Operation and performance
of the ATLAS tile calorimeter in LHC Run 2 The ATLAS tile calorimeter
(TileCal) is the hadronic sampling calorimeter covering the central region of
the ATLAS detector at the Large Hadron Collider (LHC). This paper gives an
overview of the calorimeter’s operation and performance during the years
2015–2018 (Run 2). In this period, ATLAS collected proton–proton collision
data at a centre-of-mass energy of 13 TeV and the TileCal was 99.65% efficient
for data-taking. The signal reconstruction, the calibration procedures, and
the detector operational status are presented. The performance of two ATLAS
trigger systems making use of TileCal information, the minimum-bias trigger
scintillators and the tile muon trigger, is discussed. Studies of radiation
effects allow the degradation of the output signals at the end of the LHC and
HL-LHC operations to be estimated. Finally, the TileCal response to isolated
muons, hadrons and jets from proton–proton collisions is presented. The energy
and time calibration methods performed excellently, resulting in good
stability and uniformity of the calorimeter response during Run 2. The setting
of the energy scale was performed with an uncertainty of 2%. The results
demonstrate that the performance is in accordance with specifications defined
in the Technical Design Report. TCAL-2021-01 CERN-EP-2023-266 Eur. Phys. J. C.

###### Contents

  1. 1 Introduction
  2. 2 Experimental setup
    1. 2.1 Tile calorimeter
    2. 2.2 Readout electronics
    3. 2.3 Calibration systems
      1. 2.3.1 Charge Injection system
      2. 2.3.2 Integrator readout of minimum-bias collisions
      3. 2.3.3 Caesium system
      4. 2.3.4 Laser system
  3. 3 Reconstruction and calibration of signals in physics events
    1. 3.1 Signal amplitude
      1. 3.1.1 Channel timing calibration
      2. 3.1.2 Channel timing monitoring
    2. 3.2 The conversion factor from ADC counts to pC
    3. 3.3 Signal measurement in GeV
    4. 3.4 Monitoring of the PMT, tile and fibre response with the caesium system
    5. 3.5 Monitoring of the PMT, tile and fibre response with minimum-bias collisions
    6. 3.6 Monitoring of the PMT response with the laser system
    7. 3.7 The calibration procedure
    8. 3.8 Signal reconstruction of simulated events
  4. 4 Trigger signals
    1. 4.1 Level-1 calorimeter trigger
    2. 4.2 Tile muon trigger
    3. 4.3 Minimum-bias trigger scintillators
  5. 5 Radiation exposure effects
    1. 5.1 Comparison of laser, caesium and minimum-bias measurements
    2. 5.2 Degradation of scintillator tiles and WLS fibres
    3. 5.3 Degradation of the MBTS system
  6. 6 Data quality analysis and operation
    1. 6.1 Detector control system
    2. 6.2 Calibration run validation
    3. 6.3 Online data quality assessment and monitoring
    4. 6.4 Offline data quality review
    5. 6.5 Summary of TileCal operations in Run 2
  7. 7 Performance studies
    1. 7.1 Energy response to single isolated muons
      1. 7.1.1 Selection of isolated muons
      2. 7.1.2 Cell response uniformity
      3. 7.1.3 Radial layer calibration
      4. 7.1.4 Time stability
    2. 7.2 Energy response to single isolated hadrons
    3. 7.3 Timing performance with collision data
      1. 7.3.1 Mean time and time resolution
      2. 7.3.2 Effect of pile-up on the time resolution
      3. 7.3.3 Run-to-run differences
    4. 7.4 Electronic and pile-up noise
      1. 7.4.1 Electronic noise
      2. 7.4.2 Pile-up noise
    5. 7.5 Performance of the tile muon trigger system
    6. 7.6 Performance of the minimum-bias trigger scintillators
    7. 7.7 Summary of performance studies
  8. 8 Conclusion

##  1 Introduction

ATLAS [1] is a general-purpose detector at the Large Hadron Collider (LHC) [2]
designed to reconstruct events from colliding hadrons. It has a
forward–backward symmetric cylindrical geometry and a near $4\pi$ coverage in
solid angle. ATLAS consists of an inner tracking detector surrounded by a thin
superconducting solenoid providing a $2\text{\,}\mathrm{T}$ axial magnetic
field, electromagnetic and hadronic calorimeters, and a muon spectrometer. The
inner tracking detector covers the pseudorapidity range of $|\eta|<2.5$.111
ATLAS uses a right-handed coordinate system with its origin at the nominal
interaction point (IP) in the centre of the detector and the $z$-axis along
the beam pipe. The $x$-axis points from the IP to the centre of the LHC ring,
and the $y$-axis points upwards. 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
$\eta=-\ln\tan(\theta/2)$. Angular distance is measured in units of $\Delta
R\equiv\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}}$. It consists of silicon
pixel, silicon microstrip, and transition radiation tracking detectors.
Lead/liquid-Argon (LAr) sampling calorimeters provide electromagnetic (EM)
energy measurements. A steel/scintillator-tile hadronic calorimeter covers the
central pseudorapidity range of $|\eta|<1.7$. The endcap and forward regions
are instrumented with LAr calorimeters for both the EM and hadronic energy
measurements up to $|\eta|=4.9$. The muon spectrometer (MS) surrounds the
calorimeters in the pseudorapidity range of $|\eta|<2.7$ and is based on three
large superconducting air-core toroidal magnets with eight coils each. The
field integral of the toroids ranges between $2$ and
$6\text{\,}\mathrm{T}\mathrm{m}$ across most of the detector. The muon
spectrometer includes a system of precision tracking chambers and fast
detectors for triggering.

The tile calorimeter (TileCal) is the hadronic barrel calorimeter sub-detector
of ATLAS and provides essential input to the identification of hadronic jets
and measurement of their energy and direction. It also provides information
for triggers, participates in the measurement of the missing transverse
momentum carried by non-interacting or not detected particles, and assists in
the identification of muons. The TileCal design provides a standalone energy
resolution for isolated pions of $\sigma/E=56.4\%/\sqrt{E(\text{GeV})}\oplus
5.5\%$ [1] and a linear response with a nonlinearity tolerance of 2% for jets
up to 4 TeV to be sensitive to the full range of energies expected in the LHC
lifetime. A detailed description of the ATLAS TileCal can be found in the
dedicated Technical Design Report [3]; the construction, optical
instrumentation and installation into the ATLAS detector are described in
Refs. [4, 5]; the operation and performance of the TileCal during Run 1 at the
LHC are reported in Ref. [6].

This paper presents the operation and performance of the TileCal during the
LHC Run 2 data-taking period (2015–2018).222 In ATLAS, data collected over
periods of time spanning an LHC fill or generally stable conditions are
grouped into a ‘run’, while the entire running period under similar conditions
for several years is referred to as a ‘Run’. Run 1 refers to runs collected in
the period 2008–2012. Data taken within a run are broken down into elementary
units called luminosity blocks, corresponding to about one minute of collision
data for which the detector conditions or software calibrations remain
approximately constant.  The full ATLAS detector recorded events from cosmic-
ray muons in the period February–July 2015. The first proton–proton ($pp$)
collisions at a centre of mass energy $\sqrt{\text{s}}\leavevmode\nobreak\
=\leavevmode\nobreak\ 13$ TeV were recorded in April 2015 with a bunch spacing
of $50\text{\,}\mathrm{n}\mathrm{s}$ [7]. Later in 2015 and the following
years, the LHC $pp$ collisions continued to be at
$\sqrt{\text{s}}=13\leavevmode\nobreak\ \text{TeV}$, but the instantaneous
luminosity and the number of proton collisions per bunch crossing increased
and the bunch spacing decreased to 25 ns. The total integrated recorded
(delivered) luminosity was 145.5 fb-1 (157.4 fb-1) [7, 8]. Only events
recorded during stable beam conditions and with all ATLAS sub-detectors fully
operational are considered in the analysis. The corresponding integrated
luminosity is 140.1 fb-1 [8]. A summary of the LHC beam conditions in Run 2 is
shown in Table 1. Additional special runs with low integrated luminosity and a
low average number of interactions per bunch crossing, $\langle\mu\rangle$,
used for commissioning purposes, were taken with a bunch spacing of 25 ns in
2017 and 2018. During these years ATLAS also recorded data with lower-energy
proton collisions ($\sqrt{\text{s}}=\leavevmode\nobreak\ 5\leavevmode\nobreak\
\text{TeV}$), and data produced by lead–lead or xenon–xenon ion collisions.
These runs had very low integrated luminosity.

Table 1: Summary of the proton–proton collision data collected in the four years of Run 2 and used to obtain the results presented in this paper. The ATLAS analysis integrated luminosity corresponds to the total integrated luminosity approved for analysis, passing all data quality requirements ensuring the detector and reconstruction software are properly functioning [8, 7]. | 2015 | 2016 | 2017 | 2018
---|---|---|---|---
Maximum beam energy [TeV] | 6.5 | 6.5 | 6.5 | 6.5
Delivered integrated luminosity [fb-1] | 4.0 | 39.0 | 50.6 | 63.8
Recorded integrated luminosity [fb-1] | 3.6 | 35.5 | 46.4 | 60.0
ATLAS analysis integrated luminosity [fb-1] | 3.2 | 33.4 | 44.6 | 58.8
Mean number of interactions per bunch crossing | 13 | 25 | 38 | 36
Maximum instantaneous luminosity [$10^{33}\text{cm}^{-2}\text{s}^{-1}$] | 5 | 13 | 16 | 19

The recorded events are separated into different streams according to the
trigger category for which the event is selected. Physics streams are composed
of triggers that are used to identify electrons, photons, muons, jets,
hadronically decaying $\tau$-leptons, and missing transverse momentum in
collision data. There are also calibration streams used by the various sub-
detectors for calibration and monitoring purposes.

This paper is organised as follows. Section 2 describes the experimental set-
up. The reconstruction and the calibration of physics events are the subjects
of Section 3. The calibration streams used by the TileCal for calibration
purposes were taken in dedicated runs when the beams were off. As discussed in
the paper, they include caesium, laser and charge injection system (CIS)
events. Laser events taken during empty bunches in the LHC abort gap [2] are
used for timing calibration. Physics events are also used for calibration
purposes. To minimise systematic uncertainties, as discussed at the end of the
section, the procedure used to reconstruct the experimental energy deposited
in the cells is used in the case of simulated events. The TileCal data subsets
used in the hardware-based Level-1 (L1) ATLAS trigger system are discussed in
Section 4. The deterioration of the detector performance due to the radiation
exposure is reported in Section 5. These studies allow the amplitude reduction
of the output signals at the end of the LHC and HL-LHC operations to be
estimated. The online and offline data quality (DQ) checks applied to the
hardware and data acquisition systems are explained in Section 6. The
validation of the full chain of TileCal calibration and reconstruction using
physics events is described in Section 7. The results are obtained by
analysing the physics stream containing muons, zero-bias events [9] and jets.
The performance of ATLAS trigger systems based on TileCal information is also
discussed. All results presented in this document are summarised in Section 8.

The data used in the studies were collected by the tile calorimeter sub-
detector using the full ATLAS data acquisition chain. An extensive software
suite [10] is used for real and simulated data reconstruction and analysis,
for operation, and in the trigger and data acquisition systems of the
experiment. In addition to the TileCal, the information of other ATLAS sub-
detectors is used to assist in particle identification, and track, momentum
and energy reconstruction.

##  2 Experimental setup

###  2.1 Tile calorimeter

The tile calorimeter is a sampling calorimeter consisting of tiles of plastic
scintillator as active material and low-carbon steel absorber plates. The
technical details of the scintillator tiles are described in Ref. [5]. As
shown in Figure 1(a), the TileCal surrounds the LAr calorimeter and fills the
volume from an inner radius of 2.28 m to an outer radius of 4.23 m. The amount
of material in front of the TileCal at $\eta=0$ corresponds to 2.3$\lambda$
333 The nuclear interaction length $\lambda$ is defined as the mean path
length required to reduce the flux of relativistic primary protons and
neutrons to a fraction 1/e.  [1]. The sub-detector thickness at the outer edge
of the tile instrumented region is 9.7$\lambda$ at $\eta=0$. Including
1.3$\lambda$ from the outer support, the total detector thickness is
11$\lambda$ at $\eta=0$, sufficient to reduce punch-through well below the
irreducible level of prompt decay muons. The calorimeter is mechanically
divided into three segments along the $z$-axis (the beam axis): one central
long barrel (LB) section that is 5.8 m in length ($|\eta|<1.0$), and two
extended barrel (EB) sections on either side of the LB that are each 2.6 m
long ($0.8<|\eta|<1.7$).

((a))

((b))

Figure 1: (a) Cut-away view of the ATLAS calorimeter system. The TileCal
consists of a barrel and two extended barrel sections. The sections of the
ATLAS liquid-argon (LAr) calorimeters are also indicated. (b) An illustration
of the mechanical assembly and optical readout of a single tile calorimeter
module. A total of 256 such modules comprise the full tile calorimeter. Source
tubes are used to circulate a 137Cs radioactive source contained in a capsule
for calibration purposes.

Each TileCal barrel consists of 64 modules in the angular direction $\phi$
allowing full azimuth coverage. Figure 1(b) shows a schematic of a TileCal
module. In each module, the steel and scintillator tiles have a thickness of
14 mm and 3 mm respectively. The steel and scintillator tiles are interleaved
periodically in the longitudinal direction $z$. The scintillator tiles are
organised along the radius in 11 rows of different sizes, numbered from 1 to
11 starting from the smallest radius. Each row corresponds to a group of tiles
at the same distance from the beam axis. Light from the scintillator tiles is
collected at their edges by wavelength-shifting (WLS) fibres, arranged in pre-
shaped opaque plastic ‘profiles’ attached to both sides of the modules and
running radially, as shown in Figure 1(b). The WLS fibres transport the light
to photomultiplier tubes (PMTs). The readout cell geometry is defined by
grouping the fibres from individual tiles on the given PMTs [5]. The cell
layout of the LB and EB modules is shown in Figure 2 for $z>0$. A mirroring of
those in the other direction in $z$ defines the three sections of the
calorimeter. Three longitudinal layers are obtained. In the long barrels,
layers A, BC and D cells are made of three, six and two rows corresponding to
depths of 1.5, 4.1, and 1.8$\lambda$ respectively. In the extended barrels,
layers A, B and D cells have three, four and four rows corresponding to depths
of 1.5, 2.6, and 3.3$\lambda$ respectively. The layers allow the jet energy
depositions to be measured at different depths. The cells have a granularity
of $\Delta\eta\times\Delta\phi=0.1\times 0.1$ in the two innermost layers and
$\Delta\eta\times\Delta\phi=0.2\times 0.1$ in the outermost one. As shown in
the figure, the scheme produces pseudo-projective towers. The total energy in
a tower is used for triggering purposes as discussed in Section 2.2.

