2016 071 11 March Transverse energy at midrapidity in Pb–Pb collisions ALICE
Collaboration††thanks: See Appendix A for the list of collaboration members
ALICE Collaboration

We report the transverse energy ($E_{\mathrm{T}}$) measured with ALICE at
midrapidity in Pb–Pb collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV as a
function of centrality. The transverse energy was measured using identified
single particle tracks. The measurement was cross checked using the
electromagnetic calorimeters and the transverse momentum distributions of
identified particles previously reported by ALICE. The results are compared to
theoretical models as well as to results from other experiments. The mean
$E_{\mathrm{T}}$ per unit pseudorapidity ($\eta$),
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$, in 0–5% central collisions is 1737
$\pm$ 6(stat.) $\pm$ 97 (sys.) GeV. We find a similar centrality dependence of
the shape of $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ as a function of the
number of participating nucleons to that seen at lower energies. The growth in
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ at the LHC energies exceeds
extrapolations of low energy data. We observe a nearly linear scaling of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ with the number of quark
participants. With the canonical assumption of a 1 fm/$c$ formation time, we
estimate that the energy density in 0–5% central Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV is 12.3 $\pm$ 1.0 GeV/fm3 and that the
energy density at the most central 80 fm2 of the collision is at least 21.5
$\pm$ 1.7 GeV/fm3. This is roughly 2.3 times that observed in 0–5% central
Au–Au collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 200 GeV.

##  1 Introduction

Quantum Chromodynamics (QCD) predicts a phase transition of nuclear matter to
a plasma of quarks and gluons at energy densities above about 0.2-1 GeV/fm3
[1, 2]. This matter, called Quark–Gluon Plasma (QGP), is produced in high
energy nuclear collisions [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17] and its properties are being investigated at the Super Proton Synchrotron
(SPS), the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron
Collider (LHC). The highest energy densities are achieved at the LHC in Pb–Pb
collisions.

The mean transverse energy per unit pseudorapidity
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ conveys information about how much
of the initial longitudinal energy carried by the incoming nuclei is converted
into energy carried by the particles produced transverse to the beam axis. The
transverse energy at midrapidity is therefore a measure of the stopping power
of nuclear matter. By using simple geometric considerations [18]
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ can provide information on the
energy densities attained. Studies of the centrality and
${\sqrt{s_{\mathrm{NN}}}}$ dependence of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ therefore provide insight into the
conditions prior to thermal and chemical equilibrium.

The $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ has been measured at the AGS by
E802 [19] and E814/E877 [20], at the SPS by NA34 [21], NA35 [22], NA49 [23],
and WA80/93/98 [24, 25], at RHIC by PHENIX [26, 27, 28] and STAR [29], and at
the LHC by CMS [30], covering nearly three orders of magnitude of
${\sqrt{s_{\mathrm{NN}}}}$. The centrality dependence has also been studied
extensively with $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ at midrapidity
scaling nearly linearly with the collision volume, or equivalently, the number
of participating nucleons at lower energies [31, 24, 32]. Further studies of
heavy-ion collisions revealed deviations from this simple participant scaling
law [25]. The causes of this deviation from linearity are still actively
discussed and might be related to effects from minijets [33, 34] or
constituent quark scaling [35, 36].

The ALICE detector [37] has precision tracking detectors and electromagnetic
calorimeters, enabling several different methods for measuring
$E_{\mathrm{T}}$. In this paper we discuss measurements of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ in Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV using the tracking detectors alone and
using the combined information from the tracking detectors and the
electromagnetic calorimeters. In addition we compare to calculations of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ from the measured identified
particle transverse momentum distributions. Measurements from the tracking
detectors alone provide the highest precision. We compare our results to
theoretical calculations and measurements at lower energies.

##  2 Experiment

A comprehensive description of the ALICE detector can be found in [37]. This
analysis uses the V0, Zero Degree Calorimeters (ZDCs), the Inner Tracking
System (ITS), the Time Projection Chamber (TPC), the ElectroMagnetic
Calorimeter (EMCal), and the PHOton Spectrometer (PHOS), all of which are
located inside a 0.5 T solenoidal magnetic field. The V0 detector [38]
consists of two scintillator hodoscopes covering the pseudorapidity ranges
$-$3.7 $<\eta<$ $-$1.7 and 2.8 $<\eta<$ 5.1. The ZDCs each consist of a
neutron calorimeter between the beam pipes downstream of the dipole magnet and
a proton calorimeter external to the outgoing beam pipe.

The TPC [39], the main tracking detector at midrapidity, is a cylindrical
drift detector filled with a Ne–CO2 gas mixture. The active volume is nearly
90 m3 and has inner and outer radii of 0.848 m and 2.466 m, respectively. It
provides particle identification via the measurement of the specific
ionization energy loss (d$E$/d$x$) with a resolution of 5.2% and 6.5% in
peripheral and central collisions, respectively.

The ITS [37] consists of the Silicon Pixel Detector with layers at radii of
3.9 cm and 7.6 cm, the Silicon Drift Detector with layers at radii of 15.0 cm
and 23.9 cm, and the Silicon Strip Detector with layers at radii of 38.0 and
43.0 cm. The TPC and ITS are aligned to within a few hundred $\mu$m using
cosmic ray and pp collision data [40].

The EMCal [41, 42] is a lead/scintillator sampling calorimeter covering
$|\eta|<$ 0.7 in pseudorapidity and 100∘ in azimuth in 2011. The EMCal
consists of 11520 towers, each with transverse size 6 cm $\times$ 6 cm, or
approximately twice the effective Molière radius. The relative energy
resolution is $\sqrt{0.11^{2}/E+0.017^{2}}$ where the energy $E$ is measured
in GeV [41]. Clusters are formed by combining signals from adjacent towers.
Each cluster is required to have only one local energy maximum. Noise is
suppressed by requiring a minimum tower energy of 0.05 GeV. For this analysis
we use clusters within $|\eta|<$ 0.6. The PHOS [43] is a lead tungstate
calorimeter covering $|\eta|<$ 0.12 in pseudorapidity and 60∘ in azimuth. The
PHOS consists of three modules of 64 $\times$ 56 towers each, with each tower
having a transverse size of 2.2 cm $\times$ 2.2 cm, comparable to the Molière
radius. The relative energy resolution is
$\sqrt{0.013^{2}/E^{2}+0.036^{2}/E+0.01^{2}}$ where the energy $E$ is measured
in GeV [44].

The minimum-bias trigger for Pb–Pb collisions in 2010 was defined by a
combination of hits in the V0 detector and the two innermost (pixel) layers of
the ITS [8]. In 2011 the minimum-bias trigger signals in both neutron ZDCs
were also required [45]. The collision centrality is determined by comparing
the multiplicity measured in the V0 detector to Glauber model simulations of
the multiplicity [8, 38]. These calculations are also used to determine the
number of participating nucleons, $\langle N_{\mathrm{part}}\rangle$. We
restrict our analysis to the 0–80% most central collisions. For these
centralities corrections due to electromagnetic interactions and trigger
inefficiencies are negligible. We use data from approximately 70k 0-80%
central events taken in 2011 for the tracking detector and EMCal measurements
and data from approximately 600k 0-80% central events taken in 2010 for the
PHOS measurement. We focus on a small event sample where the detector
performance was uniform in order to simplify efficiency corrections since the
measurement is dominated by systematic uncertainties.

Tracks are reconstructed using both the TPC and the ITS. Tracks are selected
by requiring that they cross at least 70 rows and requiring a $\chi^{2}$ per
space point $<$ 4\. Tracks are restricted to $|\eta|<$ 0.6. Each track is
required to have at least one hit in one of the two innermost ITS layers and a
small distance of closest approach (DCA) to the primary vertex in the $xy$
plane as a function of transverse momentum ($p_{\rm T}$), defined by DCAxy $<$
(0.0182+0.035/ $p_{\mathrm{T}}^{1.01}$) cm where $p_{\rm T}$ is in GeV/$c$.
The distance of closest approach in the $z$ direction is restricted to DCAz
$<$ 2 cm. This reduces the contribution from secondary particles from weak
decays, which appear as a background. With these selection criteria tracks
with transverse momenta $p_{\rm T}$ $>$ 150 MeV/$c$ can be reconstructed. The
typical momentum resolution for low momentum tracks, which dominate
$E_{\mathrm{T}}$ measurements, is $\Delta$$p_{\rm T}$/$p_{\rm T}$ $\approx$
1%. The reconstruction efficiency varies with $p_{\rm T}$ and ranges from
about 50% to 75% [45].

Particles are identified through their specific energy loss, d$E$/d$x$, in the
TPC when possible. The d$E$/d$x$ is calculated using a truncated-mean
procedure and compared to the d$E$/d$x$ expected for a given particle species
using a Bethe-Bloch parametrization. The deviation from the expected d$E$/d$x$
value is expressed in units of the energy-loss resolution $\sigma$ [46].
Tracks are identified as arising from a kaon if they are within 3$\sigma$ from
the expected d$E$/d$x$ for a kaon, more than 3$\sigma$ from the expected
d$E$/d$x$ for a proton or a pion, and have $p_{\rm T}$ $<$ 0.45 GeV/$c$.
Tracks are identified as arising from (anti)protons if they are within
3$\sigma$ from the expected d$E$/d$x$ for (anti)protons, more than 3$\sigma$
from the expected d$E$/d$x$ for kaons or pions, and have $p_{\rm T}$ $<$ 0.9
GeV/$c$. Tracks are identified as arising from an electron (positron) and
therefore excluded from the measurement of $E_{\mathrm{T}}^{\pi\mathrm{,K,p}}$
if they are within 2$\sigma$ from the expected d$E$/d$x$ for an electron
(positron), more than 4$\sigma$ from the expected d$E$/d$x$ for a pion, and
more than 3$\sigma$ from the expected d$E$/d$x$ for a proton or kaon. With
this algorithm approximately 0.1% of tracks arise from electrons or positrons
misidentified as arising from pions and fewer than 0.1% of tracks are
misidentified as arising from kaons or protons. Any track not identified as a
kaon or proton is assumed to arise from a pion and the measurement must be
corrected for the error in this assumption.

The PHOS and EMCal are used to measure the electromagnetic energy component of
the $E_{\mathrm{T}}$ and to demonstrate consistency between methods. Data from
2011 were used for the EMCal analysis due to the larger EMCal acceptance in
2011. Data from one run in 2010 were used for the PHOS due to better detector
performance and understanding of the calibrations in that run period. The
EMCal has a larger acceptance, but the PHOS has a better energy resolution.
There is also a lower material budget in front of the PHOS than the EMCal.
This provides an additional check on the accuracy of the measurement.

##  3 Method

Historically most $E_{\mathrm{T}}$ measurements have been performed using
calorimeters, and the commonly accepted operational definition of
$E_{\mathrm{T}}$ is therefore based on the energy $E_{j}$ measured in the
calorimeter’s $j$′th tower

$E_{\mathrm{T}}=\sum_{{\mathrm{j}}=1}^{\mathrm{M}}E_{\mathrm{j}}\sin\theta_{\mathrm{j}}$
(1)

where j runs over all M towers in the calorimeter and $\theta_{\mathrm{j}}$ is
the polar angle of the calorimeter tower. The transverse energy can also be
calculated using single particle tracks. In that case, the index, j, in Eq. 1
runs over the M measured particles instead of calorimeter towers, and
$\theta_{\mathrm{j}}$ is the particle emission angle. In order to be
compatible with the $E_{\mathrm{T}}$ of a calorimetry measurement, the energy
$E_{\mathrm{j}}$ of Eq. 1 must be replaced with the single particle energies

$E_{\mathrm{j}}=\left\\{\begin{array}[]{ll}E_{\mathrm{kin}}&\mbox{for
baryons}\\\ E_{\mathrm{kin}}+2mc^{2}&\mbox{for anti-baryons}\\\
E_{\mathrm{kin}}+mc^{2}&\mbox{for all other particles.}\end{array}\right.$ (2)

This definition of $E_{\mathrm{T}}$ was used in the measurements of the
transverse energy by CMS [30] (based on calorimetry), PHENIX [26] (based on
electromagnetic calorimetry), and STAR [29] (based on a combination of
electromagnetic calorimetry and charged particle tracking). To facilitate
comparison between the various data sets the definition of $E_{\mathrm{T}}$
given by Eqs. 1 and 2 is used here.

It is useful to classify particles by how they interact with the detector. We
define the following categories of final state particles:

A

$\pi^{\pm}$, K±, p, and $\overline{\mathrm{p}}$: Charged particles measured
with high efficiency by tracking detectors

B

$\pi^{\mathrm{0}}$, $\omega$, $\eta$, e±, and $\gamma$: Particles measured
with high efficiency by electromagnetic calorimeters

C

$\Lambda$, $\overline{\Lambda}$, K${}^{\mathrm{0}}_{\mathrm{S}}$,
$\Sigma^{+}$, $\Sigma^{-}$, and $\Sigma^{0}$: Particles measured with low
efficiency in tracking detectors and electromagnetic calorimeters

D

K${}^{\mathrm{0}}_{\mathrm{L}}$, n, and $\overline{\mathrm{n}}$: Neutral
particles not measured well by either tracking detectors or electromagnetic
calorimeters.

