale is
derived comparing the results obtained with the two pile-up reweighting
factors; it is of the order of $2\times 10^{-4}$ in the barrel and of $5\times
10^{-4}$ in the endcap. The total systematic uncertainty in the energy scale
amounts to $4\times 10^{-4}$ in the barrel and $2\times 10^{-3}$ in the
endcap.

Figure 11: Evolution of the squared noise as a function of
$\left\langle\mu\right\rangle$ in data (red points) and simulation (blue
triangles), for one particular $\eta$ bin in the second layer of the EM
calorimeter. The lines show the result of linear fits to the points for
$\left\langle\mu\right\rangle\in[15,45]$ and the dotted lines show the
extrapolation to higher $\left\langle\mu\right\rangle$.

###  5.3 Validation of the photon energy scale with
$Z\rightarrow\ell\ell\gamma$ decays

The energy scale corrections extracted from $Z\to ee$ decays, as described in
Section 5.1, are applied to correct the photon energy scale. A data-driven
validation of the photon energy scale corrections is performed using radiative
decays of the $Z$ boson, probing mainly the low-energy region. Residual energy
scale factors for photons, $\Delta\alpha$, are derived by comparing the mass
distribution of the $\ell\ell\gamma$ system in data and simulation after
applying the $Z$-based energy scale corrections. The mass distribution of the
$\ell\ell\gamma$ system in the simulation is modified by applying
$\Delta\alpha$ to the photon energy and the value of $\Delta\alpha$ that
minimizes the $\chi^{2}$ comparison between the data and the simulation is
extracted. If the energy calibration is correct, $\Delta\alpha$ should be
consistent with zero within the uncertainties described in Section 5.2. An
alternative method based on a binned extended maximum-likelihood fit with an
analytic function to describe the mass distribution is used, and gives
consistent results. The electron and muon channels are analysed separately. In
the electron channel, the electron energy scale uncertainty is accounted for
in the determination of the residual photon energy scale. The electron and
muon results are found to agree, and are combined. Figure 12 shows the
measured $\Delta\alpha$ as a function of $E_{\text{T}}$ and $|\eta|$,
separately for converted and unconverted photons. The dominant sources of
uncertainty in the extrapolation to photons of the energy corrections derived
in $Z\to ee$ decays are related to the amount of passive material in front of
the EM calorimeter, and to the intercalibration of the calorimeter layers. The
value of $\Delta\alpha$ is consistent with zero within about two standard
deviations at most.

Figure 12: Residual photon energy scale factors, $\Delta\alpha$, for
unconverted (top) and converted (bottom) photons as a function of the photon
transverse energy $E_{\text{T}}$ (left) and pseudorapidity $|\eta|$ (right),
respectively. The points show the measurement with its total uncertainty and
the band represents the full energy calibration uncertainty for photons from
$Z\rightarrow\ell\ell\gamma$ decays.

###  5.4 Energy scale and resolution corrections in low-pile-up data

Special data with low pile-up were collected in 2017 at 13 TeV, as described
in Section 3. Energy scale factors are derived for this sample using the
baseline method, described in Section 5.1. The measurement is done in 24
$\eta$ regions given the small size of the sample.

An alternative approach, used for validation, consists of measuring the energy
scale factors using high-pile-up data and extrapolating the results to the
low-pile-up conditions. Two main effects are considered in the extrapolation,
namely the explicit dependence of the energy corrections on
$\left\langle\mu\right\rangle$, and differences between the clustering
thresholds used for the two samples; other effects are sub-leading and are
treated as systematic uncertainties.

To evaluate the first effect, the high-pile-up energy scale corrections are
measured in five intervals of $\left\langle\mu\right\rangle$ in the range
$20<\left\langle\mu\right\rangle<60$, in each of the 24 $\eta$ regions
considered for the low-pile-up sample. The results are parameterized using a
linear function, which is extrapolated to $\left\langle\mu\right\rangle=2$.
Over this range, the energy correction is found to vary by about 0.01% in the
barrel, and by about 0.1% in the endcap. The statistical uncertainty in the
extrapolation is about 0.05% in each $\eta$ region. The procedure is
illustrated in Figure 13, for representative $\eta$ regions in the barrel and
in the endcap.

Figure 13: Examples of the energy scale extrapolation from high pile-up to low
pile-up in the barrel (left) and endcap (right). The blue points show the
energy scale factors $\alpha$ for the high-pile-up dataset as a function of
$\left\langle\mu\right\rangle$, the black lines show the extrapolation to
$\left\langle\mu\right\rangle\sim 2$ using a linear function and five
intervals of $\left\langle\mu\right\rangle$, the band represents the
uncertainty in the extrapolation. The extrapolation results are compared with
the energy scale factors extracted from the low-pile-up dataset, represented
by the red point.

Secondly, as described in Section 4, the low-pile-up data were reconstructed
with topo-cluster noise thresholds corresponding to $\mu=0$, while the
standard runs used thresholds corresponding to $\mu=40$. This results in an
increased cluster size and enhanced energy response for the low-pile-up
samples. The difference between the enhancements in data and simulation is
measured using $Z$-boson decays, and a correction applied. The correction
amounts to about $2\times 10^{-3}$ in the barrel and $4\times 10^{-3}$ in the
endcap, with a typical uncertainty of $3\times 10^{-4}$.

Figure 14(a) shows the comparison between the energy scale factors derived
from low-pile-up data and extrapolated from high-pile-up data after correcting
for the noise threshold effect. The observed difference is of the order of
$0.1\%$ in the barrel region and increases to $0.5\%$ in the endcap region.

Different systematic uncertainties were considered for the extrapolation
approach. In addition to the systematic uncertainties in high-pile-up data
discussed in Section 5.2, systematic uncertainties related to the functional
form chosen for the extrapolation or the number of $\mu$ intervals considered
were evaluated and are of the order of a few $10^{-4}$. The changes of the LAr
temperature, in the absence of collisions, between the low-pile-up and high-
pile-up data-taking periods, was found to induce a variation of the energy
scale by 0.006%. A systematic uncertainty in the energy scale is also added
for the non-linear variation of the LAr temperature with $\mu$ and amounts to
a few times $10^{-4}$ in the barrel and $10^{-3}$ in the endcap. The total
uncertainty in the extrapolated energy scale factors is about 0.05% in the
barrel, and on average 0.15% in the endcap, as shown in Figure 14(b).

((a))

((b))

Figure 14: (a) Energy scale corrections derived from $Z\to ee$ candidate
events as a function of $\eta$ for the low-pile-up data, high-pile-up data and
the extrapolated high-pile-up data after correction for the topo-cluster noise
threshold difference. The shaded areas correspond to the statistical
uncertainties. The bottom panel shows the differences between the energy scale
corrections measured in the 2017 high-$\mu$ dataset without any correction or
extrapolated to $\mu=2$ and the measurements using 2017 low-$\mu$ data only.
(b) Uncertainties in the energy scale corrections as a function of $\eta$ for
the low-pile-up data.

##  6 Electron identification

Further quality criteria, called ‘identification selections’ below, are used
to improve the purity of selected electron and photon objects. The
identification of prompt electrons relies on a likelihood discriminant
constructed from quantities measured in the inner detector, the calorimeter
and the combined inner detector and calorimeter. A detailed description is
given in Ref. [2]. Recent changes implemented as a result of the migration to
the supercluster reconstruction algorithm and adjustments made in parallel are
discussed in the following. The identification criteria apply to all
reconstructed electron candidates (see Section 4).