To correct for energy losses in the gap region between the TileCal and the LAr
sections, where many cables and electronics racks from other ATLAS sub-
detectors are located, a special Intermediate tile calorimeter (ITC) system is
installed. As shown in Figure 2, the ITC cells (D4, C10 and E1–E4) are located
between the LB and EB, and provide coverage in the range of $0.8<|\eta|<1.6$.
Some of the C10 and D4 cells have reduced thickness or special geometry to
accommodate services and readout electronics for other ATLAS sub-detectors [3,
11]. The gap (E1–E2) and crack (E3–E4) cells are composed of only scintillator
media and are read out by one PMT each. The minimum-bias trigger scintillators
(MBTS) [12], used to trigger events from colliding particles, are also read
out by TileCal EB electronics and provide coverage in the range of
$2.08<|\eta|<3.86$ (see Section 4.3). Most TileCal cells are read out by two
PMTs, accounting for a total of 9852 readout channels for the 5182 cells.

Figure 2: The layout of the TileCal cells with $\eta\geq 0$, denoted by one or
two letters (A to E) plus an integer number. The layer A is closest to the
beamline.The naming convention is repeated for cells with negative $\eta$. The
long barrel (extended barrel) cells are shown at the left (right).

###  2.2 Readout electronics

The PMTs and front-end electronics are placed in aluminium units housed in a
steel girder on the outer radius of each module. The units can be completely
extracted and are therefore called electronics drawers. Two contiguous
connected drawers form a super-drawer. In each module of the LB there are two
super-drawers hosting the electronics of the cells with $\eta>0$ (A-side) and
$\eta<0$ (C-side) respectively. The electronics of the cells of each of the
modules of the EBs are located in a super-drawer. In this way, from an
electronic point of view, one identifies four barrels, the LBA and EBA with
$\eta>0$ and the LBC and EBC with $\eta<0$. There are 45 and 32 channels per
super-drawer in the LB and EB, respectively.

Each channel consists of a unit called a PMT block, which contains the light-
mixer, PMT tube and High-Voltage (HV) divider, and a ‘3-in-1 card’ [13, 14].
The card receives the PMT signal and provides three output signals as follows:

  * •

A shaper with a shaping time of 50 ns shapes the fast PMT signal to the
requirements of the 10-bit, 40M sample per second ADCs used to digitise the
signal at the LHC bunch crossing rate [15]. The amplitude of the shaped signal
is proportional to the PMT signal. Two linear outputs are produced with a
relative gain of 64 and hence an overall 16-bit dynamic range using two 10-bit
ADCs. Seven samples centred around the pulse peak and synchronised with the
LHC master clock are extracted from the circular pipeline buffer. The data are
temporarily stored in another pipeline memory until a Level-1 trigger [9]
signal is received. A gain switch is used to determine which gain information
is sent to the back-end electronics for event processing. By default the high-
gain (HG) signal is used unless any of the seven samples saturates the ADC, at
which point the low-gain (LG) signal is transmitted. The signals from the
digital readout are used to measure physics and laser calibration data
(Section 2.3)

  * •

An integrator that receives less than 1% of the PMT current digitized by a
12-bit ADC card saturating at 5 V [16]. The integrator is a low-pass DC
amplifier with six switchable gain settings and a calibration input. With one
of the available gains, the currents range between 0.01 nA and 1.4 $\mu$A over
a time window of 10–20 ms. The integrator readout is used for calibration and
monitoring purposes (Section 2.3) measuring the caesium and physics runs
signals. In the case of physics runs the signals are produced essentially by
inelastic proton-proton collisions at low momentum transfer, known as minimum-
bias (MB) events. Besides response monitoring, the measurements of MB events
also allow to determine the instantaneous luminosity of the colliding beams,
not discussed in this article.

  * •

A differential signal from the LG output of the shaper is sent to the adder
boards located in the drawer to determine the total energy in a calorimeter
tower used in the ATLAS trigger (Section 4.1). The signals of the D5 and D6
cells are used as input to the tile muon trigger system (Section 4.2). The
channels reading the MBTS counters provide the analogue HG outputs to the
corresponding trigger (Section 4.3).

In addition to the PMT signals, the 3-in-1 card also contains an input path
for the calibration charge injection system described in Section 2.3.1.

In the case of the digital readout, the DMU (data management unit) chips
located on the digitiser boards are responsible for organising the digitized
samples in packets of data. There are eight digitiser boards in each super-
drawer, and each one has two DMU devices, so there are 16 DMU devices per
super-drawer. The interface board collects data from all the digitisers,
serialises and transmits them to the back-end electronics. The integrity of
the data received by the back-end is checked using a CRC (cyclic redundancy
check) algorithm. The back-end electronics are located in the counting room
approximately 100 m away from the ATLAS detector. The data acquisition system
of the TileCal is split into four logical partitions associated with the
super-drawers of the modules in LBA, LBC, EBA, and EBC. Optical fibres
transmit signals between each super-drawer and the back-end trigger, timing
and control (TTC), and readout driver (ROD [17]) crates. There are a total of
four TTC and ROD crates, one for each logical partition. The ATLAS TTC system
distributes the LHC clock, trigger decisions, and configuration commands to
the front-end electronics. If the TTC system sends the trigger acceptance
command to the front-end electronics, the corresponding digital samples for
all channels of the calorimeter are sent to the ROD where the signal is
reconstructed.

The integrator output voltage of each PMT of a module, proportional to the
input charge, is read out sequentially using a single ADC. The switching
between the corresponding 3-in-1 cards takes place about every 0.1 s. This
switching mechanism is known to induce noise for a couple of bunch crossings,
thus it is done in the LHC abort gap [2]. The ‘SHAFT board’ [18, 19] that is
responsible for handling the different Tile calibration signals during data-
taking, sends the pulse to trigger the sending of the switching command via
TTC to be distributed over the full detector. The digitized signals are sent
to an off-detector readout buffer through CAN bus.

The front-end electronics of a single super-drawer are supplied by a low-
voltage power supply (LVPS) source, which is positioned in an external steel
box mounted just outside the super-drawer. The HV is set and distributed to
each PMT using dedicated boards positioned inside the super-drawers next to
the front-end electronics.

###  2.3 Calibration systems

Figure 3: The signal paths for each of the three calibration systems used by
the TileCal. The signal produced by particles from collisions is denoted by
the thick solid line, and the path taken by each of the calibration systems is
shown with dashed lines.

The ATLAS physics performance goals for hadronic jets measurements require a
tolerance of 2% on the non-linearity of the detector response for jets up to 4
TeV. To achieve this in the ATLAS environment and over an extended period of
time requires calibration of the calorimeter response with the same precision.
Four systems, the electronic charge injection system, the integrator readout,
the caesium radioactive $\gamma$-source system [20] and the laser system [21]
are used, as depicted in Figure 3. They probe the three steps in the signal
reconstruction of TileCal and MBTS cells (see Section 4.3): production and
collection of light in scintillator tiles and fibres, conversion of light to
electrical signal in PMTs, and calibration of electrical signals in the
electronic readout. The aim is to maintain a uniform and stable response of
the measurements of the energy deposited in all cells accounting for changes
in the optics and electronics. The calibration systems allow the scale of the
cell energy measurement to be set, as described in Section 3, and the
determinations obtained using experimental and simulated data to be compared.
The caesium source, MB currents and the laser system allow to determine the
degradation of the TileCal and MBTS signals due to their exposure to a high
radiation level produced during the LHC operations. The latter is discussed in
Section 5. Moreover, the three complementary calibration systems also aid in
identifying the source of problematic channels (see Section 6.2). Problems
originating strictly in the readout electronics are seen by both the laser and
CIS, while problems related solely to the PMTs are detected exclusively by the
laser system.

####  2.3.1 Charge Injection system

The charge injection system calibrates the front-end electronics. The
calibration is performed by injecting a full dynamic range of input charge
signals, similar to what the detector experiences in physics runs, to the
readout electronics of all channels through the respective 3-in-1 cards. The
magnitude of each injected charge is controlled by a 10-bit digital to
analogue converter (DAC) with a conversion factor of 0.801 pC per DAC setting
count. The DAC setting is increased from 0 to 15 with a step size of 1 for the
HG readout, and varied from 32 to 992 with a step size of 32 for the LG. The
two readouts provide a comprehensive test of the electronics response over the
full range of energies expected during regular running of the LHC. As
discussed in Section 2.3.2, a part of this system is also used to calibrate
the gain conversion constant of the integrator readout (see Figure 3).

####  2.3.2 Integrator readout of minimum-bias collisions

The integrator readout measurements of the PMT current induced by MB $pp$
interactions are used to monitor the variations of the sub-detector response
over time. The current, proportional to the LHC luminosity, varies with the
position of the cell. To avoid saturation and maintain an adequate resolution,
the integrator gain can be selected by choosing one of the six predefined
resistors that also define the integration time. The PMT current is obtained
from the ADC voltage measurement as

$I\ \mathrm{[nA]=\frac{ADC\ [mV]-ped\ [mV]}{Int.\ gain\ [M\Omega]}}$ (1)

where ped is the pedestal, measured with circulating beams before collisions
to account for beam background sources such as beam halo and beam-gas
interactions, and Int. gain is the integrator gain constant determined by an
internal calibration circuit with a high precision DAC on the 3-in-1 card.

Dedicated runs are periodically taken to calculate the values for each of the
six gain settings by fitting the linear relationship between the injected
current and measured voltage response. For an instantaneous luminosity between
$1\times 10^{30}$ and $3\times 10^{34}$ cm-2s-1, the non–linearity of the
integrator response is $<1\%$. The deviation from stability of the integrator
gains is better than 0.05% for individual channels and better than 0.01% on
average.

####  2.3.3 Caesium system

The caesium system employs three 137Cs radioactive $\gamma$-sources, one for
the LB, one for the EBA and one for the EBC modules [20]. A hydraulic system
moves the source through the calorimeter using a network of stainless steel
tubes parallel to the beam line running through small holes in each tile
scintillator (see Figure 1(b)). It produces 0.662 MeV photons that generate
scintillation light in each tile. The average activity of the three sources
was approximately 323 MBq in March 2015 and dropped to approximately 296 MBq
in December 2018 (about $-2.3$% per year). To collect a sufficient signal, the
electrical readout of the caesium calibration is performed using the
integrator readout path (see Figure 3). The readout employs a resistor of
28.81 M$\Omega$ with corresponding integration time of 13.9 ms. The caesium
system allows the cells’ response to be equalised and the combined variations
of the optical components and the PMTs to be monitored.

####  2.3.4 Laser system

The laser calibration system consists of a single laser source, located off
detector, able to produce controlled short light pulses that are
simultaneously distributed by optical fibres to the photocathode of all 9852
PMTs. During the LHC long shutdown before the start of Run 2, a new laser
system [21, 22] was developed to correct shortcomings in electronics and light
monitoring of the first system used during Run 1, which in turn resulted in an
improved long term reliability. The new system has been used since the
beginning of Run 2. The intrinsic stability of the laser light was found to be
within 3%, so to measure the PMT gain variations to a better precision using
the laser source, the response of the PMTs is normalised to the signal
measured by a dedicated photodiode. Its stability is monitored by an
$\alpha$-source and, in 2015, the variation over one month was shown to be
0.5%, and the linearity of the associated electronics response was within
0.2%. As shown in Figure 3, the laser system monitors the PMTs and electronic
components of the digital readout. Since the optical fibres have the same
length, the system is also used to equalise the timing of the digitizers (see
Section 3.1.1).

##  3 Reconstruction and calibration of signals in physics events

To reconstruct physics events, the energy deposited in a cell is obtained by
summing the energy measurements from the connected PMT channels, with each
channel energy $E$ given by

$E\ [\text{GeV}]=\frac{A\ [\mathrm{ADC}]}{C_{\mathrm{ADC}\to\mathrm{pC}}\times
C_{\mathrm{pC}\to\text{GeV}}\times C_{\mathrm{Cs}}\times C_{\mathrm{MB}}\times
C_{\mathrm{Las}}}.$ (2)

The signal amplitude $A$ is determined by using the seven signal samples of
the digital readout (Section 2.2) as discussed in Section 3.1. The calibration
constant $C_{\mathrm{ADC}\to\mathrm{pC}}$ converting the signal from ADC
channel units to pC units is estimated using the CIS system as reported in
Section 3.2. The factor $C_{\mathrm{pC}\to\text{GeV}}$ was determined by
measuring the response of the sub-detector to electrons with test beams (TBs)
(Section 3.3). It allows the signals to be expressed in GeV and the
experimental energy determinations to be compared with the ones obtained using
simulated events. The factors $C_{\mathrm{Cs}}$, $C_{\mathrm{MB}}$ and
$C_{\mathrm{Las}}$, discussed in Section 3.4, Section 3.5 and Section 3.6
respectively, are used to monitor the stability of the responses and provide
corrections for each channel during the ATLAS operations. The procedure is
described in Section 3.7. In the case of simulated events, the cell energy
deposited is also obtained using Eq. (2) with the $C_{\mathrm{Cs}}$,
$C_{\mathrm{MB}}$ and $C_{\mathrm{Las}}$ constants being equal to 1. The
procedure is discussed in Section 3.8.

###  3.1 Signal amplitude

The optimal filtering (OF) algorithm is used to reconstruct the amplitude $A$
in units of ADC counts, the time offset $\tau$ relative to the 40 MHz clock
and the pedestal, $p$, of the pulse of the shaped PMT signal [23, 24]. The
method linearly combines the seven signal samples $S_{i}$, $i=1,...,7$ of the
digital readout, which are read with 25 ns spacing:

$A=\sum_{i=1}^{n=7}a_{i}S_{i},\hskip
30.00005ptA\tau=\sum_{i=1}^{n=7}b_{i}S_{i},\hskip
30.00005ptp=\sum_{i=1}^{n=7}c_{i}S_{i}.$ (3)

The coefficients $a_{i}$, $b_{i}$ and $c_{i}$ are optimised using TB data to
minimise the bias on the reconstructed quantities introduced by the electronic
noise (see Section 7.4.1) [24]. The normalised pulse shape function, taken as
the average pulse shape from test beam data, is used to determine the
coefficients. As shown in Figure 4, separate functions are defined for HG and
LG modes. The pulse shape and coefficients are stored in a dedicated database.
The values of $A$, $\tau$ and $p$ are obtained by solving the set of equations
in Eq. (3). The signal reconstruction is performed twice: i) in real time by
the RODs (referred to as online) for use in the trigger, and ii) after the
data have been recorded (referred to as offline) for use in the data analysis.