The total $E_{\mathrm{T}}$ is the sum of the $E_{\mathrm{T}}$ observed in
final state particles in categories A-D. Contributions from all other
particles are negligible. In HIJING 1.383 [47] simulations of Pb–Pb collisions
at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV the next largest contributions come
from the $\Xi$($\overline{\Xi}$) and $\Omega$($\overline{\Omega}$) baryons
with a total contribution of about 0.4% of the total $E_{\mathrm{T}}$, much
less than the systematic uncertainty on the final value of $E_{\mathrm{T}}$.
The $E_{\mathrm{T}}$ from unstable particles with $c\tau<$ 1 cm is taken into
account through the $E_{\mathrm{T}}$ from their decay particles.

When measuring $E_{\mathrm{T}}$ using tracking detectors, the primary
measurement is of particles in category A and corrections must be applied to
take into account the $E_{\mathrm{T}}$ which is not observed from particles in
categories B-D. In the hybrid method the $E_{\mathrm{T}}$ from particles in
category A is measured using tracking detectors and the $E_{\mathrm{T}}$ from
particles in category B is measured by the electromagnetic calorimeter. An
electromagnetic calorimeter has the highest efficiency for measuring particles
in category B, although there is a substantial background from particles in
category A. The $E_{\mathrm{T}}$ from categories C and D, which is not well
measured by an electromagnetic calorimeter, must be corrected for on average.
Following the convention used by STAR, we define
$E_{\mathrm{T}}^{\mathrm{had}}$ to be the $E_{\mathrm{T}}$ measured from
particles in category A and scaled up to include particles in categories C and
D and $E_{\mathrm{T}}^{\mathrm{em}}$ to be the $E_{\mathrm{T}}$ measured in
category B. The total $E_{\mathrm{T}}$ is given by

$E_{\mathrm{T}}=E_{\mathrm{T}}^{\mathrm{had}}+E_{\mathrm{T}}^{\mathrm{em}}.$
(3)

We refer to $E_{\mathrm{T}}^{\mathrm{had}}$ as the hadronic $E_{\mathrm{T}}$
and $E_{\mathrm{T}}^{\mathrm{em}}$ as the electromagnetic $E_{\mathrm{T}}$. We
note that $E_{\mathrm{T}}^{\mathrm{had}}$ and $E_{\mathrm{T}}^{\mathrm{em}}$
are operational definitions based on the best way to observe the energy
deposited in various detectors and that the distinction is not theoretically
meaningful.

Several corrections are calculated using HIJING [47] simulations. The
propagation of final state particles in these simulations through the ALICE
detector material is described using GEANT 3 [48]. Throughout the paper these
are described as HIJING+GEANT simulations.

###  3.1 Tracking detector measurements of
$\mathbf{{\mathit{E}}_{\mathrm{T}}}$

The measurements of the total $E_{\mathrm{T}}$ using the tracking detectors
and of the hadronic $E_{\mathrm{T}}$ are closely correlated because the direct
measurement in both cases is $E_{\mathrm{T}}^{\pi\mathrm{,K,p}}$, the
$E_{\mathrm{T}}$ from $\pi^{\pm}$, K±, p, and $\overline{\mathrm{p}}$ from the
primary vertex. All contributions from other categories are treated as
background. For $E_{\mathrm{T}}^{\mathrm{had}}$ the $E_{\mathrm{T}}$ from
categories C and D is corrected for on average and for the total
$E_{\mathrm{T}}$ the contribution from categories B, C, and D is corrected for
on average. Each of these contributions is taken into account with a
correction factor.

The relationship between the measured track momenta and
$E_{\mathrm{T}}^{\pi\mathrm{,K,p}}$ is given by

$\frac{{\mathrm{d}}E_{\mathrm{T}}^{\pi\mathrm{,K,p}}}{{\mathrm{d}}\eta}=\frac{1}{\Delta\eta}\frac{1}{f_{\mathrm{p_{T}cut}}}\frac{1}{f_{\mathrm{notID}}}\sum\limits_{{\mathrm{i}}=1}^{\mathrm{n}}\frac{f_{\mathrm{bg}}(p_{\mathrm{T}}^{\mathrm{i}})}{\epsilon(p_{\mathrm{T}}^{\mathrm{i}})}E_{\mathrm{i}}\sin\theta_{\mathrm{i}}$
(4)

where i runs over the n reconstructed tracks and $\Delta\eta$ is the
pseudorapidity range used in the analysis, $\epsilon(p_{\mathrm{T}})$ corrects
for the finite track reconstruction efficiency and acceptance,
$f_{\mathrm{bg}}(p_{\mathrm{T}})$ corrects for the $\Lambda$,
$\overline{\Lambda}$, and K${}^{\mathrm{0}}_{\mathrm{S}}$ daughters and
electrons that pass the primary track quality cuts, $f_{\mathrm{notID}}$
corrects for particles that could not be identified unambiguously through
their specific energy loss d$E$/d$x$ in the TPC, and
$f_{\mathrm{p}_{\mathrm{Tcut}}}$ corrects for the finite detector acceptance
at low momentum. Hadronic $E_{\mathrm{T}}$ is given by
$E_{\mathrm{T}}^{\mathrm{had}}$ =
$E_{\mathrm{T}}^{\pi\mathrm{,K,p}}$/$f_{\mathrm{neutral}}$ where
$f_{\mathrm{neutral}}$ is the fraction of $E_{\mathrm{T}}^{\mathrm{had}}$ from
$\pi^{\pm}$, K±, p, and $\overline{\mathrm{p}}$ and total $E_{\mathrm{T}}$ is
given by $E_{\mathrm{T}}$ =
$E_{\mathrm{T}}^{\pi\mathrm{,K,p}}$/$f_{\mathrm{total}}$ where
$f_{\mathrm{total}}$ is the fraction of $E_{\mathrm{T}}$ from $\pi^{\pm}$, K±,
p, and $\overline{\mathrm{p}}$. The determination of each of these corrections
is given below and the systematic uncertainties are summarized in Tab. 1.
Systematic uncertainties are correlated point to point.

####  3.1.1 Single track efficiency$\times$acceptance
$\mathbf{\epsilon(p_{\mathrm{T}})}$

The single track efficiency$\times$acceptance is determined by comparing the
primary yields to the reconstructed yields using HIJING+GEANT simulations, as
described in [49]. When a particle can be identified as a $\pi^{\pm}$, K±, p,
or $\overline{\mathrm{p}}$ using the algorithm described above, the efficiency
for that particle is used. Otherwise the particle-averaged efficiency is used.
The 5% systematic uncertainty is determined by the difference between the
fraction of TPC standalone tracks matched with a hit in the ITS in simulations
and data.

####  3.1.2 Background $\mathbf{{\mathit{f}}_{\mathrm{bg}}(p_{\mathrm{T}})}$

The background comes from photons which convert to $e^{+}e^{-}$ in the
detector and decay daughters from $\Lambda$, $\overline{\Lambda}$, and
K${}^{\mathrm{0}}_{\mathrm{S}}$ which are observed in the tracking detectors
but do not originate from primary $\pi^{\pm}$, K±, p, and
$\overline{\mathrm{p}}$. This is determined from HIJING+GEANT simulations. The
systematic uncertainty on the background due to conversion electrons is
determined by varying the material budget in the HIJING+GEANT simulations by
$\pm$10% and found to be negligible compared to other systematic
uncertainties. The systematic uncertainty due to $\Lambda$,
$\overline{\Lambda}$, and K${}^{\mathrm{0}}_{\mathrm{S}}$ daughters is
sensitive to both the yield and the shape of the $\Lambda$,
$\overline{\Lambda}$, and K${}^{\mathrm{0}}_{\mathrm{S}}$ spectra. To
determine the contribution from $\Lambda$, $\overline{\Lambda}$, and
K${}^{\mathrm{0}}_{\mathrm{S}}$ decay daughters and its systematic uncertainty
the spectra in simulation are reweighted to match the data and the yields are
varied within their uncertainties [50]. Because the centrality dependence is
less than the uncertainty due to other corrections, a constant correction of
0.982 $\pm$ 0.008 is applied across all centralities .

####  3.1.3 Particle identification $f_{\mathbf{{\mathrm{notID}}}}$

The $E_{\mathrm{T}}$ of particles with 0.15 $<$ $p_{\rm T}$ $<$ 0.45 GeV/$c$
with a d$E$/d$x$ within two standard deviations of the expected d$E$/d$x$ for
kaons is calculated using the kaon mass and the $E_{\mathrm{T}}$ of particles
with 0.15 $<$ $p_{\rm T}$ $<$ 0.9 GeV/$c$ with a d$E$/d$x$ within two standard
deviations of the expected d$E$/d$x$ for (anti)protons is calculated using the
(anti)proton mass. The $E_{\mathrm{T}}$ of all other particles is calculated
using the pion mass. Since the average transverse momentum is $\langle
p_{\mathrm{T}}\rangle$ = 0.678 $\pm$ 0.007 GeV/$c$ for charged particles [51]
and over 80% of the particles created in the collision are pions [46], most
particles can be identified correctly using this algorithm. At high momentum,
the difference between the true $E_{\mathrm{T}}$ and the $E_{\mathrm{T}}$
calculated using the pion mass hypothesis for kaons and protons is less than
at low $p_{\rm T}$. This is therefore a small correction. Assuming that all
kaons with 0.15 $<$ $p_{\rm T}$ $<$ 0.45 GeV/$c$ and (anti)protons with 0.15
$<$ $p_{\rm T}$ $<$ 0.9 GeV/$c$ are identified correctly and using the
identifed $\pi^{\pm}$, K±, p, and $\overline{\mathrm{p}}$ spectra [46] gives
$f_{\mathrm{notID}}$ = 0.992 $\pm$ 0.002. The systematic uncertainty is
determined from the uncertainties on the yields.

Assuming that 5% of kaons and protons identified using the particle
identification algorithm described above are misidentified as pions only
decreases $f_{\mathrm{notID}}$ by 0.0002, less than the systematic uncertainty
on $f_{\mathrm{notID}}$. This indicates that this correction is robust to
changes in the mean d$E$/d$x$ expected for a given particle and its standard
deviation. We note that either assuming no particle identification or doubling
the number of kaons and protons only decreases $f_{\mathrm{notID}}$ by 0.005.

####  3.1.4 Low $\mathbf{p_{\rm T}}$ acceptance
$\mathbf{{\mathit{f}}_{\mathrm{p}_{\mathrm{Tcut}}}}$

The lower momentum acceptance of the tracking detectors is primarily driven by
the magnetic field and the inner radius of the active volume of the detector.
Tracks can be reliably reconstructed in the TPC for particles with $p_{\rm T}$
$>$ 150 MeV/$c$. The fraction of $E_{\mathrm{T}}$ carried by particles below
this momentum cut-off is determined by HIJING+GEANT simulations. To calculate
the systematic uncertainty we follow the prescription given by STAR [29]. The
fraction of $E_{\mathrm{T}}$ contained in particles below 150 MeV/$c$ is
calculated assuming that all particles below this cut-off have a momentum of
exactly 150 MeV/$c$ to determine an upper bound, assuming that they have a
momentum of 0 MeV/$c$ to determine a lower bound, and using the average as the
nominal value. Using this prescription, $f_{\mathrm{p}_{\mathrm{Tcut}}}$ =
0.9710 $\pm$ 0.0058. We note that $f_{\mathrm{p}_{\mathrm{Tcut}}}$ is the same
within systematic uncertainties when calculated from PYTHIA simulations [52]
for pp collisions with $\sqrt{s}$ = 0.9 and 8 TeV, indicating that this is a
robust quantity.