###  6.1 Variables in the electron identification

The quantities used in the electron identification are chosen according to
their ability to discriminate prompt isolated electrons from energy deposits
from hadronic jets, from converted photons and from genuine electrons produced
in the decays of heavy-flavour hadrons. The variables can be grouped into
properties of the primary electron track, the lateral and longitudinal
development of the electromagnetic shower in the EM calorimeter, and the
spatial compatibility of the primary electron track with the reconstructed
cluster. They are described in Table 1 and summarized here.

The primary electron track is required to fulfil a set of quality
requirements, namely hits in the two inner tracking layers closest to the beam
line, as well as a number of hits in the silicon-strip detectors. The
transverse impact parameter of the track and its significance are used to
construct the likelihood discriminant. Furthermore, $\Delta p/p$ and particle
identification in the TRT are used.

The lateral development of the electromagnetic shower is characterized with
variables calculated separately in the first and second layer of the
electromagnetic calorimeter. To reject clusters from multiple incident
particles, $w_{s\,\mathrm{tot}}$ is used (see Table 1). The lateral shower
development is measured with $R_{\phi}$ and $R_{\eta}$. All lateral shower
shape variables are calculated by summing energy deposits in calorimeter cells
relative to the cluster’s most energetic cell, and no significant difference
between fixed-size EM clusters and superclusters is expected in these
variables, as shown in Figure 15(a) for $R_{\phi}$.

For the longitudinal shower shape variables, the numbers of cells contributing
to the energy measurement in each layer are chosen dynamically in the
supercluster approach, compared with fixed numbers of cells in fixed-size
clusters. The supercluster approach inherently suppresses noise in the
calorimeter cells, resulting in lower values and narrower distributions. The
electron identification uses $f_{1}$ and $f_{3}$ (see Table 1). The
distribution of $f_{3}$ is compared for fixed-size clusters and superclusters
in Figure 15(b). The significant differences between data and simulation are
caused by a known mismodelling of calorimeter shower shapes in the Geant4
detector simulation. These are accounted for in the optimisation of the
electron identification (see Section 6.3) and corrected with data-to-
simulation efficiency ratios in analyses. Further discrimination against
hadronic showers is achieved with $R_{\mathrm{had}}$.

The reconstructed track and the EM cluster are matched using $\Delta\eta_{1}$
and $\Delta\phi_{\text{res}}$.

((a))

((b))

Figure 15:  The distributions of (a) $R_{\phi}$ and (b) $f_{3}$ obtained from
$33.7$ fb-1 of data recorded in 2016 at $\sqrt{s}=13$ TeV and simulation for
prompt electrons that satisfy $40<E_{\text{T}}<45$ GeV and
$0.80<\left|\eta\right|<1.15$. The variables are shown for fixed-size EM
clusters and superclusters. The detector simulation of the corresponding
distributions is performed with the Geant4 versions 4.9.6 and 4.10,
respectively. The distributions for both the simulation and the data are
obtained using the $Z\to ee$ tag-and-probe method and KDE smoothing has been
applied.

###  6.2 Likelihood discriminant

A discriminant is formed from the likelihoods for a reconstructed electron to
originate from signal, $L_{S}$, or background, $L_{B}$. They are calculated
from probability density functions (pdfs), $P$, which are created by smoothing
histograms of the $n$ (typically 13) discriminating variables with an adaptive
kernel density estimator (KDE [35]) as implemented in TMVA [36], separately
for signal and background and in 9 bins in $\left|\eta\right|$ and 7 bins of
$E_{\text{T}}$:

$L_{S(B)}(\mathbf{x})={\displaystyle\prod_{i=1}^{n}P_{S(B),i}(x_{i})}.$

For signal and background the pdfs take the values $P_{S,i}(x_{i})$ and
$P_{B,i}(x_{i})$, respectively, for the quantity $i$ at value $x_{i}$. The
likelihood discriminant $d_{L}$ is defined as the natural logarithm of the
ratio of $L_{S}$ and $L_{B}$.

The pdfs for signal were derived from $Z\to ee$ (for $E_{\text{T}}>15$ GeV)
and $J/\psi\rightarrow ee$ events (for $E_{\text{T}}<15$ GeV) prior to the
2017 data-taking period in $36.9$ fb-1 of data recorded in the years 2015 and
2016. A reconstructed electron is selected in these events using a tag-and-
probe method [37]. One of the electrons must satisfy a strict requirement on
the likelihood discriminant of the previous electron identification [2] and
the other electron serves as a probe. To reduce the background contamination
in the selected data, probe electrons are required to satisfy a very loose
requirement on the likelihood discriminant. This requirement rejects
approximately 95% of the background with a signal efficiency of 97%, causing
only a mild distortion of the likelihood pdfs. Events with at least one
reconstructed electron are selected to derive the pdfs for background. This
sample primarily contains dijet events; contributions from genuine electrons,
mainly from $W\rightarrow e\nu$ and $Z\to ee$ decays, are suppressed to a
negligible level using dedicated selection criteria. Deriving the likelihood
pdfs in data is an improvement compared to the previous likelihood-based
identification, which used simulation. Compared to the mismodelling in
simulation, the selection applied in data and differences in the run
conditions between the years 2015, 2016, 2017 and 2018 cause only mild
differences in the pdfs.

The electron likelihood identification imposes a selection on the likelihood
discriminant and some additional requirements. The variable $f_{3}$ exhibits a
dependence on the electron $E_{\text{T}}$ and $\eta$ that cannot adequately be
captured by the seven and nine bins, respectively, in which the pdfs are
determined. It is therefore only used for electrons with
$\left|\eta\right|<2.37$ and $E_{\text{T}}<80$ GeV. Electrons are also
rejected if a two-track silicon conversion vertex was reconstructed with a
momentum closer to the cluster energy than that of the primary electron track.
To pass the Tight operating point, electrons must moreover satisfy $E/p<10$
and their primary track must satisfy $p_{\text{T}}>2$ GeV. These additional
criteria aim to reject background from converted photons. For very high
$E_{\text{T}}$ the energy dependence of the shower shape variables can cause a
degradation of efficiencies for very strict requirements on the likelihood
discriminant. To avoid efficiency losses in the Tight identification, the cuts
on $d_{L}$ are chosen to be identical to the Medium identification for
$E_{\text{T}}>150$ GeV, and the operating points differ only in the additional
requirements and an $\eta$-dependent requirement on the shower width in the
first calorimeter layer, applied to Tight electrons.

###  6.3 Efficiency of the electron identification

Figure 16: The electron identification efficiency in data for electrons with
$E_{\text{T}}>30$ GeV as a function of the average number of interactions per
bunch crossing for the Loose, Medium and Tight operating points. The
efficiencies are measured in $Z\to ee$ events in data recorded in the year
2017. The shape of the $\left\langle\mu\right\rangle$ distribution is shown as
a shaded histogram. The bottom panel shows the data-to-simulation ratios. The
total uncertainties are shown.

The operating points Loose, Medium and Tight are each optimized in 9 bins in
$\left|\eta\right|$ and 12 bins in $E_{\text{T}}$ such that reconstructed
electrons meet the requirements on the likelihood discriminant with some
predefined efficiency. The values of these requirements are determined in
simulated events. For that purpose, the electromagnetic shower quantities and
the combined track–cluster variables are shifted and adjusted in width such
that the resulting distribution of the likelihood discriminant of the
simulated electrons closely matches that in data. The discriminant threshold
is adjusted linearly as a function of pile-up level to yield a stable
rejection of background electrons. The number of reconstructed vertices
$n_{\mathrm{vtx}}$ serves as a measure for pile-up. Due to the deterioration
of the discriminating power with pile-up, the approximately constant
background rejection is accompanied by a reduction of signal efficiency as a
function of the average number of interactions per bunch crossing, as shown in
Figure 16 for a pure sample of electrons from $Z$-boson decays.