Figure 4: The reference pulse shapes for high gain (dotted curve) and low gain
(solid curve), shown in arbitrary units [11].

The expected time of the pulse peak is calibrated such that, for particles
originating from collisions at the interaction point, the pulse should peak at
the central (fourth) sample, synchronous with the LHC clock. The reconstructed
value of $\tau$ represents the time offset in nanoseconds between the expected
pulse peak and the time of the actual reconstructed signal peak, arising from
fluctuations in particle travel time and uncertainties in the electronics
readout (see Section 3.1.1).

There are two versions of the optimal filtering algorithm, iterative and non-
iterative. The coefficients $a_{i}$, $b_{i}$ and $c_{i}$ are functions of the
pulse’s true time offset relative to the 40 MHz clock. This time offset is
known only approximately a priori before the reconstruction. The iterative OF
method takes the time of the maximum sample as an initial value of the time
offset. In the subsequent iterations, the input time offset is taken to be
equal to $\tau$ calculated in the previous iteration. The algorithm converges
to the actual time offset value with an accuracy better than 0.5 ns in the
absence of pile-up pulses (see Section 7.4.2). Typically, three iterations are
needed to converge. This method is used when reconstructing events occurring
asynchronously with the LHC clock, such as cosmic-ray muons. With an
increasing number of events per bunch crossing, the non-iterative method,
which is more robust against pile-up, is used. The out-of-time pile-up, see
Section 7.3.2, can lead to a reconstructed time offset value far from the
expected one, biasing the energy measurement when the iterative method is
used. The non-iterative OF method performs only a single iteration of the
optimal filtering method and uses as input the time offset determined for each
TileCal channel from prior timing calibration runs. This is the time offset
expected for in-time pulses from the collisions of interest. By forcing the
time offset to its predetermined expected value, the non-iterative optimal
filtering method better reconstructs the energy of the in-time pulse from a
collision of interest in the presence of out-of-time pile-up. This method is
also more robust against electronic noise for very low amplitude signals.

In real time, or online, the digital signal processor (DSP) in the ROD
performs the signal reconstruction using the OF technique and provides the
channel energy and time to the High-Level Trigger [9]. The conversion between
signal amplitude in ADC counts and energy units of GeV is done by applying
channel-dependent calibration constants that are described in the following
sections. The DSP reconstruction is limited by the use of fixed point
arithmetic, which has a precision of 0.0625 ADC counts (approximately 0.75 MeV
in HG), and imposes precision limitations for the channel-dependent
calibration constants. The offline signal is reconstructed using the same
iterative or non-iterative OF technique as online but using floating point
arithmetic.

To avoid saturation of the output ROD bandwidth in high instantaneous
luminosity conditions, all LG channels and only HG channels for which the
difference between the maximum and minimum $S_{i}$ is larger than five ADC
counts (approximately 60 MeV) have the raw data transmitted from the ROD for
offline signal reconstruction. Otherwise, the ROD signal reconstruction
results are used for the offline data processing.

####  3.1.1 Channel timing calibration

To allow for optimal energy reconstruction by the non-iterative OF method and
to enable precise time-of-flight measurement in certain physics analyses, the
time difference between the digitising sampling clock and the peak of the PMT
pulses must be minimised and measured with a precision of 1 ns. To achieve
this, the clock phases in the DMUs in the front-end hardware (see Section 2.2)
are adjusted in multiples of 104 ps. The hardware time offset can be set for
groups of six channels.

The initial time calibration for Run 2 was performed using the relative timing
differences per channel relative to the end of Run 1 measured by the laser
system (see Section 2.3.4). The calibration was later refined using beam-
splash events from a single LHC beam utilising the same method as before the
start of Run 1 [11]. Finally, the time calibration is established with the
$pp$ collision data. To avoid possible bias from non-collision beam
backgrounds, only channels belonging to reconstructed jets satisfying standard
quality criteria [25, 26] are considered in each event. Given that the timing
is slightly dependent on the energy deposited in a cell, in the case of HG
signals, the offset is determined in the range
$$2\text{\,}\mathrm{GeV}$<E<$4\text{\,}\mathrm{GeV}$$. In the case of LG
signals the behaviour is smoother and a broader energy range of
$$15\text{\,}\mathrm{GeV}$<E<$50\text{\,}\mathrm{GeV}$$ is chosen. The
distributions show that more than 99.5% of the reconstructed $\tau$ values are
found to be between $-10$ ns and $+10$ ns. A non-zero value of the phase
$\tau$ causes the reconstructed amplitude to be underestimated. A correction
(parabolic correction) based on the phase is applied when the phase is
reconstructed within half the LHC bunch spacing (12.5 ns) and the channel
amplitude is larger than 15 ADC counts, to reduce contributions from noise
[6]. After applying the correction, the reconstructed amplitudes are found to
underestimate the actual signal by less than 1% in magnitude within time
phases of $\pm$10 ns. Pile-up is included in simulated events, such that the
signal amplitude reconstruction proceeds in the same way for simulated and
real events (see Section 3.8).

####  3.1.2 Channel timing monitoring

As discussed, the time settings in each channel are adjusted so that the
channel signal pulse produced by a collision particle peaks at the central
sample of the digital readout. Two complementary procedures are developed to
monitor the time calibration. The first one exploits the laser calibration
events recorded during the empty bunch crossings of physics runs with a
frequency of about 3 Hz. This tool provides the reconstructed time as a
function of the luminosity block in each channel. The second tool directly
uses physics events. Only HG signals are monitored. Both tools were
systematically used in all runs and revealed three main types of problems: the
so-called timing jumps, bunch-crossing offsets, and bad or unstable channels.

((a))

((b))

Figure 5: (a) The reconstructed time of laser events as a function of the
luminosity block. Data from six channels belonging to the same digitizer are
superimposed. The timing jump lasted the entire duration of the run and all
events are centered around $+$15\text{\,}\mathrm{n}\mathrm{s}$$. The dashed
line indicates the expected mean time value. (b) The 2D histogram shows the
average channel time in physics events on a colour scale as a function of
module number ($x$-axis) and channel number ($y$-axis).

In a timing jump, the reconstructed time suddenly changes for a group of six
channels belonging to the same digitiser board. An example of such a case,
identified by both monitoring tools, is shown in Figure 5. Timing jumps are
corrected by adjusting the corresponding time constants in the affected
period. The observed frequency of timing jumps was much lower than in Run 1
[6] due to the improved stability of the LVPS, and they have no direct impact
on the overall timing performance.

((a))

((b))

Figure 6: (a) The reconstructed time of laser events as a function of the
luminosity block. Data from three channels belonging to the same DMU are
superimposed. The majority of events, centred around zero, are well timed in.
The events affected by the the bunch-crossing offset are centred at
$+$25\text{\,}\mathrm{n}\mathrm{s}$$. (b) The reconstructed time in physics
events in the same three channels with (corrected) and without (original)
applying the algorithm mitigating the bunch-crossing offset events. The
algorithm significantly reduces events centred around
$+$25\text{\,}\mathrm{n}\mathrm{s}$$.

The bunch-crossing offsets correspond to the cases where channels have
reconstructed times occasionally deviating by one or two bunch crossings, i.e.
$\pm 25$ or $\pm$50\text{\,}\mathrm{n}\mathrm{s}$$. This feature affects three
channels connected to the same DMU [15] described in Section 2.2. The
magnitude of the observed offsets and affected events are fully correlated
across the three channels. The problem is intermittent and affected events
occur typically at a percent-level rate. The bunch-crossing offsets are
identified with laser and physics events. An example is shown in Figure 6(a).
In order to mitigate this problem, the affected channels are flagged in the
conditions database (Section 6.4) and a dedicated software algorithm was
developed to identify individual problematic events in the affected channels
and exclude them from further data processing. Figure 6(b) compares the
reconstructed time in physics events with and without this algorithm applied.
A significant fraction of affected events close to
$+$25\text{\,}\mathrm{n}\mathrm{s}$$ is removed. This algorithm was used
during the data reprocessing campaign.

Some channels have a distorted pulse shape resulting in a wrong reconstructed
time or they exhibit instabilities in the reconstruction. This is typically
caused by a malfunctioning or damaged hardware component in a given channel. A
special flag is assigned to such channels to prevent the incorrect time from
further propagation in the object reconstruction and subsequent data analysis.
In total, 35 channels were flagged as having bad or unstable timing at the end
of Run 2.

###  3.2 The conversion factor from ADC counts to pC

The CIS system described in Section 2.3.1 is used to determine the factor
$C_{\mathrm{ADC}\to\mathrm{pC}}$. Runs are typically taken daily for both
gains in the absence of colliding beams. The procedure of injecting charges,
sampling the analogue pulse, and measuring the fitted amplitude is repeated as
the DAC value is increased. The relation between the reconstructed amplitude
(in ADC counts) discussed in Section 3.1 and injected charge (in pC) is
obtained by performing a single parameter linear fit for specific ranges of
charge (3–10 pC for HG ADCs, 300–700 pC for LG ADCs).444The lower limit of
each fit range is chosen to ensure the precision of each injection to be at
least 0.04$\%$, which ensures a measured error value of less than 0.5$\%$. The
upper limit on the HG fit range eliminates injections that saturate the ADC,
as the amplitude of charge values $>$10 pC are all read out at 1023 ADC. The
slope of the linear fit yields the calibration constant
$C_{\mathrm{ADC}\to\mathrm{pC}}$ for the ADC of each channel in units of
ADC/pC. For channels where the calibration constant varies by more than 1.0%,
the constant is updated for the energy reconstruction.

Figure 7 shows the stability of the charge injection constants, as a function
of time, observed during the entire Run 2 for the HG and LG ADC channels.
There is a 0.7% systematic uncertainty present in individual calibrations,
represented by the shaded error band. This uncertainty is determined as the
characteristic channel-to-channel variation. It can be seen that the detector-
wide mean CIS constant over all non-problematic channels falls within the
systematic error band of the typical channel plotted, throughout Run 2. Figure
8 shows the change in the average CIS constant in per cent for every channel
in the detector between August 2015 (at the beginning of Run 2) and October
2018 (at the end of Run 2). In all figures shown, channels that are
unresponsive or have CIS constants that fluctuate run-to-run are not included.
For the duration of Run 2 the CIS constants of only 32 channels in the
detector changed by more than $\pm$4$\%$.

((a))

((b))

Figure 7:  The charge injection system constants
($C_{\mathrm{ADC}\to\mathrm{pC}}$) for the (a) high-gain and (b) low-gain
ADCs, as a function of time, observed during the entire Run 2 (between CIS
calibration runs taken on August 2015 and November 2018). Values for the
average over all channels and for one typical channel are shown. The RMS
values indicate the fluctuations present in calibrations. In addition, there
is a 0.7% systematic uncertainty present in individual calibrations,
represented by the shaded error band. This uncertainty comes from the observed
peak output amplitudes and is taken as characteristic of the channel-to-
channel variation from this source, prior to any calibration. Only good
channels not suffering from damaged components relevant to the charge
injection calibration are included.  Figure 8: Variations in the detector-wide
CIS constants (in per cent) between August 2015 and October 2018. The RMS
variation is approximately 0.35$\%$. Only good channels not suffering from
damaged components relevant to the charge injection calibration are included.
The first and last bins contain overflow and underflow, respectively.

###  3.3 Signal measurement in GeV

The electromagnetic (EM) scale calibration constant
$C_{\mathrm{pC}\to\text{GeV}}$, converting the cell signals measured as an
electric charge in pC to GeV, is obtained from the measured amplitude $A\
[\mathrm{ADC}]$ of the signal produced by electrons at dedicated test beam
campaigns using 11% of the production modules [11, 27]:

$C_{\mathrm{pC}\to\text{GeV}}=\frac{A\
[\mathrm{ADC}]}{C_{\mathrm{ADC}\to\mathrm{pC}}\times E_{e}}$ (4)

At TBs, the electrons hit the centre of the A cells at an angle of
$20^{\circ}$ relative to the cell surface normal. The energy $E_{e}$ of the
incident electron is completely deposited in the hit cell. The calibration
constant $C_{\mathrm{ADC}\to\mathrm{pC}}$, obtained using CIS measurements,
allows the measured amplitude in ADC counts to be converted to pC (Section
3.2). The value of $C_{\mathrm{pC}\to\text{GeV}}$ amounts to $1.050\pm 0.003$
pC/GeV with an RMS spread of ($2.4\pm 0.1$)%.

To transport to ATLAS the value of the EM scale determined at the TB, at the
start of Run 2, the response of all TileCal cells was equalised using the same
procedure as before the electron runs at the TB and the start of Run 1 [6]. In
February 2015, ahead of the start of collisions, the HV of each PMT was
adjusted so that the integrator response to the 137Cs source in the PMTs was
equal to that observed before the start of Run 1 and also equal to the
response measured during TB campaigns. Corrections were applied taking into
account the activity decrease of the 137Cs source, which is about 2.3% per
year. After the equalisation, the HV applied to the PMTs was kept unchanged
during the entirety of Run 2.

Since the scintillator tile response depends on the impact point position of
the particle on the tile, as well as on the tile size, correction factors are
applied for each layer of the calorimeter. Those values are determined from TB
data, measuring the response to muons impinging on the calorimeter with a
direction parallel to the $z$-axis (beam axis in Figure 2), and from the
measurements obtained using a 90Sr source [27].

###  3.4 Monitoring of the PMT, tile and fibre response with the caesium
system

Since a caesium scan [20] needs a pause in the $pp$ collisions of at least six
hours, this calibration cannot be performed very often. Moreover, during the
LHC technical stop at the beginning of the data-taking period in 2016, a few
traces of liquid coming from the caesium hydraulic system were found in the
detector cavern. Since then until the end of Run 2, caesium scans were
restricted to the end of year technical stops due to risk of the liquid leak
and were performed only a few times per year in Run 2.