####  3.1.5 Correction factors $\mathbf{{\mathit{f}}_{\mathrm{neutral}}}$ and
$\mathbf{{\mathit{f}}_{\mathrm{total}}}$

Under the assumption that the different states within an isospin multiplet and
particles and antiparticles have the same $E_{\mathrm{T}}$,
$f_{\mathrm{neutral}}$ can be written as

$f_{\mathrm{neutral}}=\frac{2E_{\mathrm{T}}^{\pi}+2E_{\mathrm{T}}^{\mathrm{K}}+2E_{\mathrm{T}}^{\mathrm{p}}}{3E_{\mathrm{T}}^{\pi}+4E_{\mathrm{T}}^{\mathrm{K}}+4E_{\mathrm{T}}^{\mathrm{p}}+2E_{\mathrm{T}}^{\Lambda}+6E_{\mathrm{T}}^{\Sigma}}$
(5)

and $f_{\mathrm{total}}$ can be written as

$f_{\mathrm{total}}=\frac{2E_{\mathrm{T}}^{\pi}+2E_{\mathrm{T}}^{\mathrm{K}}+2E_{\mathrm{T}}^{\mathrm{p}}}{3E_{\mathrm{T}}^{\pi}+4E_{\mathrm{T}}^{\mathrm{K}}+4E_{\mathrm{T}}^{\mathrm{p}}+2E_{\mathrm{T}}^{\Lambda}+6E_{\mathrm{T}}^{\Sigma}+E_{\mathrm{T}}^{\omega,\eta,{\mathrm{e}}^{\pm},\gamma}}.$
(6)

where $E_{\mathrm{T}}^{\mathrm{K}}$ is the $E_{\mathrm{T}}$ from one kaon
species, $E_{\mathrm{T}}^{\pi}$ is the $E_{\mathrm{T}}$ from one pion species,
$E_{\mathrm{T}}^{\mathrm{p}}$ is the average of the $E_{\mathrm{T}}$ from
protons and antiprotons, $E_{T}^{\Lambda}$ is the average $E_{\mathrm{T}}$
from $\Lambda$ and $\overline{\Lambda}$, and $E_{T}^{\Sigma}$ is the average
$E_{\mathrm{T}}$ from $\Sigma^{+}$, $\Sigma^{-}$, and $\Sigma^{0}$ and their
antiparticles. The contributions $E_{\mathrm{T}}^{\pi}$,
$E_{\mathrm{T}}^{\mathrm{K}}$, $E_{\mathrm{T}}^{\mathrm{p}}$, and
$E_{\mathrm{T}}^{\Lambda}$ are calculated from the particle spectra measured
by ALICE [46, 50] as for the calculation of $E_{\mathrm{T}}$ from the particle
spectra. The systematic uncertainties are also propagated assuming that the
systematic uncertainties from different charges of the same particle species
(e.g., $\pi^{+}$ and $\pi^{-}$) are 100% correlated and from different species
(e.g., $\pi^{+}$ and K+) are uncorrelated. The contribution from the
$\Sigma^{+}$, $\Sigma^{-}$, and $\Sigma^{0}$ and their antiparticles is
determined from the measured $\Lambda$ spectra. The total contribution from
$\Sigma$ species and their antiparticles should be approximately equal to that
of the $\Lambda$ and $\overline{\Lambda}$, but since there are three isospin
states for the $\Sigma$, each species carries roughly 1/3 of the
$E_{\mathrm{T}}$ that the $\Lambda$ carries. Since the $\Sigma^{0}$ decays
dominantly through a $\Lambda$ and has a short lifetime, the measured
$\Lambda$ spectra include $\Lambda$ from the $\Sigma^{0}$ decay. The ratio of
$F$ =
$(E_{\mathrm{T}}^{\Sigma^{+}}+E_{\mathrm{T}}^{\Sigma^{-}})/E_{\mathrm{T}}^{\Lambda}$
is therefore expected to be 0.5. HIJING [47] simulations indicate that $F$ =
0.67 and if the $E_{\mathrm{T}}$ scales with the yield, THERMUS [53] indicates
that $F$ = 0.532. We therefore use $F$ = 0.585 $\pm$ 0.085.

The contribution $E_{\mathrm{T}}^{\omega,\eta,{\mathrm{e}}^{\pm},\gamma}$ is
calculated using transverse mass scaling for the $\eta$ meson and PYTHIA
simulations for the $\omega$, $e^{\pm}$, and $\gamma$, as described earlier.
Because most of the $E_{\mathrm{T}}$ is carried by $\pi^{\pm}$, K±, p,
$\overline{\mathrm{p}}$, n, and $\overline{\mathrm{n}}$, whose contributions
appear in both the numerator and the denominator, $f_{\mathrm{total}}$ and
$f_{\mathrm{neutral}}$ can be determined to high precision, and the
uncertainty in $f_{\mathrm{total}}$ and $f_{\mathrm{neutral}}$ is driven by
$E_{\mathrm{T}}^{\Lambda}$ and $E_{\mathrm{T}}^{\omega,\eta,e^{\pm},\gamma}$.
It is worth considering two special cases. If all $E_{\mathrm{T}}$ were
carried by pions, as is the case at low energy where almost exclusively pions
are produced, Eq. 6 would simplify to $f_{\mathrm{total}}$ = 2/3. If all
$E_{\mathrm{T}}$ were only carried by kaons, (anti)protons, and
(anti)neutrons, Eq. 6 would simplify to $f_{\mathrm{total}}$ = 1/2.

In order to calculate the contribution from the $\eta$ meson and its
uncertainties, we assume that the shapes of its spectra for all centrality
bins as a function of transverse mass are the same as the pion spectra, using
the transverse mass scaling [54], and that the $\eta/\pi$ ratio is independent
of the collision system, as observed by PHENIX [55]. We also consider a
scenario where the $\eta$ spectrum is assumed to have the same shape as the
kaon spectrum, as would be expected if the shape of the $\eta$ spectrum was
determined by hydrodynamical flow. In this case we use the ALICE measurements
of $\eta/\pi$ in pp collisions [56] to determine the relative yields. We use
the $\eta/\pi$ ratio at the lowest momentum point available, $p_{\rm T}$ = 0.5
GeV/$c$, because the $E_{\mathrm{T}}$ measurement is dominated by low momentum
particles. Because no $\omega$ measurement exists, PYTHIA [52] simulations of
pp collisions were used to determine the relative contribution from the
$\omega$ and from all other particles which interact electromagnetically
(mainly $\gamma$ and e±). These contributions were approximately 2% and 1% of
$E_{\mathrm{T}}^{\pi}$, respectively. With these assumptions,
$E_{\mathrm{T}}^{\omega,\eta,e^{\pm},\gamma}/E_{\mathrm{T}}^{\pi}$ = 0.17
$\pm$ 0.11. The systematic uncertainty on this fraction is dominated by the
uncertainty in the $\eta/\pi$ ratio. We propagate the uncertainties assuming
that the $E_{\mathrm{T}}$ from the same particle species are 100% correlated
and that the uncertainties from different particle species are uncorrelated.

Figure 1: Fraction of the total $E_{\mathrm{T}}$ in pions ($f_{\pi}$), kaons
($f_{\mathrm{K}}$), p and $\overline{p}$ ($f_{{\mathrm{p}}}$), and $\Lambda$
($f_{\Lambda}$) and the correction factors $f_{\mathrm{total}}$,
$f_{\mathrm{neutral}}$, and $f_{\mathrm{em}}$ as a function of $\langle
N_{\mathrm{part}}\rangle$. The fraction $f_{\Lambda}$ is scaled by a factor of
two so that the data do not overlap with those from protons. Note that
$f_{\mathrm{neutral}}$ is the fraction of $E_{\mathrm{T}}^{\mathrm{had}}$
measured in the tracking detectors while $f_{\mathrm{total}}$ and
$f_{\mathrm{em}}$ are the fractions of the total $E_{\mathrm{T}}$ measured in
the tracking detectors and the calorimeters, respectively. The vertical error
bars give the uncertainty on the fraction of $E_{\mathrm{T}}$ from the
particle yields.

The $f_{\mathrm{neutral}}$, $f_{\mathrm{total}}$, and $f_{\mathrm{em}}$ =
$1-$$f_{\mathrm{total}}$/$f_{\mathrm{neutral}}$ are shown in Fig. 1 along with
the fractions of $E_{\mathrm{T}}$ carried by all pions $f_{\pi}$, all kaons
$f_{K}$, protons and antiprotons $f_{p}$, and $\Lambda$ baryons $f_{\Lambda}$
versus $\langle N_{\mathrm{part}}\rangle$. While there is a slight dependence
of the central value on $\langle N_{\mathrm{part}}\rangle$, this variation is
less than the systematic uncertainty. Since there is little centrality
dependence, we use $f_{\mathrm{em}}$ = 0.240 $\pm$ 0.027,
$f_{\mathrm{neutral}}$ = 0.728 $\pm$ 0.017, and $f_{\mathrm{total}}$ = 0.553
$\pm$ 0.010, which encompass the entire range for all centralities. The
systematic uncertainty is largely driven by the contribution from $\Lambda$,
$\omega$, $\eta$, e±, and $\gamma$ since these particles only appear in the
denominator of Eqs. 5 and 6. The systematic uncertainty on
$f_{\mathrm{total}}$ is smaller than that on $f_{\mathrm{neutral}}$ because
$f_{\mathrm{neutral}}$ only has $E_{\mathrm{T}}^{\Lambda}$ in the denominator.

These results are independently interesting. There is little change in the
fraction of energy carried by different species with centrality and the
changes are included in the $f_{\mathrm{total}}$ used for the measurement of
$E_{\mathrm{T}}$. Additionally, only about 1/4 of the energy is in
$E_{\mathrm{T}}^{\mathrm{em}}$, much less than the roughly 1/3 of energy in
$E_{\mathrm{T}}^{\mathrm{em}}$ at lower energies where most particles produced
are pions with the $\pi^{\mathrm{0}}$ carrying approximately 1/3 of the energy
in the collision. Furthermore, only about 3.5% of the $E_{\mathrm{T}}$ is
carried by $\omega$, $\eta$, e±, and $\gamma$. Since charged and neutral pions
have comparable spectra, this means that the tracking detectors are highly
effective for measuring the transverse energy distribution in nuclear
collisions.

####  3.1.6 $\mathbf{{\mathit{E}}_{\mathrm{T}}^{\mathrm{had}}}$ distributions

Correction | Value | % Rel. uncertainty
---|---|---
$f_{\mathrm{p}_{\mathrm{Tcut}}}$ | 0.9710 $\pm$ 0.0058 | 0.6 %
$f_{\mathrm{neutral}}$ | 0.728 $\pm$ 0.017 | 2.3 %
$f_{\mathrm{total}}$ | 0.553 $\pm$ 0.010 | 3.0 %
$f_{\mathrm{notID}}$ | 0.982 $\pm$ 0.002 | 0.2 %
$f_{\mathrm{bg}}(p_{\mathrm{T}})$ | 1.8% | 0.8%
$\epsilon(p_{\mathrm{T}})$ | 50% | 5%
Table 1: Summary of corrections and systematic uncertainties for
$E_{\mathrm{T}}^{\mathrm{had}}$ and $E_{\mathrm{T}}$ from tracking detectors.
For centrality and $p_{\rm T}$ independent corrections the correction is
listed. For centrality and $p_{\rm T}$ dependent corrections, the approximate
percentage of the correction is listed. In addition, the anchor point
uncertainty in the Glauber calculations leads to an uncertainty of 0–4%,
increasing with centrality. Figure 2: Distribution of
$E_{\mathrm{T}}^{\mathrm{had}}$ measured from $\pi^{\pm}$, K±, p, and
$\overline{\mathrm{p}}$ tracks at midrapidity for several centrality classes.
Not corrected for resolution effects. Only statistical error bars are shown.

Figure 2 shows the distributions of the reconstructed
$E_{\mathrm{T}}^{\mathrm{had}}$ measured from $\pi^{\pm}$, K±, p, and
$\overline{\mathrm{p}}$ tracks using the method described above for several
centralities. No correction was done for the resolution leaving these
distributions dominated by resolution effects. The mean
$E_{\mathrm{T}}^{\mathrm{had}}$ is determined from the average of the
distribution of $E_{\mathrm{T}}^{\mathrm{had}}$ in each centrality class.

Figure 3: Comparison of
$\langle$d$E_{\mathrm{T}}^{\mathrm{had}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ from the
measured particle spectra and as calculated from the tracking detectors. The
boxes indicate the systematic uncertainties.

###  3.2 Calculation of $\mathbf{{\mathit{E}}_{\mathrm{T}}}$ and
$\mathbf{{\mathit{E}}_{\mathrm{T}}^{\mathrm{had}}}$ from measured spectra

We use the transverse momentum distributions (spectra) measured by ALICE [46,
50] to calculate $E_{\mathrm{T}}$ and $E_{\mathrm{T}}^{\mathrm{had}}$ as a
cross check. We assume that all charge signs and isospin states of each
particle carry the same $E_{\mathrm{T}}$, e.g.
$E_{\mathrm{T}}^{\pi^{+}}=E_{\mathrm{T}}^{\pi^{-}}=E_{\mathrm{T}}^{\pi^{0}}$,
and that the $E_{\mathrm{T}}$ carried by (anti)neutrons equals the
$E_{\mathrm{T}}$ carried by (anti)protons. These assumptions are consistent
with the data at high energies where positively and negatively charged hadrons
are produced at similar rates and the anti-baryon to baryon ratio is close to
one [57, 58]. Since the $\Lambda$ spectra [50] are only measured for five
centrality bins, the $\Lambda$ contribution is interpolated from the
neighboring centrality bins. The same assumptions about the contributions of
the $\eta$, $\omega$, $\gamma$, and $e^{\pm}$ described in the section on
$f_{\mathrm{total}}$ and $f_{\mathrm{neutral}}$ are used for these
calculations. The dominant systematic uncertainty on these measurements is due
to the single track reconstruction efficiency and is correlated point to
point. The systematic uncertainty on these calculations is not correlated with
the calculations of $E_{\mathrm{T}}$ using the tracking detectors because
these measurements are from data collected in different years. The mean
$E_{\mathrm{T}}^{\mathrm{had}}$ per $\langle N_{\mathrm{part}}/2\rangle$
obtained from the tracking results of Fig. 2 are shown as a function of
$\langle N_{\mathrm{part}}\rangle$ in Fig. 3, where they are compared with
results calculated using the particle spectra measured by ALICE. The two
methods give consistent results. Data are plotted in 2.5% wide bins in
centrality for 0–40% central collisions, where the uncertainty on the
centrality is $<$1% [59]. Data for 40–80% central collisions are plotted in 5%
wide bins.