The target efficiencies are the same as in the previous identification [2], as
these have proven to suit a wide range of analyses and topologies. For typical
electroweak processes they are, on average, 93%, 88% and 80% for the Loose,
Medium, and Tight operating points and gradually increase from low to high
$E_{\text{T}}$. The reduced efficiency of the Medium and Tight operating
points is accompanied by an improved rejection of background processes by
factors of approximately 2.0 and 3.5, respectively, in the range
$20\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}<E_{\text{T}}<50$ GeV. The
background efficiency was evaluated in QCD two-to-two processes simulated as
described in Section 3.1. Figure 17 shows the resulting efficiencies in data.
With increasing $E_{\text{T}}$, the identification efficiency varies from 58%
at $E_{\text{T}}=4.5$ GeV to 88% at $E_{\text{T}}=100$ GeV for the Tight
operating point, and from 86% at $E_{\text{T}}=20$ GeV to 95% at
$E_{\text{T}}=100$ GeV for the Loose operating point. In 2015, a different gas
mixture was used in the TRT causing higher efficiencies. Similar efficiencies
are obtained for the data recorded in the years 2016 and 2017 and residual
differences are caused by their dependence on pileup. The discontinuity in the
efficiency curve at $E_{\text{T}}=15$ GeV is caused by a known mismodelling of
the variables used in the likelihood discriminant at low $E_{\text{T}}$:
performing the optimization of the discriminant cuts using simulated events
leads to a higher efficiency in data in this region, resulting in the rise at
low $E_{\text{T}}$ observed in the lower panels of Figure 17.

The uncertainties in the efficiency are $\pm 7\%$ at
$E_{\text{T}}=4.5\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$ and decrease
with transverse energy, reaching better than $\pm 1\%$ for
$30\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}<E_{\text{T}}<250\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}$. The systematic uncertainties in the measurements
are dominated by background subtraction uncertainties at low $E_{\text{T}}$,
and are derived as decribed in Ref. [2]. For larger values of $E_{\text{T}}$,
additional systematic uncertainties of $\pm 0.5\%$, $\pm 1.0\%$, $\pm 1.5\%$
assigned due to variations in the electron efficiency with $E_{\text{T}}$ for
Loose, Medium and Tight identification, respectively, limit the precision.

Figure 17: The electron identification efficiency in $Z\to ee$ events in data
as a function of $E_{\text{T}}$ (left) and as a function of $\eta$ (right) for
the Loose, Medium and Tight operating points. The efficiencies are obtained by
applying data-to-simulation efficiency ratios measured in $J/\psi\rightarrow
ee$ and $Z\to ee$ events to $Z\to ee$ simulation. The inner uncertainties are
statistical and the total uncertainties are the statistical and systematic
uncertainties in the data-to-simulation efficiency ratio added in quadrature.
For both plots, the bottom panel shows the data-to-simulation ratios.

##  7 Photon identification

###  7.1 Optimization of the photon identification

The photon identification criteria are designed to efficiently select prompt,
isolated photons and reject backgrounds from hadronic jets. The photon
identification is constructed from one-dimensional selection criteria, or a
cut-based selection, using the shower shape variables described in Table 1.
The variables using the EM first layer play a particularly important role in
rejecting $\pi^{0}$ decays into two highly collimated photons.

The primary identification selection is labelled as Tight, with less
restrictive selections called Medium and Loose, which are used for trigger
algorithms. The Loose identification criteria have remained unchanged since
the beginning of Run 2, and Loose was the main selection used in the
triggering of photon and diphoton events in 2015 and 2016. It uses the
$R_{\mathrm{had}}$, $R_{\mathrm{had_{1}}}$, $R_{\eta}$, and $w_{\eta_{2}}$
shower shape variables. The Medium selection, which adds a loose cut on
$E_{\mathrm{ratio}}$, became the main trigger selection in the beginning of
2017, in order to maintain an acceptable trigger rate. Because the
reconstruction of photons in the ATLAS trigger system does not differentiate
between converted and unconverted photons, the Loose and Medium identification
criteria are the same for converted and unconverted photons. The Tight
identification criteria described in this paper are designed to select a
subset of the photon candidates passing the Medium criteria. Because the
shower shapes vary due to the geometry of the calorimeter, the cut-based
selection of Loose, Medium and Tight are optimized separately in bins of
$|\eta|$. The Tight identification presented here is also optimized in
separate bins of $E_{\text{T}}$, and compared with an earlier version of the
Tight identification that makes an $E_{\text{T}}$-independent selection.

The Tight identification is optimized using TMVA, and performed separately for
converted and unconverted photons. The shower shapes of converted photons
differ from unconverted photons due to the opening angle of the $e^{+}e^{-}$
conversion pair, which is amplified by the magnetic field, and from the
additional interaction of the conversion pair with the material upstream of
the calorimeters.

The Tight identification is optimized using a series of MC samples that
provide prompt photons and representative backgrounds at different transverse
momenta. For photons with $10<E_{\text{T}}<25$ GeV, the $Z\to\ell\ell\gamma$
MC sample with the selection described in Section 3.1 is used as a signal. The
corresponding background sample is obtained from data consisting of $Z$+jets
events collected using a similar event selection, but with relaxed
requirements on the dilepton and dilepton+photon invariant masses
$m_{\ell\ell}$ and $m_{\ell\ell\gamma}$. Above $E_{\text{T}}=25$ GeV, the
inclusive-photon production MC sample described in Section 3.2 is compared
with a dijet background MC sample that is enriched in high-$E_{\text{T}}$
energy deposits using a generator-level filter. No isolation selection is
applied to the training samples, and the shower shape variables are corrected
to match the shower shapes observed in data using the correction procedure
described in Ref. [1].

Figures 18 and 19 show the result of the Tight identification optimization in
terms of the efficiencies as a function of $E_{\text{T}}$ for the signal and
background MC training samples. The optimized selection, labelled
$E_{\text{T}}$-dependent, is compared with a reference selection that uses
criteria that do not change with $E_{\text{T}}$ ($E_{\text{T}}$-independent).
The new, $E_{\text{T}}$-dependent Tight identification allows the efficiencies
of low- and high-$E_{\text{T}}$ photon regions to be tuned separately. The
Tight identification is tuned to give a $\sim$20% higher efficiency at low
$E_{\text{T}}$, and an improved background rejection at high $E_{\text{T}}$.
The $\left\langle\mu\right\rangle$ dependence of the photon identification is
depicted in Figure 20 for photons from $Z\to\ell\ell\gamma$ decays.

Figure 18:  Efficiencies of the Tight photon identification for unconverted
(left) and converted (right) signal photons, plotted as a function of photon
$E_{\text{T}}$. The signal events are taken from the sample of
$Z{\rightarrow}\ell\ell\gamma$ photons with $E_{\text{T}}<25$ GeV, and from
inclusive-photon production above 25 GeV. In each case, the
$E_{\text{T}}$-independent and $E_{\text{T}}$-dependent selections are
compared. The Loose isolation (see Section 8.2) is applied as a preselection.
For both plots, the bottom panel shows the ratios between the
$E_{\text{T}}$-dependent and the $E_{\text{T}}$-independent identification
efficiencies.