Figure 9(a) shows the response deviation from the expected value, $\Delta
R_{\mathrm{Cs}}$ in per cent, as a function of time, averaged over all cells
in a given radial layer. These drifts are a combination of different sources
(scintillator tiles, WLS fibres and PMTs) as detailed in Section 5.1. Due to
higher radiation exposure, the most affected cells are located at the inner
radius in layer A. Figure 9(b) shows the difference in cell responses recorded
over the period of Run 2 (between February 2015 and October 2018), for cells
located at different $\eta$. It can be seen that the degradation is not
uniform across $\eta$, an effect of the different radiation doses received. At
the end of Run 2, the most irradiated cells in layer A had their response
drifted downward by 18%, while central cells in outer layer D drifted up by
2%.

((a))

((b))

Figure 9:  (a) The average response variation of the TileCal cells to the
137Cs source relative to the expected value, $\Delta R_{\mathrm{Cs}}$, as a
function of time. The average runs over all cells in three radial layers. The
increasing response corresponds to the periods without collisions. The LHC
delivered integrated luminosity is shown by the shaded area. (b) The average
response variation of the TileCal cells to the 137Cs source relative to the
expected value, $\Delta R_{\mathrm{Cs}}$, after Run 2 data-taking, as a
function of the cell position in $\eta$, for three different layers.

In each channel, the calibration constant, $C_{\mathrm{Cs}}$ in Eq. (2) is
related to $\Delta R_{\mathrm{Cs}}$ according to

$C_{\mathrm{Cs}}=1+\Delta R_{\mathrm{Cs}}.$ (5)

The precision of the caesium calibration in a typical cell is approximately
0.3%. For cells on the extreme sides of a partition, the precision is 0.5% due
to larger uncertainties associated with the source position. The precision for
the narrow C10 and D4 ITC cells is 3% and 1%, respectively.

###  3.5 Monitoring of the PMT, tile and fibre response with minimum-bias
collisions

Corrections based on MB measurements are applied during the reprocessing of
the data. Since the MB response is proportional to the instantaneous
luminosity, the cell response to MB events is normalised to luminosity
measurements obtained using the inner tracker [8]. The response deviation in
each cell type, $\Delta R_{\mathrm{MB}}$, is determined relative to a nominal
value and then turned into a calibration constant, $C_{\mathrm{MB}}$ in Eq.
(2), as described in Section 3.7. The precision of the measurements is
approximately 1.2%. As an example, Figure 10 shows the variation of the
average response to MB events for the cells in the gap/crack region of the
Extended Barrel as a function of time. These cells are exposed to high
radiation doses.

Figure 10: The variation of the average response to MB events $\Delta
R_{\mathrm{MB}}$ for the cells in the gap/crack region of the extended barrel
as a function of time. This quantity is derived relative to the luminosity
measured using the inner tracker. The error bars correspond to the RMS of all
the response distributions. The results are normalised to the values measured
in the first run of Run 2 (16th July 2015). The integrated luminosity
delivered by the LHC is shown by the shaded area.

###  3.6 Monitoring of the PMT response with the laser system

The laser system is used to monitor the variation of the PMT response [21].
Deviation in each channel response relative to its nominal value, $\Delta
R_{\mathrm{Las}}$, is translated into a calibration constant,
$C_{\mathrm{Las}}$ in Eq. (2) using the equation

$C_{\mathrm{Las}}=1+\Delta R_{\mathrm{Las}}.$ (6)

The laser calibration runs are usually taken daily for both gains, in the
absence of colliding beams (standalone runs). To address the fast drift of PMT
response caused by the large instantaneous luminosity, the laser calibration
constants were updated every 1–2 weeks.

Figure 11 showns the mean of the $\Delta R_{\mathrm{Las}}$ values for each
cell type (average over $\phi$) measured with the laser system during the
entire $pp$ collisions period in 2018. The most affected cells are those
located at the inner radius and in the gap and crack region with down-drift up
to 4.5% and 6%, respectively. Those cells are the most irradiated and their
readout PMTs experience the largest anode current. The EB partitions
experience larger current draws than the LBs due to higher exposure. Figure 12
shows the time evolution of the mean response variation in the PMTs of each
layer observed during the entire Run 2. The PMT response exhibits a
correlation with the LHC operation, as detailed in Section 5.1. For data taken
in 2015 and 2016, the laser calibration constants were calculated and applied
for channels with PMT response variations larger than 1.5% (2%) in the LB
(EB). In 2017 and 2018, the thresholds on PMT response variations were removed
and all channels were corrected weekly. The total statistical and systematic
errors in the laser calibration constants depend on the integrated luminosity
$\mathscr{L}$ and are found to be
$\sigma/C_{\mathrm{Las}}=0.16\%(0.32\%)\cdot\mathscr{L}(\mathrm{fb^{-1}})\oplus
0.5\%$ for the LB (EBs).

Figure 11: The mean response variation $\Delta R_{\mathrm{Las}}$ in the PMTs
for each cell type, in percent, averaged over $\phi$, observed during the
entire $pp$ collisions data-taking period in 2018 (between standalone laser
calibration runs taken on 18 April 2018 and 22 October 2018). For each cell
type, the response variation is defined as the mean of a Gaussian function fit
to the response variations in the channels associated with given cell type. A
total of 64 modules in $\phi$ are used for each cell type, with the exclusion
of known bad channels. Figure 12: The mean response variation $\Delta
R_{\mathrm{Las}}$ in the PMTs for each layer, as a function of time, observed
during the entire Run 2 (between standalone laser calibration runs taken on 17
July 2015 and 22 October 2018). For each layer, the response variation is
defined as the mean of a Gaussian function fit to the response variations in
the channels associated with given layer. Known bad channels are excluded. The
LHC integrated delivered luminosity is shown by the shaded area.

###  3.7 The calibration procedure

During Run 2, data from the four sub-detector calibration systems CIS,
caesium, integrator readout and laser, were used to correct for the response
variation of the different calorimeter components. The detector calibration
constants entering in Eq. (2) $C_{\mathrm{ADC}\to\mathrm{pC}}$,
$C_{\mathrm{Cs}}$, $C_{\mathrm{MB}}$ and $C_{\mathrm{Las}}$ are stored in a
database consulted during online and offine energy reconstruction and are
defined within a time interval or a range of run numbers or a range of
luminosity blocks where they are applicable.

The calibration activities started in 2015 with the equalisation of the
detector calibration through HV adjustments to all PMTs and the channel timing
calibration, as discussed in Sections 3.3 and 3.1.1, respectively. Afterwards,
regular updates of the caesium, laser and CIS calibration constants in Eq. (2)
were performed during the data-taking period for prompt data processing. The
laser system was used to calibrate the response of the PMTs and readout
electronics by frequently updating the $C_{\mathrm{Las}}$ factors calculated
relative to the previous caesium scan. When the rare caesium scans were
performed, the values of the $C_{\mathrm{Cs}}$ constants were updated, the
laser reference signals for each PMT were written to the database and the
laser constants were reset to 1. This procedure permitted the overall response
of the detector to be calibrated with a negative offset smaller than 1% in
absolute value for most of the detector cells, which have not been harmed by
significant radiation damage. Due to the accumulated radiation exposure, since
2016 it is not possible to correct for the response reduction of the most
exposed cells with an accuracy down to 2% by relying exclusively on the sparse
caesium scans and laser measurements.

Every year, the data recorded by the ATLAS detector are reprocessed to apply
finer calibrations and improved algorithms in the ATLAS reconstruction chain,
as well as to rectify any missed or previously unattainable corrections during
prompt data processing. In particular, in the LHC Long Shutdown 2 at the end
of Run 2, the full Run 2 data set was reprocessed. For the TileCal
calibration, the reprocessing campaigns also included the determination of the
calibration constant $C_{\mathrm{MB}}$ appearing in Eq. (2) from the analysis
of the acquired collision data. The correction was introduced to address the
residual miscalibration effects due to scintillator and WLS fibre degradation
beyond the PMT response variation, more precisely calibrated with the laser
system, as follows:

$C_{\mathrm{MB}}=1+\langle\Delta R_{\mathrm{MB}}-\Delta
R_{\mathrm{Las}}\rangle.$ (7)

The cell response variations to MB events, $\Delta R_{\mathrm{MB}}$, are
calculated yearly relative to their nominal values at the beginning of the
data-taking campaign and close to the Cs scan, when $C_{\mathrm{MB}}$ is reset
to 1. These are computed as an average of the values per cell type since the
optics response variations are found to be similar accross the different
detector modules. They were introduced for the E-cells and a few cells mostly
in layer A (A13 in 2016, A12 and A13 in 2017, and A12, A13, A14 and especially
narrow C10 in 2018), which show larger response variations during LHC
operation.

###  3.8 Signal reconstruction of simulated events

In physics analysis, the measured energy is compared with that obtained by
analysing simulated events. The ATLAS Monte Carlo (MC) simulation [28] relies
on the Geant4 toolkit [29] to model the detector and the interactions of
particles with the detector material. The MC process is divided into four
steps: event generation, simulation, digitisation, and reconstruction. Various
event generators are used for the ATLAS physics analyses and performance
studies, see Section 7. During Run 2, ATLAS used the ‘FTFP_BERT_ATL’ physics
model to describe the hadronic interactions with matter, where at high
energies the hadron showers are modelled using the Fritiof string model. The
Bertini intra-nuclear cascade model is used for lower-energy hadrons [30]. The
transition between those two models takes place in the energy region 9–12 GeV
[31].

The input to the digitisation is a collection of hits in the active
scintillator material, characterised by energy, time and position. The amount
of energy deposited in the scintillator is divided by the calorimeter sampling
fraction to correct for energy deposited in the inactive material. To obtain
the channel energy at the electromagnetic scale [32] the sampling fraction is
obtained by simulating electrons with the same kinematics features as the ones
used at the TBs (Section 3.3). In the case of a cell read out by two PMTs, the
energy is shared between the two PMTs according to the distance in $r\phi$ of
each hit from the edges of the cell. Moreover, the cell energy response has an
azimuthal dependence as measured using $W\to\mu\nu$ events in the 2012 $pp$
collision data [33]. This dependence is implemented in the MC simulations.

To follow the same procedure used in the reconstruction of experimental
events, in the digitisation step, the channel energy in GeV is converted into
its equivalent charge using the electromagnetic scale constant measured at
TBs. The charge is subsequently translated into the signal amplitude in ADC
counts using the corresponding calibration constant as explained in Section
3.2. The amplitude is convoluted with the pulse shape and digitized every 25
ns as in real data. The effects of the electronics are emulated and added to
the digitized samples as described in Section 7.4.1. The generation of the
simulated event samples includes the effect of multiple $pp$ interactions per
bunch crossing, and the effect on the detector response as described in
Section 7.4.2, due to neighbouring bunch crossings on the one containing the
analysed interaction.

##  4 Trigger signals

A two-level trigger system [9] was used by ATLAS in Run 2 to reduce the event
rate from a maximum raw rate of 40 MHz to 1 kHz, which is written to disk. The
Level-1 trigger is implemented in hardware and uses a subset of calorimeter
and muon sub-detector information to accept events at a rate below
$100\text{\,}\mathrm{kHz}$. The data are searched for signatures such as large
energy deposits (Level-1 calorimeter trigger) or high-pT muon tracks (Level-1
muon trigger). This is followed by a software-based high-level trigger (HLT),
implemented in a large dedicated computer farm adjacent to the cavern, which
reduces the accepted event rate to $1\text{\,}\mathrm{kHz}$ on average
depending on the data-taking conditions. The TileCal data subsets used in the
L1 trigger are discussed in the next sections. As discussed in Section 4.3,
information collected by the TileCal is also used to select events during low
luminosity LHC runs.

###  4.1 Level-1 calorimeter trigger

The Level-1 calorimeter trigger exploits the tower structure in the
$\eta-\phi$ plane of the TileCal (see Figure 1(b)) and the LAr calorimeter.
The TileCal information used in L1 comes from the adder boards, referred to in
Section 2.2. These boards sum the 3-in-1 card low-gain analogue signals of the
six channels connected to cells with the same $\eta$ and $\phi$ in the layers
A, BC and D of the LB and in the layers A, B and D of the EB.

###  4.2 Tile muon trigger

The tile muon trigger uses information from the TileCal outermost layer cells
(D cells) of the EB to reduce the rate of the ATLAS L1 muon trigger [1]
background events due to low momentum protons emerging from the endcap toroid
and beam shielding. Figure 13 shows that muons arising from $pp$ collisions
with $1.0<|\eta|<1.3$, cross the D5 and D6 cells of the TileCal extended
barrel before reaching the endcap muon chambers (TGC) [1]. This is not the
case for background events. The requirement of a coincidence between the
TileCal and the muon sub-detector signals reduces the background rate.

Figure 13: Schematic of a partial longitudinal cut of the ATLAS detector
showing the $\eta$ region covered by the tile muon trigger system. The azimuth
angle coverage is $0\leq\phi<2\pi$. The sub-systems not used in the tile muon
trigger are sketched for completeness and their drawings do not represent the
accurate geometry.

The tile muon trigger is based on the information of $2\times 64$ TileCal
azimuth sectors, each corresponding to one EB module, and $2\times 24$ TGC
chamber sectors. To provide the TileCal and TGC sector matching, a tile muon
digitiser board (TMDB) is required to process the D5 and D6 signals from eight
TileCal modules and interface with three Level-1 TGC sector logic blocks [34,
35] (Figure 14). To cover the entire detector, 16 TMDBs housed in a VME 9U
crate in the ATLAS service cavern are required.

For each TileCal sector, the TMDB provides four energy values, one for each of
the two PMT’s of the D5 and D6 cells. The analogue signals are digitized at a
frequency of 40 MHz and a window of seven samples in time is used to represent
the readout pulses. The energies are estimated by performing an inner product
between the matched filter (MF) coefficients and the incoming time samples in
ADC counts [36]. Compared to the OF method discussed in Section 3.1, this
method maximises the signal-to-noise ratio for muon signals while increasing
detection efficiency. The presence of a signal produced by a muon in the D5,
in the D6, and in the D5 and D6 cells is obtained by comparing the four energy
determinations with the corresponding threshold values. The MF coefficients
and threshold values are loaded in the TMDB. The board transmits the $\eta$
and $\phi$ coordinates of the identified cells to the three TGC logic blocks
through three Gigabit links (GLink). The information is also transmitted to
neighbour receiver boards to accommodate the non-perfect matching between the
eight TileCal modules and the three muon sector logic blocks. Each TGC sector
Logic board performs the coincidence. The performance of the tile muon trigger
systems is discussed in Section 7.5.

Figure 14: The basic architecture of the tile muon trigger system.