###  3.3 Electromagnetic calorimeter measurements of
$\mathbf{{\mathit{E}}_{\mathrm{T}}^{\mathrm{em}}}$

The $E_{\mathrm{T}}^{\mathrm{em}}$ is defined as the transverse energy of the
particles of category B discussed above, which are the particles measured well
by an electromagnetic calorimeter. While the definition of
$E_{\mathrm{T}}^{\mathrm{em}}$ includes $\pi^{\mathrm{0}}$, $\omega$, $\eta$,
e±, and $\gamma$, the majority of the $E_{\mathrm{T}}$ comes from
$\pi^{\mathrm{0}}$ $\rightarrow$ $\gamma\gamma$ (85%) and $\eta$ $\rightarrow$
$\gamma\gamma$ (12%) decays, meaning that the vast majority of
$E_{\mathrm{T}}^{\mathrm{em}}$ arises from photons reaching the active area of
the electromagnetic calorimeters. Reconstructed clusters are used for the
analysis, with most clusters arising from a single $\gamma$. Clusters reduce
contributions from detector noise to a negligible level, as compared to using
tower energies as done by STAR [29]. However, clusters also require additional
corrections for the reconstruction efficiency, nonlinearity, and minimum
energy reconstructed. In addition, both the EMCal and the PHOS have limited
nominal acceptances so an acceptance correction must be applied. Backgrounds
come from charged hadrons in category A ($\pi^{\pm}$, K±, p, and
$\overline{\mathrm{p}}$), kaon decays into $\pi^{\mathrm{0}}$ from both
category A (K±) and category C ($K^{\mathrm{0}}_{\mathrm{S}}$), neutrons from
category D, and particles produced by secondary interactions with the detector
material.

The corrected $E_{\mathrm{T}}^{\mathrm{em}}$ is given by

$\frac{{\mathrm{d}}E_{\mathrm{T}}^{\mathrm{em}}}{{\mathrm{d}}\eta}=\frac{1}{\Delta\eta}\frac{1}{f_{\mathrm{acc}}}\frac{1}{f_{\mathrm{E}_{\mathrm{Tmin}}}}\bigg{(}\sum\limits_{\mathrm{j}}\delta_{\mathrm{m}}\frac{\sin\theta_{\mathrm{j}}}{\epsilon_{\gamma}f_{E_{\mathrm{NL}}}}E_{\mathrm{j}}~{}-~{}E_{\mathrm{T}}^{\mathrm{bkgd}}\bigg{)}$
(7)

where j runs over the reconstructed clusters in the calorimeter and
$\Delta\eta$ is the pseudorapidity range used in the analysis. The correction
factor $f_{\mathrm{acc}}$ corrects for the finite nominal azimuthal detector
acceptance, $f_{E_{\mathrm{Tmin}}}$ is a correction for the minimum cluster
energy used in the analysis, $\delta_{\mathrm{m}}$ is zero when a cluster is
matched to a track and one otherwise, $\epsilon_{\gamma}$ is the product of
the active acceptance and the reconstruction efficiency in the nominal
acceptance of the detector, $f_{E_{\mathrm{NL}}}$ is the correction for the
nonlinear response of the calorimeter, and $E_{\mathrm{T}}^{\mathrm{bkgd}}$ is
the sum of the contributions from charged hadrons, kaons, neutrons, and
particles created by secondary interactions. These correction factors are
discussed below and their systematic uncertainties are summarized in Tab. 2.
All of the systematic uncertainties except for that due to the background
subtraction are correlated point to point. Systematic uncertainties on
measurements of $E_{\mathrm{T}}^{\mathrm{em}}$ from the EMCal and the PHOS and
calculations of $E_{\mathrm{T}}^{\mathrm{em}}$ from the spectra are not
correlated. Systematic uncertainties on hybrid measurements are dominated by
systematic uncertainties on $E_{\mathrm{T}}^{\mathrm{had}}$ and are therefore
dominantly correlated point to point and with the tracking detector
measurements.

####  3.3.1 Acceptance correction $\mathbf{{\mathit{f}}_{\mathrm{acc}}}$ and
cluster reconstruction efficiency $\mathbf{\epsilon_{\gamma}}$

The correction for the acceptance is divided into two parts, the correction
due to the nominal acceptance of the detector and the correction due to
limited acceptance within the nominal acceptance of the detector due to dead
regions and edge effects. To reduce edge effects, clusters in the PHOS are
restricted to $|\eta|<$ 0.1 and in the EMCal to $|\eta|<$ 0.6. The correction
$f_{\mathrm{acc}}$ accounts for the limited nominal acceptance in azimuth and
is therefore 5/18 for the EMCal, which has a nominal acceptance of 100∘, and
1/6 for the PHOS, which has a nominal acceptance of 60∘. It does not correct
for acceptance effects due to dead regions in the detector or for noisy towers
omitted from the analysis. This is accounted for by the cluster reconstruction
efficiency$\times$acceptance within the nominal detector acceptance,
$\epsilon_{\gamma}$, calculated from HIJING+GEANT simulations using photons
from the decay of the $\pi^{\mathrm{0}}$ meson. The efficiency is calculated
as a function of the energy of the cluster.

####  3.3.2 Minimum cluster energy $\mathbf{f_{E_{\mathrm{Tmin}}}}$

There is a minimum energy for usable clusters analogous to the minimum $p_{\rm
T}$ in the acceptance of the tracking detectors. A threshold of 250 MeV for
PHOS and 300 MeV for the EMCal is applied. These energies are above the peak
energy for minimum ionizing particles (MIPs), reducing the background
correction due to charged hadrons. We apply the threshold in $E_{\mathrm{T}}$
rather than energy because it simplifies the calculation of the correction for
this threshold and its systematic uncertainty. We use the charged pion spectra
to calculate the fraction of $E_{\mathrm{T}}^{\mathrm{em}}$ below these
thresholds. PYTHIA is used to simulate the decay kinematics and the measured
charged pion spectra are used to determine the fraction of $E_{\mathrm{T}}$
from pions within the acceptance. As for the calculation of
$f_{\mathrm{total}}$ for the measurement of $E_{\mathrm{T}}^{\mathrm{had}}$
described above, we assume transverse mass scaling to determine the shape of
the $\eta$ spectrum and the $\eta/\pi$ ratio measured by ALICE [56] to
estimate the contribution of the $\eta$ meson to $f_{E_{\mathrm{Tmin}}}$. The
uncertainty on the shape of the charged pion spectrum and on the $\eta/\pi$
ratio is used to determine the uncertainty on $f_{E_{\mathrm{Tmin}}}$. This
correction is centrality dependent and ranges from 0.735 to 0.740 for the PHOS
and from 0.640 to 0.673 for the EMCal with a systematic uncertainty of 3.5–5%.

####  3.3.3 Nonlinearity correction $\mathbf{f_{E_{\mathrm{NL}}}}$ and energy
scale uncertainty

For an ideal calorimeter the signal observed is proportional to the energy. In
practice, however, there is a slight deviation from linearity in the signal
observed, particularly at low energies. A nonlinearity correction is applied
to take this into account. For the EMCal this deviation from linearity reaches
a maximum of about 15% for the lowest energy clusters used in this analysis.
The systematic uncertainty for the EMCal is determined by comparing the
nonlinearity observed in test beam and the nonlinearity predicted by
HIJING+GEANT simulations and reaches a maximum of about 5% for the lowest
energy clusters. The PHOS nonlinearity is determined by comparing the location
of the $\pi^{\mathrm{0}}$ mass peak to HIJING+GEANT simulations and cross
checked using the energy divided by the momentum for identified electrons. The
systematic uncertainty is derived from the accuracy of the location of the
$\pi^{\mathrm{0}}$ mass peak. The nominal correction is about 1% with a
maximum systematic uncertainty of around 3% for the lowest energy clusters.
The raw $E_{\mathrm{T}}^{\mathrm{em}}$ is calculated with the maxima and
minima of the nonlinearities and the difference from the nominal value is
assigned as a systematic uncertainty. The final systematic uncertainty on the
measurement with the EMCal due to nonlinearity is about 0.8% and 1.3% for the
PHOS. For both the PHOS and the EMCal, the energy scale uncertainty was
determined by comparing the location of the $\pi^{\mathrm{0}}$ mass peak and
the ratio of energy over momentum for electrons. This systematic uncertainty
is 2% for the EMCal [60] and 0.5% for the PHOS [61].

####  3.3.4 Background $\mathbf{E_{\mathrm{T}}^{\mathrm{bkgd}}}$

Charged particles (category A) are the largest source of background in
$E_{\mathrm{T}}^{\mathrm{em}}$. Clusters matched to tracks are omitted from
the analysis. The track matching efficiency determined from HIJING+GEANT
simulations is combined with information from clusters matched to tracks to
calculate the number and mean energy of remaining deposits from charged
particles. The systematic uncertainty on this contribution comes from the
uncertainty on the track matching efficiency and the uncertainty in the mean
energy. The former is dominated by the uncertainty on the single track
reconstruction efficiency and the latter is determined by comparing central
and peripheral collisions, assuming that the energy of clusters matched to
tracks in central collisions may be skewed by overlapping clusters due to the
high occupancy.

The background contributions from both charged kaons (category A) through
their K± $\rightarrow$ X$\pi^{\mathrm{0}}$ decays and
$K^{\mathrm{0}}_{\mathrm{S}}$ (category C) through its
$K^{\mathrm{0}}_{\mathrm{S}}$ $\rightarrow$ $\pi^{\mathrm{0}}$
$\pi^{\mathrm{0}}$ decay are non-negligible. The amount of energy deposited by
a kaon as a function of $p_{\rm T}$ is determined using HIJING+GEANT
simulations. This is combined with the kaon spectra measured by ALICE [46] to
calculate the energy deposited in the calorimeters by kaons. The systematic
uncertainty on the background from kaons is determined by varying the yields
within the uncertainties of the spectra. Contributions from both neutrons and
particles from secondary interactions are determined using HIJING+GEANT
simulations. The systematic uncertainty on these contributions is determined
by assuming that they scale with either the number of tracks (as a proxy for
the number of charged particles) or with the number of calorimeter clusters
(as a proxy for the number of neutral particles).

The background contribution is centrality dependent and ranges from 61% to 73%
with both the background and its systematic uncertainty dominated by
contributions from charged hadrons. This correction is so large because
$E_{\mathrm{T}}^{\mathrm{em}}$ comprises only about 25% of the
$E_{\mathrm{T}}$ in an event while $\pi^{\pm}$, K±, p, and
$\overline{\mathrm{p}}$ carry roughly 57% of the $E_{\mathrm{T}}$ in an event.

####  3.3.5 Acceptance effects

The limited calorimeter acceptance distorts the distribution of
$E_{\mathrm{T}}^{\mathrm{em}}$ for events with very low
$E_{\mathrm{T}}^{\mathrm{em}}$ because it is difficult to measure the mean
$E_{\mathrm{T}}$ when the mean number of clusters observed is small (about
1–10). While it is possible to correct for acceptance, this was not done since
the measurement of $E_{\mathrm{T}}$ from the tracking method has the highest
precision. The hybrid method using both the calorimeters and the tracking
detectors is therefore restricted to the most central collisions where
distortions of the $E_{\mathrm{T}}^{\mathrm{em}}$ distribution are negligible.

####  3.3.6 $\mathbf{{\mathit{E}}_{\mathrm{T}}^{\mathrm{em}}}$ distributions

| PHOS | EMCal
---|---|---
| Correction | Uncertainty | Correction | Uncertainty
$f_{\mathrm{acc}}$ | 6 | 0 | 3.6 | 0
Energy scale | – | 0.5% | – | 2%
$\epsilon_{\gamma}$ | 40% | 5% | 80% | 5%
$f_{E_{\mathrm{Tmin}}}$ | 0.735 – 0.740 | 3.5% | 0.64 – 0.673 | 4.1 – 5.0%
$f_{E_{\mathrm{NL}}}$ |  $<$ 0.5% | 1.3% |  $<$ 5% | 0.8%
$f_{\mathrm{bkgd}}$ | 0.616 – 0.753 | 9 – 20% | 0.659 – 0.732 | 8 – 13%
$E_{\mathrm{T}}^{\mathrm{em}}$ | – | 10 – 20% | – | 10 – 15%
Table 2: Summary of corrections and systematic uncertainties for
$E_{\mathrm{T}}^{\mathrm{em}}$. The approximate size of the correction is
listed for $\epsilon_{\gamma}$ and the ranges are listed for centrality
dependent corrections. The fraction $f_{\mathrm{bkgd}}$ =
$E_{\mathrm{T}}^{\mathrm{bkgd}}/E_{\mathrm{T}}^{\mathrm{raw}}$ where
$E_{\mathrm{T}}^{\mathrm{raw}}=\sum\limits_{\mathrm{j}}\delta_{\mathrm{m}}\frac{\sin\theta_{\mathrm{j}}}{\epsilon_{\gamma}f_{E_{\mathrm{NL}}}}E_{\mathrm{j}}$
is given in order to compare $E_{\mathrm{T}}^{\mathrm{bkgd}}$ across
centralities. In addition, the anchor point uncertainty in the Glauber
calculations leads to an uncertainty of 0–4%, increasing with centrality.