Figure 19:  Efficiencies of the Tight photon identification for unconverted
(left) and converted (right) background photons from jets, plotted as a
function of photon $E_{\text{T}}$. The background is taken from
$Z{\rightarrow}\ell\ell+$jets production below 25 GeV, and filtered dijet
production above 25 GeV. In each case, the $E_{\text{T}}$-independent and
$E_{\text{T}}$-dependent selections are compared. The Loose isolation (see
Section 8.2) is applied as a preselection. For both plots, the bottom panel
shows the ratios between the $E_{\text{T}}$-dependent and the
$E_{\text{T}}$-independent identification efficiencies.

Figure 20: Photon identification efficiency as a function of
$\left\langle\mu\right\rangle$ for unconverted (left) and converted photons
(right), as measured by the radiative $Z$ method, for photons with
$20<E_{\text{T}}<40$ GeV. Backgrounds, which are not subtracted in this plot,
are estimated to be below 1%. The error bars show the statistical
uncertainties. For both plots, the bottom panel shows the data-to-simulation
ratios.

###  7.2 Efficiency of the photon identification

To assess the performance of the ($E_{\text{T}}$-dependent) Tight photon
identification on data, three photon efficiency measurements are performed
using distinct data samples. The first uses an inclusive-photon production
data selection, the second uses photons radiated from leptons in
$Z\to\ell\ell\gamma$ decays, and the third uses electrons from $Z\to ee$
decays, with a method that transforms the electron shower shapes to resemble
the photon shower shapes. These efficiency measurements are described in
detail in Ref. [1], and summarized below. All three procedures measure photons
that are isolated, using the Loose working-point definition (see Section 8.2).

The three measurements use a common method to characterize the imperfect
modelling of shower shapes in simulated samples, in order to estimate its
impact on the efficiency measurement in data. Nominally, the MC shower shapes
are compared with data in control regions enriched in real photons and
corrected by applying a simple shift to the distributions, whose magnitude is
determined by a $\chi^{2}$ minimization procedure. However, some data–MC
differences cannot be corrected by this procedure, such as the widths of the
distributions. In order to estimate any residual data–MC differences, the
$\chi^{2}$ minimisation is repeated considering only the tail of the
distribution, defined as the region containing 30% of the distribution on the
side closer to the identification cut value. The shift value obtained when
comparing the data and simulation tails is used to define a systematic
uncertainty in the modelling of the shower shapes, and is derived for all
variables for which a mismodelling is observed. Four variations are defined
using sets of correlated variables; the variables within each set are shifted
together: {$R_{\mathrm{had}}$}, {$R_{\phi}$}, {$R_{\eta}$,$w_{\eta_{2}}$}, and
{$w_{s\,3}$,$f_{\mathrm{side}}$,$w_{s\,\mathrm{tot}}$}. The result is
equivalent to four sets of MC simulated samples, which can be used to assign
systematic uncertainties for mismodelling effects that impact the data
measurement, and which are considered to be uncorrelated variations.

The method using $Z\to\ell\ell\gamma$ decays selects data as described in
Section 3.1. Additional requirements on the invariant mass of the three-body
system, $80<m_{\ell\ell\gamma}<100$ GeV, and on the lepton-pair invariant
mass, $40<m_{\ell\ell}<83$ GeV, select radiative $Z$-boson decays while
rejecting backgrounds from $Z+\gamma$ and $Z+$jets production. The efficiency
and purity of the samples with and without the Tight identification
requirement are determined from fits of signal and background templates,
extracted from simulated $Z\to\ell\ell\gamma$ and $Z+$jets events, to the
observed three-body invariant-mass distribution.

The systematic uncertainties in the photon efficiency measurement using
$Z\to\ell\ell\gamma$ decays include a closure test using simulated signal and
background samples to assess the validity of the measurement. To assess the
impact of simulation mismodelling, the measurement is repeated comparing the
Powheg-Pythia8 and Sherpa $Z\to\ell\ell$ samples and the difference is taken
as a systematic uncertainty. The shower shape correction uncertainties are
considered by repeating the measurement with each of the four sets of modified
simulation samples, and the observed differences are added in quadrature.
Finally, as a test of the background description, the fit range of the
$m_{\ell\ell\gamma}$ distribution is varied from its nominal value of [65,105]
GeV using two variations, [45,95] GeV and [80,120] GeV, and the efficiency
differences are assigned as a systematic uncertainty.

The method to extract the photon efficiency using inclusive-photon production
relies on data collected with prescaled photon triggers that feature a Loose
identification requirement, as described in Section 3.1. This data sample
contains a mixture of real photons and backgrounds from jet production, and a
matrix method is used to extract the photon efficiency. The matrix method
constructs four regions by categorizing Loose photon candidates according to
whether they pass or fail the Tight identification, and whether they pass or
fail track-based isolation cuts. The four regions contain eight unknowns (i.e.
the numbers of signal and background events in each region); if the isolation
efficiencies for signal and background from each region are known, the
efficiency for Loose photons to pass the Tight identification can be
extracted. The isolation efficiencies for loosely and tightly identified
signal photons are determined from the Monte Carlo samples, and the isolation
efficiencies for backgrounds are obtained in a jet-enriched control region
constructed by inverting identification criteria. Finally, the efficiency for
reconstructed photon candidates to pass the Loose identification is determined
from simulation, as this contribution is not measured in data by this method.
The magnitude of the correction is typically less than 5%, and smaller at high
$E_{\text{T}}$.

Systematic uncertainties assigned to the matrix method include a closure
uncertainty that quantifies the agreement between the background isolation
efficiencies derived in the data control region and in the regions to which
they are applied. This effect is estimated using simulation, and is the
largest source of uncertainty in the measurement. The robustness of the method
is tested by varying the track-based isolation requirement, and assigning any
difference in measured efficiency as a systematic uncertainty. The impact of
uncertainties in the shower shape corrections is estimated using simulation;
the effects of the four shower shape variations described above are added in
quadrature. Finally, an uncertainty is assigned for a potential mismodelling
in the MC-based correction to extrapolate from Loose to reconstructed photons.
This uncertainty is based on the Loose identification efficiency measured with
radiative photons in $Z\rightarrow\ell\ell\gamma$ events.

Photon efficiencies can be estimated in a data sample of electrons from $Z\to
ee$ decays whose shower shape variables have been modified to resemble photon
shower shapes, a technique referred to as the electron extrapolation method.
This efficiency measurement, described in Ref. [1], uses the $Z\to ee$ sample
defined in Section 3.1, with the photon Loose isolation requirement applied to
the electron candidates. Electron shower shape variables are modified using a
Smirnov transform [38] derived from simulated $Z\to ee$ and inclusive-photon
production samples. The candidate electrons in data contain a small background
from $W+$jets and multijet production; this background is subtracted by
fitting simulated signal samples and background templates derived from data
control regions to the $m_{ee}$ data distributions. The electron candidates
are counted for events in the range $70<m_{ee}<110$ GeV, and the efficiencies
are measured using the tag-and-probe method as described in Section 6.

The systematic uncertainties in the electron extrapolation method are as
follows. First, a closure test is performed to determine whether the
transformed electrons can reproduce the expected photon efficiency, using the
simulation and in the absence of background. The difference in relative
efficiency, which can be as high as 3%, is applied as a correction to the
measured data efficiency, and the magnitude of the correction is assigned as
the systematic uncertainty. Systematic effects that affect the Smirnov
transformations include the fraction of fragmentation photons in the simulated
inclusive-photon sample, which is varied by $\pm 50$%, and the predicted
fraction of true converted photons, which is varied by $\pm 10$%, to assess
the impact of the imperfect simulation on the efficiency measurement. The
uncertainty in the modelling of identification variables in simulation is
assessed by defining Smirnov transformations for each of the four sets of
variations of the shower shape modelling, recalculating the efficiency for
each case; the total modelling uncertainty is taken as the sum in quadrature
of the individual variations. The uncertainty due to the limited size of the
MC samples used to derive the Smirnov transformations is assessed using the
bootstrap method. Finally, the uncertainty associated with the subtraction of
the $W+$jets and multijet backgrounds in the signal region is tested by
reducing the level of background through a restriction of the selected
invariant-mass range to $80<m_{\ell\ell}<100$ GeV, and repeating the
measurement procedure. The resulting difference in the measured efficiency is
taken as the systematic uncertainty.