###  4.3 Minimum-bias trigger scintillators

During low luminosity LHC runs, the MBTS system allowed the online selection
of events with the highest efficiency and the lowest possible bias [12]. The
system consists of 2 cm thick polystyrene scintillator counters made by PS-
PTP-POPOP polyethylene located on both sides, A-side and C-side, of the inner
sub-detector at a distance of 3.6 m from the interaction point. Each side is
composed of eight inner counters ($2.76\leq|\eta|<3.86$) and eight outer
counters ($2.08\leq|\eta|<2.76$) instrumented with WLS fibres embedded in
grooves at the edges of the counters. The light going through the fibres is
directed to PMTs [5] where the signal readout is done using the same
electronics as the TileCal cells (Section 2.2). The signals from the shaper
output (Section 2.2) are fed into leading edge discriminators and sent as 25
ns NIM pulses to the Central Trigger Processor [37]. As shown in Figure 15, in
the period 2015–2017 there are twelve readout channels in total in each side.
Each inner counter is connected to one PMT and adjacent pairs of outer
counters are read by a single PMT grouping the corresponding WLS fibres.

Due to the high irradiation dose, the performance of the scintillators, fibres
and PMTs of the MBTS degraded throughout Run 2 and a large signal reduction
was observed. This is discussed in detail in Section 5.3. The MBTS
efficiencies, observed at the beginning of Run 2 and after two years of LHC
operations, are reported in Section 7.6. Due to the very large degradation of
the response, the MBTS counters, installed before the start of Run 2, were
replaced at the beginning of Run 3.

Figure 15: The layout of one side of the MBTS sub-detector in the period
2015–2017. The energy deposited in each sensitive region is read by one
readout channel. Due to the large reduction of the scintillator response, the
number of sensitive regions in the outer layer was doubled in 2018.

##  5 Radiation exposure effects

The LHC operation affects the performance of the TileCal and of the MBTS.
Prolonged exposure to intense radiation causes a decrease in the optical
transmission of the scintillator tiles and of the WLS fibres, inducing a
decrease in pulse height and a deterioration of the energy resolution of the
detector. The accumulated charge affects the gain of the PMTs (see Section
5.1). The laser measurements allow the effects of the PMTs on the calorimeter
response to be determined while the caesium system and the MB events probe the
effects of PMTs, tiles and fibres, as described in Section 3. Combining their
information allows to study the degradation of the optical system (tiles and
fibres) of the TileCal, presented in Sections 5.2 and 5.3.

###  5.1 Comparison of laser, caesium and minimum-bias measurements

The effects of the LHC conditions on the cell response during Run 2 are
discussed in this section. Figure 16 shows the relative response variations of
the A13 calorimeter cells to caesium, MB events and laser pulses, respectively
$\Delta R_{\mathrm{Cs}}$, $\Delta R_{\mathrm{MB}}$ and $\Delta
R_{\mathrm{Las}}$, as a function of time in Run 2. The assessment of these
quantities is detailed in Sections 3.4 and 3.5 and Section 3.6. The cell A13
is located in the EB, and due to the smaller amount of upstream material, it
is exposed to one of the highest radiation doses as shown in Figure 2.

Figure 16:  The average response variation of A13 cells measured by the laser,
caesium and minimum-bias integrator systems as a function of time during the
entire Run 2. Known bad channels are excluded. As discussed in the text the
response behaviours are connected to the LHC delivered luminosity shown by the
shaded area.

The PMT gain, monitored with the laser system, is known to decrease with
increasing light exposure due to lower secondary emissions from the dynode
surfaces [38]. The decrease in gain depends on several factors, including
temperature, intensity and duration of light exposure, as well as the previous
history of the PMT. When a PMT is initially exposed to light after a long ‘no
light’ period, its gain decreases rapidly and then slow stabilisation occurs
[39]. This behaviour is demonstrated in Figures 12 and 16. The data-taking in
each year started after periods of inactivity. The recovery periods, in which
the PMT response to the laser tends towards the initial conditions, coincide
with the periods in which the LHC was not colliding protons. This is
consistent with the known behaviour of fatigued PMTs that gradually return to
their original operating condition after the exposure is removed [40]. A
global PMT gain increase of 0.9% per year is observed without any exposure
(e.g. between data-taking periods).

As already discussed, the responses to the caesium system and MB events are
sensitive to both the PMT gain changes and the scintillator/fibre degradation.
The transparency of these systems is reduced after radiation exposure [41]. In
the TileCal this is evident in the continued downward response to caesium (or
MB events) with increasing integrated luminosity of the collisions, despite
the eventual slow recovery of the PMTs as described above. In the absence of
the radiation source the annealing process is believed to slowly restore the
scintillator material, hence improving the collected light yield. This can be
seen in Figures 9(a), 10 and 16. The rate and amount of scintillator damage
and recovery are complex combinations of factors, such as particle energies,
temperatures, exposure rates and duration, and are difficult to quantify.

To disentangle the effects of PMT and scintillator changes one can study the
laser compared to MB or caesium responses. It can be seen in Figure 16, that
the responses to caesium, laser and MB integrator systems show similar
behaviour in 2015. This indicates no effect of scintillator/fibre irradiation.
In 2016–2018, when the LHC delivered significantly larger luminosity, the
response to MB (and caesium) events compared to the laser system diverges,
indicating the degradation of the scintillators and the fibers. At the end of
Run 2, the maximum response loss in A13 is approximately 16%, where around 8%
is associated with PMT response loss and the remaining 8% with scintillator
degradation.

###  5.2 Degradation of scintillator tiles and WLS fibres

Scintillator tile and WLS fibre ageing effects were determined during Run 2
using the signals produced by the 137Cs source, MB collision events and the
laser pulses. The relative light yield $I/I_{0}$ of the cells due to
scintillator and fibre degradation is defined as:

$\centering I/I_{0}=(1+\Delta R_{\mathrm{Cs/MB}}-\Delta
R_{\mathrm{Las}}).\@add@centering$ (8)

Figure 17:  The measured relative light yield $I/I_{0}$ (Eq. (8)) of the
TileCal cells at the end of Run 2. The uncertainty is of the order of 1%.

Figure 17 shows the relative light yield measured at the end of Run 2 averaged
over all TileCal barrel cells [42]. The innermost layer A and the B11 and C10
cells have a light yield loss between 4 and 10%. The uncertainty is around 1%
and the measurements are not yet sensitive to light yield degradation of B/BC
and D cells. The observed light response degradation is more important in the
innermost cells, subjected to larger particle fluence and thus more ionising
dose. The ionisation doses deposited in the different calorimeter cells are
obtained from simulation of $pp$ collisions at a centre-of-mass energy of
$\sqrt{s}=13$ TeV using the Pythia 8 event generator and Geant4 [43, 44].
Figure 18 shows the simulated ionising dose corresponding to an integrated
luminosity of 1 fb-1. The largest doses, up to 20 Gy/fb-1, occur in the E
cells. The most irradiated cells in the calorimeter barrel are the A12 and A13
cells, with doses of 0.5 and 0.4 Gy/fb-1, respectively.

Figure 18:  Simulated ionisation dose deposited in the scintillator tiles of
the cells and in the gap/crack scintillators in $4\times 4$ cm2 bins in
$r\times z$. The study was performed using 50 000 inelastic $pp$ collisions at
$\sqrt{s}=13$ TeV generated with Pythia 8. The response of the detector was
obtained using the simulation program Geant4. The results are normalised to a
cross-section of $\sigma_{\mathrm{inel}}$ = 78.42 mb and an integrated
luminosity of 1 fb-1 [43, 44].

To further investigate the effects of radiation exposure on the performance of
the TileCal active material, $I/I_{0}$ was monitored during Run 2. The study
allows the light yield till the end of LHC operations and during the HL-LHC
data-taking period to be estimated. Figure 19 shows these measurements as a
function of the integrated delivered luminosity and the average simulated dose
deposited for A13 cells. The Run 2 integrated dose is obtained by normalising
the cell averaged dose coefficients presented in Figure 18 to the measured
integrated luminosity delivered by the LHC [8]. The loss of light yield is
quite smooth and increases with exposure to radiation. In the study, the
damage as a function of dose $d$ is modelled by an exponential function:

$I/I_{0}=p_{0}e^{-d/p_{1}}$ (9)

The parameters $p_{0}$ and $p_{1}$ are obtained by minimising the $\chi^{2}$
function considering only the statistical uncertainty in $I/I_{0}$. The
systematic uncertainties in the caesium, MB and laser calibration systems
(around 0.5%, 1.2% and 0.5%) are propagated to the $I/I_{0}$ uncertainty. This
uncertainty is represented by the opaque band, which additionally covers the
spread of the dose within the large cell volume (around 50%). Based on the fit
result, the extrapolated light output of the A13 cells is $76^{+9}_{-24}\%$ at
the end of the LHC operation (dose around 180 Gy).

Figure 19:  Average relative light yield ($I/I_{0}$) measurements based on the
caesium system (dots) and integrated minimum-bias currents (triangles) for A13
cells as a function of average simulated dose $d$ and LHC integrated
luminosity. The dashed curve corresponds to the fit to the function in Eq. (9)
to the data. The surrounding opaque band represents the total uncertainty in
the fit including the RMS of the dose distribution within the cell and
systematic uncertainties in $I/I_{0}$ due to the intrinsic precision of the
caesium, MB and laser measurements. The solid curve represents the expected
average $I/I_{0}$ of the A13 cells in the HL-LHC phase including dose rate
effects (see the text). The surrounding semi-transparent band is the total
uncertainty on this extrapolation, obtained by propagating the uncertainty
sources of the study. Results from measurements of bare scintillators
performed one month after irradiations made in the laboratory before the
detector construction are also shown [45]. An exponential function is fitted
to the data obtained from irradiations with $\gamma$s (open squares) and
hadrons (full squares). Dashed vertical lines represent the expected dose by
the end of the LHC (450 fb-1) and HL-LHC (4000 fb-1) [46].  Figure 20:  The
degradation rate parameter $p_{1}$ obtained from the simple exponential model
($I/I_{0}=p_{0}e^{-d/p_{1}}$) as a function of the average simulated dose rate
$\dot{d}$ for the most exposed cells. Results from a similar study performed
using the CMS Hadron Endcap Calorimeter measurements are also displayed
(crosses) [47]. The vertical error bars on the TileCal data points represent
the total uncertainty including the $I/I_{0}$ measurement uncertainty and the
dose spread within the cell volume. The nominal points are fitted with a power
law function (continuous curve). This function is extrapolated to the higher
dose rate region (dashed curve) expected at the HL-LHC phase and populated by
the CMS data. The dashed vertical line indicates the expected dose rate of the
A13 cells in the HL-LHC.

While it is important to carefully monitor the performance of the TileCal
active material and make predictions well ahead of time, doing such an
extrapolation with current data is affected by uncertainties not taken into
account in this study. For instance, no explicit recovery is incorporated in
the degradation model for long shutdown times. Furthermore, dose rate
conditions may affect significantly the degradation rate. Measurements from
the CMS-HCAL Collaboration [47] conclude that smaller dose rates produce
larger degradation rates. In this scenario, the degradation rate, with respect
to dose, of TileCal cells would substantially decrease in the HL-LHC phase
given the increase of collision (dose) rate. To estimate the decrease of the
degradation effects, fits of the function in Eq. (9) are performed to the
relative light yield determinations as a function of the simulated dose for
the TileCal cells exhibiting the largest degradation, i.e. those in the A
layer, B11 and C10, see Figure 17. The obtained fitted parameters, driving the
degradation rate, $p_{1}$, are represented as a function of the average dose
rates of the cells in Figure 20. The average dose rates correspond to the cell
averaged dose coefficients presented in Figure 18 multiplied by the LHC
average instantaneous luminosity in Run 2. The results obtained by CMS [47]
are also shown in the figure and, despite the differences between the
calorimeter arrangement and scintillator material, the agreement between
TileCal and CMS-HCAL is good. The TileCal data are fitted with a power law
function to model the dose rate dependency of the cell ageing allowing an
extrapolation to the HL-LHC that takes into account an expected dose rate
being seven times larger (dashed vertical line). The obtained $p_{1}$ value
for the A13 cells in the HL-LHC phase is 1724 Gy. This extrapolation is also
drawn in Figure 19 (solid curve). According to this study, one expects for the
A13 cells a normalised light response of $37^{+17}_{-27}\%$ at the end of the
HL-LHC runs, approximately two times larger than the value obtained without
taking into account the different dose rate expected at HL-LHC (dashed curve).
In the figure, the extrapolated curve can also be compared with the results of
laboratory irradiations [45] where the dose rates were enormously higher and
the scintillators were measured one month after irradiations, having recovered
most of the suffered damage. Also the results obtained by analysing the MBTS
data discussed in Section 5.3 highlight the reduction of the response
degradation by increasing the dose rate.

###  5.3 Degradation of the MBTS system

The counters of the MBTS system are read out using the same electronics as the
TileCal. Due to high irradiation dose, scintillator, fibre and PMT
performances degraded throughout Run 2 and large MBTS signal reductions were
observed. The average total ionising doses, estimated by using the method
described in Section 5.2, are $0.62\times 10^{3}$ Gy/fb-1 for inner counters
and $0.83\times 10^{2}$ Gy/fb-1 for outer counters [43, 44]. The degradation
of the MBTS system is determined using laser and MB data collected during $pp$
collision runs. The PMTs were operated at 500 V. The MBTS response is obtained
by normalising the measured MB currents to the ATLAS instantaneous luminosity
[8].

Figure 21(a) shows the response variation of the inner and outer counters
relative to the first run of Run 2, as a function of time. The relative
variations of the PMT responses as measured by the laser system are also
shown.

((a))

((b))

Figure 21: (a) The average response variation of the MBTS inner (down
triangles) and outer (up triangles) counters as a function of time during Run
2. The circle (diamond) markers show the relative response of the PMTs of the
inner (outer) counters. The LHC delivered luminosity is shown by the shaded
area. (b) The average relative light yield ($I/I_{0}$) of scintillators and
fibres of inner (down triangles) and outer (up triangles) counters as a
function of total ionising dose during Run 2. The values are the averages of
the corresponding determinations obtained for the inner and outer counters.
The uncertainties correspond to the RMS of the counter response distributions.
The function obtained by fitting the inner MBTS data points is also shown
(solid curve).

At the beginning of Run 2, the MB PMT currents were at the level of 15 and 10
nA/1030s-1cm-2 for the inner and outer counters respectively. By end of 2015
(3.2 fb-1 of integrated luminosity), the inner (outer) counters have lost
almost 55% (35%) of their response. This difference is due to the larger
irradiation density of the inner counters, being closer to the beam line. At
the beginning of each new year’s data-taking period, a relative recovery of
the response of about 30% is observed. This is due to the technical stop
periods where the scintillators and fibres are not irradiated further and
partially recover some of their efficiency.