Figure 4 shows the distributions of the reconstructed
$E_{\mathrm{T}}^{\mathrm{em}}$ measured using the EMCal and Fig. 5 shows the
distributions of the reconstructed $E_{\mathrm{T}}^{\mathrm{em}}$ measured
using the PHOS. No resolution correction was applied for the resolution
leaving the distributions in Fig. 4 and Fig. 5 dominated by resolution
effects. The resolution is primarily determined by the finite acceptance of
the detectors in azimuth, limiting the fraction of
$E_{\mathrm{T}}^{\mathrm{em}}$ sampled by the calorimeter. The distributions
are broader for PHOS than EMCal because of the smaller azimuthal acceptance of
the PHOS. The mean $E_{\mathrm{T}}^{\mathrm{em}}$ is determined from the
average of the distribution of $E_{\mathrm{T}}^{\mathrm{em}}$ in each
centrality bin. The $E_{\mathrm{T}}^{\mathrm{em}}$ per $\langle
N_{\mathrm{part}}\rangle$ pair measured using the electromagnetic calorimeters
is compared to that calculated using the measured pion spectra in Fig. 6,
demonstrating that these methods lead to comparable results. The
$E_{\mathrm{T}}^{\mathrm{em}}$ calculated from the spectra is determined using
the same ratio of
$E_{\mathrm{T}}^{\omega,\eta,{\mathrm{e}}^{\pm},\gamma}/E_{\mathrm{T}}^{\pi}$
= 0.171 $\pm$ 0.110 for all centralities.

Figure 4: Distribution of $E_{\mathrm{T}}^{\mathrm{em}}$ measured with the
EMCal at midrapidity for several centrality bins. Not corrected for resolution
effects. Only statistical error bars are shown. Figure 5: Distribution of
$E_{\mathrm{T}}^{\mathrm{em}}$ measured with the PHOS at midrapidity for
several centrality bins. Not corrected for resolution effects. Only
statistical error bars are shown. Figure 6: Comparison of
$\langle$d$E_{\mathrm{T}}^{\mathrm{em}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ at
midrapidity from the PHOS, from the EMCal, and as calculated from the measured
pion spectra. The boxes indicate the systematic uncertainties.

##  4 Results

Figure 7: Comparison of total $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ at
midrapidity using tracking detectors, using EMCal+tracking, using
PHOS+tracking, and as calculated from the measured particle spectra. The boxes
indicate the systematic uncertainties.

The $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ is shown
in Fig. 7 using tracking detectors, using EMCal+tracking, using PHOS+tracking,
and as calculated from the measured particle spectra. All methods lead to
comparable results, although the systematic errors are largely correlated due
to the dominant correction from the tracking inefficiency. The determination
of $\langle N_{\mathrm{part}}\rangle$ and its uncertainties are calculated
using a Glauber model as in [59, 62] and the uncertainties on $\langle
N_{\mathrm{part}}\rangle$ are added in quadrature to the uncertainties on
$E_{\mathrm{T}}$.

As discussed above, the small number of clusters observed in the calorimeters
in peripheral collisions make acceptance corrections difficult. Since the
measurements with the tracking detectors alone has higher precision, only
these measurements are used in the following.

Figure 8 compares $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ in Pb–Pb
collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from CMS [30] and ALICE,
and in Au–Au collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 200 GeV from STAR [29]
and PHENIX [26, 27]. Data from RHIC have been scaled by a factor of 2.7 for
comparison of the shapes. The factor of 2.7 is approximately the ratio of
$\langle p_{\mathrm{T}}\rangle\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$ at the
LHC [46] to that at RHIC [63, 64]. The shapes observed by ALICE and PHENIX are
comparable for all $\langle N_{\mathrm{part}}\rangle$. STAR measurements are
consistent with PHENIX measurements for the most central collisions and above
the PHENIX measurements, although consistent within systematic uncertainties,
for more peripheral collisions. CMS measurements are consistent with ALICE
measurements for peripheral collisions but deviate beyond the systematic
uncertainties for more central collisions. The $E_{\mathrm{T}}$ in 0–5% Pb–Pb
collisions is 1737 $\pm$ 6(stat.) $\pm$ 97 (sys.) GeV and the $E_{\mathrm{T}}$
per participant is 9.02 $\pm$ 0.03(stat.) $\pm$ 0.50 (sys.) GeV, two standard
deviations below the value observed by CMS [30]. All methods resulted in a
lower $E_{\mathrm{T}}$ than that reported by CMS, although the systematic
errors on the measurements are significantly correlated. One possible
explanation of the differences is that the corrections for the CMS calorimetry
measurement are determined by Monte Carlo [30] while the corrections for the
ALICE measurement are mainly data-driven.

Figure 8: Comparison of $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ at midrapidity in Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from CMS [30] and ALICE and in Au–Au
collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 200 GeV from STAR [29] and PHENIX
[26, 27]. Data from RHIC were scaled by a factor of 2.7 for comparison of the
shapes. The boxes indicate the systematic uncertainties.

PHENIX [28] reported that while $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$
scaled by $\langle N_{\mathrm{part}}\rangle$ has a pronounced centrality
dependence, as seen in Fig. 8, $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$
scaled by the number of constituent quarks, $\langle
N_{\mathrm{quark}}\rangle$, $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{quark}}/2\rangle$ shows little centrality dependence within the
systematic uncertainties for collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 62.4 –
200 GeV. This indicates that $E_{\mathrm{T}}$ might scale linearly with the
number of quarks participating in the collision rather than the number of
participating nucleons. Figure 9 shows
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{quark}}/2\rangle$
as a function of $\langle N_{\mathrm{part}}\rangle$. To calculate $\langle
N_{\mathrm{quark}}\rangle$ the standard Monte Carlo Glauber technique [32] has
been used with the following Woods-Saxon nuclear density parameters: radius
parameter $R_{\mathrm{WS}}=6.62\pm 0.06$ fm, diffuseness $a=0.546\pm 0.010$
fm, and hard core $d_{\mathrm{min}}=0.4\pm 0.4$ fm. The three constituent
quarks in each nucleon have been sampled from the nucleon density distribution
$\rho_{\mathrm{nucleon}}=\rho_{0}e^{-ar}$ with $a=4.28fm^{-1}$ using the
method developed by PHENIX [65]. The inelastic quark-quark cross section at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV was found to be
$\sigma_{\mathrm{qq}}^{\mathrm{inel}}=15.5\pm 2.0$ mb corresponding to
$\sigma_{\mathrm{NN}}^{\mathrm{inel}}=64\pm 5$ mb [59]. The systematic
uncertainties on the $\langle N_{\mathrm{quark}}\rangle$ calculations were
determined following the procedure described in [59, 62]. Unlike at RHIC, we
observe an increase in $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{quark}}/2\rangle$ with centrality below $\langle
N_{\mathrm{part}}\rangle$ $\approx$200.

Figure 9: Measurements of $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{quark}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ at
midrapidity in Pb–Pb collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV. Note
the suppressed zero. The boxes indicate the systematic uncertainties.

Figure 10 shows
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$,
a measure of the average transverse energy per particle, versus $\langle
N_{\mathrm{part}}\rangle$ in Pb–Pb collisions at ${\sqrt{s_{\mathrm{NN}}}}$ =
2.76 TeV from ALICE, and in Au–Au collisions at ${\sqrt{s_{\mathrm{NN}}}}$ =
200 GeV from STAR [29] and PHENIX [26, 27]. No centrality dependence is
observed within uncertainties at either RHIC or LHC energies. The
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
increases by a factor of approximately 1.25 from ${\sqrt{s_{\mathrm{NN}}}}$ =
200 GeV [26, 27, 29] to ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV. This is
comparable to the increase in $\langle p_{\mathrm{T}}\rangle$ from
${\sqrt{s_{\mathrm{NN}}}}$ = 200 GeV to ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV,
which also shows little dependence on the charged-particle multiplicity except
in peripheral collisions [51]. The absence of a strong centrality dependence
is consistent with the development of radial flow seen in the spectra of
identified particles [51] where the kinetic energy is conserved during the
hydrodynamic expansion instead of producing a higher $\langle
p_{\mathrm{T}}\rangle$.

Figure 10: Comparison of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
versus $\langle N_{\mathrm{part}}\rangle$ at midrapidity in Pb–Pb collisions
at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from ALICE and in Au–Au collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 200 GeV from STAR [29] and PHENIX [26, 27].
Figure 11: Comparison of $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ at midrapidity versus ${\sqrt{s_{\mathrm{NN}}}}$
in 0–5% central Pb–Pb collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from
ALICE and CMS [30] and central collisions at other energies [29, 26, 65] at
midrapidity. All measurements are from 0–5% central collisions except the NA49
data, which are from 0–7% collisions.

Figure 11 shows a comparison of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$
versus ${\sqrt{s_{\mathrm{NN}}}}$ in 0–5% central Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from ALICE and CMS [30] and central
collisions at other energies [29, 26, 65] at midrapidity. The data are
compared to an extrapolation from lower energy data [26], which substantially
underestimates the $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ at the LHC. The data are also compared to the EKRT
model [66, 67]. The EKRT model combines perturbative QCD minijet production
with gluon saturation and hydrodynamics. The EKRT calculation qualitatively
describes the ${\sqrt{s_{\mathrm{NN}}}}$ dependence at RHIC and SPS energies
[29]. However, at LHC energies EKRT overestimates $E_{\mathrm{T}}$
substantially, indicating that it is unable to describe the collision energy
dependence.

Figure 12: Comparison of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
at midrapidity versus ${\sqrt{s_{\mathrm{NN}}}}$ in Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from ALICE and measurements at other
energies [68, 19, 23, 25, 26, 29, 65]. The band shows the extrapolation from
lower energies with the width representing the uncertainty on the fit [26].

Figure 12 shows a comparison of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
versus ${\sqrt{s_{\mathrm{NN}}}}$ in 0-5% central Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV from ALICE and in central collisions at
other energies. Previous measurements indicated that
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
had either saturated at RHIC energies or showed only a weak dependence on
${\sqrt{s_{\mathrm{NN}}}}$ [26, 29, 65]. An empirical extrapolation of the
data to LHC energies assuming that both $E_{\mathrm{T}}$ and $\langle
N_{\mathrm{ch}}\rangle$ have a linear dependence on ${\sqrt{s_{\mathrm{NN}}}}$
predicted that
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
would be 0.92 $\pm$ 0.06 [26] and we observe 1.06 $\pm$ 0.05. Increasing the
incident energy increases both the particle production and the mean energy per
particle at LHC energies, in contrast to lower energies
(${\sqrt{s_{\mathrm{NN}}}}$ = 19.6 – 200 GeV) where increasing the incident
energy only led to increased particle production [26].

Figure 13: Comparison of $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{part}}/2\rangle$ versus $\langle N_{\mathrm{part}}\rangle$ at
midrapidity to AMPT [69], HYDJET 1.8 [70], and UDG [71]. The boxes indicate
the systematic uncertainties.

Figure 13 shows a comparison of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$
versus $\langle N_{\mathrm{part}}\rangle$ to various models. AMPT [69] is a
Monte Carlo event generator which builds on HIJING [47], adding explicit
interactions between initial minijet partons and final state hadronic
interactions. HYDJET 1.8 [70] is a Monte Carlo event generator that introduces
jet quenching via gluon bremsstrahlung to PYTHIA [52] events. The HYDJET
values use the $E_{\mathrm{T}}$ from HYDJET and the $\langle
N_{\mathrm{part}}\rangle$ from ALICE, similar to comparisons to HYDJET by CMS
[30]. The curves labeled UDG are calculations from a Color Glass Condensate
model [71] with different normalization K factors. None of the available
models is able to describe the data very well, but we find that AMPT does best
in describing the shape and level of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$.
HYDJET describes the relative shape changes as a function of centrality as
well as AMPT, but overestimates
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$.
Both CGC calculations overestimate
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$
and predict a larger increase as a function of centrality than is observed in
the data.

The volume-averaged energy density $\epsilon$ can be estimated from
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ using the following expression [18]

$\epsilon=\frac{1}{\mathrm{A}c\tau_{0}}{\mathrm{J}}\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}$
(8)

where A is the effective transverse collision area, $c$ is the speed of light,
J is the Jacobian for the transformation between
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ and
$\langle$d$E_{\mathrm{T}}/$dy$\rangle$, and $\tau_{0}$ is the formation time.
The Jacobian is calculated from the measured particle spectra [46, 50]. While
J has a slight centrality dependence, it is smaller than the systematic
uncertainty so a constant Jacobian of J = 1.12 $\pm$ 0.06 is used. The
formation time of the system $\tau_{0}$ is highly model dependent and we
therefore report $\epsilon\tau_{0}$.

The transverse overlap area corresponding to the measured
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ was determined by a calculation
using a Glauber Monte Carlo method. Using the Glauber parameters from [59] and
assuming each participating nucleon has an effective transverse radius of
$R=(\sigma_{\mathrm{NN}}^{\mathrm{inel}}/{4\pi})^{1/2}=0.71$ fm results in
$A=162.5$ fm2 for central collisions ($b=0$ fm). This is equivalent to a
transverse overlap radius of $R=7.19$ fm, which is close to the value of 7.17
fm often used in estimates of energy densities using a Woods-Saxon
distribution to determine the effective area [28, 65]. The centrality
dependence of A is obtained by assuming it scales as
$(\sigma_{\mathrm{x}}^{2}\sigma_{\mathrm{y}}^{2}-\sigma_{\mathrm{xy}}^{2})^{1/2}$
[72], where $\sigma_{\mathrm{x}}^{2}$ and $\sigma_{\mathrm{y}}^{2}$ are the
variances and $\sigma_{\mathrm{xy}}^{2}$ is the covariance of the spatial
distribution of the participating nucleons in the transverse plane in the
Glauber Monte Carlo calculation. For 0–5% central collisions this leads to a
reduction of A by 3% resulting in $\epsilon\tau_{0}=$ 12.5 $\pm$ 1.0
GeV/fm2/$c$. For comparison using $R=7.17$ fm gives $\epsilon\tau_{0}=$ 12.3
$\pm$ 1.0 GeV/fm2/$c$, roughly 2.3 times that observed in 0–5% central Au–Au
collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 200 GeV. Some of this increase
comes from the higher $\langle N_{\mathrm{part}}\rangle$ in central Pb–Pb
collisions relative to central Au–Au collisions The energy density times the
formation time $\epsilon\tau_{0}$ is shown in Fig. 14 for $R$ = 7.17 fm, the
same value of R used by PHENIX at RHIC energies [28, 65].