The three efficiency measurements are compared with MC simulation in order to
obtain scale factors, in bins of $E_{\text{T}}$ and $|\eta|$, that are used to
correct the MC simulations so that the simulations closely resemble data.
Before determining these scale factors, the shower shapes in these MC
simulations were corrected to match data using the procedure described in Ref.
[1].

Figures 21 and 22 depict the Tight identification efficiencies for unconverted
and converted photons as measured with the three efficiency methods. The
data/MC scale factors are also shown for each measurement separately. The
three efficiency measurements are performed using different processes, with
different event topologies that may impact the photon efficiency. Despite this
fact, the efficiency measurements are compatible within their statistical and
systematic uncertainties.

Figure 21: The photon identification efficiency, and the ratio of data to MC
efficiencies, for unconverted photons with a Loose isolation requirement
applied as preselection, as a function of $E_{\text{T}}$ in four different
$|\eta|$ regions. The combined scale factor, obtained using a weighted average
of scale factors from the individual measurements, is also presented; the band
represents the total uncertainty.

Figure 22: The photon identification efficiency, and the ratio of data to MC
efficiencies, for converted photons with a Loose isolation requirement applied
as preselection, as a function of $E_{\text{T}}$ in four different $|\eta|$
regions. The combined scale factor, obtained using a weighted average of scale
factors from the individual measurements, is also presented; the band
represents the total uncertainty.

The scale factors from each of the three efficiency measurements are combined
using a weighted average. The statistical and systematic uncertainties are
assumed to be uncorrelated between the methods. The total uncertainty of the
combined scale factors ranges between 7% at low $E_{\text{T}}$ and 0.5% at
high $E_{\text{T}}$ for unconverted photons, and between 12% (low
$E_{\text{T}}$) and less than 1% (high $E_{\text{T}}$) for converted photons.
For $E_{\text{T}}$ > 1.5 TeV, where no measurement is performed, the scale
factor measured in the $E_{\text{T}}$ bin [0.25,1.5] TeV is used, with the
same uncertainty.

##  8 Electron and photon isolation

The activity near leptons and photons can be quantified from the tracks of
nearby charged particles, or from energy deposits in the calorimeters, leading
to two classes of isolation variables.

The raw calorimeter isolation [2] ($E_{\mathrm{T,raw}}^{\mathrm{isol}}$) is
built by summing the transverse energy of positive-energy topological clusters
whose barycentre falls within a cone centred around the electron or photon
cluster barycentre. The topological cluster energy scale is the EM scale. The
raw calorimeter isolation includes the EM particle energy
($E_{\mathrm{T,core}}$), which is subtracted by removing the energy of the EM
calorimeter cells contained in a $\Delta\eta\times\Delta\phi=5\times 7$ (in
EM-middle-layer units) rectangular cluster around the barycentre of the EM
particle cluster. The advantage of this simple method is a stable subtraction
for real or fake/non-prompt objects for any transverse momentum and pile-up.
The disadvantage is that it does not subtract all the EM particle energy and
an additional leakage correction is needed. This leakage is parameterized as a
function of $E_{\text{T}}$ and $|\eta|$ using MC samples of single electrons
or photons without pile-up. Additionally, a correction for the pile-up and
underlying-event contribution to the isolation cone is also estimated [39].

Finally, the fully corrected calorimeter isolation variable is computed as:

$E_{\text{T}}^{\text{coneXX}}=E_{\mathrm{T,raw}}^{\mathrm{isol\mathrm{XX}}}-E_{\mathrm{T,core}}-E_{\mathrm{T,leakage}}(E_{\text{T}},\eta,\Delta
R)-E_{\mathrm{T,\textrm{pile-up}}}(\eta,\Delta R),$

where $\mathrm{XX}$ refers to the size of the employed cone, $\Delta
R=\mathrm{XX}/100$. A cone size $\Delta R=0.2$ is used for the electron
working points whereas cone sizes $\Delta R=0.2$ and 0.4 are used for photon
working points.

The track isolation variable ($p_{\text{T}}^{\text{coneXX}}$) is computed by
summing the transverse momentum of selected tracks within a cone centred
around the electron track or the photon cluster direction. Tracks matched to
the electron or converted photon are excluded. Since for electrons produced in
the decay of high-momentum heavy particles, other decay products can be very
close to the electron direction, the track isolation for electrons is defined
with a variable cone size ($p_{\text{T}}^{\text{varconeXX}}$) – the cone size
shrinks for larger transverse momentum of the electron:

$\Delta R=\min\left(\frac{10}{p_{\text{T}}[\text{Ge\kern-1.00006ptV}]},\Delta
R_{\mathrm{max}}\right),$

where $\Delta R_{\mathrm{max}}$ is the maximum cone size (typically 0.2).

The tracks considered are required to have $p_{\text{T}}>1\
\text{Ge\kern-1.00006ptV}$ and $|\eta|<2.5$, at least seven silicon (Pixel +
SCT) hits, at most one shared hit (defined as
$n^{\text{sh}}_{\text{Pixel}}+n^{\text{sh}}_{\text{SCT}}/2$, where
$n^{\text{sh}}_{\text{Pixel}}$ and $n^{\text{sh}}_{\text{SCT}}$ are the
numbers of hits assigned to several tracks in the Pixel and SCT detectors), at
most two silicon holes (i.e. missing hits in the pixel and SCT detectors) and
at most one pixel hole. In addition, for electron isolation, the tracks are
required to have a loose vertex association, i.e. the track was used in the
primary vertex fit, or it was not used in any vertex fit but satisfies
$|\Delta z_{0}|\sin\theta<3$ mm, where $|\Delta z_{0}|$ is the longitudinal
impact parameter relative to the chosen primary vertex; for photon isolation,
all selected tracks satisfying $|\Delta z_{0}|\sin\theta<3$ mm are used.

In this section, the isolation efficiency measurements are illustrated with
the data recorded in 2017; nevertheless, the measurements are performed for
the full high-$\mu$ dataset described in Section 3.1.

###  8.1 Electron isolation criteria and efficiency measurements

The implementation of isolation criteria is specific to the physics analysis
needs, as it results from a compromise between a highly-efficient
identification of prompt electrons, isolated or produced in a busy
environment, and a good rejection of electrons from heavy-flavour decays or
light hadrons misidentified as electrons. The different electron-isolation
working points used in ATLAS are presented in Table 2.

The working points can be defined in two different ways, targeting a fixed
value of efficiency or with fixed cuts on the isolation variables. The
Gradient working point is designed to give an efficiency of 90% at
$p_{\text{T}}=25\ \text{Ge\kern-1.00006ptV}$ and $99\%$ at $p_{\text{T}}=60\
\text{Ge\kern-1.00006ptV}$, uniform in $\eta$. The requirements on
$E_{\text{T}}^{\text{cone20}}$ and $p_{\text{T}}^{\text{varcone20}}$ (cut
maps) for this working point are derived from $J/\psi\to ee$
($E_{\text{T}}<15\ \text{Ge\kern-1.00006ptV}$) and $Z\to ee$
($E_{\text{T}}>15\ \text{Ge\kern-1.00006ptV}$) MC simulations and Tight
identification requirements. The three other working points, HighPtCaloOnly,
Loose and Tight, have a fixed requirement on the calorimeter and/or the track
isolation variables.