Laser data allowed the PMT variations over the Run 2 period to be evaluated.
The inner and outer counters show a rapid decrease of the average PMT response
by about 20% at the beginning of Run 2. This degradation is expected as the
PMTs are receiving high light output from the scintillators at that time,
inducing a large anode current and a significant amount of charge being
integrated. After this rapid decrease, the responses of the PMTs become more
stable and a general up-drift can be noticed. This behaviour is understood by
the rapid degradation of the MBTS scintillators/fibres that results in much
less light received by the PMTs. Consequently the integrated PMT anode
currents decrease causing the down-drift to cease and eventually to reverse
its course.

To measure the light yield degradation of the MBTS scintillators and fibres,
PMT variations are factored out from MB data as expressed in Eq. (8). The
results as a function of the total ionising dose are shown in Figure 21(b).
The decline appears to follow an exponential decay curve up to 15 kGy with
similar degradation rate for inner and outer counters. With the increase of
the doses, the inner counters continue to decrease exponentially with a
slowing rate caused presumably by saturation effects in the scintillating
material.

##  6 Data quality analysis and operation

A collection of tools continuously monitors the detector hardware and data
acquisition systems during their operation. Some are fully automated to
effectively address problems in real time (online) to protect hardware and
scrutinise the quality of the output data. In the following, the Detector
Control System (DCS), Section 6.1, and the use of calibration runs to check
for faulty hardware components, Section 6.2, are discussed. Online data
quality assessment and monitoring are presented in Section 6.3. After data are
recorded, offline monitoring tools provide key information for analysers to
improve data quality and to address more challenging data corruption issues.
For cases of (semi-) permanent problems, data quality flags are assigned to
portions of the affected data, indicating whether those data are usable for
physics analyses with care (on an analysis-dependent basis) or must be
discarded entirely.

###  6.1 Detector control system

The ATLAS detector control system (DCS) ensures the coherent and safe
operation of the whole experiment [48]. The TileCal DCS [49] is part of the
ATLAS DCS being responsible for the control of the low- and high-voltage
systems and the detector’s infrastructure. The DCS executes actions
initialised by the operator or automatic actions based on conditions for the
monitored data, such as automatic recovery of power supplies from an abnormal
shutdown or shutdown electronics due to high temperature or over-current.
Alarms and other notifications (email, SMS) are triggered to alert the experts
about any abnormality. The relevant monitored data and all alarms are stored
in databases, allowing easy access to the data. For example, the DCS is able
to adjust the various high-voltage levels for each of the TileCal’s PMTs, in
the range of $[\mathrm{HV_{input}+1\leavevmode\nobreak\ V}$,
$\mathrm{HV_{input}+360\leavevmode\nobreak\ V}]$ [50], while monitoring it
with 0.1 V accuracy. Keeping a stable applied voltage is the main goal of the
high-voltage system since the gain of the PMT is a function of the applied
voltage, HV:

$G=\alpha\times\mathrm{HV}^{\beta}$ (10)

where $\alpha$ and $\beta$ are characteristic parameters of each PMT. In the
TileCal LB and EB, the average HV is 640 V and 700 V, respectively, while the
average $\beta$ is 7.07 and 6.95. Therefore, a variation in voltage of 1 V
causes a gain variation of 1.1% (1%) in the LB (EB).

The archived DCS data allow the stability of the HV applied to the TileCal’s
PMTs to be studied. During Run 2, 99.7% of the PMT channels operated with
stable HV. A portion of the faulty channels may be due to monitoring problems.
However, hardware failures are the most common cause.

Figure 22: The hierarchy of the TileCal DCS within the ATLAS DCS [49].

The ATLAS DCS is based on a supervisory control and data acquisition (SCADA)
[51] commercial software. The DCS uses a set of guidelines and software
framework components that allow an easy and coherent integration of the ATLAS
detectors as a single control system. The TileCal DCS is distributed among two
of the three functional levels of the DCS back-end (BE) hierarchy, as can be
seen in Figure 22. It is distributed among six SCADA systems. Four of them are
identical and independent in functionality, each being responsible for the low
and high-voltage systems of one TileCal partition. The infrastructure
supervises the detector’s common components (detector cooling, calibration
systems, etc) while the sub-detector control station acts as the top layer of
the TileCal hierarchy combining all the SCADA systems. A finite state machine
(FSM) toolkit [52] is used to model the DCS BE hierarchy. This allows for full
control of the detector and, at the same time, visualisation of either the
global detector state and the status at the top level or the individual
voltages at the lower level. Due to its simplicity of usage, the FSM is the
most commonly used tool by detector experts and users. In preparation for Run
2, the DCS went through important updates and upgrades [49]. The main
improvement was the migration of the non-SCADA software to a fully Linux based
system. For example, the OLE (object linking and embedding) for process
control data access was migrated to Open Platform Communications Unified
Architecture. Apart from the changes required by software migration, it was
also necessary to replace control blocks due to the replacement of hardware (a
new 200 V DC system and new laser calibration system).

###  6.2 Calibration run validation

The analysis of calibration runs mainly allows checks for faulty hardware
components. During the long shutdowns, the faulty components are included in
the repair list of the maintenance team. The following types of calibration
runs are monitored:

  * •

Laser calibration runs. There are two types of laser runs: ‘Laser LG’ and
‘Laser HG’, which use two different intensities of the laser signal.

  * •

Charge injection runs. Three types of runs are used: ‘CIS’ calibration runs
where a scan with the variable injected charge and phase is performed, and
‘MonoCIS LG’ and ‘Mono-CIS HG’ runs with a constant value of injected charge.

  * •

Pedestal runs with no beams circulating in the LHC and thus with no signal in
the detector.

Raw data from calibration runs are reconstructed offline using the dedicated
software based on the ATLAS data processing framework Athena [10]. It produces
plots and histograms that undergo futher tests to identify potential problems.
Two types of tests are employed. The first checks the consistency of data
(e.g. parity bits, data header, etc) sent by individual DMU chips. The second
type of tests monitors the quality of the signal read from individual channels
(e.g. digital errors, RMS of signal amplitude, timing shifts, etc). The first
type of tests provides a result for each DMU on the module while the second
type provides a result for each channel. Some tests are run for all types of
calibration runs while other tests are run-type specific. Each test takes some
specific value obtained for each channel or DMU and compares it to a
predefined threshold or a range of values. Based on this comparison it assigns
a status (called data quality monitor or DQM status) to each channel (or DMU).
The status is Green if the expected value is observed. If a problem is found,
the status can be Yellow or Red depending on its severity. Statuses of
individual channels or DMUs are then propagated into the DQM module test
status:

  * •

Green status: all channels/DMUs test results are within expected range.

  * •

Yellow status: some problems, usually no more than one channel affected.

  * •

Orange status: more serious problems, usually two or more channels affected.

  * •

Red status: serious problems.

  * •

Undefined status: there is not enough data to evaluate the test.

The module’s overall DQM status is then treated as the worst status of all
module tests.

###  6.3 Online data quality assessment and monitoring

Data quality monitoring begins in real time in the ATLAS control room. Online
shifters on duty serve as a first line of defence to identify serious
detector-related issues. During periods of physics collisions, the TileCal has
experts in the ATLAS control room 24 hours per day and a handful of remote
experts available on call to assist in advanced interventions. The primary
goal is to quickly identify and possibly correct any problem that cannot be
fixed later in software, and that can result in overall data loss.

The ATLAS data quality framework is designed to perform automatic checks of
the data and to alert experts to potential problems that warrant further
investigation [53]. This framework allows data quality monitoring at various
levels of the ATLAS data flow. The subset of data reconstructed online is
quickly made available to the online shifters via display tools. The automatic
tests performed on the reconstruction output include compatibility checks
between the observed distributions from the monitoring data and reference
histograms taken from a past run that is both free of data quality issues and
taken with similar machine operating conditions. Other tests might involve
checks on the number of bins in a histogram above a predefined threshold, or
checks on the gradient of a distribution. For example, histograms that monitor
readout errors should always be empty under ‘ideal’ conditions. If a bin in
such a histogram has a non-zero number of entries, a flag would be raised to
alert the shifter to the problem. Online event reconstruction also allows
control room experts to monitor reconstructed physics objects, such as jets or
missing transverse momentum, permitting real-time monitoring of combined
performance in addition to detector status. The data quality monitoring
framework takes the results of tests on individual histograms and propagates
them upwards through a tree, resulting in a set of top-level status flags,
which can be viewed on the data quality monitoring display. Monitoring
histograms are updated to include additional data every few minutes as newly
available data are reconstructed. In this way, online monitoring allows
hardware- or software-related issues to be caught in real time and rectified
to minimise their impact on collected data.

In addition to the global ATLAS data quality monitoring, TileCal specific data
are reconstructed and validated. This allows more events to be reconstructed
and more detailed monitoring histograms to be produced. Online reconstruction
is done in the same way as it is done offline (see Section 6.4). TileCal
specific automatic checks are focused mainly on monitoring histograms that
accumulate entries per luminosity block (one luminosity block nominally spans
one minute). These allow detection of problems and to address them within that
period during the run. For example, if a test detects that the fraction of
corrupted data in a single TileCal module goes above a certain threshold, a
request to power-cycle the corresponding module is issued. Then the DCS
decides if a power-cycle should be performed immediately or be ignored because
the module is in the exclusion list or was recently power-cycled. During
physics runs, in addition to collisions data, the TileCal also collects
special laser data when every TileCal PMT receives laser light. These laser
data are reconstructed online to monitor timing and address timing jumps, as
described in Section 3.1.2.

Common problems identified by TileCal experts during the online shifts include
hardware failures that do not automatically recover, or software configuration
problems that might present themselves as data corruption flags from the ROD
data integrity checks. The trigger efficiency and data acquisition, as well as
higher-level reconstruction data quality, might be influenced by such
problems.

###  6.4 Offline data quality review

Once the data are recorded, a two-stage offline DQ assessment ensues [7]. Soon
after the data are taken, a small fraction is quickly reconstructed using the
ATLAS Athena software framework [10]. Reconstructed data are then used by the
offline data quality experts with more complex tools to evaluate the quality
of the data. The experts are given 48 hours to identify, and, where possible,
to correct problems, before the bulk reconstruction of the entire run is made.
The TileCal offline experts can update the conditions database, where
information such as the calibration constants and status of each channel is
stored. Channels that suffer from high levels of noise have calibration
constants in the database updated accordingly. For channels that suffer from
intermittent data corruption problems, data quality flags are assigned to the
affected data to exclude the channels in the full reconstruction during the
problematic period. This 48-hour period is also used to identify cases of
digitiser timing jumps and to add the additional time phases to the time
constants of the digitiser affected to account for the magnitude of the time
jump.

Luminosity blocks can be flagged as defective to identify periods of time when
the TileCal is not operating in its nominal configuration. These defects can
either be tolerable whereby corrections are applied but additional caution
should be taken while analysing these data, or intolerable in which case the
data are not deemed suitable for physics analyses. Defects are entered into
the ATLAS data quality defect database [54] with the information propagating
to analyses and to integrated luminosity calculations. Removing all data
within that time can accumulate to a significant data loss. For rare
situations where only a few events are affected by the data corruption, an
additional error-state flag is introduced into the reconstruction data. This
flag is used to remove such events from the analysis. Once all offline teams
perform the review, the entire run is reconstructed using the most up-to-date
conditions database. Subsequently the data can be re-reconstructed when
reconstruction algorithms are improved and the conditions database is further
refined to improve the description of the detector. These data reprocessing
campaigns typically occur several months after the data are taken.

###  6.5 Summary of TileCal operations in Run 2

The TileCal operated very smoothly during Run 2. In 2015, there were no data
lost due to DQ issues in the TileCal. In 2016 most of the inefficiency
attributed to the TileCal was due to data lost in two cases when four
consecutive modules were disabled due to a failure in the ROD-ROS links. These
events induced a loss of 61 $\mathrm{pb}^{-1}$ and 42 $\mathrm{pb}^{-1}$
(0.29% of the total integrated luminosity of 35.5 fb-1 in 2016). Most of the
data loss from the TileCal during 2017 corresponded to a single run when four
consecutive modules were disabled for eight hours due to an auxiliary board
[3] issue. During the attempt to fix the auxiliary board the entire LBA
partition went off for two hours. This event induced a loss of 265
$\mathrm{pb}^{-1}$ (0.57% of the total integrated luminosity of 46.4 fb-1 in
2017). In 2018, there was no data lost due to DQ issues in the TileCal. The DQ
efficiency for each year of Run 2 and for the entire Run 2 are summarised in
Table 2.

Table 2: The TileCal DQ efficiency during stable-beams $pp$ collision physics runs at $\sqrt{s}=13$ TeV for each year of Run 2 and for the entire Run 2. For completeness the corresponding ATLAS efficiencies are reported [7]. | 2015 | 2016 | 2017 | 2018 | Entire Run2
---|---|---|---|---|---
TileCal DQ efficiency [%] | 100.00 | 99.31 | 99.41 | 100.00 | 99.65
ATLAS DQ efficiency [%] | 88.79 | 93.07 | 95.67 | 97.46 | 95.60
Figure 23: The fraction of channels and cells removed from the reconstruction
(masked) as a function of time during Run 1 and Run 2. The number of masked
cells (channels) at the end of Run 2, 3 December 2018, is about 0.5% (1%). The
hatched area represents the maintenance periods of the detector.

Failure of some components, like cooling or an interface card, causes the
exclusion of all channels (thus all cells) of a module from the
reconstruction. Failure of other components affects only a part of a module.
For example, a failure of a HV card renders every second channel of a half-
module non-operational, while keeping all readout cells operational thanks to
the readout redundancy. The next example is a failure of a digitiser [3]. In
this case, six corresponding channels and two or three cells are excluded.
Figure 23 shows the fraction of channels and cells removed (masked) as a
function of time in Run 1 and Run 2. The shaded regions correspond to
maintenance periods. The most common issues, which are addressed and repaired
during this time, correspond to cooling, HV, front-end electronics or the
trigger. Regular maintenance helped to keep the fraction of inefficient cells
below 1.1%.