Figure 14: $\epsilon\tau_{\mathrm{0}}$ versus $\langle
N_{\mathrm{part}}\rangle$ estimated using Eq. 8, $R=7.17$ fm, and the measured
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$. The boxes indicate the systematic
uncertainties.

In addition to estimating the volume averaged energy density it is also
interesting to estimate the energy density attained at the core of the
collision area. This can be done by rewriting the Bjorken Eq. 8 as

$\epsilon_{\mathrm{c}}\tau_{0}=\frac{\mathrm{J}}{c}\frac{\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}_{\mathrm{c}}}{A_{\mathrm{c}}}=\frac{\mathrm{J}}{c}\frac{\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}}{\langle
N_{\mathrm{part}}\rangle}\sigma_{\mathrm{c}}$ (9)

where $A_{\mathrm{c}}$ is the area of the transverse core,
$\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}_{\mathrm{c}}$
is
$\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}$
produced in the core, and $\sigma_{\mathrm{c}}=\langle
N_{\mathrm{part}}\rangle_{\mathrm{c}}/A_{\mathrm{c}}$ is the transverse area
density of nucleon participants at the core. The area $A_{\mathrm{c}}$ was
chosen arbitrarily to be a circle with a radius of 1 fm at the center of the
collision. Equation 9 assumes that the local energy density scales with the
participant density in the transverse plane and that the measured value of
$\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}/\langle
N_{\mathrm{part}}\rangle$, which is averaged over the total transverse
collision area, is also representative of the transverse energy production at
the core,
$\Big{\langle}\frac{{\mathrm{d}}E_{\mathrm{T}}}{{\mathrm{d}}\eta}\Big{\rangle}_{\mathrm{c}}/\langle
N_{\mathrm{part}}\rangle_{\mathrm{c}}$. The increase of this quantity with
increasing centrality indicates that this is a conservative estimate. From a
Glauber Monte Carlo calculation we find for 0–5% centrality
$\sigma_{\mathrm{c}}=4.2\pm 0.1$ nucleon/fm2 resulting in a core energy
density of $\epsilon_{\mathrm{c}}\tau_{0}=21\pm 2$ GeV/fm2/$c$. For the most
central 80 fm2 (half the total overlap area) the energy density is still above
80% of the core energy density emphasizing that the core energy density may be
more relevant for judging the initial conditions of the QGP than the volume
averaged energy density.

##  5 Conclusions

We have measured $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ at midrapidity in
Pb–Pb collisions at ${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV using four different
methods. All methods lead to comparable results, although the systematic
uncertainties are largely correlated. Our results are consistent with results
from CMS [30] for 10–80% central collisions, however, we observe a lower
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ in 0–10% central collisions. The
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$ observed at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV in 0–5% central collisions is 1737 $\pm$
6(stat.) $\pm$ 97 (sys.) GeV. The shape of the centrality dependence of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$
is similar for RHIC and the LHC. No centrality dependence of
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
is observed within uncertainties, as was observed at RHIC. Unlike at RHIC, we
observe an increase in $\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle
N_{\mathrm{quark}}/2\rangle$ with centrality below $\langle
N_{\mathrm{part}}\rangle$ $\approx$200\. Both
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle/\langle N_{\mathrm{part}}/2\rangle$
and
$\langle$d$E_{\mathrm{T}}/$d$\eta\rangle$/$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$
in central collisions exceed the value expected from naive extrapolations from
data at lower collision energies. Assuming that the formation time
$\tau_{\mathrm{0}}$ is 1 fm/$c$ the energy density is estimated to be at least
12.3 $\pm$ 1.0 GeV/fm3 in 0–5% central Pb–Pb collisions at
${\sqrt{s_{\mathrm{NN}}}}$ = 2.76 TeV and the energy density at the core of
the collision exceeds 21 $\pm$ 2 GeV/fm3.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: State
Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds
Kidagan, Armenia; Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de
Amparo à Pesquisa do Estado de São Paulo (FAPESP); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; Danish Natural Science Research Council, the
Carlsberg Foundation and the Danish National Research Foundation; The European
Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und
Technologie (BMBF) and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; National Research,
Development and Innovation Office (NKFIH), Hungary; Department of Atomic
Energy and Department of Science and Technology of the Government of India;
Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi - Museo Storico
della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Italy; Japan Society
for the Promotion of Science (JSPS) KAKENHI and MEXT, Japan; Joint Institute
for Nuclear Research, Dubna; National Research Foundation of Korea (NRF);
Consejo Nacional de Cienca y Tecnologia (CONACYT), Direccion General de
Asuntos del Personal Academico(DGAPA), México, Amerique Latine Formation
academique - European Commission (ALFA-EC) and the EPLANET Program (European
Particle Physics Latin American Network); Stichting voor Fundamenteel
Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway
(NFR); National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and National Council of Scientific
Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Education
and Science of Russian Federation, Russian Academy of Sciences, Russian
Federal Agency of Atomic Energy, Russian Federal Agency for Science and
Innovations and The Russian Foundation for Basic Research; Ministry of
Education of Slovakia; Department of Science and Technology, South Africa;
Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas
(CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA),
Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia
(Consellería de Educación), Centro de Aplicaciones Tecnológicas y Desarrollo
Nuclear (CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy
Agency); Swedish Research Council (VR) and Knut $\&$ Alice Wallenberg
Foundation (KAW); Ukraine Ministry of Education and Science; United Kingdom
Science and Technology Facilities Council (STFC); The United States Department
of Energy, the United States National Science Foundation, the State of Texas,
and the State of Ohio; Ministry of Science, Education and Sports of Croatia
and Unity through Knowledge Fund, Croatia; Council of Scientific and
Industrial Research (CSIR), New Delhi, India; Pontificia Universidad Católica
del Perú.

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##  Appendix A The ALICE Collaboration