Table 2: Definition of the electron isolation working points and isolation
efficiency $\epsilon$. In the Gradient working point definition, the unit of
$p_{\text{T}}$ is GeV. All working points use a cone size of $\Delta R=0.2$
for calorimeter isolation and $\Delta R_{\mathrm{max}}=0.2$ for track
isolation.

Working point | Calorimeter isolation | Track isolation
---|---|---
Gradient |  $\epsilon=0.1143\times p_{\text{T}}+92.14\%$ (with $E_{\text{T}}^{\text{cone20}}$) |  $\epsilon=0.1143\times p_{\text{T}}+92.14\%$ (with $p_{\text{T}}^{\text{varcone20}}$)
HighPtCaloOnly | $E_{\text{T}}^{\text{cone20}}<\text{max}(0.015\times p_{\text{T}},3.5\leavevmode\nobreak\ \text{$\text{Ge\kern-1.00006ptV}$})$ | -
Loose | $E_{\text{T}}^{\text{cone20}}/p_{\text{T}}<0.20$ | $p_{\text{T}}^{\text{varcone20}}/p_{\text{T}}<0.15$
Tight | $E_{\text{T}}^{\text{cone20}}/p_{\text{T}}<0.06$ | $p_{\text{T}}^{\text{varcone20}}/p_{\text{T}}<0.06$

Figure 23: Efficiency of the different isolation working points for electrons
from inclusive $Z\to ee$ events as a function of the electron $E_{\text{T}}$
(top left), electron $\eta$ (top right) and the number of interactions per
bunch crossing $\left\langle\mu\right\rangle$ (bottom). The electrons are
required to fulfil the Medium selection from the likelihood-based electron
identification. The lower panel shows the ratio of the efficiencies measured
in data and in MC simulations. The total uncertainties are shown, including
the statistical and systematic components.

Figure 23 shows the electron isolation efficiency measured in data recorded in
2017 and the corresponding data-to-MC simulation ratios as a function of the
electron $E_{\text{T}}$ and $\eta$, and of the number of interactions per
bunch crossing for the isolation working points summarized in Table 2. The
pile-up correction to the calorimeter isolation is applied, and reduces the
dependence of the isolation efficiency by about a factor of five. These
results are obtained using a sample enriched in $Z\to ee$ events, where the
electrons satisfy the Medium identification. The method used to compute the
electron isolation efficiency and the associated uncertainties are described
in Ref. [2]. For Gradient, a jump in the efficiency is observed at the
transition point of 15 GeV because the value of the isolation efficiency is
process dependent: the cut maps are optimized with $J/\psi\to ee$ events below
15 GeV, while the measurement is performed with $Z\to ee$ events in the full
range. The Tight operating point gives the highest background rejection below
60 GeV and the most significant difference in shape in $\eta$. As the name
suggests, HighPtCaloOnly gives the highest rejection in the
high-$E_{\text{T}}$ region ($E_{\text{T}}>100\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}$). The Gradient and Tight operating points give the
highest pile-up dependency, the isolation efficiency decreasing from $\sim$95%
at low $\left\langle\mu\right\rangle$ to $\sim$85% when
$\left\langle\mu\right\rangle$ is around 70–80.

The overall differences between data and MC simulation are less than
approximately 1–5% depending on the working point, with the largest difference
observed for Tight isolation. For electrons with $E_{\text{T}}$ higher than
$500\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$ no measurement can be
performed because of the limited number of data events, and the results from
the $E_{\text{T}}$ bin [300,500] GeV are used with an additional systematic
uncertainty varying betwen 0.1% and 1.7%, depending on the isolation working
point. The overall scale factor uncertainties range from about 5% for
electrons with $E_{\text{T}}$ below 7 GeV, to less than 0.5% towards high
$E_{\text{T}}$.

###  8.2 Photon isolation criteria and efficiency measurements

Table 3: Definition of the photon isolation working points. Working point | Calorimeter isolation | Track isolation
---|---|---
Loose | $E_{\text{T}}^{\text{cone20}}<0.065\times E_{\text{T}}$ | $p_{\text{T}}^{\text{cone20}}/E_{\text{T}}<0.05$
Tight |  $E_{\text{T}}^{\text{cone40}}<0.022\times E_{\text{T}}+2.45$ GeV | $p_{\text{T}}^{\text{cone20}}/E_{\text{T}}<0.05$
TightCaloOnly |  $E_{\text{T}}^{\text{cone40}}<0.022\times E_{\text{T}}+2.45$ GeV | -

Figure 24: The data-driven shifts for $E_{\text{T}}^{\text{cone20}}$ (top) and
$E_{\text{T}}^{\text{cone40}}$ (bottom) obtained with 2017 data and Pythia8 MC
simulations; the Tight isolation working point is applied as preselection to
decrease the level of background. The results are shown as a function of
photon $E_{\text{T}}$, in two $\eta$ regions of the detector ($|\eta|<0.6$ and
$1.81<|\eta|<2.37$), separately for converted (left) and unconverted (right)
photons. Only the uncertainties associated with the fit parameters are shown.

Figure 25: Distribution of $E_{\text{T}}^{\text{cone40}}$ in data and
simulation using $Z\to\ell\ell\gamma$ events, in the central region of the
detector ($|\eta|<0.6$), separately for converted (left) and unconverted
(right) photons after the data-driven shifts are applied. Only the statistical
uncertainties are shown.

Three photon isolation operating points are defined using requirements on the
calorimeter and track isolation variables, as summarized in Table 3. For the
calorimeter-based photon isolation variables a discrepancy between the peak
positions of their distributions in data and simulation has been observed
since Run 1 [40], pointing to a mismodelling in simulation of the lateral
profile development of the electromagnetic showers. As a result, the photon
isolation efficiencies in data and simulations disagree, leading to scale
factors significantly different from 1.

These discrepancies are mitigated by applying data-driven shifts to the
calorimeter isolation variables for photons in simulation. The shifts are
obtained by performing fits to the calorimeter isolation variable
distribution, using Crystal Ball pdfs [41], in regions dominated by real
photons, in data and simulation. The fits are performed in bins of photon
$\eta$, $E_{\text{T}}$ and conversion status, separately for
$E_{\text{T}}^{\text{cone20}}$ and $E_{\text{T}}^{\text{cone40}}$ isolation
variables. The difference in the fitted peak values between data and
simulation defines the shift value, which is added to the photon calorimeter
isolation values in simulation. Figure 24 illustrates the data-driven shifts
obtained with 2017 data and the Pythia8 simulation for the
$E_{\text{T}}^{\text{cone20}}$ and $E_{\text{T}}^{\text{cone40}}$ isolation
variables in two $\eta$ regions. Figure 25 shows the distribution of the
$E_{\text{T}}^{\text{cone40}}$ isolation variable in 2017 data and simulation,
using $Z\to\ell\ell\gamma$ events after the data-driven shifts are applied.

The photon isolation efficiency is studied in two main signatures: radiative
$Z$ decays (valid for $10<E_{\text{T}}<100\ \text{Ge\kern-1.00006ptV}$) and
inclusive photons (used in the $25\
\text{Ge\kern-1.00006ptV}<E_{\text{T}}<\,\sim$1.5 TeV range).

####  8.2.1 Measurement of photon isolation efficiency with radiative $Z$
decays

As detailed in Section 7, final-state radiation in $Z$-boson decays provides a
clean environment to probe photons in the low-$E_{\text{T}}$ range. Using the
same method as for the photon identification, photon isolation efficiencies
are measured for the operating points presented in Table 3. The evolution of
the isolation efficiency measured in 2017 data as a function of $\eta$ and
$E_{\text{T}}$ is illustrated in Figure 26, together with the data-to-
simulation efficiency ratio. The overall differences between data and
simulation are less than approximately 5%. The decrease of efficiency with
increasing pile-up activity is shown in Figure 27. A loss of efficiency of
$\sim$10% is measured when increasing $\left\langle\mu\right\rangle$ from 15
to 60. This loss is well described by the simulation.

Figure 26: Efficiency of the isolation working points defined in Table 3,
using $Z\to\ell\ell\gamma$ events, for converted (left) and unconverted
(right) photons as a function of photon $\eta$ (top) and $E_{\text{T}}$
(bottom). The lower panel shows the ratio of the efficiencies measured in data
and in simulation. The total uncertainties are shown, including the
statistical and systematic components.

Figure 27: Efficiency of the isolation working points defined in Table 3,
using $Z\to\ell\ell\gamma$ events, for converted (left) and unconverted
(right) photons as a function of $\left\langle\mu\right\rangle$. The lower
panel shows the ratio of the efficiencies measured in data and in simulation.
The total uncertainties are shown, including the statistical and systematic
components.

####  8.2.2 Photon calorimeter isolation efficiency measurement with
inclusive-photon events

Photon isolation studies with inclusive-photon events are performed using two
different methods for the calorimeter-based and track-based isolations. This
is because the distribution of the track isolation variable shows a large peak
at $p_{\text{T}}^{\text{cone20}}=0$ followed by a 1 GeV gap, due to the
selection of the tracks entering the $p_{\text{T}}^{\text{cone20}}$
computation, and by a small tail, and cannot be fitted with an analytic
function. In consequence, the efficiency measurement is done separately for
the track isolation and calorimeter isolation criteria applied to define the
working points presented in Table 3. When the measurement is performed for the
track-based (calorimeter-based) isolation, the requirements on the
calorimeter-based (track-based) isolation are applied at preselection level to
reduce the background from jets.

The photon calorimeter isolation (calo-only) efficiency with inclusive-photon
events is obtained by fitting the distribution of the calorimeter isolation,
$E_{\text{T}}^{\text{cone40}}$ or $E_{\text{T}}^{\text{cone20}}$, minus the
relevant $E_{\text{T}}$ fraction ($0.022\times E_{\text{T}}$ for Tight and
$0.065\times E_{\text{T}}$ for Loose), hereafter simply called the isolation
distribution. The measurement is performed in bins of photon $\eta$,
$E_{\text{T}}$, conversion status and data-taking period. The Pythia8
inclusive-photon sample described in Section 3.2 is used for the true photon
template.

A set of alternate selections is used to determine the isolation distributions
for the backgound and their uncertainty. These criteria, denoted
LoosePrime$N$, select photon candidates that pass the Loose identification but
fail at least one out of $N$ shower shape cuts used in the Tight
identification. 999The sets of criteria of which at least one is not satisfied
are requirements on {$w_{s\,3}$, $f_{\mathrm{side}}$} for $N$=2; {$w_{s\,3}$,
$f_{\mathrm{side}}$, $\Delta{}E_{s}$} for $N$=3; {$w_{s\,3}$,
$f_{\mathrm{side}}$, $\Delta{}E_{s}$, $E_{\mathrm{ratio}}$} for $N$=4 and
{$w_{s\,3}$, $f_{\mathrm{side}}$, $\Delta{}E_{s}$, $E_{\mathrm{ratio}}$,
$w_{s\,\mathrm{tot}}$} for $N$=5. The nominal background template is obtained
from photon candidates passing the LoosePrime4 identification. As in the
measurements of the data-driven shifts, the photon isolation efficiency is
obtained by performing a set of fits in regions defined in simulation and
data. Although background enriched, the sample passing LoosePrime4 also
contains true photons that fail the Tight identification requirement; these
are defined as ‘leakage’ photons and subtracted. The sequence of fits proceeds
as follows:

  * 1.

A model for the isolation distribution for signal photons is defined from a
fit, using a Crystal Ball function, to the isolation distribution obtained for
tightly identified photons in simulation.

  * 2.

The corresponding model for leakage photons is defined from a fit to the
isolation distribution obtained for LoosePrime4 photons in simulation.

  * 3.

The isolation distribution for background photons (i.e. the sum of fake and
leakage photons) is parameterized using a two-component fit to the
distribution observed for photons satisfying the LoosePrime4 requirement in
data. An unconstrained Crystal Ball function is used to model the isolation
distribution for fake photons, and the model for leakage photons is defined in
point 2.

  * 4.

Finally, the number of signal photons is estimated from a two-component fit to
the isolation distribution observed for tightly identified photons in data.
The background component uses the model defined in point 3, and the signal
photon component uses the model defined in point 1.

The fits described in points 3 and 4 above are performed twice. The first
time, they are performed to estimate the number of leakage photons from the
ratio of the number of photon candidates passing the Tight and LoosePrime4
identification selection. When the fit in the LoosePrime4 sample is performed
again (point 3), the number of leakage photons is constrained, allowing a
better estimation of the fake photon isolation distribution. Finally the fit
in the tightly identified sample is also redone, with the background component
formed only by fake photons. Once the background component is subtracted, only
real photons meeting the Tight identification criterion remain and are used
for the isolation efficiency measurements.

Finally, the calo-only isolation efficiency in data is obtained by integrating
the background-subtracted isolation distribution for tightly identified
photons in data, up to the working point cut-off of 0 GeV (Loose) or 2.45 GeV
(Tight and TightCaloOnly). Three sources of systematic uncertainty are
considered: discrepancies between the fitted isolation distribution and that
observed for photons in data; differences between results obtained using
LoosePrime3 and LoosePrime5 instead of LoosePrime4 for the determination of
the background templates; and uncertainties in the estimation of the number of
leakage photons in the LoosePrime4 sample. A binomial statistical error in the
scale factors is also calculated and added in quadrature to the systematic
components.

Figure 28: Efficiency of the different calo-only isolation working points for
photons from inclusive-photon events, as a function of photon $E_{\text{T}}$
in two $\eta$ bins ($|\eta|<0.6$ top, and $|\eta|>1.81$ bottom). The results
are shown for converted (left) and unconverted (right) photons. The lower
panel shows the ratio of the efficiencies measured in data and in simulation.
The total uncertainties are shown, including the statistical and systematic
components.

The calo-only isolation efficiencies measured with inclusive-photon events in
2017 data are shown in Figure 28. The overall differences between data and
simulation increase from a few percent in the low $E_{\text{T}}$ region up to
15% at high $E_{\text{T}}$ ($>200$ GeV) for the TightCaloOnly working point,
and only up to 5% for Loose and Tight.

####  8.2.3 Photon track-based isolation efficiency measurement with
inclusive-photon events

As in the measurement of the calo-only photon isolation efficiency, the main
source of background comes from jets misidentified as photons. This background
is estimated with a template fit to the track isolation distribution, in a
region enriched in background photons satisfying LoosePrime4 but failing the
Tight identification criterion. The track-only photon isolation efficiency is
measured in a signal region enriched in tightly identified photons, after the
background is subtracted. To assign the systematic uncertainties, the fit
range is varied as well as the definition of the background template, where
the photons are required to pass LoosePrime2, LoosePrime3 or LoosePrime5
instead of the LoosePrime4 criterion. Efficiencies for each configuration are
computed, and with them the corresponding scale factors. Once the different
scale factors are calculated, a bin-by-bin scan is performed, keeping the
largest deviation from the nominal value among the considered variations. The
total uncertainty is obtained by adding the systematic and statistical
components in quadrature.

Figure 29: Efficiency of the different track-only isolation working points for
photons from inclusive-photon events, as a function of photon $E_{\text{T}}$
in two $\eta$ bins ($|\eta|<0.6$ top, and $|\eta|>1.81$ bottom). The results
are shown for converted (left) and unconverted (right) photons. The lower
panel shows the ratio of the efficiencies measured in data and in simulation.
The total uncertainties are shown, including the statistical and systematic
components.

The track-only isolation efficiencies measured with inclusive-photon events in
2017 data are shown in Figure 29. The ratio of the data to MC simulation is
close to unity.

####  8.2.4 Combination of photon isolation scale factors

The photon isolation scale factors are measured for the three isolation
working points detailed in Table 3 using radiative $Z$ decays and inclusive-
photon events. The different results are combined to obtain one set of scale
factors per working point, data-taking year, and photon conversion status. The
combination is performed in two steps. First, the track-only and calo-only
scale factors determined with inclusive-photon events are multiplied together
to obtain a single set per configuration. These inclusive-photon scale factors
are further combined with those determined with radiative $Z$ decay events
using a simple weighted average. The uncertainties in the track-only and calo-
only results obtained with inclusive-photon events are treated as fully
correlated in the combination, while the uncertainties in the radiative-$Z$
and inclusive-photon measurement results are treated as uncorrelated. The
combination is performed for $25<E_{\text{T}}<100$ GeV; below 25 GeV, only
results from radiative $Z$ decays are available, while above 100 GeV the
results are obtained with inclusive-photon events only. If, in a given
($|\eta|$, $E_{\text{T}}$) bin, the total uncertainty in the combined scale
factor does not cover the difference between the values obtained from the two
samples, it is scaled such that $\chi^{2}=1$. Above $1.5\
\text{Te\kern-1.00006ptV}$, the results obtained in the last bin used for the
measurement are considered, with no change in the systematic uncertainty.

For $E_{\text{T}}$ < 25 GeV, the measurements achieve a typical uncertainty of
about 2%, and at worst 5–10% for $E_{\text{T}}$ < 15 GeV. For $E_{\text{T}}$ >
100 GeV, uncertainties around 1–2% are obtained. For $25<E_{\text{T}}<100$
GeV, the combination of the two channels reduces the scale factor
uncertainties to about 1% on average.

##  9 Electron charge misidentification

The reconstruction of the electric charge of an electron relies solely on the
measurement of the curvature of its associated track in the inner detector.
Interactions of an electron with the detector material can create secondary
particles: photons and electron–positron pairs. The production of these
secondary particles can lead to distortions of the primary electron track,
e.g. hits from the secondary particle being included in the fit of the primary
electron track, and the presence of additional tracks of secondary particles
in the vicinity of the primary electron track. Incorrect charge reconstruction
can thus be caused either by an incorrect determination of the track
curvature, or by the choice of an incorrect track.

For electrons at high transverse momentum, the first effect becomes dominant
and leads to an almost linear increase with energy in the probability to
determine the sign of the curvature incorrectly. Final-state radiation emitted
collinearly off the electron can also cause charge misidentification if the
radiated photon subsequently converts to an electron–positron pair in the
detector material. Here, the correct or incorrect charge is assigned with
equal probability. The electric charge is heavily used as a selection
criterion in measurements with the ATLAS experiment, and hence understanding
the effects of charge misidentification is important. Some specific signatures
also require the suppression of electron charge misidentification in order to
reduce background.

###  9.1 Suppression of electron charge misidentification

The suppression of electron charge misidentification is based on the output
discriminant of a boosted decision tree (BDT). A previous version, optimized
for data recorded in 2015 and 2016, rejected 90% of electrons with incorrectly
reconstructed charge, removing only 3% of electrons with correctly
reconstructed charge [2]. The optimization was based on simulated electrons
and showed a higher rejection than observed in data. In the following, a re-
optimization of the BDT is described. Data from $Z\to ee$ decays are used to
reduce efficiency losses due to mismodelling of the input variables in the BDT
training. Furthermore, additional input variables have been studied.

To select a relatively clean sample of electrons with correctly and
incorrectly reconstructed charge, one of the electrons is restricted to
$\left|\eta\right|<0.6$, required to satisfy Tight identification and to pass
the 97% operating point of the previous BDT discriminant. These requirements
minimize charge misidentification for this electron. Any additional
reconstructed electron in the event is used to train the BDT, as a signal
electron if it has an electric charge different from the first electron, and
as a background electron if the electric charge is the same. To reduce
background from converted photons from initial- or final-state radiation, the
invariant mass of any pairs of electrons must lie within 5 GeV of 90 GeV in
opposite-charge events and within 5 GeV of 88 GeV in same-charge events. The
lower value used in same-charge events accounts for the fact that electrons
with the incorrect charge have a higher probability for energy loss as
discussed in Section 9.2 and illustrated in Figure 30(a).

Input quantities to the BDT are the electron $E_{\text{T}}$ and $\eta$, and a
set of additional variables. In decreasing order of separation power, these
are: the transverse impact parameter multiplied by the electron electric
charge $q\times d_{0}$, the average charge of all tracks matched to the
electron weighted by their number of hits in the SCT detector
$\bar{q}_{\mathrm{SCT}}$, $E/p$ and $\Delta\phi_{\mathrm{res}}$. With
$\bar{q}_{\mathrm{SCT}}$ the BDT includes for the first time the reconstructed
properties of additional tracks in the vicinity of the electron, which
improves rejection in cases where the incorrect track is chosen as the primary
electron track.

The efficiency of the requirement on the BDT is 98% in $Z\to ee$ events for
electrons satisfying Medium or Tight identification with the Tight isolation
requirement, and that have the correct electric charge. Approximately 90% of
electrons with the same identification and isolation requirements but
incorrect electric charge are removed. This re-optimization of the BDT
variables has improved the efficiency of the selection criterion, leaving the
rejection of electrons with misidentified charge unchanged.

###  9.2 Measurement of the probability for charge misidentification

The probability for electron charge misidentification is measured in seven
bins in $\eta$ and six $E_{\text{T}}$ bins in the range
$20\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}<E_{\text{T}}<95\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}$ in $Z\to ee$ events. The events were collected with
the dielectron triggers discussed in Section 3.1 with transverse momentum
thresholds of 17 GeV or less and Loose trigger identification, allowing the
measurement to be extended to lower values of $E_{\text{T}}$ and looser
identification criteria than previous measurements. Both electrons in the
event are selected with the same identification and isolation criteria and,
respectively, fall into bins $i$ and $j$ in $\left(\eta,E_{\text{T}}\right)$,
yielding $N_{ij}$ $Z\to ee$ events. Their invariant mass must lie within 10
GeV of the nominal $Z$-boson mass. The probabilities of the electron charge
misidentification in bins $i$ and $j$, $\epsilon_{i}$ and $\epsilon_{j}$,
maximize the Poisson probability
$P\left(\lambda_{ij}|n_{ij}^{\mathrm{sc}}\right)$, where:

$\lambda_{ij}=\left(\epsilon_{i}\left(1-\epsilon_{j}\right)+\left(1-\epsilon_{i}\right)\epsilon_{j}\right)N_{ij}+B_{ij}^{\mathrm{sc}},$

and $n_{ij}^{\mathrm{sc}}$ is the number of same-charge $Z\to ee$ events. The
number of background events in the sample where both electrons have the same