##  7 Performance studies

The studies reported in this section allow the performance of the
reconstruction and calibration methods described in the previous sections to
be verified. The results obtained by analysing isolated muons, single hadrons
and jets are discussed. The cell noise levels obtained by analysing
experimental and simulated data are compared. The performance of the minimum-
bias trigger system and the improvements made to the ATLAS muon trigger system
by implementing the information provided by the TileCal are also presented.

###  7.1 Energy response to single isolated muons

The interaction of muons with matter is a well-understood process [55, 56],
and events with muons allow comparison of the equalisation of the cell
response, its stability and the EM scale setting. In this Section, results of
the studies of the calorimeter response to muons produced by $W\to\mu\nu$
decays from $pp$ collisions are reported. These muons have momenta in the
range 20 to 80 GeV and lose energy in the TileCal primarily due to ionisation.
The energy loss per unit path is close to the minimum ionising level for the
momenta considered and hence small compared to the muon energy over the full
path traversed in the calorimeter. This makes the muons from $W\to\mu\nu$
ideal test particles to scan the entire TileCal volume.

In the analysis, the muon tracks measured by the pixel and SCT detectors are
extrapolated through the calorimeter volume taking into account detector
material and the magnetic field [57]. To compute the path, $\Delta x$,
travelled by the muon in a cell, a linear interpolation is performed to
determine the entry and exit points of the muon in the crossed cell. The path
and the energy deposited in the cell, $\Delta E$, are used to compute the muon
energy loss per unit distance, $\Delta E/\Delta x$. The distributions of this
quantity can be described by a Landau function convoluted with a Gaussian
distribution, where the Landau part describes the actual energy loss and the
Gaussian part accounts for resolution effects. However, due to long tails from
rare energy loss mechanisms, such as energetic delta electrons and
bremsstrahlung, the fits show small $\chi^{2}$ probability values. For this
reason the truncated mean $\langle\Delta E/\Delta x\rangle_{F=1\%}$,
calculated without considering 1% of the events in the high tail of the
distributions, is used to define the muon response. The truncated mean shows
slight non-linear behaviour with $\Delta x$. This effect and other non-
uniformities, such as pile-up, the differences in momentum and incident angle
spectra are, to a large extent, reproduced by the MC simulation. To compensate
for these effects, the ratio of the $\langle\Delta E/\Delta x\rangle_{F=1\%}$
obtained using experimental and simulated data:

$R\equiv\frac{\langle\Delta E/\Delta
x\rangle^{\mathrm{data}}_{F=1\%}}{\langle\Delta E/\Delta
x\rangle^{\mathrm{MC}}_{F=1\%}}$ (11)

is then used in the analysis. Differences between the $R$ values obtained for
different cells may indicate cell miscalibration. Deviations of the values
from unity may indicate an inaccurate setting of the EM energy scale.

####  7.1.1 Selection of isolated muons

The results presented here were obtained by analysing proton–proton collision
data collected in 2015–2016, 2017 and 2018. The 2015 and 2016 samples were
merged together due to low numbers of events in each of them. Events were
collected using the L1 muon trigger that accepts events with muons originating
from the interaction point [58]. Three further kinematic cuts are used to
select $W\to\mu\nu$ events and to suppress background from multijet processes:
number of muon tracks $N_{\mu}=1$, transverse mass 555The transverse mass
$m_{\text{T}}$ of a single heavy particle in a semi-invisible decay into
particles 1 and 2 is defined by
$m_{\text{T}}=2p_{\text{T},1}p_{\text{T},2}(1-\text{cos}\phi_{12})$ in the
approximation of massless decay products ($m_{1}=m_{2}=0$), with
$p_{\text{T},1(2)}$ denoting the transverse momentum magnitude of the particle
1 (2) and $\phi_{12}$ the azimuthal distance between the decay products [56].
$40\leavevmode\nobreak\ \text{GeV}\leq m_{\mathrm{T}}\leq
140\leavevmode\nobreak\ \text{GeV}$ and missing transverse momentum [59]
$30\leavevmode\nobreak\ \text{GeV}\leq E_{\mathrm{T}}^{\mathrm{miss}}\leq
120\leavevmode\nobreak\ \text{GeV}$. The muons with momentum
$20\leavevmode\nobreak\ \text{GeV}\leq p\leq 80\leavevmode\nobreak\
\text{GeV}$ are retained. The lower limit reduces multiple scattering effects
while the upper limit ensures that muons lose their energy primarily via
ionisation. The contribution from nearby particles in the energy deposited in
a cell is suppressed by only considering well isolated muon tracks [6]. The
selection requirements $\Delta x>100$ mm and $\Delta E>60$ MeV are applied to
reduce noise contributions. The cells with $|\eta|<0.1$ are not considered in
the analysis since in the TileCal the scintillator tiles are oriented radially
and the energy deposited by muons with a trajectory close to this direction is
measured with poor accuracy due to large variations of sampling fraction as
function of the impact point. The number of retained tracks is about 300
million.

The MC simulation uses the Geant4 toolkit that provides the physics models of
particle interactions with material, the ATLAS geometry description and the
tracking tools as described in Section 3.8. The simulated $W\to\mu\nu$ events
were generated using Sherpa [60] at next-to-leading order interfaced with
Pythia 8 [61] for the parton showering. The number of simulated events is
approximately 200 million. The energy deposited in the cells was digitized and
reconstructed using the same procedure as applied in the case of experimental
data. The retained events pass the same criteria used in the selection of
experimental data. The relevant kinematic distributions show good agreement
between data and MC with observed discrepancies only in bins whose contents
are a negligible proportion of the total yield. Using MC events, the purity of
the selected track sample is estimated to be 98%.

####  7.1.2 Cell response uniformity

As shown in Figure 24, in the calorimeter one can distinguish 74 rings of
cells, 46 in the LB and 28 in EB, each consisting of $N_{r}=64$ cells with the
same values of the coordinates $r$ and $z$ and different value of $\phi$. Due
to the symmetry of the calorimeter and of the particles produced in $pp$
collisions, one expects that the ratios in Eq. (11) computed using muons
crossing any cell $c$ of the same ring $r$, $R_{r,c}$, are equal.

The estimated value for the ratio defined by Eq. (11) for a given ring,
$R_{r}$, is determined by maximising the Gaussian likelihood function:

$\mathcal{L}=\prod_{c=1}^{N_{r}}\frac{1}{\sqrt{2\pi}\sqrt{\sigma_{r,c}^{2}+s_{r}^{2}}}\exp\left[-\frac{1}{2}\frac{\left(R_{r,c}-R_{r}\right)^{2}}{\sigma_{r,c}^{2}+s_{r}^{2}}\right]$
(12)

Figure 24: Visualisation of the TileCal in the ($z$, $r$) plane showing the
2017 estimated values of the ratios $R_{r}$ of the cells of a given ring $r$
(see the text). The values are obtained by maximising the likelihood function
in Eq. (12). The statistical uncertainty in each determination is about 0.5%.

where $\sigma_{r,c}$ is the statistical uncertainty in the determination of
$R_{r,c}$. The other parameter determined in the likelihood function
maximisation, $s_{r}$, describes the response non-uniformity of the cells due
to differences in the optical and electronic read-out systems not described in
the simulation and potential miss-calibration of cells of the ring. The
parameter, $s_{r}$, is estimated to be 2.4%. The cell non-uniformity was
previously measured in ATLAS using cosmic rays [6] and at test beams [11]
using electrons incident at the centre of A cells with an angle of 20∘.
Similar results are obtained. The analysis shows no problematic cells with a
value of $R_{r,c}$ that deviates significantly from $R_{r}$.

Figure 24 shows the estimates of $R_{r}$ obtained for the different rings by
analysing 2017 data. For a given radial layer, the values are uniform within
about 1%. Similar results are found by analysing the 2015–2016 and 2018 data.

####  7.1.3 Radial layer calibration

The estimated response $R_{l}$ for the six radial layers $l$: LB-A, LB-BC,
LB-D, EB-A, EB-B, and EB-D are obtained from the truncated mean ratios (Eq.
(11)) of the experimental and simulated $\Delta E/\Delta x$ distributions of
all the cells belonging to the layer. The results obtained by analysing the
data collected in the three periods are reported in Table 3. The statistical
and systematic uncertainties are shown separately. To estimate systematic
uncertainties, the selection parameters were varied around their nominal
values (see Section 7.1.1). The systematic uncertainties dominate. In each
year the standard deviation of the distributions of the measurements listed in
the Table is $1.5\%$. The maximum deviation of the values of $R_{l}$ from 1 is
0.029.

Table 3: The response ratio $R_{l}$ of the cells of different radial layers in the LB and EB obtained by analysing 2015–2016, 2017 and 2018 data. Statistical (first value) and systematic (second value) uncertainties are shown. Layer | $R_{l}(2015-2016)$ | $R_{l}(2017)$ | $R_{l}(2018)$
---|---|---|---
LB-A | 0.988 $\pm$ 0.001 $\pm$ 0.003 | 0.996 $\pm$ 0.002 $\pm$ 0.007 | 0.996 $\pm$ 0.001 $\pm$ 0.004
LB-BC | 0.984 $\pm$ 0.001 $\pm$ 0.001 | 0.993 $\pm$ 0.001 $\pm$ 0.002 | 0.992 $\pm$ 0.001 $\pm$ 0.003
LB-D | 1.014 $\pm$ 0.001 $\pm$ 0.004 | 1.019 $\pm$ 0.001 $\pm$ 0.003 | 1.024 $\pm$ 0.001 $\pm$ 0.002
EB-A | 1.006 $\pm$ 0.003 $\pm$ 0.006 | 1.029 $\pm$ 0.002 $\pm$ 0.006 | 1.016 $\pm$ 0.002 $\pm$ 0.006
EB-B | 0.978 $\pm$ 0.002 $\pm$ 0.002 | 0.990 $\pm$ 0.001 $\pm$ 0.006 | 0.989 $\pm$ 0.001 $\pm$ 0.004
EB-D | 0.982 $\pm$ 0.001 $\pm$ 0.004 | 0.990 $\pm$ 0.001 $\pm$ 0.007 | 0.997 $\pm$ 0.001 $\pm$ 0.004

####  7.1.4 Time stability

The determination of the stability of the $R_{r}$ values discussed in Section
7.1.2 allows quantification of how well the calibration compensates for time-
dependent variations of the calorimeter response. For the cells of each ring
$r$, a determination is obtained by maximising the likelihood function:

$\mathcal{L}=\exp(-\frac{1}{2}(\vec{R}_{r}-\vec{\hat{R}}_{r})^{T}[C_{r}]^{-1}(\vec{R}_{r}-\vec{\hat{R}}_{r}))$
(13)

The components of the vector $\vec{R}_{r}$ = ($R^{1}_{r},R^{2}_{r},R^{3}_{r}$)
are the responses of the cells of a ring $r$ obtained by maximising the
likelihood function (Eq. (12)) using data collected in 2015–2016
($R^{1}_{t}$), 2017 ($R^{2}_{t}$) and 2018 ($R^{3}_{t}$) respectively. The
components of the vector $\vec{\hat{R}}_{r}$ =
($\hat{R}^{1}_{r},\hat{R}^{2}_{r},\hat{R}^{3}_{r}$) are the corresponding
parameter estimates. The covariance matrix $C_{r}$ takes into account
correlations between the determinations performed in the different periods.

((a))

((b))

Figure 25: Visualisation of the TileCal in the ($z$, $r$) plane showing the
relative difference of the fitted response ratios (a) $\Delta_{r}(2015-2016\to
2017)$, obtained in 2015–2016 and 2017, and $\Delta_{r}(2017\to 2018)$,
obtained in 2017 and 2018. The average statistical error in the determinations
is about 0.8%.

Figures 25(a) and 25(b) show the relative variations of the ring responses
between 2015–2016 and 2017:

$\Delta_{r}(\textrm{2015--2016}\to
2017)\equiv\frac{\hat{R}_{r}(2017)-\hat{R}_{r}(\textrm{2015--
2016})}{\hat{R}_{r}(\textrm{2015--2016})}$ (14)

and between 2017 and 2018:

$\Delta_{r}(2017\to
2018)\equiv\frac{\hat{R}_{r}(2018)-\hat{R}_{r}(2017)}{\hat{R}_{r}(2017)}$ (15)

respectively. The uncertainties are obtained by combining statistical and
systematic effects in quadrature and taking into account correlation effects.
In both cases the most probable value is +0.5%. The 95% confidence intervals
of the variations of the cell response between 2015–2016 and 2017 and between
2017 and 2018 are found to be $[-1.3\%,3.3\%]$ and $[-2.4\%,+2.5\%]$
respectively.

###  7.2 Energy response to single isolated hadrons

The calorimeter energy response is probed by measuring the energy deposited in
the calorimeter by isolated hadrons produced in the $pp$ collisions. The
determination is obtained using the ratio:

$R=E/p$ (16)

where $E$ is the energy measured by the calorimeters and $p$ the momentum
measured by the inner detector. The particles have a momentum below 20 GeV and
the precision of the measurement is dominated by the energy resolution [1].
The events analysed were produced in $pp$ interactions in 2017 at a centre-of-
mass energy $\sqrt{s}=13$ TeV with an average of the mean number of
interactions per bunch crossing within a luminosity block,
$\langle\mu\rangle$, of about 2.

At the trigger level, the events were selected requiring at least one counter
with a signal above the threshold value in each side of the MBTS system (see
Section 4.3). Each event is required to have a well reconstructed vertex with
at least four well reconstructed associated tracks with
$p_{\text{T}}>400\leavevmode\nobreak\ \text{MeV}$. Each track selected for
this study is required to have $p_{\text{T}}>500$ MeV and $|\eta|<2.5$. The
reconstruction of the momentum $p$ is described in [1]. To select isolated
single charged hadrons, no other track is allowed within a cone of $\Delta
R<0.4$ centred on the considered track. The energy measurement $E$ is obtained
using ensembles of cells (topological clusters) [62]. A cluster of cells $i$
is associated with the track $k$ if:

$\Delta
R=\sqrt{(\Delta\eta(\textrm{track}_{kj},\textrm{cluster}_{i}))^{2}+(\Delta\phi(\textrm{track}_{kj},\textrm{cluster}_{i}))^{2}}<0.2$
(17)

where $\Delta\phi(\textrm{track}_{kj},\textrm{cluster}_{i})$ is the smallest
angle in the transverse plane between track $k$ and cluster $i$. The
$\eta(\textrm{track}_{kj})$ and $\phi(\textrm{track}_{kj})$ are the values of
the extrapolated track in the layer $j$ of the cluster with the largest
deposited energy. The energy of a track corresponds to the sum of the energy
deposited in all the cells of the clusters associated with the track [63]. The
cell energies are reconstructed and calibrated at EM scale using the
procedures described in Sections 2 and 3.

Additional requirements are applied to ensure that tracks reach and deposit
their energy in the TileCal layers, and to reduce the contamination from
neutral particles and muons. These are:

  * •

Momentum of the track, $p_{\mathrm{track}}$, larger than
$2\leavevmode\nobreak\ \text{GeV}$ and $|\eta_{\mathrm{track}}|<1.7$.

  * •

The energy deposited by the hadron in the LAr EM calorimeter [64],
$E_{\mathrm{LAr}}<1\leavevmode\nobreak\ \text{GeV}$, compatible with that of a
minimum ionising particle (MIP), so that the hadron deposits almost all its
energy in the TileCal.

  * •

The energy deposited in TileCal is required to be at least 70% of the total
energy deposited in the calorimeters,
$E_{\mathrm{Tile}}/(E_{\mathrm{LAr}}+E_{\mathrm{Tile}})>0.7$.

The last two criteria effectively reduce the contribution from neutral
particles decaying electromagnetically since these events deposit most of
their energy in the EM calorimeter [63]. The experimental results are compared
with those obtained analysing simulated data. The simulation program Pythia
8.186 [61] was used to generate multijet events with the A14 set of tuned
parameters (tune) [65] and the NNPDF23 leading-order parton distribution
function set. The detector response was simulated using the Geant4 simulation
program. The transverse momentum of the tracks was re-weighted to match the
observed spectrum in data. The same selection criteria and signal
reconstruction procedures used in the analysis of the experimental data are
used in the analysis of the simulated data.

Figure 26: The distribution of the ratio of the energy of isolated hadrons
measured by the calorimeters divided by the momentum of the track measured by
the inner detector ($E/p$). The distribution obtained by analysing simulated
data is also shown. The distributions are normalised to an integrated area of
one. The ratios of the experimental values to the simulated ones are plotted
in the lower panel. The MC statistical uncertainties are shown.

Good agreement is found between the experimental and simulated results. The
$E/p$ distribution of the selected events is shown in Figure 26. The mean of
the distribution obtained by analysing experimental (simulated) data is
$\langle E/p\rangle$ is 0.5896 $\pm$ 0.0001 (0.593 $\pm$ 0.001). Only
statistical uncertainties are quoted. The values are smaller than one because
of the non-compensating nature of the calorimeter. Also energy leakage affects
the result. Figure 27 shows the distributions of $\langle E/p\rangle$ as a
function of the hadron $p$, $\eta$ and $\phi$. The $R$ values obtained by
comparing experimental and simulated events in three $\eta$ regions
($|\eta|<0.7$, $0.7\leq|\eta|\leq 1.0$ and $1.0<|\eta|\leq 1.7$) are reported
in Table 4. For each of three pseudorapidity regions, the values refer to
isolated hadrons with momenta $2.0\leavevmode\nobreak\ \text{GeV}\leq
p<3.0\leavevmode\nobreak\ \text{GeV}$, $3.0\leavevmode\nobreak\ \text{GeV}\leq
p<4.0\leavevmode\nobreak\ \text{GeV}$, $4.0\leavevmode\nobreak\ \text{GeV}\leq
p<5.0\leavevmode\nobreak\ \text{GeV}$, $5.0\leavevmode\nobreak\ \text{GeV}\leq
p<7.0\leavevmode\nobreak\ \text{GeV}$ and $p\geq 7\leavevmode\nobreak\
\text{GeV}$ respectively.

Table 4: Ratios of the $\langle E/p\rangle$ values obtained from experimental and simulated data. The results were obtained by analysing isolated hadrons with different pseudorapidity and momentum values. Statistical and systematic uncertainties are combined in quadrature.  | $|\eta|<0.7$ | $0.7\leq|\eta|\leq 1.0$ | $1.0<|\eta|\leq 1.7$
---|---|---|---
2.0 GeV $\leq p<3.0$ GeV | 0.98 $\pm$ 0.010 | 0.97 $\pm$ 0.010 | 1.03 $\pm$ 0.050
3.0 GeV $\leq p<4.0$ GeV | 0.98 $\pm$ 0.010 | 0.97 $\pm$ 0.010 | 1.00 $\pm$ 0.030
4.0 GeV $\leq p<5.0$ GeV | 0.97 $\pm$ 0.020 | 0.98 $\pm$ 0.020 | 0.99$\pm$ 0.020
5.0 GeV $\leq p<7.0$ GeV | 0.98 $\pm$ 0.010 | 0.96 $\pm$ 0.020 | 0.97 $\pm$ 0.020
$p\geq 7.0$ GeV | 1.01 $\pm$ 0.030 | 1.02 $\pm$ 0.050 | 0.98 $\pm$ 0.020

((a))

((b))

((c))

Figure 27: The average ratio of energy to momentum ($\langle E/p\rangle$)
measurements as a function of (a) $p$, (b) $\eta$ and (c) $\phi$. The ratios
of experimental to simulated data are plotted in the lower panels. MC
statistical and experimental systematic uncertainties are shown.

Two sources of systematic uncertainty are identified. The first one is from
the contamination of neutral particles. The effects on the ratio of the
experimental and simulation results are estimated by varying the selection
criteria for $E_{\mathrm{LAr}}$ and
$E_{\mathrm{Tile}}/(E_{\mathrm{LAr}}+E_{\mathrm{Tile}})$. To this end,
different cuts on the reconstructed number of clusters are also applied. A
systematic uncertainty of about 1%, almost independent of $\eta$, is found. It
corresponds to the maximum difference of the results obtained by applying the
different cuts. In particular for large values of $|\eta|$, another source of
systematic uncertainty comes from the description in the simulation of the
dead material in front of TileCal. Effects of few percent are observed by
varying the energy deposited in the gap/crack scintillators in the dead
material region. Statistical and systematic uncertainties are combined in
quadrature in Table 4. The comparison between the results obtained by
analysing experimental and simulated data shows a good reconstruction of the
energy at the EM scale of low momentum hadrons with an uncertainty better than
5%.

###  7.3 Timing performance with collision data

Correct channel timing obtained by analysing jets as discussed in Section
3.1.1 is essential for energy reconstruction, particle identification and
searches for hypothetical long-lived particles. The performance of time
calibration is presented in this section.

####  7.3.1 Mean time and time resolution

Figure 28: The mean reconstructed cell time as a function of the cell energy.
Results obtained in Run 2 (2015, 2016, 2017 and 2018), are shown. Statistical
uncertainties are smaller than the size of the markers. The discontinuity
close to 22 GeV corresponds to the ADC high-/low-gain transition.

Figure 28 compares the mean of the cell time (average of the reconstructed
times of channels associated with that cell) as a function of the cell energy
measurements of all TileCal cells in each of the four years of Run 2, 2015,
2016, 2017 and 2018. For each energy bin, the mean cell time corresponds to
the mean value, $\mu$, of a Gaussian function fit to the cell time
distribution in the range of $\mu\pm 2\sigma$ ($\sigma$ is the standard
deviation of the Gaussian function). To do this, an iterative procedure is
applied. The mean cell time decreases with the cell energy, reaching the
plateau at energies above 40 GeV. The time behaviour remains essentially
unchanged during the whole Run 2. The differences appear only in the two
lowest energy bins, below 4 GeV, dominated by pile-up conditions. At higher
energies, the year-to-year differences are within 0.05 ns in agreement with
previous results [66].

((a))

((b))

Figure 29: (a) The time resolution (full circles) and RMS of the time
distribution (open squares) as a function of the cell energy. The results were
obtained by analysing 2018 data. Statistical uncertainties are smaller than
the size of the markers. The fits of the function in Eq. (18) are superimposed
on high- and low-gain resolution data as indicated by solid and dashed curves,
respectively. (b) A comparison of the time resolution fit functions obtained
by analysing 2015, 2016, 2017, 2018 data samples [66] as a function of the
cell energy. The 2017 high-gain fit is affected by a worse time resolution in
the lower energy bin that leads to slightly different fit parameters $p_{0}$
and $p_{1}$ (see Eq. (18)) compared to the results of the other years. The
effect translates into an increase of the 2017 and 2015 resolution ratio near
the high-gain end point. The lower panel shows the fitted time resolution
obtained by analysing 2016, 2017 and 2018 data relative to the values obtained
analysing 2015 data.

Time resolution corresponds to the $\sigma$ of the Gaussian function fit to
the cell time distribution discussed above. The values of time resolution and
of the root mean square (RMS) of the cell time distribution in each cell
energy bin obtained using 2018 data are shown in Figure 29(a). The time
resolution is relatively stable between individual runs. The RMS values, being
more affected by the tails of the time distribution driven by the pile-up
conditions in the given run, are more unstable. The fit functions

$\sigma=\sqrt{p_{0}^{2}+(p_{1}/\sqrt{E})^{2}+(p_{2}/E)^{2}}$ (18)

are superimposed on HG and LG resolution data in the figure. The fit functions
obtained for the four different data-taking years of Run 2 are compared in
Figure 29(b). Since the calibration procedure for the HG setting remained
unchanged during the whole Run 2, the differences in time resolution for cell
energies smaller than 22 GeV are mainly caused by different pile-up
conditions. The best resolution is observed in 2015. The difference relative
to other years is 10% for cell energies around 20 GeV at LG.

The time calibration for LG was the same during the years 2016–2018. The time
resolution is slightly worse in 2015 due to an older calibration procedure. It
relied on the HG time calibration taking into account a constant offset due to
faster signal propagation at LG instead of direct determination of the LG time
calibration constants. The updated procedure, as described in Section 3.1.1,
improves the time resolution for LG by up to 5% despite higher pile-up in
2016–2018 compared to 2015.

####  7.3.2 Effect of pile-up on the time resolution

The dependence of time resolution on pile-up was investigated by analysing the
data on a run-to-run basis. The mean number of reconstructed primary vertices
per bunch crossing within a luminosity block, $N_{\text{PV}}$, is used as a
proxy for the pile-up conditions in each run. Results are shown in Figure 30.
Low pile-up runs show slightly better time resolution than runs with higher
pile-up. This feature is fully compatible with the differences in the time
resolution reported in Figure 29(b).

Figure 30: The cell time resolution ($\sigma$) determined in the energy range
$$8\text{\,}\mathrm{GeV}$<E_{\mathrm{cell}}<$10\text{\,}\mathrm{GeV}$$ as a
function of the mean number of reconstructed primary vertices per bunch
crossing within a luminosity block, $N_{\text{PV}}$, in the run. Each point
corresponds to one run and is obtained using all the cells of the detector. In
the analysis, only runs with 25 ns bunch spacing and the number of bunches in
the LHC larger than 1000 are used. The worse resolution in 2015 is compatible
with the larger run-to-run differences provided the phase changes are not
strictly coupled to individual run boundaries, as discussed in Section 7.3.3.

####  7.3.3 Run-to-run differences

The differences in the mean reconstructed time were also investigated on run-
to-run basis. These differences are due to a phase between the LHC clock
signal and the bunch-crossings in ATLAS that can vary slightly in time. Large
run-to-run differences can negatively influence the time resolution integrated
over several runs. While the run-to-run RMS was rather large in 2015 (up to
0.1 ns), it significantly improved since the beginning of 2016 and stayed at
the level of 0.03 ns or better. This value is negligible compared to the time
resolution constant term $p_{0}$ shown in Figure 29(a) and the run-to-run
differences have no impact on the time resolution even if integrating over
many runs.

ATLAS monitors this phase with the beam pick-up based timing system (BPTX)
[67].666The BPTX stations are beam position monitors installed in the LHC
tunnel $175\text{\,}\mathrm{m}$ away from the ATLAS interaction point. The
improvement in the run-to-run RMS observed in the TileCal is in line with the
automated correction for large phases based on BPTX measurements that was
adopted in ATLAS in 2016.

###  7.4 Electronic and pile-up noise

The total noise per cell is calculated taking into account two components,
electronic noise and a contribution from pile-up interactions (pile-up noise).
These two contributions are added in quadrature to estimate the total noise
(see Section 7.4.2). The total cell noise is used as input to the topological
clustering algorithm [62]. See also Section 7.2.

####  7.4.1 Electronic noise

The electronic noise is measured by fluctuations of the channel pedestal $p$
(Eq. (3)) and is largely independent of LHC beam conditions. The distributions
are obtained using dedicated runs with no beam in the LHC. The reconstruction
of pedestal data mirrors that of the data-taking period, using the non-
iterative OF technique. The cell electronic noise is given by

$\sigma_{\text{electronic}}=\sqrt{\sum^{N_{c}}_{i}{(\sigma^{i}_{\text{electronic}})^{2}}}$
(19)

where $\sigma^{i}_{\text{electronic}}$ is the standard deviation (RMS) of the
distribution of pedestal values of channel $i$ and $N_{c}$ is the number of
channels in the cell. Most of the TileCal cells are read out by two channels.
Both are read out in HG and LG. Therefore, for each cell there are four
combinations (low–low, low–high, high–low and high–high). The high–high
combination is typically used when the deposited energy in a cell is below 15
GeV while above that the low–low one is most commonly used. In the region
around 15 GeV the combination of low–high/high–low is used. Figure 31 shows
the $\phi$-averaged electronic noise (RMS) for all cells as a function of
$\eta$, for the high–high gain combination, measured in a single
representative run taken in 2017. Different calorimeter layers are presented.
The average cell noise for regular cells is approximately 20.5 MeV with a
standard deviation of 2.5 MeV. However, cells located in the region
$|\eta|\approx 1$ show noise values closer to 27.5 MeV. These cells are formed
by channels physically located near the LVPS. Detailed discussions of the
electronic noise is given in Ref. [6].

Figure 31: The $\phi$-averaged electronic noise as a function of $\eta$ of the
cell, with both contributing read-out channels in high-gain mode. For each
cell type the average value over all modules is taken. The statistical
uncertainties are smaller than the marker size. Values are extracted using a
single representative pedestal calibration run taken in 2017. The different
cell types are shown separately for each layer. The transition between the
long and extended barrels can be seen in the range of $0.7<|\eta|<1.0$.

####  7.4.2 Pile-up noise

The total noise is the sum of all sources of noise contributing to the signals
in TileCal cells. The electronic noise introduced in Section 7.4.1 and the
pile-up noise described in this section are the two main contributions. Pile-
up noise has two components that lead to the overlay of multiple signals, they
are called in-time and out-of-time pile-up. In-time pile-up results in the