J. Adamorg39&D. Adamováorg84&M.M. Aggarwalorg88&G. Aglieri Rinellaorg35&M.
Agnelloorg110&N. Agrawalorg47&Z. Ahammedorg133&S. Ahmadorg19&S.U. Ahnorg68&S.
Aiolaorg137&A. Akindinovorg58&S.N. Alamorg133&D.S.D. Albuquerqueorg121&D.
Aleksandrovorg80&B. Alessandroorg110&D. Alexandreorg101&R. Alfaro
Molinaorg64&A. Aliciorg12,org104&A. Alkinorg3&J.R.M. Almarazorg119&J.
Almeorg37,org18&T. Altorg42&S. Altinpinarorg18&I. Altsybeevorg132&C. Alves
Garcia Pradoorg120&C. Andreiorg78&A. Andronicorg97&V. Anguelovorg94&T.
Antičićorg98&F. Antinoriorg107&P. Antonioliorg104&L. Aphecetcheorg113&H.
Appelshäuserorg53&S. Arcelliorg27&R. Arnaldiorg110&O.W. Arnoldorg93,org36&I.C.
Arseneorg22&M. Arslandokorg53&B. Audurierorg113&A. Augustinusorg35&R.
Averbeckorg97&M.D. Azmiorg19&A. Badalàorg106&Y.W. Baekorg67&S.
Bagnascoorg110&R. Bailhacheorg53&R. Balaorg91&S. Balasubramanianorg137&A.
Baldisseriorg15&R.C. Baralorg61&A.M. Barbanoorg26&R. Barberaorg28&F.
Barileorg32&G.G. Barnaföldiorg136&L.S. Barnbyorg101,org35&V. Barretorg70&P.
Bartaliniorg7&K. Barthorg35&J. Bartkeorg117&E. Bartschorg53&M. Basileorg27&N.
Bastidorg70&S. Basuorg133&B. Bathenorg54&G. Batigneorg113&A. Batista
Camejoorg70&B. Batyunyaorg66&P.C. Batzingorg22&I.G. Beardenorg81&H.
Beckorg53,org94&C. Beddaorg110&N.K. Beheraorg48,org50&I. Belikovorg55&F.
Belliniorg27&H. Bello Martinezorg2&R. Bellwiedorg122&R. Belmontorg135&E.
Belmont-Morenoorg64&V. Belyaevorg75&G. Bencediorg136&S. Beoleorg26&I.
Berceanuorg78&A. Bercuciorg78&Y. Berdnikovorg86&D. Berenyiorg136&R.A.
Bertensorg57&D. Berzanoorg35&L. Betevorg35&A. Bhasinorg91&I.R. Bhatorg91&A.K.
Bhatiorg88&B. Bhattacharjeeorg44&J. Bhomorg128,org117&L. Bianchiorg122&N.
Bianchiorg72&C. Bianchinorg135&J. Bielčíkorg39&J. Bielčíkováorg84&A.
Bilandzicorg81,org36,org93&G. Biroorg136&R. Biswasorg4&S. Biswasorg4,org79&S.
Bjelogrlicorg57&J.T. Blairorg118&D. Blauorg80&C. Blumeorg53&F.
Bockorg74,org94&A. Bogdanovorg75&H. Bøggildorg81&L. Boldizsárorg136&M.
Bombaraorg40&J. Bookorg53&H. Borelorg15&A. Borissovorg96&M.
Borriorg124,org83&F. Bossúorg65&E. Bottaorg26&C. Bourjauorg81&P. Braun-
Munzingerorg97&M. Bregantorg120&T. Breitnerorg52&T.A. Brokerorg53&T.A.
Browningorg95&M. Brozorg39&E.J. Bruckenorg45&E. Brunaorg110&G.E. Brunoorg32&D.
Budnikovorg99&H. Bueschingorg53&S. Bufalinoorg35,org26&P. Buncicorg35&O.
Buschorg128&Z. Butheleziorg65&J.B. Buttorg16&J.T. Buxtonorg20&J.
Cabalaorg115&D. Caffarriorg35&X. Caiorg7&H. Cainesorg137&L. Calero
Diazorg72&A. Calivaorg57&E. Calvo Villarorg102&P. Cameriniorg25&F.
Carenaorg35&W. Carenaorg35&F. Carnesecchiorg27&J. Castillo
Castellanosorg15&A.J. Castroorg125&E.A.R. Casulaorg24&C. Ceballos
Sanchezorg9&J. Cepilaorg39&P. Cerelloorg110&J. Cerkalaorg115&B. Changorg123&S.
Chapelandorg35&M. Chartierorg124&J.L. Charvetorg15&S. Chattopadhyayorg133&S.
Chattopadhyayorg100&A. Chauvinorg93,org36&V. Chelnokovorg3&M. Cherneyorg87&C.
Cheshkovorg130&B. Cheynisorg130&V. Chibante Barrosoorg35&D.D.
Chinellatoorg121&S. Choorg50&P. Chochulaorg35&K. Choiorg96&M.
Chojnackiorg81&S. Choudhuryorg133&P. Christakoglouorg82&C.H.
Christensenorg81&P. Christiansenorg33&T. Chujoorg128&S.U. Chungorg96&C.
Cicaloorg105&L. Cifarelliorg12,org27&F. Cindoloorg104&J. Cleymansorg90&F.
Colamariaorg32&D. Colellaorg59,org35&A. Colluorg74&M. Colocciorg27&G. Conesa
Balbastreorg71&Z. Conesa del Valleorg51&M.E. Connorsidp1775680,org137&J.G.
Contrerasorg39&T.M. Cormierorg85&Y. Corrales Moralesorg110&I. Cortés
Maldonadoorg2&P. Corteseorg31&M.R. Cosentinoorg120&F. Costaorg35&P.
Crochetorg70&R. Cruz Albinoorg11&E. Cuautleorg63&L. Cunqueiroorg54,org35&T.
Dahmsorg93,org36&A. Daineseorg107&M.C. Danischorg94&A. Danuorg62&D.
Dasorg100&I. Dasorg100&S. Dasorg4&A. Dashorg79&S. Dashorg47&S. Deorg120&A. De
Caroorg12,org30&G. de Cataldoorg103&C. de Contiorg120&J. de Cuvelandorg42&A.
De Falcoorg24&D. De Gruttolaorg30,org12&N. De Marcoorg110&S. De
Pasqualeorg30&A. Deistingorg94,org97&A. Delofforg77&E. Dénesorg1360&C.
Deplanoorg82&P. Dhankherorg47&D. Di Bariorg32&A. Di Mauroorg35&P. Di
Nezzaorg72&M.A. Diaz Corcheroorg10&T. Dietelorg90&P. Dillensegerorg53&R.
Diviàorg35&Ø. Djuvslandorg18&A. Dobrinorg82,org62&D. Domenicis
Gimenezorg120&B. Dönigusorg53&O. Dordicorg22&T. Drozhzhovaorg53&A.K.
Dubeyorg133&A. Dublaorg57&L. Ducrouxorg130&P. Dupieuxorg70&R.J.
Ehlersorg137&D. Eliaorg103&E. Endressorg102&H. Engelorg52&E.
Eppleorg93,org36,org137&B. Erazmusorg113&I. Erdemirorg53&F. Erhardtorg129&B.
Espagnonorg51&M. Estienneorg113&S. Esumiorg128&J. Eumorg96&D. Evansorg101&S.
Evdokimovorg111&G. Eyyubovaorg39&L. Fabbiettiorg93,org36&D. Fabrisorg107&J.
Faivreorg71&A. Fantoniorg72&M. Faselorg74&L. Feldkamporg54&A.
Felicielloorg110&G. Feofilovorg132&J. Ferenceiorg84&A. Fernández
Téllezorg2&E.G. Ferreiroorg17&A. Ferrettiorg26&A. Festantiorg29&V.J.G.
Feuillardorg15,org70&J. Figielorg117&M.A.S. Figueredoorg124,org120&S.
Filchaginorg99&D. Finogeevorg56&F.M. Fiondaorg24&E.M. Fioreorg32&M.G.
Fleckorg94&M. Florisorg35&S. Foertschorg65&P. Fokaorg97&S. Fokinorg80&E.
Fragiacomoorg109&A. Francesconorg35,org29&U. Frankenfeldorg97&G.G.
Fronzeorg26&U. Fuchsorg35&C. Furgetorg71&A. Fursorg56&M. Fusco
Girardorg30&J.J. Gaardhøjeorg81&M. Gagliardiorg26&A.M. Gagoorg102&M.
Gallioorg26&D.R. Gangadharanorg74&P. Ganotiorg89&C. Gaoorg7&C.
Garabatosorg97&E. Garcia-Solisorg13&C. Gargiuloorg35&P. Gasikorg93,org36&E.F.
Gaugerorg118&M. Germainorg113&M. Gheataorg35,org62&P. Ghoshorg133&S.K.
Ghoshorg4&P. Gianottiorg72&P. Giubellinoorg110,org35&P. Giubilatoorg29&E.
Gladysz-Dziadusorg117&P. Glässelorg94&D.M. Goméz Coralorg64&A. Gomez
Ramirezorg52&A.S. Gonzalezorg35&V. Gonzalezorg10&P. González-Zamoraorg10&S.
Gorbunovorg42&L. Görlichorg117&S. Gotovacorg116&V. Grabskiorg64&O.A.
Grachovorg137&L.K. Graczykowskiorg134&K.L. Grahamorg101&A. Grelliorg57&A.
Grigorasorg35&C. Grigorasorg35&V. Grigorievorg75&A. Grigoryanorg1&S.
Grigoryanorg66&B. Grinyovorg3&N. Grionorg109&J.M. Gronefeldorg97&J.F. Grosse-
Oetringhausorg35&R. Grossoorg97&F. Guberorg56&R. Guernaneorg71&B.
Guerzoniorg27&K. Gulbrandsenorg81&T. Gunjiorg127&A. Guptaorg91&R.
Guptaorg91&R. Haakeorg35&Ø. Haalandorg18&C. Hadjidakisorg51&M. Haiducorg62&H.
Hamagakiorg127&G. Hamarorg136&J.C. Hamonorg55&J.W. Harrisorg137&A.
Hartonorg13&D. Hatzifotiadouorg104&S. Hayashiorg127&S.T. Heckelorg53&E.
Hellbärorg53&H. Helstruporg37&A. Herghelegiuorg78&G. Herrera Corralorg11&B.A.
Hessorg34&K.F. Hetlandorg37&H. Hillemannsorg35&B. Hippolyteorg55&D.
Horakorg39&R. Hosokawaorg128&P. Hristovorg35&T.J. Humanicorg20&N.
Hussainorg44&T. Hussainorg19&D. Hutterorg42&D.S. Hwangorg21&R. Ilkaevorg99&M.
Inabaorg128&E. Incaniorg24&M. Ippolitovorg75,org80&M. Irfanorg19&M.
Ivanovorg97&V. Ivanovorg86&V. Izucheevorg111&N. Jacazioorg27&P.M.
Jacobsorg74&M.B. Jadhavorg47&S. Jadlovskaorg115&J. Jadlovskyorg115,org59&C.
Jahnkeorg120&M.J. Jakubowskaorg134&H.J. Jangorg68&M.A. Janikorg134&P.H.S.Y.
Jayarathnaorg122&C. Jenaorg29&S. Jenaorg122&R.T. Jimenez Bustamanteorg97&P.G.
Jonesorg101&A. Juskoorg101&P. Kalinakorg59&A. Kalweitorg35&J. Kaminorg53&J.H.
Kangorg138&V. Kaplinorg75&S. Karorg133&A. Karasu Uysalorg69&O.
Karavichevorg56&T. Karavichevaorg56&L. Karayanorg97,org94&E. Karpechevorg56&U.
Kebschullorg52&R. Keidelorg139&D.L.D. Keijdenerorg57&M. Keilorg35&M. Mohisin
Khanidp3130944,org19&P. Khanorg100&S.A. Khanorg133&A. Khanzadeevorg86&Y.
Kharlovorg111&B. Kilengorg37&D.W. Kimorg43&D.J. Kimorg123&D. Kimorg138&H.
Kimorg138&J.S. Kimorg43&M. Kimorg138&S. Kimorg21&T. Kimorg138&S.
Kirschorg42&I. Kiselorg42&S. Kiselevorg58&A. Kisielorg134&G. Kissorg136&J.L.
Klayorg6&C. Kleinorg53&J. Kleinorg35&C. Klein-Bösingorg54&S. Klewinorg94&A.
Klugeorg35&M.L. Knichelorg94&A.G. Knospeorg118,org122&C. Kobdajorg114&M.
Kofaragoorg35&T. Kolleggerorg97&A. Kolojvariorg132&V. Kondratievorg132&N.
Kondratyevaorg75&E. Kondratyukorg111&A. Konevskikhorg56&M. Kopcikorg115&P.
Kostarakisorg89&M. Kourorg91&C. Kouzinopoulosorg35&O. Kovalenkoorg77&V.
Kovalenkoorg132&M. Kowalskiorg117&G. Koyithatta Meethaleveeduorg47&I.
Králikorg59&A. Kravčákováorg40&M. Krivdaorg59,org101&F. Krizekorg84&E.
Kryshenorg86,org35&M. Krzewickiorg42&A.M. Kuberaorg20&V. Kučeraorg84&C.
Kuhnorg55&P.G. Kuijerorg82&A. Kumarorg91&J. Kumarorg47&L. Kumarorg88&S.
Kumarorg47&P. Kurashviliorg77&A. Kurepinorg56&A.B. Kurepinorg56&A.
Kuryakinorg99&M.J. Kweonorg50&Y. Kwonorg138&S.L. La Pointeorg110&P. La
Roccaorg28&P. Ladron de Guevaraorg11&C. Lagana Fernandesorg120&I.
Lakomovorg35&R. Langoyorg41&K. Lapidusorg93,org36&C. Laraorg52&A.
Lardeuxorg15&A. Lattucaorg26&E. Laudiorg35&R. Leaorg25&L. Leardiniorg94&G.R.
Leeorg101&S. Leeorg138&F. Lehasorg82&R.C. Lemmonorg83&V. Lentiorg103&E.
Leograndeorg57&I. León Monzónorg119&H. León Vargasorg64&M. Leoncinoorg26&P.
Lévaiorg136&S. Liorg7,org70&X. Liorg14&J. Lienorg41&R. Lietavaorg101&S.
Lindalorg22&V. Lindenstruthorg42&C. Lippmannorg97&M.A. Lisaorg20&H.M.
Ljunggrenorg33&D.F. Lodatoorg57&P.I. Loenneorg18&V. Loginovorg75&C.
Loizidesorg74&X. Lopezorg70&E. López Torresorg9&A. Loweorg136&P.
Luettigorg53&M. Lunardonorg29&G. Luparelloorg25&T.H. Lutzorg137&A.
Maevskayaorg56&M. Magerorg35&S. Mahajanorg91&S.M. Mahmoodorg22&A.
Maireorg55&R.D. Majkaorg137&M. Malaevorg86&I. Maldonado Cervantesorg63&L.
Malininaidp3839168,org66&D. Mal’Kevichorg58&P. Malzacherorg97&A.
Mamonovorg99&V. Mankoorg80&F. Mansoorg70&V. Manzariorg35,org103&M.
Marchisoneorg26,org65,org126&J. Marešorg60&G.V. Margagliottiorg25&A.
Margottiorg104&J. Marguttiorg57&A. Marínorg97&C. Markertorg118&M.
Marquardorg53&N.A. Martinorg97&J. Martin Blancoorg113&P. Martinengoorg35&M.I.
Martínezorg2&G. Martínez Garcíaorg113&M. Martinez Pedreiraorg35&A.
Masorg120&S. Masciocchiorg97&M. Maseraorg26&A. Masoniorg105&A.
Mastroserioorg32&A. Matyjaorg117&C. Mayerorg117&J. Mazerorg125&M.A.
Mazzoniorg108&D. Mcdonaldorg122&F. Meddiorg23&Y. Melikyanorg75&A. Menchaca-
Rochaorg64&E. Meninnoorg30&J. Mercado Pérezorg94&M. Meresorg38&Y.
Miakeorg128&M.M. Mieskolainenorg45&K. Mikhaylovorg58,org66&L.
Milanoorg74,org35&J. Milosevicorg22&A. Mischkeorg57&A.N. Mishraorg48&D.
Miśkowiecorg97&J. Mitraorg133&C.M. Mituorg62&N. Mohammadiorg57&B.
Mohantyorg79&L. Molnarorg55&L. Montaño Zetinaorg11&E. Montesorg10&D.A. Moreira
De Godoyorg54&L.A.P. Morenoorg2&S. Morettoorg29&A. Morrealeorg113&A.
Morschorg35&V. Mucciforaorg72&E. Mudnicorg116&D. Mühlheimorg54&S.
Muhuriorg133&M. Mukherjeeorg133&J.D. Mulliganorg137&M.G. Munhozorg120&R.H.
Munzerorg53,org93,org36&H. Murakamiorg127&S. Murrayorg65&L. Musaorg35&J.
Musinskyorg59&B. Naikorg47&R. Nairorg77&B.K. Nandiorg47&R. Naniaorg104&E.
Nappiorg103&M.U. Naruorg16&H. Natal da Luzorg120&C. Nattrassorg125&S.R.
Navarroorg2&K. Nayakorg79&R. Nayakorg47&T.K. Nayakorg133&S. Nazarenkoorg99&A.
Nedosekinorg58&L. Nellenorg63&F. Ngorg122&M. Nicassioorg97&M.
Niculescuorg62&J. Niedzielaorg35&B.S. Nielsenorg81&S. Nikolaevorg80&S.
Nikulinorg80&V. Nikulinorg86&F. Noferiniorg104,org12&P. Nomokonovorg66&G.
Noorenorg57&J.C.C. Norisorg2&J. Normanorg124&A. Nyaninorg80&J.
Nystrandorg18&H. Oeschlerorg94&S. Ohorg137&S.K. Ohorg67&A. Ohlsonorg35&A.
Okatanorg69&T. Okuboorg46&L. Olahorg136&J. Oleniaczorg134&A.C. Oliveira Da
Silvaorg120&M.H. Oliverorg137&J. Onderwaaterorg97&C. Oppedisanoorg110&R.
Oravaorg45&M. Oravecorg115&A. Ortiz Velasquezorg63&A. Oskarssonorg33&J.
Otwinowskiorg117&K. Oyamaorg94,org76&M. Ozdemirorg53&Y. Pachmayerorg94&D.
Paganoorg131&P. Paganoorg30&G. Paićorg63&S.K. Palorg133&J. Panorg135&A.K.
Pandeyorg47&V. Papikyanorg1&G.S. Pappalardoorg106&P. Pareekorg48&W.J.
Parkorg97&S. Parmarorg88&A. Passfeldorg54&V. Paticchioorg103&R.N.
Patraorg133&B. Paulorg100,org110&H. Peiorg7&T. Peitzmannorg57&H. Pereira Da
Costaorg15&D. Peresunkoorg80,org75&C.E. Pérez Laraorg82&E. Perez
Lezamaorg53&V. Peskovorg53&Y. Pestovorg5&V. Petráčekorg39&V. Petrovorg111&M.
Petroviciorg78&C. Pettaorg28&S. Pianoorg109&M. Piknaorg38&P.
Pillotorg113&L.O.D.L. Pimentelorg81&O. Pinazzaorg104,org35&L.
Pinskyorg122&D.B. Piyarathnaorg122&M. Płoskońorg74&M. Planinicorg129&J.
Plutaorg134&S. Pochybovaorg136&P.L.M. Podesta-Lermaorg119&M.G.
Poghosyanorg85,org87&B. Polichtchoukorg111&N. Poljakorg129&W.
Poonsawatorg114&A. Poporg78&S. Porteboeuf-Houssaisorg70&J. Porterorg74&J.
Pospisilorg84&S.K. Prasadorg4&R. Preghenellaorg104,org35&F. Prinoorg110&C.A.
Pruneauorg135&I. Pshenichnovorg56&M. Puccioorg26&G. Pudduorg24&P.
Pujahariorg135&V. Puninorg99&J. Putschkeorg135&H. Qvigstadorg22&A.
Rachevskiorg109&S. Rahaorg4&S. Rajputorg91&J. Rakorg123&A.
Rakotozafindrabeorg15&L. Ramelloorg31&F. Ramiorg55&R. Raniwalaorg92&S.
Raniwalaorg92&S.S. Räsänenorg45&B.T. Rascanuorg53&D. Ratheeorg88&K.F.
Readorg85,org125&K. Redlichorg77&R.J. Reedorg135&A. Rehmanorg18&P.
Reicheltorg53&F. Reidtorg35,org94&X. Renorg7&R. Renfordtorg53&A.R.
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Mansoorg82&K. Røedorg22&E. Rogochayaorg66&D. Rohrorg42&D. Röhrichorg18&F.
Ronchettiorg35,org72&L. Ronfletteorg113&P. Rosnetorg70&A. Rossiorg29,org35&F.
Roukoutakisorg89&A. Royorg48&C. Royorg55&P. Royorg100&A.J. Rubio
Monteroorg10&R. Ruiorg25&R. Russoorg26&B.D. Ruzzaorg107&E. Ryabinkinorg80&Y.
Ryabovorg86&A. Rybickiorg117&S. Saarinenorg45&S. Sadhuorg133&S.
Sadovskyorg111&K. Šafaříkorg35&B. Sahlmullerorg53&P. Sahooorg48&R.
Sahooorg48&S. Sahooorg61&P.K. Sahuorg61&J. Sainiorg133&S. Sakaiorg72&M.A.
Salehorg135&J. Salzwedelorg20&S. Sambyalorg91&V. Samsonovorg86&L.
Šándororg59&A. Sandovalorg64&M. Sanoorg128&D. Sarkarorg133&N. Sarkarorg133&P.
Sarmaorg44&E. Scapparoneorg104&F. Scarlassaraorg29&C. Schiauaorg78&R.
Schickerorg94&C. Schmidtorg97&H.R. Schmidtorg34&S. Schuchmannorg53&J.
Schukraftorg35&M. Schulcorg39&Y. Schutzorg35,org113&K. Schwarzorg97&K.
Schwedaorg97&G. Scioliorg27&E. Scomparinorg110&R. Scottorg125&M.
Šefčíkorg40&J.E. Segerorg87&Y. Sekiguchiorg127&D. Sekihataorg46&I.
Selyuzhenkovorg97&K. Senosiorg65&S. Senyukovorg35,org3&E.
Serradillaorg10,org64&A. Sevcencoorg62&A. Shabanovorg56&A. Shabetaiorg113&O.
Shaduraorg3&R. Shahoyanorg35&M.I. Shahzadorg16&A. Shangaraevorg111&A.
Sharmaorg91&M. Sharmaorg91&M. Sharmaorg91&N. Sharmaorg125&A.I. Sheikhorg133&K.
Shigakiorg46&Q. Shouorg7&K. Shtejerorg9,org26&Y. Sibiriakorg80&S.
Siddhantaorg105&K.M. Sielewiczorg35&T. Siemiarczukorg77&D. Silvermyrorg33&C.
Silvestreorg71&G. Simatovicorg129&G. Simonettiorg35&R. Singarajuorg133&R.
Singhorg79&S. Singhaorg79,org133&V. Singhalorg133&B.C. Sinhaorg133&T.
Sinhaorg100&B. Sitarorg38&M. Sittaorg31&T.B. Skaaliorg22&M. Slupeckiorg123&N.
Smirnovorg137&R.J.M. Snellingsorg57&T.W. Snellmanorg123&J. Songorg96&M.
Songorg138&Z. Songorg7&F. Soramelorg29&S. Sorensenorg125&R.D.de Souzaorg121&F.
Sozziorg97&M. Spacekorg39&E. Spiritiorg72&I. Sputowskaorg117&M. Spyropoulou-
Stassinakiorg89&J. Stachelorg94&I. Stanorg62&P. Stankusorg85&E.
Stenlundorg33&G. Steynorg65&J.H. Stillerorg94&D. Stoccoorg113&P.
Strmenorg38&A.A.P. Suaideorg120&T. Sugitateorg46&C. Suireorg51&M.
Suleymanovorg16&M. Suljicorg250&R. Sultanovorg58&M. Šumberaorg84&S.
Sumowidagdoorg49&A. Szaboorg38&A. Szanto de Toledoorg1200&I. Szarkaorg38&A.
Szczepankiewiczorg35&M. Szymanskiorg134&U. Tabassamorg16&J.
Takahashiorg121&G.J. Tambaveorg18&N. Tanakaorg128&M. Tarhiniorg51&M.
Tariqorg19&M.G. Tarzilaorg78&A. Tauroorg35&G. Tejeda Muñozorg2&A.
Telescaorg35&K. Terasakiorg127&C. Terrevoliorg29&B. Teyssierorg130&J.
Thäderorg74&D. Thakurorg48&D. Thomasorg118&R. Tieulentorg130&A.
Tikhonovorg56&A.R. Timminsorg122&A. Toiaorg53&S. Trogoloorg26&G.
Trombettaorg32&V. Trubnikovorg3&W.H. Trzaskaorg123&T. Tsujiorg127&A.
Tumkinorg99&R. Turrisiorg107&T.S. Tveterorg22&K. Ullalandorg18&A.
Urasorg130&G.L. Usaiorg24&A. Utrobicicorg129&M. Valaorg59&L. Valencia
Palomoorg70&S. Valleroorg26&J. Van Der Maarelorg57&J.W. Van Hoorneorg35&M. van
Leeuwenorg57&T. Vanatorg84&P. Vande Vyvreorg35&D. Vargaorg136&A. Vargasorg2&M.
Vargyasorg123&R. Varmaorg47&M. Vasileiouorg89&A. Vasilievorg80&A.
Vauthierorg71&O. Vázquez Doceorg36,org93&V. Vecherninorg132&A.M. Veenorg57&M.
Veldhoenorg57&A. Velureorg18&E. Vercellinorg26&S. Vergara Limónorg2&R.
Vernetorg8&M. Verweijorg135&L. Vickovicorg116&J. Viinikainenorg123&Z.
Vilakaziorg126&O. Villalobos Baillieorg101&A. Villatoro Telloorg2&A.
Vinogradovorg80&L. Vinogradovorg132&Y. Vinogradovorg990&T. Virgiliorg30&V.
Vislaviciusorg33&Y.P. Viyogiorg133&A. Vodopyanovorg66&M.A. Völklorg94&K.
Voloshinorg58&S.A. Voloshinorg135&G. Volpeorg32,org136&B. von Hallerorg35&I.
Vorobyevorg93,org36&D. Vranicorg97,org35&J. Vrlákováorg40&B. Vulpescuorg70&B.
Wagnerorg18&J. Wagnerorg97&H. Wangorg57&M. Wangorg7,org113&D.
Watanabeorg128&Y. Watanabeorg127&M. Weberorg112,org35&S.G. Weberorg97&D.F.
Weiserorg94&J.P. Wesselsorg54&U. Westerhofforg54&A.M. Whiteheadorg90&J.
Wiechulaorg34&J. Wikneorg22&G. Wilkorg77&J. Wilkinsonorg94&M.C.S.
Williamsorg104&B. Windelbandorg94&M. Winnorg94&P. Yangorg7&S. Yanoorg46&Z.
Yasinorg16&Z. Yinorg7&H. Yokoyamaorg128&I.-K. Yooorg96&J.H. Yoonorg50&V.
Yurchenkoorg3&I. Yushmanovorg80&A. Zaborowskaorg134&V. Zaccoloorg81&A.
Zamanorg16&C. Zampolliorg104,org35&H.J.C. Zanoliorg120&S. Zaporozhetsorg66&N.
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Zbroszczykorg134&I.S. Zguraorg62&M. Zhalovorg86&H. Zhangorg18&X.
Zhangorg74,org7&Y. Zhangorg7&C. Zhangorg57&Z. Zhangorg7&C. Zhaoorg22&N.
Zhigarevaorg58&D. Zhouorg7&Y. Zhouorg81&Z. Zhouorg18&H. Zhuorg18&J.
Zhuorg7,org113&A. Zichichiorg27,org12&A. Zimmermannorg94&M.B.
Zimmermannorg54,org35&G. Zinovjevorg3&M. Zyzakorg42

## Affiliation notes

0Deceased

idp1775680Also at: Georgia State University, Atlanta, Georgia, United States

idp3130944Also at: Also at Department of Applied Physics, Aligarh Muslim
University, Aligarh, India

idp3839168Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn
Institute of Nuclear, Physics, Moscow, Russia

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi”, Rome, Italy

org13Chicago State University, Chicago, Illinois, USA

org14China Institute of Atomic Energy, Beijing, China

org15Commissariat à l’Energie Atomique, IRFU, Saclay, France

org16COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org17Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org18Department of Physics and Technology, University of Bergen, Bergen,
Norway

org19Department of Physics, Aligarh Muslim University, Aligarh, India

org20Department of Physics, Ohio State University, Columbus, Ohio, United
States

org21Department of Physics, Sejong University, Seoul, South Korea

org22Department of Physics, University of Oslo, Oslo, Norway

org23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN
Rome, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org31Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy

org32Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org33Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org34Eberhard Karls Universität Tübingen, Tübingen, Germany

org35European Organization for Nuclear Research (CERN), Geneva, Switzerland

org36Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org37Faculty of Engineering, Bergen University College, Bergen, Norway

org38Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org41Faculty of Technology, Buskerud and Vestfold University College,
Vestfold, Norway

org42Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org43Gangneung-Wonju National University, Gangneung, South Korea

org44Gauhati University, Department of Physics, Guwahati, India

org45Helsinki Institute of Physics (HIP), Helsinki, Finland

org46Hiroshima University, Hiroshima, Japan

org47Indian Institute of Technology Bombay (IIT), Mumbai, India

org48Indian Institute of Technology Indore, Indore (IITI), India

org49Indonesian Institute of Sciences, Jakarta, Indonesia

org50Inha University, Incheon, South Korea

org51Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org52Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org53Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org54Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org55Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org56Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org57Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org58Institute for Theoretical and Experimental Physics, Moscow, Russia

org59Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org60Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org61Institute of Physics, Bhubaneswar, India

org62Institute of Space Science (ISS), Bucharest, Romania

org63Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org64Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org65iThemba LABS, National Research Foundation, Somerset West, South Africa

org66Joint Institute for Nuclear Research (JINR), Dubna, Russia

org67Konkuk University, Seoul, South Korea

org68Korea Institute of Science and Technology Information, Daejeon, South
Korea

org69KTO Karatay University, Konya, Turkey

org70Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org71Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org72Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org73Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org74Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org75Moscow Engineering Physics Institute, Moscow, Russia

org76Nagasaki Institute of Applied Science, Nagasaki, Japan

org77National Centre for Nuclear Studies, Warsaw, Poland

org78National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org79National Institute of Science Education and Research, Bhubaneswar, India

org80National Research Centre Kurchatov Institute, Moscow, Russia

org81Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org82Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org83Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org84Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org85Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org86Petersburg Nuclear Physics Institute, Gatchina, Russia

org87Physics Department, Creighton University, Omaha, Nebraska, United States

org88Physics Department, Panjab University, Chandigarh, India

org89Physics Department, University of Athens, Athens, Greece

org90Physics Department, University of Cape Town, Cape Town, South Africa

org91Physics Department, University of Jammu, Jammu, India

org92Physics Department, University of Rajasthan, Jaipur, India

org93Physik Department, Technische Universität München, Munich, Germany

org94Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org95Purdue University, West Lafayette, Indiana, United States

org96Pusan National University, Pusan, South Korea

org97Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany

org98Rudjer Bošković Institute, Zagreb, Croatia

org99Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org100Saha Institute of Nuclear Physics, Kolkata, India

org101School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org102Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org103Sezione INFN, Bari, Italy

org104Sezione INFN, Bologna, Italy

org105Sezione INFN, Cagliari, Italy

org106Sezione INFN, Catania, Italy

org107Sezione INFN, Padova, Italy

org108Sezione INFN, Rome, Italy

org109Sezione INFN, Trieste, Italy

org110Sezione INFN, Turin, Italy

org111SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org112Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org113SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

org114Suranaree University of Technology, Nakhon Ratchasima, Thailand

org115Technical University of Košice, Košice, Slovakia

org116Technical University of Split FESB, Split, Croatia

org117The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org118The University of Texas at Austin, Physics Department, Austin, Texas,
USA

org119Universidad Autónoma de Sinaloa, Culiacán, Mexico

org120Universidade de São Paulo (USP), São Paulo, Brazil

org121Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org122University of Houston, Houston, Texas, United States

org123University of Jyväskylä, Jyväskylä, Finland

org124University of Liverpool, Liverpool, United Kingdom

org125University of Tennessee, Knoxville, Tennessee, United States

org126University of the Witwatersrand, Johannesburg, South Africa

org127University of Tokyo, Tokyo, Japan

org128University of Tsukuba, Tsukuba, Japan

org129University of Zagreb, Zagreb, Croatia

org130Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France

org131Università di Brescia

org132V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org133Variable Energy Cyclotron Centre, Kolkata, India

org134Warsaw University of Technology, Warsaw, Poland

org135Wayne State University, Detroit, Michigan, United States

org136Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org137Yale University, New Haven, Connecticut, United States

org138Yonsei University, Seoul, South Korea

org139Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany