2017 216 21 Aug

$\pi^{0}$ and $\eta$ in pp collisions at $\sqrt{s}=8$ TeV

ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

An invariant differential cross section measurement of inclusive $\pi^{0}$ and
$\eta$ meson production at mid-rapidity in pp collisions at $\sqrt{s}=8$ TeV
was carried out by the ALICE experiment at the LHC. The spectra of $\pi^{0}$
and $\eta$ mesons were measured in transverse momentum ranges of
$0.3<p_{\mbox{\tiny T}}<35$ $\mbox{GeV}/c$ and $0.5<p_{\mbox{\tiny T}}<35$
$\mbox{GeV}/c$, respectively. Next-to-leading order perturbative QCD
calculations using fragmentation functions DSS14 for the $\pi^{0}$ and AESSS
for the $\eta$ overestimate the cross sections of both neutral mesons,
although such calculations agree with the measured $\eta/\pi^{0}$ ratio within
uncertainties. The results were also compared with PYTHIA 8.2 predictions for
which the Monash 2013 tune yields the best agreement with the measured neutral
meson spectra. The measurements confirm a universal behavior of the
$\eta/\pi^{0}$ ratio seen for NA27, PHENIX and ALICE data for pp collisions
from $\sqrt{s}=27.5$ GeV to $\sqrt{s}=8$ TeV within experimental
uncertainties. A relation between the $\pi^{0}$ and $\eta$ production cross
sections for pp collisions at $\sqrt{s}=8$ TeV is given by $m_{\mbox{\tiny
T}}$ scaling for $p_{\mbox{\tiny T}}>3.5$ $\mbox{GeV}/c$. However, a deviation
from this empirical scaling rule is observed for transverse momenta below
$p_{\mbox{\tiny T}}<3.5$ $\mbox{GeV}/c$ in the $\eta/\pi^{0}$ ratio with a
significance of $6.2\sigma$.

##  1 Introduction

Measuring identified particle production in proton-proton (pp) collisions over
wide kinematic ranges is considered an informative probe of strong
interactions at high energies. Quantum Chromodynamics (QCD) is the fundamental
theory of the strong interaction [1]. It succeeds in providing a qualitative
description of a wide range of phenomena in hadronic collisions. At typical
hadron collider energies its perturbative expansion (pQCD) permits a detailed
quantitative comparison with experimental data. However, it remains a
challenge to provide a consistent description of hadron spectra at all
collision energies reached experimentally. In theoretical models, particle
production is usually divided into two categories: the “soft” scattering
regime describing particle production involving small momentum transfers and
the “hard” scattering regime, responsible for producing particles with momenta
of several $\mbox{GeV}/c$ or more.

Only “hard” scattering processes with a sufficiently large transverse momentum
transfer, $Q^{2}$, can be calculated using methods based on pQCD. High-
momentum particles originate from the fragmentation of partons produced in
scattering processes with large $Q^{2}$. The theoretical description of a
“hard” scattering process can be factorized into parton distribution functions
(PDFs), the QCD matrix element and fragmentation functions (FFs). PDFs
describe the fraction of the proton’s longitudinal momentum carried by a
scattered parton, $x$, and FFs describe the ratio of the observed hadron
momentum to the final-state parton momentum, $z$, respectively. Comprehensive
parametrizations of PDFs and FFs are derived from global fits to the
experimental data at various collision energies. The energies reached at the
LHC [2] open up the domains in $x$ and $z$ not accessible at lower energy. In
the past, experiments at the LHC consequently found discrepancies between the
measured $\pi^{0}$ and $\eta$ meson spectra [3, 4, 5] and pQCD calculations
based on fragmentation functions, which include mostly data from experiments
below the TeV scale [6]. Since the gluon contribution becomes more dominant
with increased center of mass energy, $\sqrt{s}$, [7], $\pi^{0}$ and $\eta$
meson spectra at LHC energies provide new constraints on the gluon to light-
flavor hadron fragmentation functions. Recent progress in comprehensive global
QCD analysis of parton-to-pion fragmentation functions at next-to-leading
order (NLO) [8] derived from inclusive pion production in semi-inclusive
electron-positron annihilation, deep-inelastic scattering and pp collisions
over a wide energy range, including the LHC results [3], achieves a good and
consistent description of pion spectra, including the latest measurements of
$\pi^{0}$ and $\eta$ spectra in pp collisions at $\sqrt{s}=2.76$ TeV [9] and 7
TeV [3]. One of the conclusions of that analysis was that meson production
from gluon fragmentation is reduced, which turns out to be at tension with
previously available data obtained at RHIC [10]. In the quark model, the
$\pi^{0}$ consists of light-flavor quark-antiquark pairs, $u\bar{u}$ and
$d\bar{d}$, whereas the $\eta$ additionally contains hidden strangeness,
$s\bar{s}$. Measurements of both neutral mesons are thus of particular
interest due to their different quark content as they help to constrain the
PDFs and FFs [11] of the $s$ quark.

The majority of particles at low transverse momenta, $p_{\mbox{\tiny T}}$, are
produced in “soft” processes involving a small $Q^{2}$. In this regime, the
pQCD calculations are not applicable for description of the production
mechanisms and phenomenological models are based on previous measurements of
neutral meson production cross sections or other light mesons by other
experiments at lower collision energies. Particle production measurements at
transverse momenta down to a few hundred $\mbox{MeV}/c$, as reported here, are
particularly important to further constrain such models.

The importance of precise identified particle production measurements is
underlined by various empirical rules observed in relative particle yields
which allow estimates of the hadronic background of rare probes such as direct
photons, dileptons and heavy-quark production. Almost all lower-energy
experiments from ISR to RHIC report the observation of such an empricial rule,
so-called $m_{\mbox{\tiny T}}$ scaling, in particle production over wide
$p_{\mbox{\tiny T}}$ ranges [12, 13]. The practical use of $m_{\mbox{\tiny
T}}$ scaling is the ability to derive the $p_{\mbox{\tiny T}}$-dependent
differential yields of most of particles from the well measured light-flavor
mesons, like pions and kaons, by assuming that the meson spectra can be
described as a function of transverse mass $m_{\mbox{\tiny T}}$: $E{\rm
d^{3}}\sigma/{\rm d}p^{3}=C^{h}f(m_{\mbox{\tiny T}})$, where the function
$f(m_{\mbox{\tiny T}})$ is universal for all hadron species, so that their
spectra share the same shape up to a normalization factor $C^{h}$ [14]. In the
context of rare probes, this empirical relation is hence widely used to
estimate the various background sources, for which no measurements are
available. However, phenomenological analyses of new data delivered by the LHC
experiments show that $m_{\mbox{\tiny T}}$ scaling is violated at higher
$p_{\mbox{\tiny T}}$ compared to lower collision energies [15, 14]. Therefore,
precise measurements of identified hadron spectra over wide transverse
momentum ranges at different LHC energies are of particular importance for the
quantitative description of particle production at the LHC.

In this paper, the differential invariant production cross sections, $E{\rm
d}^{3}\sigma/{\rm d}p^{3}$, of $\pi^{0}$ and $\eta$ mesons and the particle
production ratio $\eta/\pi^{0}$ are presented, measured over wide
$p_{\mbox{\tiny T}}$ ranges at mid-rapidity in pp collisions at
$\sqrt{s}=~{}8$ TeV by ALICE. The new experimental results are compared with
pQCD calculations using MSTW08 (PDF) [16] with DSS14 (FF) [8] for the
$\pi^{0}$ and accordingly CTEQ6M5 (PDF) [17] with AESSS (FF) [11] for the
$\eta$, as well as the PYTHIA8.210 Monte Carlo (MC) event generator [18] with
the tunes Tune 4C [19] and Monash 2013 [20].

This paper is organized as follows: In Sec. 2, the ALICE experiment is briefly
described with the focus on the detectors used in this analysis, namely the
calorimeters and the central tracking systems. Sec. 3 describes the datasets,
the event selection and also introduces the calorimeter triggers used in this
analysis. In Sec. 4, the reconstruction principles for neutral mesons are
introduced. Furthermore, the determination of correction factors, which are
used to calculate the differential invariant cross sections from the measured
raw yields, is described. Sec. 5 discusses the various contributions to the
statistical and systematic uncertainties of the measurements. In Sec. 6, the
$p_{\mbox{\tiny T}}$ differential invariant cross sections for $\pi^{0}$ and
$\eta$ meson production in pp collisions at $\sqrt{s}=~{}8$ TeV are presented
and compared with pQCD calculations. Subsequently, the measured ratio of
$\eta/\pi^{0}$ is presented and compared to the same theoretical models. Sec.
7 concludes the paper with a summary of the obtained results.

##  2 Detector description

Neutral mesons, $\pi^{0}$ and $\eta$, decay into photons, which are
reconstructed via two fundamentally different detection methods. The first
method exploits the measurement of photons using electromagnetic calorimeters.
Two such calorimeters are available in ALICE [21, 22]: the Electromagnetic
Calorimeter (EMCal) [23] and the Photon Spectrometer (PHOS) [24]. The second
method of photon detection makes use of photons converted into $e^{+}e^{-}$
pairs within the inner detector material located between the interaction point
and a radius which corresponds to the midpoint between the inner and outer
field cage of the Time Projection Chamber (TPC) [25]. These electron-positron
pairs, originating at secondary vertices (${\rm V^{0}}$), are reconstructed by
the main tracking systems in ALICE centered at mid-rapidity and consisting of
the Inner Tracking System (ITS) [26] and the TPC [25]. The aforementioned
detectors are described below, noting the detector configurations during pp
data taking at $\sqrt{s}=~{}8$ TeV in 2012.

The EMCal detector [23] is a sampling electromagnetic calorimeter. Its active
elements, called cells, are composed of 77 alternating layers of lead and
plastic scintillator providing a radiation length of $20.1\,X_{0}$. The
scintillation light in each layer is collected by wavelength shifting fibers
perpendicular to the face of each cell. The fibers are connected to $5\times
5$ mm2 active area Avalanche Photo Diodes (APDs) to detect the generated
scintillation light. Each cell has a size of
$\Delta\eta\times\Delta\phi=0.0143\times 0.0143$ ($\approx 6.0\times 6.0$
cm2), corresponding to approximately twice the Molière radius. Groups of
$2\times 2$ cells are combined into modules, which are further combined into
arrays of $12\times 24$ modules called supermodules. In total, there are ten
active, full EMCal supermodules, covering $\Delta\phi=100^{\circ}$ in azimuth
and $|\eta|<0.7$ in pseudorapidity with a total number of 11,520 cells. The
EMCal is located at a radial distance of 4.28 m at the closest point from the
nominal collision vertex. The intrinsic energy resolution of the EMCal is
parametrized as $\sigma_{E}/E=4.8\%/E\oplus 11.3\%/\sqrt{E}\oplus 1.7\%$ with
$E$ in units of GeV [27]. The relative energy calibration of the detector is
performed by measuring, in each cell, the reconstructed $\pi^{0}$ mass in the
invariant mass distribution of photon pairs built with one photon in the given
cell. The achieved calibration level is estimated to be 3% and adds up
quadratically to the constant term of the energy resolution.

The PHOS [24, 21] is a homogeneous electromagnetic calorimeter composed of
lead tungstate, $\rm{PbWO_{4}}$. The size of its elementary active units, also
called cells, is $\Delta\eta\times\Delta\phi=0.004\times 0.004$ ($\approx
2.2\times 2.2$ cm2). Thus, the lateral dimensions of the cells are slightly
larger than the $\rm{PbWO_{4}}$ Molière radius of 2 cm. APDs with an active
area of $5\times 5$ mm2 detect the scintillation light generated within the
detector cells. The spectrometer covers $\Delta\phi=60^{\circ}$ in azimuth and
$|\eta|<0.12$ in pseudorapidity and is located at a distance of 4.6 m from the
interaction point. It is operated at a temperature of $-25^{\circ}\rm{C}$, at
which the light yield of $\rm{PbWO_{4}}$ increases by about a factor of three
compared to room temperature. The energy resolution of the PHOS is
$\sigma_{E}/E=1.8\%/E\oplus 3.3\%/\sqrt{E}\oplus 1.1\%$, with $E$ in units of
GeV. The fine granularity of the detector enables the measurement of $\pi^{0}$
candidates up to $p_{\mbox{\tiny T}}\approx 50$ GeV/$c$.

The ITS [26] consists of three sub-detectors each with two layers to measure
the trajectories of charged particles and to reconstruct primary vertices. The
two innermost layers are the Silicon Pixel Detectors (SPD) positioned at
radial distances of $3.9$ cm and $7.6$ cm. The middle two layers are Silicon
Drift Detectors (SDD) located at $15.0$ cm and $23.9$ cm relative to the beam
line. The outer two layers are Silicon Strip Detectors (SSD) located at radial
distances of $38$ cm and $43$ cm. The two layers of SPD cover pseudorapidity
ranges of $|\eta|<2$ and $|\eta|<1.4$, respectively. The SDD and SSD cover
$|\eta|<0.9$ and $|\eta|<1.0$, accordingly.

The TPC [25] is a large (90 ${\rm m}^{3})$ cylindrical drift detector filled
with a gas mixture of ${\rm Ne}$-${\rm CO_{2}}$ ($90$%-$10$%). It covers a
pseudorapidity range of $|\eta|<0.9$ over full azimuth, providing up to 159
reconstructed space points per track. A magnetic field of $B=0.5$ T is
generated by a large solenoidal magnet surrounding the central barrel
detectors. Charged tracks originating from the primary vertex can be
reconstructed down to $p_{\mbox{\tiny T}}\approx 100$ MeV/$c$ and charged
secondaries down to $p_{\mbox{\tiny T}}\approx 50$ MeV/$c$ [22]. The TPC
provides particle identification via the measurement of energy loss,
d$E$/d$x$, with a resolution of $\approx 5\%$ [25]. Beyond the outer radius of
the TPC, the Transition Radiation Detector (TRD) and the Time-Of-Flight
detector (TOF) provide additional particle identification information, as well
as allowing for improved momentum resolution and added triggering capability.
The detectors represent most of the material between the TPC and the EMCal and
hence dominate the material budget in front of the EMCal. These detectors are
missing in front of PHOS in order to provide a minimal radiation length to
profit from the high resolution of the spectrometer.

The V0 detector is made up of two scintillator arrays (V0A and V0C) [28]
covering $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$. It is used to provide a minimum
bias (MB) trigger [29] and reduce background events [22]. It is also involved
in the definition of calorimeter triggers [30, 31] and is used for luminosity
determination as described in the next section.

In addition, the T0 detector [32] was used for luminosity determination. It
consists of two arrays of Cherenkov counters, T0A and T0C, which respectively
cover $4.61<\eta<4.92$ and $-3.28<\eta<-2.97$. The T0 furthermore provides a
precise timing signal to other detectors with a resolution of better than 50
ps, used as starting signal for the TOF detector for example.

##  3 Datasets and event selection

During the data taking period of pp collisions at $\sqrt{s}=~{}8$ TeV in 2012,
the LHC operated at high beam intensities of approximately
$2\,\times\,10^{14}$ protons per beam. Collisions at the ALICE interaction
point were realized using a so-called ”main-satellite” bunch scheme, which
involved proton collisions between the high intensity main bunches and low
intensity satellite bunches. The interaction probability per bunch-satellite
crossing was about $0.01$, corresponding to an average instantaneous
luminosity of about $5\times 10^{30}~{}\rm{cm^{-2}s^{-1}}$. Background events
caused by beam-gas interactions or detector noise are rejected in the analysis
using the V0A and V0C timing information [22]. Pileup events, with more than
one pp collision per bunch crossing, are rejected based on SPD pileup
identification algorithms looking for multiple primary vertices in a single
event [22]. Additionally, the SPD is used to reject background events by
comparing the number of SPD clusters to the multiplicity of SPD track
candidates found in the respective collision. Only events with a $z$-vertex
position of $|z|<10$ cm in the global ALICE coordinate system are accepted for
the analysis.

Two different types of triggers were used during data taking to select the
events to be recorded: the minimum bias (MB) trigger and the calorimeter
triggers, which are provided by the EMCal and the PHOS, to enhance statistics
at high $p_{\mbox{\tiny T}}$ by selectively recording events with high energy
deposits in the calorimeters. The MB trigger is a hardware Level-0 (L0)
trigger [29]. It requires at least one hit in each V0A and V0C [28]. Both
calorimeters also provide L0 triggers: EMC-L0 [30] and PHOS-L0 [31]. These L0
calorimeter triggers are required to be in coincidence with the MB trigger and
select events with a deposited energy exceeding a nominal threshold in
$4\times 4$ adjacent cells, which is set to $\overline{E}_{{\rm
EMC}\text{-}\rm{L0}}\approx 2$ GeV and $\overline{E}_{{\rm
PHOS}\text{-}\rm{L0}}\approx 4$ GeV, respectively. A software Level-1 (L1)
trigger is also deployed for the EMCal which inspects events preselected by
the EMC-L0 trigger [33]. The trigger algorithm is similar to the EMC-L0, but
combines information from different trigger region units to enhance the
trigger efficiency and overcome hardware boundary effects [33]. Additionally,
a larger trigger threshold of $\overline{E}_{{\rm EMC}\text{-}\rm{L1}}\approx
8.4$ GeV is set to further obtain statistics at higher transverse momenta.

In order to correctly normalize each trigger, the trigger rejection factors
($RF$) are determined by constructing the ratio of cluster energy spectra from
MB and calorimeter triggered events as a function of the cluster energy, $E$,
which are shown in Fig. 1. The ratios are expected to follow a constant for
high cluster energies, the so-called plateau region, assuming the triggers
only enhance the rate of clusters but do not affect their reconstruction
efficiency. To reduce the statistical uncertainties, the $RF$s are always
determined with respect to the next lower threshold trigger. The cluster
energy ratios have a steep turn-on near the respective trigger threshold
energies. Since the EMC-L0 trigger becomes fully efficient only above its
triggering threshold of $\overline{E}_{{\rm EMC}\text{-}\rm{L0}}\approx 2$
GeV, there is a change of slope visible in the turn-on region of the EMC-L1
trigger. The turn-on curve of the PHOS-L0 trigger also changes its slope due
to a non-uniformity of the channels hardware gains. However, only the $RF$
plateau regions are mainly relevant for analysis, as they are needed to
correctly normalize the triggered data, which are found to be: $RF_{\rm
EMC\text{-}L0}=67.0\pm 1.1$, $RF_{\rm PHOS\text{-}L0}=(12.4\pm 1.5)\times
10^{3}$ and $RF_{\rm EMC\text{-}L1}=(14.9\pm 0.3)\times 10^{3}$. The last
factor is obtained by multiplying the two given rejection factors of the two
EMCal triggers, see Fig. 1, as the $RF$ for EMC-L1 to MB trigger is of
interest.

Figure 1: Determination of $RF$s for the PHOS-L0 and EMC-L0/L1 triggers. In
the plateau region, the $RF$s are obtained by fits of constants in the given
cluster energy ranges, illustrated by the dotted lines. The uncertainties of
the determined $RF$s are indicated by light colored uncertainty bands, which
are obtained by varying the fit ranges.

The luminosity determination is based on the cross-section of the MB trigger
condition, $\sigma_{\rm MB_{AND}}$, measured in a van der Meer (vdM) scan [34,
35]. The stability of the measured cross section throughout the whole data
taking period is assessed by comparing the V0-based luminosity measurement
with an independent luminosity signal, issued by the T0 detector. As discussed
in Ref. [35], this comparison results in an overall normalization uncertainty
of 2.6%, which includes contributions from both the vdM-based measurement and
its stability over time. The integrated luminosity of each triggered sample is
calculated with the number of analyzed events, $N_{\text{events}}$, the
respective rejection factors, $RF$, and the MB cross section, $\sigma_{\rm
MB_{AND}}=55.80\pm 1.45_{\text{(stat+sys)}}$ mb [35], given by:

$\mathscr{L_{\rm int}}=\frac{N_{\rm events}}{\sigma_{\rm MB_{AND}}}\times RF,$
(1)

for which $RF=1$ holds for the MB trigger. As the good run lists for each
detection method do not coincide, integrated luminosities are individually
quoted for all cases in Tab. 1.

|  $\mathscr{L_{\rm int}}$ (nb-1)
---|---
Reconstruction method | EMC & PCM-EMC | PHOS | PCM
MB trigger | $1.94\pm 0.05_{\text{norm}}$ | $1.25\pm 0.04_{\text{norm}}$ | $2.17\pm 0.06_{\text{norm}}$
EMC-/PHOS-L0 trigger | $40.9\pm 0.7_{\text{sys}}\pm 1.1_{\text{norm}}$ | $135.6\pm 16.8_{\text{sys}}\pm 3.6_{\text{norm}}$ | -
EMC-L1 trigger | $615.0\pm 15.0_{\text{sys}}\pm 16.0_{\text{norm}}$ | - | -
Table 1: The analyzed luminosities considering the individual statistics for
the different reconstruction methods and triggers. The EMCal related
measurements use the same list of good runs as indicated by the combined
column. The uncertainties denoted with “sys” reflect the systematical
uncertainty of $RF$ determination, whereas “norm” represents the uncertainties
entering from the cross section determination of the MB trigger [35].

##  4 Neutral meson reconstruction

Both $\pi^{0}$ and $\eta$ mesons are reconstructed via their two-photon decay
channels with branching ratios of $98.823\pm 0.034\%$ and $39.31\pm 0.20\%$
[36] by means of an invariant mass analysis. The neutral mesons are
reconstructed using the two electromagnetic calorimeters, EMCal and PHOS, a
photon conversion method (PCM) and a hybrid method, PCM-EMCal, which combines
one photon candidate from the PCM and one from the EMCal, resulting in four
(three) different methods for the reconstruction of $\pi^{0}$ ($\eta$) mesons.
The reconstruction of $\eta$ mesons is not accessible by PHOS due to the
limited detector acceptance and, compared to the $\pi^{0}$, the wider opening
angle of the decay photons. The hybrid PCM-EMCal method benefits from the high
momentum resolution of the PCM, a high reconstruction efficiency and,
crucially, the triggering capabilities of the EMCal. Moreover, an extended
$p_{\rm T}$ coverage is achieved compared to the standalone EMCal measurement,
as there is no limitation due to cluster merging effects, discussed later in
this section.

Photons and electrons/positrons generate electromagnetic showers when they
enter an electromagnetic calorimeter. They usually spread their energy over
multiple adjacent calorimeter cells. In order to reconstruct the full energy
of impinging particles, those adjacent cells need to be grouped into clusters,
which is realized by a clusterization algorithm. In the first step, the
algorithm looks for the cell that recorded the highest energy in the event,
exceeding the seed energy, $E_{\rm seed}$. After the identification of such a
seed cell, adjacent cells with recorded energies above a minimum energy,
$E_{\rm min}$, are added to the cluster. For the EMCal, the clusterization
algorithm adds cells to the cluster as long as their recorded energy is
smaller than the previous cell’s energy and does not aggregate the respective
cell, if it recorded a higher energy than the previous one. The clusterization
process continues in the same way with the remaining cells, until all cells
above the energy thresholds are grouped into clusters. Cluster energies are
then calculated by $E=\sum^{N_{\rm cell}}_{i}e_{i}$, where $e_{i}$ stands for
the energy recorded by the indicated cell. The values of $E_{\rm seed}$ and
$E_{\rm min}$ depend on the energy resolution and the noise level of the
front-end electronics. For the EMCal, values of $E_{\rm seed}=500$ MeV and
$E_{\rm min}=100$ MeV are chosen. For the PHOS, these parameters are set to
$E_{\rm seed}=200$ MeV and $E_{\rm min}=15$ MeV. Large clusters due to
overlapping photon showers in the PHOS are separated into individual clusters
by an unfolding method based on the knowledge of the lateral shape of the
electromagnetic shower [37].

Figure 2: Example invariant mass spectra in selected $p_{\rm T}$ slices for
PCM (top left), PHOS (top right), EMC (bottom left) and PCM-EMC (bottom right)
in the $\pi^{0}$ mass region. The black histograms show raw invariant mass
distributions before any background subtraction. The grey points show mixed-
event and residual correlated background contributions, which have been
subtracted from raw real events to obtain the signal displayed with red data
points. The blue curves represent fits to the background-subtracted invariant
mass spectra. Additional examples of invariant mass distributions for the
different methods are given in Ref. [38].

Cell energies are calibrated for both calorimeters to provide best estimates
for the cluster energies. After the cell-by-cell energy calibration of the
EMCal [23, 27], an improved correction for the relative energy scale as well
as for the residual geometrical misalignment of the EMCal between data and MC
simulations is derived by making use of the good momentum resolution of the
PCM photon in the hybrid PCM-EMCal method. Using this method, the $\pi^{0}$
mass is evaluated as a function of EMCal cluster energy, $E_{\rm cluster}$,
for data and MC. Therefrom, a cluster energy correction is deduced for the
simulation, for which the reconstructed $\pi^{0}$ masses are adjusted to the
measured mass positions in data. For $E_{\rm cluster}\approx 1$ GeV, the
correction is of the order of 2% and rises up to 4% for higher energies. Thus,
a precise energy calibration scheme for the relevant energy regions is
available which is found to be consistent for the EMCal and hybrid PCM-EMCal
methods for $\pi^{0}$ as well as $\eta$ mesons at the same time, hence
demonstrating the validity of the procedure. After applying this calibration
in the analysis, the $\pi^{0}$ and $\eta$ mass values in data and MC are
obtained for each $p_{\mbox{\tiny T}}$ bin and their ratio is computed. Then,
the ratios are plotted versus $p_{\mbox{\tiny T}}$ and fitted with a constant,
giving access to the residual miscalibration of the meson mass values between
data and MC. Such residual offsets of 0.005$\pm$0.043% and 0.14$\pm$0.13% are
found for $\pi^{0}$ and $\eta$ mesons for the EMCal analysis, whereas
0.002$\pm$0.042% and 0.02$\pm$0.14% are obtained for PCM-EMCal, illustrating
the performance of the calibration procedure. For the PHOS, the energy
deposition in each cell is calibrated by adjusting the $\pi^{0}$ peak position
in the invariant mass spectra of photon pairs to the true mass of the
$\pi^{0}$ meson. The accuracy of this calibration procedure is estimated to be
better than 1%. It is evaluated from a comparison of the $\pi^{0}$ peak width
in calibrated data and MC simulations by introducing random, normal-
distributed decalibration parameters to the MC simulation.

Photon identification criteria are applied to the sample of reconstructed
clusters in order to primarily select clusters generated by true photon
candidates. For the photon reconstruction with PHOS, relatively loose
identification cuts are applied because the shower overlap is negligible and
the combinatorial background is found to be small in pp collisions. A minimum
cluster energy, $E_{\rm cluster}>0.3$ GeV, as well as a minimum number of
cells forming a cluster, $N_{\rm cell}\geq 3$, are required in order to reject
electronic noise and minimum ionizing particles which deposit about $270$ MeV
in the PHOS. For the EMCal, a minimum energy cut of $E_{\rm cluster}>0.7$ GeV
is applied and the minimum number of cells grouped in a cluster is set to
$N_{\rm cell}\geq 2$. Furthermore, the selection criteria of $|\eta|<0.67$ and
$1.40$ rad $<\varphi<3.15$ rad are imposed for EMCal clusters. Pileup from
multiple events, which may occur within a readout interval of the front-end
electronics, is rejected by applying a cluster timing cut relative to the
collision time of $-25<t_{\rm cluster}<25$ ns for the PHOS and $-35<t_{\rm
cluster}<25$ ns for the EMCal. Thus, photon candidates from different bunch
crossings are removed with high efficiency of $\rm{>}99\%$. For the EMCal, all
clusters matched with a primary charged track are rejected. This track
matching procedure, referred to as general track matching, uses a track
$p_{\mbox{\tiny T}}$-dependent matching in $\eta$ and $\varphi$, beginning
from $|\Delta\eta|<0.04$ and $|\Delta\varphi|<0.09$ for very low track momenta
of $p_{\mbox{\tiny T}}<0.5$ $\mbox{GeV}/c$ and going down to
$|\Delta\eta|<0.01$ and $|\Delta\varphi|<0.015$ for highest track momenta,
using the $p_{\mbox{\tiny T}}$-dependent matching conditions
$|\Delta\eta|<0.01+(p_{\mbox{\tiny T}}+4.07)^{-2.5}$ and
$|\Delta\varphi|<0.015+(p_{\mbox{\tiny T}}+3.65)^{-2}$. Applying these
conditions, a primary track to cluster matching efficiency of more than 95% is
obtained over the full $p_{\mbox{\tiny T}}$ range, rising above 98% for the
analyzed EMCal triggered datasets for $p_{\mbox{\tiny T}}$ beyond 10
$\mbox{GeV}/c$. To further enhance the photon purity and to reject neutral
hadrons, a cluster shape cut of $0.1\leq\sigma^{2}_{\rm long}\leq 0.7$ is
applied for EMCal clusters, where $\sigma^{2}_{\rm long}$ stands for the
smaller eigenvalue of the dispersion matrix of the shower shape ellipse
defined by the responding cells and their energy contributions to the cluster
[39, 9]. The lower threshold of $\sigma^{2}_{\rm long}$ is chosen to remove
contamination caused by neutrons hitting the APDs of the readout electronics.

Photons convert into lepton pairs within the detector material of ALICE with a
probability of about 8.5%. The reconstruction of such photon conversion
candidates using PCM may be divided into three major steps: (i) tracking of
charged particles and secondary vertex (${\rm V^{0}}$) finding [37]; (ii)
particle identification and (iii) photon candidate reconstruction and
subsequent selection. The ${\rm V^{0}}$s used in this analysis are obtained
during data reconstruction using all available tracking information,
recalculating the momenta of the daughter tracks under the assumption that
both daughters are created with parallel momentum vectors at the ${\rm
V^{0}}$. The tracks associated with secondary vertices are required to have a
minimum momentum of $p_{\rm T}^{\rm track}>50$ MeV/$c$ and at least 60% of
clusters from the maximum possible number of clusters, that a particle track
can create in the TPC along its path, need to be found. In order to reduce the
contamination from Dalitz decays, conversion candidates are only considered
with a vertex at a radial distance of at least $R>5$ cm. In addition, a line-
cut is applied to restrict the geometrical $\eta$ distribution of the ${\rm
V^{0}}$s in order to remove photon candidates that would otherwise appear
outside the angular dimensions of the detector. The condition $R_{\rm
conv}>|Z_{\rm conv}|S_{\rm ZR}-7$ cm is applied with $S_{\rm
ZR}=\tan\left(2\arctan(\exp(-\eta_{\rm cut}))\right)$ and $\eta_{\rm
cut}=0.9$, where the coordinates $R_{\rm conv}$ and $Z_{\rm conv}$ are
determined with respect to the nominal center of the detector. Additional
constraints are imposed on $R_{\rm conv}<180$ cm and $|Z_{\rm conv}|<240$ cm
to ensure that the reconstruction of secondary tracks is performed inside the
TPC. Electrons and positrons from photon conversions are identified via their
energy deposit, d$E$/d$x$, in the TPC. The difference of the measured
d$E$/d$x$ value from the hypothesis of the electron/positron energy loss is
used for particle identification. The d$E$/d$x$ of measured charged tracks is
required to be within $-3<{n\sigma_{e}<5}$ of the expected energy loss, which
is a $p_{\mbox{\tiny T}}$-dependent observable defined by
$n\sigma_{e}=(d$E$/d$x$-\langle$d$E/$d$x\rangle_{e})/\sigma_{e}$ with the
average energy loss of the electron/positron, $\langle$d$E/$d$x\rangle_{e}$,
and the Gaussian width of the fit to the measured d$E$/d$x$ distribution,
$\sigma_{e}$. To further reduce charged pion contamination as the pion
d$E$/d$x$-band begins to merge with the electron/positron d$E$/d$x$-band above
$p\gtrsim 4$ $\mbox{GeV}/c$, a cut based on the separation from the hypothesis
of charged pion energy loss is applied in $n\sigma_{\pi}$, analog to the
previous definition. Tracks with energy losses closer to the pion line than
$|n\sigma_{\pi}|<1$ are removed, which is done up to $3.5$ $\mbox{GeV}/c$. The
non-photon ${\rm V^{0}}$ candidate contamination is further suppressed by a
triangular two-dimensional cut, $|\Psi_{\rm pair}|<\Psi_{\rm
pair,max}(1-\chi^{2}_{\rm red}/\chi^{2}_{\rm red,max})$, with $\chi^{2}_{\rm
red,max}=30$ and $\Psi_{\rm pair,max}=0.1$. This cut is based on the reduced
$\chi^{2}$ of the Kalman-Filter [40] hypothesis for the $e^{+}e^{-}$ pair and
on the angle $\Psi_{\rm pair}$ between the plane perpendicular to the magnetic
field of the ALICE magnet and the $e^{+}e^{-}$ pair plane. Furthermore, a cut
on the cosine of the pointing angle of $\cos(\theta_{\rm PA})>0.85$ is
performed, where the pointing angle, $\theta_{\rm PA}$, is the angle between
the reconstructed photon momentum vector and the vector joining the collision
vertex. The remaining ${\rm K^{0}_{S}}$, ${\rm\Lambda}$ and
${\rm\overline{\Lambda}}$ contamination is removed by selecting $q_{\rm
T}<q_{\rm T,max}\sqrt{1-\alpha^{2}/\alpha^{2}_{\rm max}}$ on the Armenteros-
Podolanski plot [41] with $q_{\rm T,max}=0.05$ $\mbox{GeV}/c$ and $\alpha_{\rm
max}=0.95$. Additionally, the PCM measurement requires an out-of-bunch pileup
correction which estimates the contamination of photon candidates from
multiple events overlapping in the TPC. The correction is based on a study of
the distance of closest approach (DCA) of the conversion photon candidates
which is the smallest distance in beam direction, $z$, between the primary
vertex and the momentum vector of the photon candidate. Photon candidates from
different events generate a broad underlying Gaussian-like DCA distribution,
which is fitted in order to estimate the out-of-bunch pileup contribution. The
correction is found to be $p_{\mbox{\tiny T}}$-dependent and ranges from 42%
at low $p_{\mbox{\tiny T}}$ $\approx 0.35$ $\mbox{GeV}/c$ to 10% at high
$p_{\mbox{\tiny T}}$ $\approx 11$ $\mbox{GeV}/c$.

Figure 3: Example invariant mass spectra in selected $p_{\mbox{\tiny T}}$
slices in PCM (top left), PCM-EMCal (top right) and EMCal (bottom plots) in
the $\eta$ mass region. The black histograms show raw invariant mass
distributions before any background subtraction. The grey points show mixed-
event and residual correlated background contributions, which have been
subtracted from raw real events to obtain the signal displayed with red data
points. The blue curves represent fits to the background-subtracted invariant
mass spectra. Additional examples of invariant mass distributions for the
different methods are given in Ref. [38].

The hybrid PCM-EMCal method practically uses the same cuts on photon
candidates as the respective standalone reconstruction methods. In context of
the PCM, a wider cut of $-4<{\rm n\sigma_{e}<5}$ concerning the
electron/positron energy loss hypothesis is used for the hybrid method and the
$p_{\mbox{\tiny T}}$ restriction of the charged pion d$E$/d$x$ cut is
loosened. Only the upper value of the cut on the short axis of the moment of
the shower shape for the EMCal is changed and required to be $\sigma^{2}_{\rm
long}\leq 0.5$ in order to further reject contamination of hadrons [9]. Due to
the timing constraint of the EMCal restricting clusters to triggered bunch
crossings, no DCA or additional out-of-bunch pileup rejection is needed for
the hybrid method. In addition to the general matching of primary charged
particles to EMCal clusters already described, a dedicated track matching
procedure for the two charged ${\rm V^{0}}$ daughters with respect to EMCal
clusters is applied. This cluster-${\rm V^{0}}$ track matching is the most
important ingredient for the hybrid analysis, as pairing one leg of the ${\rm
V^{0}}$ candidate with the EMCal cluster generated by one of these secondary
charged tracks itself, leads to an auto-correlation and causes a broad peak
between the masses of the $\pi^{0}$ and $\eta$ mesons at around 300 MeV/$c$.
The same parameters from the general track matching procedure are found to
remove about 99% of such candidates.

Invariant mass distributions of photon pairs, shown in Figs. 2 and 3, include
combinatorial background as well as the neutral meson signal for photon
candidate pairs from the same, real event. An opening angle cut of 17 mrad for
the angle between the momentum vectors of the two paired photon candidates is
applied for the EMCal measurement. Requiring a minimum separation between such
pairs is needed to ensure a proper background description by event mixing, in
which two clusters from different events might otherwise be separated by an
arbitrarily small distance. In same events, such cluster configurations would
overlap partially or even merge into single clusters, which has been
explicitly considered for event mixing by not allowing the cells with largest
deposited energies of respective clusters to be direct neighbors on the EMCal
surface. For the PCM and hybrid PCM-EMCal methods, an opening angle cut of 5
mrad is further applied between the momentum vectors of the pair of conversion
photon candidates and accordingly, the pair of PCM and EMCal photon
candidates. Furthermore, pairs are restricted to a rapidity of $|y|<0.12$ for
the PHOS and $|y|<0.8$ for all other methods.

The uncorrelated combinatorial background is estimated by using an event
mixing technique, in which photon candidates from different events are paired
in order to prevent correlations between the candidates. Different event pools
are used for this purpose, binned by primary vertex position, photon candidate
multiplicity and transverse momentum to ensure the mixing of similar events
only. In contrast to same-event combinations to extract the neutral meson
signal, the mixed-event background is obtained with up to 80 different events,
stored in each of the event pools, in order to minimize its statistical
uncertainties. Therefore, the mixed-event background needs to be scaled to
match the integral of the raw signal in the vicinity of the right side of the
neutral meson peak, just outside the peak integration interval, after which it
is subtracted from the raw distribution. The background-subtracted signal is
then fitted to determine the mass peak position and width of $\pi^{0}$ and
$\eta$ mesons for every $p_{\mbox{\tiny T}}$ bin. A function composed of a
Gaussian modified by an exponential tail at the low mass side [42] is used for
this purpose. The low mass tail accounts for late conversions of one or both
photons for the EMCal method and for energy loss effects due to bremsstrahlung
for the PCM and hybrid PCM-EMCal methods. To reflect the residual correlated
background components which remain after the subtraction of the mixed-event
background, the fitting is performed by including an additional first order
polynomial function (deduced from MC simulations), which is also shown in
Figs. 2 and 3 and which is further being subtracted from the invariant mass
distribution. In contrast, a slightly different approach for the background
description is followed for the PHOS as its limited acceptance results in a
more complicated shape of the combinatorial background around the signal peak,
especially at low $p_{\mbox{\tiny T}}$. As both correlated and combinatorial
backgrounds are influenced in the same manner, the ratio of the raw signal and
mixed-event distributions is constructed and fitted with first or second order
polynomial function outside the peak region. Then, the mixed-event
distribution is scaled with the obtained polynomial function and subtracted
from the raw signal, which can be followed in Fig. 2. A Crystal Ball function
[43] is used as the main fit function for the PHOS method which also
reproduces the tail at the low mass region to take into account the late
conversion of photons in front of the calorimeter. The signal distribution is
then obtained by subtracting the scaled mixed-event background from the raw
invariant mass distribution. The resulting background-subtracted signal
distributions as well as raw signals from real events, the normalized mixed-
event and residual background distributions are shown in Figs. 2, 3 and in
Ref. [38] for the $\pi^{0}$ and $\eta$ meson mass region, respectively, for
given example $p_{\mbox{\tiny T}}$ bins, illustrating the meson reconstruction
over the full reported $p_{\mbox{\tiny T}}$ range.

The neutral meson raw yields are extracted by integrating the background-
subtracted invariant mass distributions. The integration windows are defined
by the reconstructed mass position and width obtained by the respective fits
of the signal distribution in a given $p_{\mbox{\tiny T}}$ bin. For the PHOS
method, the integration range for $\pi^{0}$ is asymmetrically defined as
$[-5\sigma,+3\sigma]$ around reconstructed peak position, where $\sigma$ is
the standard deviation of the Gaussian part of the Crystal Ball function to
take the asymmetric shape into account. For the other methods, the integration
windows for both neutral mesons are chosen to cover at least
$[-3\sigma,+3\sigma]$ around the reconstructed peak position, where $\sigma$
is the standard deviation of the Gaussian part of the fit function. For each
reconstruction method, the peak position and width used for the signal
extraction are shown in Fig. 4 as a function of reconstructed $p_{\mbox{\tiny
T}}$.

Figure 4: The left plots show reconstructed $\pi^{0}$ peak positions (left-
bottom) and widths (left-top) of each reconstruction method compared to MC
simulations for the transverse momentum bins used in the analysis.
Corresponding plots for the $\eta$ meson are on the right for peak masses
(right-bottom) and widths (right-top).

Corrections for geometrical acceptance and reconstruction efficiencies are
evaluated using MC simulations. PYTHIA8 [18] and PHOJET [44] event generators
with minimum bias processes are used for this purpose. The correction factors
for both MC productions are found to be consistent and, hence, are combined.
To generate enough statistics for high meson momenta to be able to correct the
raw yields obtained with triggered data, a PYTHIA8 simulation is used that is
enriched with jets, generated in bins of hard scatterings, $p_{\mbox{\tiny T,
hard}}$. Particles generated by the event generators are propagated through
the ALICE detector using GEANT3 [45] which realistically reproduces
interactions between the particles and the detector material. In the
simulation, the same reconstruction algorithms and analysis cuts are applied
as for real data. In Fig. 4, the reconstructed $\pi^{0}$ and $\eta$ mass peak
positions and widths are compared as a function of $p_{\mbox{\tiny T}}$
between data and MC to confirm a proper detector response in the simulation.
The normalized correction factors, $\epsilon$, for each method, containing the
specific detector acceptances as well as the full reconstruction efficiencies,
are shown in Fig. 5. For the EMCal analysis, the correction factor for the
$\pi^{0}$ is observed to decrease for $p_{\mbox{\tiny T}}\gtrsim 10$
$\mbox{GeV}/c$. This is due to the effect of cluster merging, as due to the
Lorentz boost the opening angles of $\pi^{0}$ mesons become too small to
resolve adjacent clusters given the finite segmentation of the calorimeter.
While the dominant symmetric decays are first to merge, the asymmetric decay
contributions become more relevant at higher momenta. Above a certain limiting
momentum, it is no longer possible to separate the two decay photons of the
$\pi^{0}$, creating merged clusters that significantly reduce the
reconstruction efficiency in the EMCal as seen in Fig. 5. Thus, the natural
upper limit for the $\pi^{0}$ reconstruction with the EMCal is of the order of
$p_{\mbox{\tiny T}}^{\pi^{0}}\approx 20$ GeV/$c$. In contrast, the PCM-EMCal
hybrid approach overcomes the limitations of the EMCal cell segmentation and
makes it possible to reconstruct $\pi^{0}$ mesons up to $p_{\mbox{\tiny
T}}\approx 35$ $\mbox{GeV}/c$ as reported in this paper. For the PHOS, such
cluster merging effects are negligible for the reported $p_{\mbox{\tiny T}}$
range owing to the high granularity of the calorimeter. Since the opening
angles of photons from $\eta$ meson decays are much larger compared to the
$\pi^{0}$, merging effects are negligible for all approaches over the full
reported $p_{\mbox{\tiny T}}$ range in this case.

Figure 5: The normalized correction factors, $\epsilon$, for each
reconstruction method for $\pi^{0}$ (left) and $\eta$ mesons (right) plotted
versus $p_{\mbox{\tiny T}}$ bins used in the analysis. The factors contain the
detector acceptances and the respective reconstruction efficiencies, where
acceptances are further normalized by the rapidity windows accessible with
each method, $\Delta y$, and full azimuth coverage of $2\pi$, in order to
enable a direct comparison between the different methods.

The contributions of secondary $\pi^{0}$ from weak decays and hadronic
interactions with the detector material are estimated and removed for the
$\pi^{0}$ measurements. Weak decays of ${\rm K_{S}^{0}}$ represent the main
source of secondaries. For all reconstruction methods, the spectra of the
three main particles relevant for the secondary correction due to weak decays,
${\rm K_{S}^{0}}$, ${\rm K_{L}^{0}}$ and $\Lambda$, are obtained from Refs.
[46, 47, 48] with extrapolation of spectra to $\sqrt{s}=8$ TeV, assuming a
power law for each $p_{\mbox{\tiny T}}$ bin as function of $\sqrt{s}$. These
spectra are used as weights in a PYTHIA6.4 simulation, where the respective
particle decays are simulated on generator level, taking into account the full
decay kinematics. Using this procedure, the invariant yields of secondary
$\pi^{0}$s from weakly decaying particles are obtained. From the full ALICE
GEANT3 MC simulations, the acceptance and reconstruction efficiencies are
calculated for these secondaries and multiplied with the respective invariant
yields from the generator level MC simulation to arrive at the secondary
$\pi^{0}$ raw yields from the different particles. On the other hand, the
$\pi^{0}$ raw yield from interactions with the detector material is purely
obtained from the full MC simulation, which is the only viable approach. All
the estimated, secondary $\pi^{0}$ raw yields are subtracted from the
reconstructed number of $\pi^{0}$s, as indicated in Eq. 2. The corrections are
of the order of 1-3% for ${\rm K_{S}^{0}}$, $<$0.5% for ${\rm K_{L}^{0}}$,
$\lesssim$0.02% for $\Lambda$ and 0.1-2% for material, varying within the
given values for the different methods and triggers used.

As there are three different triggers available for the EMCal and hybrid PCM-
EMCal methods, and two different ones for the PHOS measurement, each with its
own statistical and systematic uncertainties, as well as correlations between
the different systematical uncertainties, the results from each trigger class
are properly combined in order to obtain the final result for each
reconstruction method. Statistical uncertainties are ensured to be
uncorrelated since different triggers use non-overlapping data samples. For
the systematic uncertainties, the $p_{\mbox{\tiny T}}$-dependent correlation
coefficients are determined. Only a few systematic uncertainties are found to
be uncorrelated, such as the uncertainty of signal extraction and partly
“efficiency” and “trigger” related uncertainties, for which further details
are contained in Sec. 5. The correlation coefficients are found to be
generally above 0.8. The respective $p_{\mbox{\tiny T}}$-dependent weights are
calculated according to the BLUE algorithm [49, 50, 51, 52, 53], which are
used to combine the spectra from each method.

##  5 Systematic uncertainties

Systematic uncertainties are respectively summarized in Tabs. 2, 3 and 4 for
the neutral mesons $\pi^{0}$, $\eta$ and their ratio $\eta/\pi^{0}$. The
values are given in percent and refer to relative systematic uncertainties of
the measured values. Three different example $p_{\mbox{\tiny T}}$ bins are
listed for each reconstruction method in order to illustrate their relative
strengths. An additional, more detailed description of the systematic sources
and the determination of uncertainties for all methods except PHOS may be
found in Ref. [9], which is fully applicable to this paper.

$p_{\mbox{\tiny T}}$ interval |  $1.4-1.6$ GeV/$c$ |  $5.0-5.5$ GeV/$c$ |  $15.0-16.0$ GeV/$c$
---|---|---|---
Method | PCM | PCM- | EMC | PHOS | PCM | PCM- | EMC | PHOS | PCM- | EMC | PHOS
EMC | EMC | EMC
Signal extraction | $4.8$ | $1.9$ | $2.3$ | $3.0$ | $5.4$ | $2.4$ | $1.5$ | $1.8$ | $3.3$ | $4.6$ | $1.0$
Inner material | $9.0$ | $4.5$ | - | - | $9.0$ | $4.5$ | - | - | $4.5$ | - | -
Outer material | - | $2.1$ | $4.2$ | $3.5$ | - | $2.1$ | $4.2$ | $3.5$ | $2.1$ | $4.2$ | $3.5$
PCM track rec. | $1.0$ | $0.5$ | - | - | $1.0$ | $0.9$ | - | - | $2.1$ | - | -
PCM electron PID | $1.8$ | $0.6$ | - | - | $1.1$ | $1.3$ | - | - | $3.1$ | - | -
PCM photon PID | $1.7$ | $0.5$ | - | - | $2.1$ | $1.1$ | - | - | $3.5$ | - | -
Cluster description | - | $2.5$ | $4.4$ | - | - | $2.5$ | $3.7$ | - | $4.3$ | $4.0$ | -
Cluster energy calib. | - | $1.8$ | $2.5$ | $2.6$ | - | $1.9$ | $1.8$ | $0.6$ | $2.8$ | $2.0$ | $0.6$
Track match to cluster | - | $0.2$ | $3.1$ | - | - | $0.5$ | $2.0$ | - | $3.3$ | $3.7$ | -
Efficiency | - | $2.0$ | $2.5$ | $7.0$ | - | $2.8$ | $2.7$ | $7.0$ | $2.7$ | $3.7$ | $7.5$
Trigg. norm.&pileup | $3.4$ | $0.1$ | $0.1$ | $1.2$ | $2.2$ | $0.7$ | $0.3$ | $1.2$ | $2.3$ | $2.4$ | $12.5$
Total syst. uncertainty | $11.1$ | $6.5$ | $8.0$ | $8.9$ | $11.0$ | $7.3$ | $6.9$ | $8.2$ | $10.6$ | $9.6$ | $15.0$
Statistical uncertainty | $1.5$ | $1.5$ | $3.4$ | $7.2$ | $7.5$ | $3.3$ | $2.2$ | $8.2$ | $7.9$ | $4.4$ | $10.6$
Combined stat. unc. | 2.1 | 2.2 | 4.0
Combined syst. unc. | 5.1 | 5.1 | 7.6

Table 2: Summary of relative systematic uncertainties in percent for selected
$p_{\mbox{\tiny T}}$ bins for the reconstruction of $\pi^{0}$ mesons. The
statistical uncertainties are given in addition to the total systematic
uncertainties for each bin. Moreover, the combined statistical and systematic
uncertainties are also listed, obtained by applying the BLUE method [49, 50,
51, 52, 53] for all reconstruction methods available in the given
$p_{\mbox{\tiny T}}$ bin, considering the uncertainty correlations for the
different methods (see Sec. 6 for further details). The uncertainty from
$\sigma_{\rm MB_{AND}}$ determination of 2.6%, see Ref. [35], is independent
from the reported measurements and is separately indicated in the following
plots below.

For the $\pi^{0}$ measurement by PHOS, the systematic uncertainty related to
the signal extraction is evaluated by varying the fitting range and the
assumptions about the mass peak and background shapes. The systematic
uncertainty related to the material budget is taken from Ref. [3], which is
estimated by comparing the results of the analysis with and without magnetic
field in the ALICE solenoid. Photons, which converted to $e^{+}e^{-}$ pairs
within the detector material, are most likely being reconstructed as two
clusters in the presence of a magnetic field. Without a field, the secondary
tracks from photon conversions are less separated and can be dominantly
detected as single clusters, building the correct invariant masses for
$\pi^{0}$s in a di-cluster analysis. Therefore, comparing the $\pi^{0}$
spectra from data and MC with nominal and zero magnetic fields is a
straightforward method to evaluate the uncertainty of the material budget
description in simulations. Systematic uncertainties due to the cluster energy
calibration are decomposed into the uncertainty of the energy scale of
clusters and non-linearity effects. The energy scale uncertainty of $0.1\%$ is
estimated from a comparison of the $\pi^{0}$ mass peak position for the two-
photon invariant mass spectra in data and MC. This energy uncertainty is
translated to an uncertainty of the $\pi^{0}$ yield by convolution with the
shape of the $p_{\mbox{\tiny T}}$ spectrum. The systematic uncertainty due to
the non-linearity correction is evaluated by introducing different non-
linearity correction schemes and calibration parameters for the MC simulation,
whereas the $p_{\mbox{\tiny T}}$ dependence of the $\pi^{0}$ peak position and
width is always kept consistent with data. The efficiency uncertainty consists
of acceptance variations and differences between MC event generators. The
acceptance uncertainty is estimated by changing the good cluster selection
criteria, and the MC generator-dependent uncertainty is evaluated by comparing
efficiencies of MB MC generators and single particle MC simulation which
generates events containing single neutral mesons with realistic transverse
momentum and rapidity distributions. Moreover, it includes the trigger
efficiency uncertainty for the high energy photon trigger analysis, which is
estimated by comparing the trigger turn-on curve from data with MC
simulations. “Trigger normalization & pileup” summarizes systematic
uncertainties due to the trigger normalization factor and pileup effects. The
uncertainty related to the trigger normalization factor is estimated by
changing the range of the fit to determine the rejection factor ($RF$).
Furthermore, the out-of-bunch pileup contribution is evaluated by varying the
timing cut to accept clusters.

For the PCM measurement, the main source of systematic uncertainty is the
material budget, for which the same value is used as previously calculated in
Ref. [3]. The signal extraction uncertainty is estimated by changing the
integration window around the invariant mass peak, the normalization range of
the mixed-event background and by using different order polynomials as well as
other fit functions to evaluate the remaining background contribution. “Track
reconstruction” summarizes the systematic uncertainties found by requiring
different numbers of TPC clusters and by applying different minimum transverse
momentum cuts on tracks. The systematic uncertainties due to the electron
identification (“electron PID” and “PCM photon PID”) are determined by varying
the PID cuts, which are elaborated in Sec. 4, and by comparing the respective
results. For PCM, the “trigger normalization & pileup” uncertainty is
dominated by the uncertainty of the DCA$z$ background description for the out-
of-bunch pileup estimation. Furthermore, it contains the systematic
uncertainty due to the pileup rejection by the SPD due to its finite
efficiency to remove pileup events.

$p_{\mbox{\tiny T}}$ interval |  $2.0-2.4$ GeV/$c$ |  $5.0-6.0$ GeV/$c$ |  $18.0-20.0$ GeV/$c$
---|---|---|---
Method | PCM | PCM- | EMC | PCM | PCM- | EMC | PCM- | EMC
EMC | EMC | EMC
Signal extraction | $5.1$ | $9.0$ | $9.3$ | $7.3$ | $7.2$ | $6.0$ | $10.6$ | $8.1$
Inner material | $9.0$ | $4.5$ | - | $9.0$ | $4.5$ | - | $4.5$ | -
Outer material | - | $2.1$ | $4.2$ | - | $2.1$ | $4.2$ | $2.1$ | $4.2$
PCM track rec. | $1.5$ | $1.8$ | - | $2.0$ | $2.4$ | - | $3.3$ | -
PCM electron PID | $2.4$ | $1.8$ | - | $2.2$ | $2.9$ | - | $6.5$ | -
PCM photon PID | $3.6$ | $2.9$ | - | $6.3$ | $3.0$ | - | $7.9$ | -
Cluster description | - | $3.1$ | $4.6$ | - | $4.0$ | $4.9$ | $6.0$ | $4.9$
Cluster energy calib. | - | $3.2$ | $3.5$ | - | $3.9$ | $3.4$ | $4.5$ | $3.5$
Track match to cluster | - | $1.5$ | $4.0$ | - | $1.7$ | $3.2$ | $4.2$ | $3.3$
Efficiency | - | $5.0$ | $4.3$ | - | $9.7$ | $5.5$ | $10.0$ | $6.3$
Trigg. norm.&pileup | $2.1$ | $0.1$ | $0.1$ | $1.4$ | $1.4$ | $1.5$ | $3.0$ | $2.8$
Total syst. uncertainty | $11.5$ | $13.0$ | $13.1$ | $13.6$ | $15.2$ | $11.5$ | $20.9$ | $13.3$
Statistical uncertainty | $10.1$ | $12.1$ | $16.8$ | $18.3$ | $6.8$ | $5.4$ | $21.3$ | $8.2$
Combined stat. unc. | 7.4 | 5.0 | 7.9
Combined syst. unc. | 8.7 | 9.0 | 12.3

Table 3: Summary of relative systematic uncertainties in percent for selected
$p_{\mbox{\tiny T}}$ bins for the reconstruction of $\eta$ mesons, see Tab. 2
for further explanations which also apply here.

For the EMCal, one main systematic uncertainty arises from the knowledge of
the outer material budget, which is defined by all detector components from
the radial center of the TPC up to the EMCal. The uncertainty is assessed by
running the analysis only with/without TRD modules in front of the EMCal,
since part of the data taking in 2012 occurred with the EMCal only partially
obscured by the TRD. Since TRD and TOF have similar material budgets, the same
uncertainty is assigned to the TOF as well, which covered the full polar angle
so that a similar assessment as for the TRD is not feasible. Both
uncertainties are quadratically combined to arrive at the given uncertainties
which are listed in the tables. The signal extraction uncertainty contains the
systematic uncertainties obtained from variations of the background
normalization region, the choice of the background fit function and
integration intervals, analog to the PCM method, as well as from variations of
the minimum opening angle cut on the meson level. The systematic uncertainty
denoted as “cluster description” reflects the mismatch of the description of
the clusterization process between data and MC simulations, giving rise to
modified reconstruction efficiencies, which includes the following cluster
related quantities: minimum energy, shower shape, number of cells and timing
as well as variations of the energy thresholds used for the clusterization
process. Moreover, cell timing cut variations are also included in this
category. “Cluster energy calibration” considers the systematic uncertainties
due to non-linearity effects and the energy scale of clusters. Different non-
linearity schemes are used in this analysis from which this uncertainty is
obtained. Moreover, the energy scale uncertainty is determined by obtaining
the residual differences of reconstructed meson mass values from data and MC
simulations. The systematic uncertainty induced by the charged particle veto
on cluster level, introduced as “general track matching” in Sec. 4, is
determined by variations of the matching residuals. The “efficiency”
uncertainty reflects differences between MB MC generators for the calculation
of reconstruction efficiencies. Moreover, it contains the uncertainty of the
actual trigger turn-on, obtained by comparing the turn-on curves in data and
MC. The uncertainties from the determination of trigger rejection factors
($RF$) as well as from the pileup rejection by the SPD, which has a finite
efficiency for pileup removal, are summarized with “trigger normalization &
pileup”.

$p_{\mbox{\tiny T}}$ interval |  $2.0-2.4$ GeV/$c$ |  $5.0-6.0$ GeV/$c$ |  $18.0-20.0$ GeV/$c$
---|---|---|---
Method | PCM | PCM- | EMC | PCM | PCM- | EMC | PCM- | EMC
EMC | EMC | EMC
Signal extraction | $5.9$ | $9.0$ | $9.3$ | $8.2$ | $7.5$ | $6.6$ | $11.2$ | $12.8$
PCM track rec. | $1.5$ | $1.9$ | - | $2.0$ | $2.4$ | - | $3.8$ | -
PCM electron PID | $2.4$ | $1.9$ | - | $2.2$ | $3.5$ | - | $7.4$ | -
PCM photon PID | $3.6$ | $3.2$ | - | $6.3$ | $3.6$ | - | $9.0$ | -
Cluster description | - | $3.5$ | $4.9$ | - | $4.1$ | $5.1$ | $8.9$ | $5.5$
Cluster energy calib. | - | $3.4$ | $4.2$ | - | $4.6$ | $4.2$ | $5.5$ | $4.5$
Track match to cluster | - | $1.5$ | $3.9$ | - | $1.8$ | $3.2$ | $6.1$ | $3.3$
Efficiency | - | $5.4$ | $4.5$ | - | $9.8$ | $5.8$ | $10.5$ | $7.5$
Total syst. uncertainty | $7.5$ | $12.4$ | $12.8$ | $10.8$ | $15.0$ | $11.6$ | $23.1$ | $16.8$
Statistical uncertainty | $10.2$ | $12.2$ | $5.4$ | $19.2$ | $7.4$ | $2.7$ | $23.3$ | $19.0$
Combined stat. unc. | 5.5 | 3.9 | 15.1
Combined syst. unc. | 7.1 | 8.7 | 13.0

Table 4: Summary of relative systematic uncertainties in percent for selected
$p_{\mbox{\tiny T}}$ bins for the determination of the $\eta/\pi^{0}$ ratio.
The statistical uncertainties are given in addition to the total systematic
uncertainties for each bin. Moreover, the combined statistical and systematic
uncertainties are listed as well, see also explanations in caption of Tab. 2.

For the hybrid method PCM-EMCal, the same cut variations are performed as for
the standalone methods. However, given the fact that only one photon candidate
of each system is used, most systematic uncertainties are found to be of
different size or behavior, e.g. the minimum opening angle cut variations. The
“track matching to cluster” uncertainty reflects the ${\rm V^{0}}$-track to
cluster matching, which is assessed by varying the matching residuals.

As indicated in Tab. 4, many uncertainties cancel for the $\eta/\pi^{0}$
ratio, such as the material-related systematics. For the remaining categories,
the respective uncertainties of the $\pi^{0}$ and $\eta$ measurements are
added quadratically and canceled partially beforehand, if applicable.

##  6 Results

The invariant differential cross sections of $\pi^{0}$ and $\eta$ production
are obtained by

$\displaystyle E\frac{{\rm d^{3}}\sigma^{pp\rightarrow\pi^{0}(\eta)+X}}{{\rm
d}p^{3}}=\frac{1}{2\pi p_{\mbox{\tiny T}}}\,\frac{1}{\mathcal{L}_{\rm
int}}\,\frac{1}{A\cdot\varepsilon_{\rm
rec}}\,\frac{1}{Br_{\pi^{0}(\eta)\rightarrow\gamma\gamma}}\,\frac{N^{\pi^{0}(\eta)}-N^{\pi^{0}}_{\rm
sec}}{\Delta y\Delta p_{\mbox{\tiny T}}},$ (2)

where $N^{\pi^{0}(\eta)}$ is the number of reconstructed $\pi^{0}(\eta)$ meson
in a given $p_{\mbox{\tiny T}}$ bin, $N^{\pi^{0}}_{\rm sec}$ represents the
estimated number of secondary $\pi^{0}$ mesons, $\mathcal{L}_{\rm int}$ is the
integrated luminosity, $A\cdot\varepsilon_{\rm rec}$ is the product of the
geometrical acceptance and reconstruction efficiency, also referred to as
$\epsilon$ in Fig. 5, $Br_{\pi^{0}(\eta)\rightarrow\gamma\gamma}$ is the
branching ratio for the two-gamma decay channel and $\Delta y\Delta
p_{\mbox{\tiny T}}$ is the bin width in rapidity and transverse momentum. For
the measurement of $\pi^{0}$ mesons by PCM, the out-of-bunch pileup correction
has to be noted for completeness and to be applied as well.

The invariant differential cross sections are independently calculated for
each method. The final spectra are obtained by combining the results in the
overlap regions using the BLUE method [49, 50, 51, 52, 53], properly taking
into account the correlations of the systematic uncertainties of the different
methods. Possible statistical correlations between the measurements, for
instance due to the conversions at small distances relative to the beam axis,
are negligible due to the small conversion probability and the small
likelihood of reconstructing the respective electron in the calorimeters
leading to a meson candidate which finally ends up in the respective
integration window. As there are no common uncertainties present for PCM,
EMCal and PHOS, all systematic uncertainties are considered to be completely
uncorrelated in those cases. On the other hand, the correlations introduced by
including the hybrid PCM-EMCal measurement have to be taken into account. By
construction, there are different numbers of conversion photons entering the
two methods. Thus, all systematic uncertainty sources from PCM are found to be
partially correlated in the PCM-EMCal method. Half of the size of the material
budget uncertainty, for example, is assumed to be uncorrelated. Furthermore,
the uncorrelated systematic uncertainties from PCM-EMCal with respect to PCM
are, with full size, all the calorimeter related uncertainties as well as
trigger and efficiency uncertainties.

Due to finite bin widths of the measured production cross sections, the
neutral meson spectra are shifted along the horizontal axis [54]. All bin
width corrections are of the order of $1\%$ and below. In contrast, the
reported $\eta/\pi^{0}$ ratios are shifted along the vertical axis, as
otherwise the ratio could not be computed and the different measurements could
not be combined. The correction is below $1\%$ for $p_{\mbox{\tiny T}}>2$
$\mbox{GeV}/c$, but becomes significant for smaller momenta and rises to $8\%$
for the lowest bin.

The combined invariant cross sections of inclusive $\pi^{0}$ and $\eta$ meson
production cover transverse momentum ranges of $0.3<p_{\mbox{\tiny T}}<35$
$\mbox{GeV}/c$ and $0.5<p_{\mbox{\tiny T}}<35$ $\mbox{GeV}/c$, respectively.
The total uncertainties of the measurements, obtained by quadratically adding
the combined statistical and systematic uncertainties, are of the order of
$5$% for the $\pi^{0}$ and $10$% for the $\eta$ meson for most of the
$p_{\mbox{\tiny T}}$ bins covered, increasing for lowest and highest momenta
due to statistical limitations as well as systematic effects. Both combined
neutral meson spectra are fitted with a two-component model (TCM), proposed in
Ref. [55], by using the total uncertainties for each $p_{\mbox{\tiny T}}$ bin.
The functional form of the TCM is a combination of a Boltzmann component and a
power-law part, which, in general, should be the dominant components at low
and high $p_{\mbox{\tiny T}}$, respectively. The fit function is able to
reproduce the spectra over the full $p_{\mbox{\tiny T}}$ range and is
described as:

$\displaystyle E\frac{{\rm d}^{3}\sigma}{{\rm d}p^{3}}=A_{\rm
e}\,\exp\left(-E_{\rm T,kin}/T_{\rm e}\right)+A\left(1+\frac{p_{\mbox{\tiny
T}}^{2}}{T^{2}n}\right)^{-n},$ (3)

where $E_{\rm T,kin}=\sqrt{p_{\mbox{\tiny T}}^{2}+m^{2}}-m$ is the transverse
kinematic energy with the meson rest mass $m$ and $A_{\rm e}$, $A$, $T_{e}$,
$T$ as well as $n$ are the free parameters. To compare the different methods,
the ratios of spectra measured by each reconstruction method to the TCM fit of
the combined spectrum are shown in Fig. 6. The vertical error bars represent
the statistical uncertainties, whereas the boxes quantify the bin widths in
horizontal direction and the systematic uncertainties in vertical direction.
All measurements agree within uncertainties over the full $p_{\mbox{\tiny T}}$
range.

Figure 6: Ratios of the fully corrected $\pi^{0}$ (left) and $\eta$ (right)
spectra for each reconstruction method to the TCM fit of the combined
spectrum.

The $\pi^{0}$ and $\eta$ meson cross sections are also fitted with a Tsallis
function [56], which has been used in previous measurements of $\pi^{0}$ and
$\eta$ meson production in pp collisions reported by ALICE [3, 4]:

$\displaystyle E\frac{{\rm d}^{3}\sigma}{{\rm
d}p^{3}}=\frac{C}{2\pi}\,\frac{(n-1)(n-2)}{nT(nT+m(n-2))}\left(1+\frac{m_{\mbox{\tiny
T}}-m}{nT}\right)^{-n},$ (4)

where $C$, $n$ and $T$ are free parameters of the fit with $m$ and
$m_{\mbox{\tiny T}}$ being the rest as well as the transverse mass of the
meson. The fit parameters extracted from both the TCM and Tsallis fits are
summarized in Tab. 5. The TCM is chosen as the standard fit function, since it
better describes the spectra at low and high $p_{\mbox{\tiny T}}$ than the
Tsallis counterpart [38]. This is also reflected in the smaller values
obtained for the reduced $\chi^{2}_{\rm red}$ of the respective fits, which
are also recorded in Tab. 5. These values are calculated without assuming any
correlation of systematic uncertainties and are found to be rather small for
both fits, as the total uncertainties of meson spectra are used for their
calculation. A direct comparison of TCM and Tsallis fits can be found in Fig.
7, where both fits are plotted, in addition to the measured spectra and theory
calculations.

TCM |  $A_{e}$ (pb GeV${}^{-2}c^{3}$) |  $T_{e}$ (GeV) |  $A$ (pb GeV${}^{-2}c^{3}$) |  $T$ (GeV) | $n$ | $\chi^{2}_{\rm red}$
---|---|---|---|---|---|---
$\pi^{0}$ | (6.84$\pm$2.79)$\times 10^{11}$ | 0.142$\pm$0.020 | (3.68$\pm$0.89)$\times 10^{10}$ | 0.597$\pm$0.030 | 3.028$\pm$0.018 | 0.28
$\eta$ | (1.62$\pm$4.35)$\times 10^{9}$ | 0.229$\pm$0.203 | (2.89$\pm$1.81)$\times 10^{9}$ | 0.810$\pm$0.103 | 3.043$\pm$0.045 | 0.33
|
Tsallis |  $C$ (pb) |  $T$ (GeV) | $n$ | $\chi^{2}_{\rm red}$
$\pi^{0}$ | (2.46$\pm$0.18)$\times 10^{11}$ | 0.121$\pm$0.004 | 6.465$\pm$0.042 | 0.57
$\eta$ | (1.56$\pm$0.19)$\times 10^{10}$ | 0.221$\pm$0.012 | 6.560$\pm$0.113 | 0.59

Table 5: Parameters of the fits to the $\pi^{0}$ and $\eta$ invariant
differential cross sections using the TCM fit [55] from Eq. 3 as well as using
a Tsallis fit [56] from Eq. 4.

Figure 7: Invariant cross sections for neutral meson production are shown
together with NLO pQCD predictions using PDFs MSTW08 (CTEQ6M5) with FFs DSS14
(AESSS) for $\pi^{0}$ ($\eta$) as well as PYTHIA8.210 calculations, for which
two different tunes are available. The data points are fitted using a TCM fit,
Eq. 3, and a Tsallis fit, Eq. 4.

The measured invariant differential cross sections are compared with NLO pQCD
calculations [8, 11] using MSTW08 (PDF) [16] with DSS14 (FF) [8] for $\pi^{0}$
and CTEQ6M5 (PDF) [17] with AESSS (FF) [11] for the $\eta$ meson. The same
factorization scale value, $\mu$, ($0.5p_{\mbox{\tiny T}}<\mu<2p_{\mbox{\tiny
T}}$) is chosen for the factorization, renormalisation and fragmentation
scales used in the NLO pQCD calculations. For the $\pi^{0}$ the NLO PDF, pQCD
and FF combination describes the RHIC data rather well [57], whereas for
$\sqrt{s}=2.76$ TeV pQCD overpredicts ALICE data by 30% at moderate
$p_{\mbox{\tiny T}}$ and agrees at higher $p_{\mbox{\tiny T}}$ [9]. The ratios
of data and NLO pQCD predictions to the TCM fits of neutral meson spectra are
shown in Fig. 7. The largest uncertainty of the NLO pQCD calculation is due to
the choice of $\mu$. For all $\mu$ values, these calculations overestimate the
measured data for both $\pi^{0}$ and $\eta$ mesons. This is also observed for
meson measurements at $\sqrt{s}=2.76$ TeV by ALICE [9], although better
description of data is achieved for $\mu=2p_{\mbox{\tiny T}}$, for which
calculations are above data by $10-40\%$ depending on $p_{\mbox{\tiny T}}$. It
has to be noted that FF uncertainties of NLO pQCD calculations have been
considerably reduced after including the published $\pi^{0}$ measurement at
$\sqrt{s}=7$ TeV [3] for DSS14. Including precise new data for $\eta$ meson
production measured at $\sqrt{s}=2.76$, $7$ and $8$ TeV [9, 3] will also help
to considerably reduce NLO pQCD uncertainty bands in that case. In addition,
the reported neutral meson measurements at $\sqrt{s}=8$ TeV are compared to
PYTHIA8.210 [18] references; Tune 4C [19] and Monash 2013 tune [20]. To enable
a proper comparison of the PYTHIA tunes with the measured neutral meson
spectra, $\pi^{0}$ from decays of long-living strange particles ($K^{0}_{S}$,
$\Lambda$, $\Sigma$ and $\Xi$) are excluded. The Tune 4C calculation is about
$30\%$ above the $\pi^{0}$ measurement for $p_{\mbox{\tiny T}}>1.5$
$\mbox{GeV}/c$. In contrast, the Monash 2013 tune reproduces the $\pi^{0}$
spectrum within 10% for almost the complete transverse momentum range,
although both tunes are not able to describe the shape of the measured
spectrum indicated by the bump at approximately 3 $\mbox{GeV}/c$. Concerning
the $\eta$ meson, both tunes reproduce the measured spectrum for
$p_{\mbox{\tiny T}}>1.5$ $\mbox{GeV}/c$ within uncertainties. At lower momenta
$p_{\mbox{\tiny T}}<1.5$ $\mbox{GeV}/c$, both tunes follow the same trend and
deviate significantly in magnitude and shape from data. The tuning parameters
of the soft QCD part of PYTHIA apparently fail to describe the measured $\eta$
meson spectrum below $p_{\mbox{\tiny T}}<1.5$ $\mbox{GeV}/c$, whereas there is
further tension up to $p_{\mbox{\tiny T}}\approx 3.5$ $\mbox{GeV}/c$. On the
other hand, both PYTHIA tunes are consistent within uncertainties with the
measured $\pi^{0}$ spectrum for the low transverse momentum interval
$0.3<p_{\mbox{\tiny T}}<1.5$ $\mbox{GeV}/c$.

The mean transverse momenta, $\langle p_{\mbox{\tiny T}}\rangle$, are
determined for the neutral meson spectra shown in Fig. 7. Three different fit
functions are used in this context: a TCM, Eq. 3, a Tsallis, Eq. 4, and a
modified Hagedorn [58] fit that is used as the default fit function, since it
yields the best agreement with data at lowest $p_{\mbox{\tiny T}}$ measured
[38]. The obtained values for $\pi^{0}$ and $\eta$ mesons are listed in Tab.
6, where statistical and systematic uncertainties are quoted. The additional
uncertainty term denoted with “fit sys” reflects the choice of the fitting
function. Moreover, the introduced fit functions are also used to calculate
the integrated yields, $\text{d}N/\text{d}y|_{y\,\,\approx\,\,0}$, for both
neutral mesons in inelastic events. The cross section for inelastic pp
collisions at $\sqrt{s}=8$ TeV, $\sigma_{\rm INEL}=74.7\pm 1.7$ mb [59], is
used for this purpose. The obtained yields are given in Tab. 6, which are
based on extrapolation fractions, $F_{\rm extpol}$, of about 45% for the
$\pi^{0}$ and about 34% for the $\eta$ meson. Additionally, the integrated
$\eta/\pi^{0}$ ratio is estimated and can be found in Tab. 6 as well. For the
recent paper by ALICE on neutral meson production in pp collisions at
$\sqrt{s}=2.76$ TeV [9], the mean $p_{\mbox{\tiny T}}$ as well as the
integrated yields are also calculated for the reported spectra, which are
furthermore added to Tab. 6. The inelastic pp cross section at $\sqrt{s}=2.76$
TeV, quoted in Ref. [9] as well, is used to calculate the integrated yields
which include extrapolation fractions of about 59% for the $\pi^{0}$ and about
52% for the $\eta$ meson. The obtained values for $\langle p_{\mbox{\tiny
T}}\rangle$ and $\text{d}N/\text{d}y|_{y\,\,\approx\,\,0}$ for both neutral
mesons are compared with measurements of average transverse momenta of charged
particles [60] and with results concerning charged-particle multiplicity [61].
Due to a large extrapolation fraction of the $\pi^{0}$ and $\eta$ meson
spectra with respect to charged particles and the given systematics for the
lowest transverse momenta, the uncertainties of $\langle p_{\mbox{\tiny
T}}\rangle$ and $\text{d}N/\text{d}y|_{y\,\,\approx\,\,0}$ are found to be
larger. Hence, the integrated $\eta/\pi^{0}$ ratios are also affected.
Nevertheless, all values quoted in this paragraph are consistent within
experimental uncertainties with the results from charged particle measurements
[47, 62]. Within their substantial uncertainties, the $\eta/\pi^{0}$ ratios at
both pp energies are found to be consistent as well.

$\sqrt{s}=8$ TeV |  $\langle p_{\mbox{\tiny T}}\rangle$ ($\mbox{GeV}/c$) | $\text{d}N/\text{d}y|_{y\,\,\approx\,\,0}$ | $F_{\rm extpol}$
---|---|---|---
$\pi^{0}$ | $0.431\pm 0.006_{\mbox{\tiny(stat)}}\pm 0.020_{\mbox{\tiny(sys)}}\pm 0.012_{\mbox{\tiny(fit sys)}}$ | $3.252\pm 0.128_{\mbox{\tiny(stat)}}\pm 0.918_{\mbox{\tiny(sys)}}\pm 0.146_{\mbox{\tiny(fit sys)}}$ | 45%
$\eta$ | $0.929\pm 0.110_{\mbox{\tiny(stat)}}\pm 0.126_{\mbox{\tiny(sys)}}\pm 0.085_{\mbox{\tiny(fit sys)}}$ | $0.164\pm 0.033_{\mbox{\tiny(stat)}}\pm 0.052_{\mbox{\tiny(sys)}}\pm 0.023_{\mbox{\tiny(fit sys)}}$ | 34%
$\eta/\pi^{0}$ | $0.050\pm 0.010_{\mbox{\tiny(stat)}}\pm 0.022_{\mbox{\tiny(sys)}}\pm 0.008_{\mbox{\tiny(fit sys)}}$ |
$\sqrt{s}=2.76$ TeV |  $\langle p_{\mbox{\tiny T}}\rangle$ ($\mbox{GeV}/c$) | $\text{d}N/\text{d}y|_{y\,\,\approx\,\,0}$ | $F_{\rm extpol}$
$\pi^{0}$ | $0.451\pm 0.008_{\mbox{\tiny(stat)}}\pm 0.014_{\mbox{\tiny(sys)}}\pm 0.152_{\mbox{\tiny(fit sys)}}$ | $1.803\pm 0.058_{\mbox{\tiny(stat)}}\pm 0.352_{\mbox{\tiny(sys)}}\pm 0.646_{\mbox{\tiny(fit sys)}}$ | 59%
$\eta$ | $0.647\pm 0.068_{\mbox{\tiny(stat)}}\pm 0.040_{\mbox{\tiny(sys)}}\pm 0.140_{\mbox{\tiny(fit sys)}}$ | $0.250\pm 0.050_{\mbox{\tiny(stat)}}\pm 0.052_{\mbox{\tiny(sys)}}\pm 0.063_{\mbox{\tiny(fit sys)}}$ | 52%
$\eta/\pi^{0}$ | $0.139\pm 0.028_{\mbox{\tiny(stat)}}\pm 0.040_{\mbox{\tiny(sys)}}\pm 0.061_{\mbox{\tiny(fit sys)}}$ |

Table 6: The mean transverse momenta, $\langle p_{\mbox{\tiny T}}\rangle$, and
integrated yields, $\text{d}N/\text{d}y|_{y\,\,\approx\,\,0}$, for ALICE
measurements of $\pi^{0}$ and $\eta$ mesons at $\sqrt{s}=2.76$ and 8 TeV are
summarized [38]. It has to be noted that the uncertainties from the
measurements of the inelastic cross sections are not included for the given
numbers, which are ${}^{+3.9\%}_{-6.4\%}(model)\pm 2.0(lumi)$% for
$\sqrt{s}=2.76$ TeV [29] and $\pm 2.3$% for 8 TeV [59]. Moreover, the
integrated $\eta/\pi^{0}$ ratios are quoted for the different energies.

Both meson spectra, which are shown in Fig. 7, exhibit a similar power-law
behavior, $E{\rm d}^{3}\sigma/{\rm d}p^{3}\propto p_{\mbox{\tiny T}}^{-n}$,
with $n_{\pi^{0}}=5.936\pm 0.012\mbox{(stat)}\pm 0.023\mbox{(sys)}$ and
$n_{\eta}=5.930\pm 0.029\mbox{(stat)}\pm 0.044\mbox{(sys)}$ for high momenta
of $p_{\mbox{\tiny T}}>3.5$ $\mbox{GeV}/c$. This is also reflected in the
$\eta/\pi^{0}$ ratio which is shown in Fig. 8. The ratio is flat for
$p_{\mbox{\tiny T}}>3.5$ $\mbox{GeV}/c$ with a constant value of
$C^{\eta/\pi^{0}}=0.455\pm 0.006\mbox{(stat)}\pm 0.014\mbox{(sys)}$. Despite
of the inability of NLO calculations to describe individual $\pi^{0}$ and
$\eta$ meson spectra, the $\eta/\pi^{0}$ ratio is reproduced fairly well, as
it can be followed from left part of Fig. 8. It has to be noted that a
different FF for the $\pi^{0}$ is used to compile the theory curve, namely
DSS07, since there is no recent calculation for the $\eta$ meson available
which could be compared to the recent DSS14 $\pi^{0}$ prediction. The
agreement of pQCD calculations with the data can be viewed as an indication
that the $\eta/\pi^{0}$ ratio is driven by the $\pi^{0}$ and $\eta$ meson FFs
in the factorized picture of pQCD. A comparison of the reported $\eta/\pi^{0}$
ratio to the different PYTHIA tunes indicates an agreement within
uncertainties down to $p_{\mbox{\tiny T}}\approx 1.5$ $\mbox{GeV}/c$, although
the shape, as well as the ratio, cannot be fully reproduced below
$p_{\mbox{\tiny T}}<1.5$ $\mbox{GeV}/c$ due to the already mentioned
deviations of PYTHIA tunes from data in this region.

Figure 8: Left: $\eta/\pi^{0}$ ratio compared to NLO pQCD predictions using
PDF CTEQ6M5 and FFs DSS07 for the $\pi^{0}$ and AESSS for the $\eta$, and
PYTHIA8.210 calculations using Tune 4C and Monash 2013 tune. The total
uncertainties of the measured $\eta/\pi^{0}$ ratio are of the order of $10$%
for most of the $p_{\mbox{\tiny T}}$ bins covered, increasing for lower and
higher momenta due to limited statistics as well as systematic effects. Right:
Comparison of the $\eta/\pi^{0}$ ratio to related, previous ALICE measurements
as well as other experiments at lower collision energies, for which total
uncertainties are drawn. Furthermore, a comparison to the $\eta/\pi^{0}$ ratio
obtained with $m_{\mbox{\tiny T}}$ scaling is added.

The validity of $m_{\mbox{\tiny T}}$ scaling is tested by means of the
$\eta/\pi^{0}$ ratio. For this purpose, the TCM parameterization of the
measured $\pi^{0}$ spectrum, given in Tab. 5, is used to obtain the $\eta$
spectrum via the application of $m_{\mbox{\tiny T}}$ scaling by replacing the
$\pi^{0}$ mass with the $\eta$ mass and using the normalization ratio
$C^{\eta}/C^{\pi^{0}}=0.455$. From these two spectra, the $\eta/\pi^{0}$ ratio
is constructed, plotted as blue curve in the right part of Fig. 8. The
measured $\eta/\pi^{0}$ ratio is consistent with the $m_{\mbox{\tiny T}}$
scaling prediction (blue curve) above $p_{\mbox{\tiny T}}>3.5$ $\mbox{GeV}/c$.
However, for smaller transverse momenta of $p_{\mbox{\tiny T}}<3.5$
$\mbox{GeV}/c$ the ratio of the measured $\eta/\pi^{0}$ ratio over the
$\eta/\pi^{0}$ ratio obtained with $m_{\mbox{\tiny T}}$ scaling, which can be
found in Ref. [38], constantly decreases and reaches about 45% at around $1$
$\mbox{GeV}/c$. For the region below $3.5$ $\mbox{GeV}/c$, $m_{\mbox{\tiny
T}}$ scaling is observed to be clearly broken with a significance of
6.2$\sigma$. Given this observation, the measured $\eta/\pi^{0}$ ratios in pp
collisions at $\sqrt{s}=2.76$ TeV and $7$ TeV, previously reported by ALICE
[9, 3], are re-evaluated. Whereas there is indication for a $m_{\mbox{\tiny
T}}$ scaling violation with 2.1$\sigma$ for $2.76$ TeV, we also observe a
significant disagreement of 5.7$\sigma$ for $7$ TeV. Hence, both ratios are
found to be consistent with our observation at $8$ TeV. Furthermore, both
$\eta/\pi^{0}$ ratios are fitted with a constant for $p_{\mbox{\tiny T}}>3.5$
$\mbox{GeV}/c$, yielding values of $C^{\eta/\pi^{0}}=0.474\pm
0.015\mbox{(stat)}\pm 0.024\mbox{(sys)}$ for $2.76$ TeV and
$C^{\eta/\pi^{0}}=0.476\pm 0.020\mbox{(stat)}\pm 0.020\mbox{(sys)}$ for $7$
TeV. They are consistent within uncertainties with the measured $\eta/\pi^{0}$
ratio at $8$ TeV for the given $p_{\mbox{\tiny T}}$ range. Therefore, all
three ALICE measurements are simultaneously fitted with a constant for
$p_{\mbox{\tiny T}}>3.5$ $\mbox{GeV}/c$ in order to obtain a combined value of
$C^{\eta/\pi^{0}}=0.459\pm 0.006\mbox{(stat)}\pm 0.011\mbox{(sys)}$. For the
region $p_{\mbox{\tiny T}}<3.5$ $\mbox{GeV}/c$, all collision energies covered
by ALICE also agree within experimental uncertainties, so that $\eta/\pi^{0}$
ratios may be claimed to be consistent within accuracy for ALICE measurements
in pp collisions at $\sqrt{s}=2.76$, $7$ and $8$ TeV.

Before the LHC era, the precision of $\eta/\pi^{0}$ measurements was not
sufficient to probe $m_{\mbox{\tiny T}}$ scaling over broad ranges of
$p_{\mbox{\tiny T}}$ with high statistics. PHENIX and NA27 provide the
$\eta/\pi^{0}$ ratio with highest accuracy at high and low $p_{\mbox{\tiny
T}}$ and therefore are compared to the reported measurement. PHENIX
measurements for pp collisions at $\sqrt{s}=200$ GeV are available only for
$p_{\mbox{\tiny T}}$ region $>2.25$ $\mbox{GeV}/c$ [63], where $\pi^{0}$ and
$\eta$ spectra are already described by $m_{\mbox{\tiny T}}$ scaling. However,
PHENIX notably does not apply any secondary $\pi^{0}$ correction concerning
weak decays, which further has to be taken into account when comparing with
data points from ALICE. Measurements of $\pi^{0}$ and $\eta$ spectra in pp
collisions at $\sqrt{s}=27.5$ GeV from NA27 [64] are used to obtain the
$\eta/\pi^{0}$ ratio in the $p_{\mbox{\tiny T}}$ range of $0.4<p_{\mbox{\tiny
T}}<1.6$ $\mbox{GeV}/c$. The paper does not mention a secondary correction of
$\pi^{0}$ spectrum; however, it cannot significantly change the conclusions to
be drawn from the measurement. Although the NA27 measurement provides the
world’s most precise published data points for the $\eta/\pi^{0}$ ratio at low
$p_{\mbox{\tiny T}}<2.0$ $\mbox{GeV}/c$ in the pre-LHC era for pp collisions,
it is not conclusive concerning $m_{\mbox{\tiny T}}$ scaling violation. The
first NA27 points at $p_{\mbox{\tiny T}}<1$ $\mbox{GeV}/c$ are consistent with
both the $m_{\mbox{\tiny T}}$ scaling curve and the new data from pp
collisions at $\sqrt{s}=2.76$, $7$ and $8$ TeV within uncertainties, whereas
for $p_{\mbox{\tiny T}}>1$ $\mbox{GeV}/c$ the results of NA27 show a tendency
to be above the $m_{\mbox{\tiny T}}$ scaling prediction, although
uncertainties become significant. A clearer confirmation of the
$m_{\mbox{\tiny T}}$ scaling at low $p_{\mbox{\tiny T}}$ is observed for other
particle species, such as kaons, $\phi$ and $J/\psi$ in pp collisions at
$\sqrt{s}=200$ GeV [13]. Whether the magnitude of $m_{\mbox{\tiny T}}$ scaling
violation depends on the collision energy can be clarified in future by
ongoing analysis of hadron spectra measurements in pp collisions at
$\sqrt{s}=13$ TeV delivered by the LHC.

##  7 Conclusion

The invariant differential cross sections of $\pi^{0}$ and $\eta$ mesons in pp
collisions at $\sqrt{s}$ = 8 TeV have been measured at mid-rapidity over a
wide $p_{\mbox{\tiny T}}$ range by the ALICE experiment, using four different
reconstruction methods for the $\pi^{0}$, and three for the $\eta$ meson. NLO
pQCD calculations with MSTW08 (PDF) with DSS14 (FF) for the $\pi^{0}$ and
CTEQ6M5 (PDF) with AESSS (FF) for the $\eta$ meson overestimate the measured
spectra of both neutral mesons. This discrepancy is also reported for pp
collisions at $\sqrt{s}=2.76$ TeV by ALICE. However, the ratio of
$\eta/\pi^{0}$ is reproduced by NLO pQCD calculations within uncertainties,
which is a test for the FFs in the factorized picture of pQCD. The prediction
from PYTHIA8.2 Tune 4C describes the $\eta$ spectrum within uncertainties for
$p_{\mbox{\tiny T}}>1.5$ $\mbox{GeV}/c$, but it is about $30\%$ larger than
the measured $\pi^{0}$ production cross section. On the other hand, the Monash
2013 tune agrees with the reported neutral meson measurements within 10% for
$p_{\mbox{\tiny T}}>1.5$ $\mbox{GeV}/c$. Both PYTHIA8.2 tunes are able to
reproduce the $\pi^{0}$ spectrum below $p_{\mbox{\tiny T}}<1.5$ $\mbox{GeV}/c$
within uncertainties, but fail to describe the $\eta$ spectrum in this region.
The $\eta/\pi^{0}$ ratio is described by $m_{\mbox{\tiny T}}$ scaling for
$p_{\mbox{\tiny T}}>3.5$ $\mbox{GeV}/c$, whereas a deviation from this
empirical scaling law is found for $p_{\mbox{\tiny T}}<3.5$ $\mbox{GeV}/c$
with a significance of $6.2\sigma$. Within experimental uncertainties, the
$\eta/\pi^{0}$ ratios measured by NA27, PHENIX and ALICE are in agreement for
the covered transverse momentum intervals of each measurement, representing pp
collisions starting at center of mass energies of $\sqrt{s}=27.5$ GeV up to
$\sqrt{s}=8$ TeV.

## Acknowledgements

We thank Werner Vogelsang and Marco Stratmann for providing the pQCD
calculations.

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: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung,
Technologie und Entwicklung, Austria; Ministry of Communications and High
Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional
de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science, Education and Sport and Croatian Science Foundation,
Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech
Republic; The Danish Council for Independent Research — Natural Sciences, the
Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark;
Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie
Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des
Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS),
France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie
(BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany;
General Secretariat for Research and Technology, Ministry of Education,
Research and Religions, Greece; National Research, Development and Innovation
Office, Hungary; Department of Atomic Energy Government of India (DAE) and
Council of Scientific and Industrial Research (CSIR), New Delhi, India;
Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion
of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y
Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología
(FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA),
Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO),
Netherlands; The Research Council of Norway, Norway; Commission on Science and
Technology for Sustainable Development in the South (COMSATS), Pakistan;
Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher
Education and National Science Centre, Poland; Korea Institute of Science and
Technology Information and National Research Foundation of Korea (NRF),
Republic of Korea; Ministry of Education and Scientific Research, Institute of
Atomic Physics and Romanian National Agency for Science, Technology and
Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of
Education and Science of the Russian Federation and National Research Centre
Kurchatov Institute, Russia; Ministry of Education, Science, Research and
Sport of the Slovak Republic, Slovakia; National Research Foundation of South
Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear
(CEADEN), Cubaenergía, Cuba, Ministerio de Ciencia e Innovacion and Centro de
Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain;
Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW),
Sweden; European Organization for Nuclear Research, Switzerland; National
Science and Technology Development Agency (NSDTA), Suranaree University of
Technology (SUT) and Office of the Higher Education Commission under NRU
project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey;
National Academy of Sciences of Ukraine, Ukraine; Science and Technology
Facilities Council (STFC), United Kingdom; National Science Foundation of the
United States of America (NSF) and United States Department of Energy, Office
of Nuclear Physics (DOE NP), United States of America.

## References

  * [1] D. J. Gross and F. Wilczek, “Asymptotically Free Gauge Theories. 1,” Phys. Rev. D8 (1973) 3633–3652.
  * [2] L. Evans and P. Bryant, “LHC Machine,” JINST 3 (2008) S08001.
  * [3] ALICE Collaboration, B. Abelev et al., “Neutral pion and $\eta$ meson production in proton-proton collisions at $\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV,” Phys. Lett. B717 (2012) 162–172, arXiv:1205.5724 [hep-ex].
  * [4] ALICE Collaboration, B. B. Abelev et al., “Neutral pion production at midrapidity in pp and Pb-Pb collisions at $\sqrt{s}$= 2.76 TeV,” Eur. Phys. J. C74 (2014) 3108, arXiv:1405.3794 [nucl-ex].
  * [5] D. d’Enterria, K. J. Eskola, I. Helenius, and H. Paukkunen, “Confronting current NLO parton fragmentation functions with inclusive charged-particle spectra at hadron colliders,” Nucl. Phys. B883 (2014) 615–628, arXiv:1311.1415 [hep-ph].
  * [6] D. de Florian, R. Sassot, and M. Stratmann, “Global analysis of fragmentation functions for pions and kaons and their uncertainties,” Phys. Rev. D75 (2007) 114010, arXiv:hep-ph/0703242 [hep-ph].
  * [7] D. de Florian, R. Sassot, and M. Stratmann, “Global analysis of fragmentation functions for protons and charged hadrons,” Phys. Rev. D76 (2007) 074033, arXiv:0707.1506 [hep-ph].
  * [8] D. de Florian, R. Sassot, M. Epele, R. J. Hernández-Pinto, and M. Stratmann, “Parton-to-Pion Fragmentation Reloaded,” Phys. Rev. D91 (2015) 014035, arXiv:1410.6027 [hep-ph].
  * [9] ALICE Collaboration, S. Acharya et al., “Production of ${\pi^{0}}$ and $\eta$ mesons up to high transverse momentum in pp collisions at 2.76 TeV,” Eur. Phys. J. C77 (2017) 339, arXiv:1702.00917 [hep-ex].
  * [10] D. d’Enterria, K. J. Eskola, I. Helenius, and H. Paukkunen, “LHC data challenges the contemporary parton-to-hadron fragmentation functions,” PoS DIS2014 (2014) 148, arXiv:1408.4659 [hep-ph].
  * [11] C. A. Aidala, F. Ellinghaus, R. Sassot, J. P. Seele, and M. Stratmann, “Global Analysis of Fragmentation Functions for Eta Mesons,” Phys. Rev. D83 (2011) 034002, arXiv:1009.6145 [hep-ph].
  * [12] M. Bourquin and J.-M. Gaillard, “A simple phenomenological description of hadron production,” Nucl. Phys. B114 (1976) 334 – 364.
  * [13] P. K. Khandai, P. Shukla, and V. Singh, “Meson spectra and $m_{T}$ scaling in $p+p$, $d+$Au, and Au + Au collisions at $\sqrt{s_{NN}}=200$ GeV,” Phys. Rev. C84 (2011) 054904, arXiv:1110.3929 [hep-ph].
  * [14] L. Altenkämper, F. Bock, C. Loizides, and N. Schmidt, “Applicability of transverse mass scaling in hadronic collisions at the LHC,” arXiv:1710.01933 [hep-ph].
  * [15] K. Jiang, Y. Zhu, W. Liu, H. Chen, C. Li, L. Ruan, Z. Tang, Z. Xu, and Z. Xu, “Onset of radial flow in p+p collisions,” Phys. Rev. C91 (2015) 024910, arXiv:1312.4230 [nucl-ex].
  * [16] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, “Parton distributions for the LHC,” Eur. Phys. J. C63 (2009) 189–285, arXiv:0901.0002 [hep-ph].
  * [17] W. Tung, H. Lai, A. Belyaev, J. Pumplin, D. Stump, and C.-P. Yuan, “Heavy quark mass effects in deep inelastic scattering and global QCD analysis,” JHEP 02 (2007) 053, arXiv:hep-ph/0611254 [hep-ph].
  * [18] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, “An Introduction to PYTHIA 8.2,” Comput. Phys. Commun. 191 (2015) 159–177, arXiv:1410.3012 [hep-ph].
  * [19] R. Corke and T. Sjöstrand, “Interleaved Parton Showers and Tuning Prospects,” JHEP 03 (2011) 032, arXiv:1011.1759 [hep-ph].
  * [20] P. Skands, S. Carrazza, and J. Rojo, “Tuning PYTHIA 8.1: the Monash 2013 Tune,” Eur. Phys. J. C74 (2014) 3024, arXiv:1404.5630 [hep-ph].
  * [21] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC,” JINST 3 (2008) S08002.
  * [22] ALICE Collaboration, B. B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC,” Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [23] ALICE Collaboration, P. Cortese et al., “ALICE electromagnetic calorimeter technical design report,” CERN-LHCC-2008-014, CERN-ALICE-TDR-014.
  * [24] ALICE Collaboration, G. Dellacasa et al., “ALICE technical design report of the photon spectrometer (PHOS),” CERN-LHCC-99-04.
  * [25] J. Alme et al., “The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events,” Nucl. Instrum. Meth. A622 (2010) 316–367, arXiv:1001.1950 [physics.ins-det].
  * [26] ALICE Collaboration, K. Aamodt et al., “Alignment of the ALICE Inner Tracking System with cosmic-ray tracks,” JINST 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det].
  * [27] ALICE EMCal Collaboration, U. Abeysekara et al., “ALICE EMCal Physics Performance Report,” arXiv:1008.0413 [physics.ins-det].
  * [28] ALICE Collaboration, P. Cortese et al., “ALICE technical design report on forward detectors: FMD, T0 and V0,” CERN-LHCC-2004-025.
  * [29] ALICE Collaboration, B. Abelev et al., “Measurement of inelastic, single- and double-diffraction cross sections in proton–proton collisions at the LHC with ALICE,” Eur. Phys. J. C73 (2013) 2456, arXiv:1208.4968 [hep-ex].
  * [30] J. Kral, T. Awes, H. Muller, J. Rak, and J. Schambach, “L0 trigger for the EMCal detector of the ALICE experiment,” Nucl. Instrum. Meth. A693 (2012) 261–267.
  * [31] D. Wang et al., “Level-0 trigger algorithms for the ALICE PHOS detector,” Nucl. Instrum. Meth. A629 (2011) 80–86.
  * [32] J. Adam et al., “Determination of the event collision time with the ALICE detector at the LHC,” Eur. Phys. J. Plus 132 (2017) 99, arXiv:1610.03055 [physics.ins-det].
  * [33] O. Bourrion, R. Guernane, B. Boyer, J. L. Bouly, and G. Marcotte, “Level-1 jet trigger hardware for the ALICE electromagnetic calorimeter at LHC,” JINST 5 (2010) C12048, arXiv:1010.2670 [physics.ins-det].
  * [34] S. van der Meer, “Calibration of the Effective Beam Height in the ISR.” CERN-ISR-PO-68-31, 1968.
  * [35] ALICE Collaboration, “ALICE luminosity determination for pp collisions at $\sqrt{s}=8$ TeV,”. https://cds.cern.ch/record/2255216.
  * [36] Particle Data Group Collaboration, C. Patrignani et al., “Review of Particle Physics,” Chin. Phys. C40 (2016) 100001.
  * [37] ALICE Collaboration, P. Cortese et al., “ALICE: Physics performance report, volume II,” J. Phys. G32 (2006) 1295–2040.
  * [38] ALICE Collaboration, “Supplemental figures: $\pi^{0}$ and $\eta$ meson production in proton-proton collisions at $\sqrt{s}=8$ TeV,”. http://cds.cern.ch/record/2282851.
  * [39] T. Awes, F. Obenshain, F. Plasil, S. Saini, S. Sorensen, and G. Young, “A simple method of shower localization and identification in laterally segmented calorimeters,” Nucl. Instrum. Meth. A311 (1992) 130 – 138.
  * [40] R. Fruhwirth, “Application of Kalman filtering to track and vertex fitting,” Nucl. Instrum. Meth. A262 (1987) 444–450.
  * [41] J. Podolanski and R. Armenteros, “III. Analysis of V-events,” Phil. Mag. 45 (1954) 13–30.
  * [42] T. Matulewicz et al., “Response of BaF2 detectors to photons of 3-50 MeV energy,” Nucl. Instrum. Meth. A289 (1990) 194–204.
  * [43] M. J. Oreglia, ”A Study of the Reactions $\psi^{\prime}\to\gamma\gamma\psi$”.  PhD thesis, SLAC, Stanford University, Stanford, California 94305, 1980\.  http://www.slac.stanford.edu/pubs/slacreports/slac-r-236.html.
  * [44] R. Engel, J. Ranft, and S. Roesler, “Hard diffraction in hadron hadron interactions and in photoproduction,” Phys. Rev. D52 (1995) 1459–1468, arXiv:hep-ph/9502319 [hep-ph].
  * [45] R. Brun, F. Bruyant, M. Maire, A. McPherson, and P. Zanarini, “GEANT3,” CERN-DD-EE-84-1 (1987) BASE001 1–3.
  * [46] ALICE Collaboration, K. Aamodt et al., “Strange particle production in proton-proton collisions at $\sqrt{s}=0.9$ TeV with ALICE at the LHC,” Eur. Phys. J. C71 (2011) 1594, arXiv:1012.3257 [hep-ex].
  * [47] ALICE Collaboration, B. B. Abelev et al., “Production of charged pions, kaons and protons at large transverse momenta in pp and Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ =2.76 TeV,” Phys. Lett. B736 (2014) 196–207, arXiv:1401.1250 [nucl-ex].
  * [48] ALICE Collaboration, J. Adam et al., “Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions,” Nature Phys. 13 (2017) 535–539, arXiv:1606.07424 [nucl-ex].
  * [49] L. Lyons, D. Gibaut, and P. Clifford, “How to Combine Correlated Estimates of a Single Physical Quantity,” Nucl. Instrum. Meth. A270 (1988) 110.
  * [50] A. Valassi, “Combining correlated measurements of several different physical quantities,” Nucl. Instrum. Meth. A500 (2003) 391–405.
  * [51] L. Lyons, Statistics For Nuclear And Particle Physicists.  Cambridge, UK: Univ. Pr., 1986.
  * [52] R. J. Barlow, Statistics: a guide to the use of statistical methods in the physical sciences, vol. 29.  John Wiley & Sons, 1989.
  * [53] A. Valassi and R. Chierici, “Information and treatment of unknown correlations in the combination of measurements using the BLUE method,” Eur. Phys. J. C74 (2014) 2717, arXiv:1307.4003 [physics.data-an].
  * [54] G. Lafferty and T. Wyatt, “Where to stick your data points: The treatment of measurements within wide bins,” Nucl. Instrum. Meth. A355 (1995) 541–547.
  * [55] A. Bylinkin, N. S. Chernyavskaya, and A. A. Rostovtsev, “Predictions on the transverse momentum spectra for charged particle production at LHC-energies from a two component model,” Eur. Phys. J. C75 (2015) 166, arXiv:1501.05235 [hep-ph].
  * [56] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” J. Statist. Phys. 52 (1988) 479–487.
  * [57] PHENIX Collaboration, A. Adare et al., “Inclusive cross section and double-helicity asymmetry for $\pi^{0}$ production at midrapidity in $p$$+$$p$ collisions at $\sqrt{s}=510$ GeV,” Phys. Rev. D93 (2016) 011501, arXiv:1510.02317 [hep-ex].
  * [58] PHENIX Collaboration, A. Adare et al., “Detailed measurement of the ${e}^{+}{e}^{-}$ pair continuum in $p+p$ and $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV and implications for direct photon production,” Phys. Rev. C 81 (2010) 034911, arXiv:0912.0244 [nucl-ex].
  * [59] TOTEM Collaboration, G. Antchev et al., “Luminosity-Independent Measurement of the Proton-Proton Total Cross Section at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$,” Phys. Rev. Lett. 111 (2013) 012001.
  * [60] ALICE Collaboration, B. B. Abelev et al., “Multiplicity dependence of the average transverse momentum in pp, p-Pb, and Pb-Pb collisions at the LHC,” Phys. Lett. B727 (2013) 371–380, arXiv:1307.1094 [nucl-ex].
  * [61] ALICE Collaboration, J. Adam et al., “Charged-particle multiplicities in proton–proton collisions at $\sqrt{s}=0.9$ to 8 TeV,” Eur. Phys. J. C77 (2017) 33, arXiv:1509.07541 [nucl-ex].
  * [62] ALICE Collaboration, J. Adam et al., “Measurement of pion, kaon and proton production in proton–proton collisions at $\sqrt{s}=7$ TeV,” Eur. Phys. J. C75 (2015) 226, arXiv:1504.00024 [nucl-ex].
  * [63] PHENIX Collaboration, A. Adare et al., “Cross section and double helicity asymmetry for eta mesons and their comparison to neutral pion production in p+p collisions at $\sqrt{s}=200$ GeV,” Phys. Rev. D83 (2011) 032001, arXiv:1009.6224 [hep-ex].
  * [64] LEBC-EHS Collaboration, M. Aguilar-Benitez et al., “Inclusive particle production in 400 GeV/c pp-interactions,” Z. Phys. C50 (1991) 405–426.

##  Appendix A The ALICE Collaboration

S. Acharyaorg137&J. Adamorg96&D. Adamováorg93&J. Adolfssonorg32&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg33&M. Agnelloorg29&N. Agrawalorg46&Z.
Ahammedorg137&N. Ahmadorg15&S.U. Ahnorg78&S. Aiolaorg141&A. Akindinovorg63&M.
Al-Turanyorg106&S.N. Alamorg137&J.L.B. Albaorg111&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg89&B. Alessandroorg57&R. Alfaro Molinaorg73&A.
Aliciorg11,org25,org52&A. Alkinorg3&J. Almeorg20&T. Altorg69&L.
Altenkamperorg20&I. Altsybeevorg136&C. Alves Garcia Pradoorg121&C.
Andreiorg86&D. Andreouorg33&H.A. Andrewsorg110&A. Andronicorg106&V.
Anguelovorg103&C. Ansonorg96&T. Antičićorg107&F. Antinoriorg55&P.
Antonioliorg52&R. Anwarorg124&L. Aphecetcheorg114&H. Appelshäuserorg69&S.
Arcelliorg25&R. Arnaldiorg57&O.W. Arnoldorg104,org34&I.C. Arseneorg19&M.
Arslandokorg103&B. Audurierorg114&A. Augustinusorg33&R. Averbeckorg106&M.D.
Azmiorg15&A. Badalàorg54&Y.W. Baekorg59,org77&S. Bagnascoorg57&R.
Bailhacheorg69&R. Balaorg100&A. Baldisseriorg74&M. Ballorg43&R.C.
Baralorg66,org87&A.M. Barbanoorg24&R. Barberaorg26&F. Barileorg51,org31&L.
Barioglioorg24&G.G. Barnaföldiorg140&L.S. Barnbyorg92&V. Barretorg131&P.
Bartaliniorg7&K. Barthorg33&E. Bartschorg69&M. Basileorg25&N. Bastidorg131&S.
Basuorg139&G. Batigneorg114&B. Batyunyaorg76&P.C. Batzingorg19&I.G.
Beardenorg90&H. Beckorg103&C. Beddaorg62&N.K. Beheraorg59&I. Belikovorg133&F.
Belliniorg25,org33&H. Bello Martinezorg2&R. Bellwiedorg124&L.G.E.
Beltranorg120&V. Belyaevorg82&G. Bencediorg140&S. Beoleorg24&A.
Bercuciorg86&Y. Berdnikovorg95&D. Berenyiorg140&R.A. Bertensorg127&D.
Berzanoorg33&L. Betevorg33&A. Bhasinorg100&I.R. Bhatorg100&A.K. Bhatiorg98&B.
Bhattacharjeeorg42&J. Bhomorg118&A. Bianchiorg24&L. Bianchiorg124&N.
Bianchiorg49&C. Bianchinorg139&J. Bielčíkorg37&J. Bielčíkováorg93&A.
Bilandzicorg34,org104&G. Biroorg140&R. Biswasorg4&S. Biswasorg4&J.T.
Blairorg119&D. Blauorg89&C. Blumeorg69&G. Bocaorg134&F.
Bockorg103,org81,org33&A. Bogdanovorg82&L. Boldizsárorg140&M. Bombaraorg38&G.
Bonomiorg135&M. Bonoraorg33&J. Bookorg69&H. Borelorg74&A.
Borissovorg17,org103&M. Borriorg126&E. Bottaorg24&C. Bourjauorg90&L.
Bratrudorg69&P. Braun-Munzingerorg106&M. Bregantorg121&T.A. Brokerorg69&M.
Brozorg37&E.J. Bruckenorg44&E. Brunaorg57&G.E. Brunoorg33,org31&D.
Budnikovorg108&H. Bueschingorg69&S. Bufalinoorg29&P. Buhlerorg113&P.
Buncicorg33&O. Buschorg130&Z. Butheleziorg75&J.B. Buttorg14&J.T.
Buxtonorg16&J. Cabalaorg116&D. Caffarriorg33,org91&H. Cainesorg141&A.
Calivaorg62,org106&E. Calvo Villarorg111&P. Cameriniorg23&A.A. Caponorg113&F.
Carenaorg33&W. Carenaorg33&F. Carnesecchiorg25,org11&J. Castillo
Castellanosorg74&A.J. Castroorg127&E.A.R. Casulaorg53&C. Ceballos
Sanchezorg9&P. Cerelloorg57&S. Chandraorg137&B. Changorg125&S.
Chapelandorg33&M. Chartierorg126&S. Chattopadhyayorg137&S.
Chattopadhyayorg109&A. Chauvinorg34,org104&C. Cheshkovorg132&B.
Cheynisorg132&V. Chibante Barrosoorg33&D.D. Chinellatoorg122&S. Choorg59&P.
Chochulaorg33&M. Chojnackiorg90&S. Choudhuryorg137&T. Chowdhuryorg131&P.
Christakoglouorg91&C.H. Christensenorg90&P. Christiansenorg32&T.
Chujoorg130&S.U. Chungorg17&C. Cicaloorg53&L. Cifarelliorg11,org25&F.
Cindoloorg52&J. Cleymansorg99&F. Colamariaorg31&D. Colellaorg33,org64,org51&A.
Colluorg81&M. Colocciorg25&M. Concasorg57orgI&G. Conesa Balbastreorg80&Z.
Conesa del Valleorg60&M.E. Connorsorg141orgII&J.G. Contrerasorg37&T.M.
Cormierorg94&Y. Corrales Moralesorg57&I. Cortés Maldonadoorg2&P.
Corteseorg30&M.R. Cosentinoorg123&F. Costaorg33&S. Costanzaorg134&J.
Crkovskáorg60&P. Crochetorg131&E. Cuautleorg71&L. Cunqueiroorg70&T.
Dahmsorg34,org104&A. Daineseorg55&M.C. Danischorg103&A. Danuorg67&D.
Dasorg109&I. Dasorg109&S. Dasorg4&A. Dashorg87&S. Dashorg46&S.
Deorg47,org121&A. De Caroorg28&G. de Cataldoorg51&C. de Contiorg121&J. de
Cuvelandorg40&A. De Falcoorg22&D. De Gruttolaorg28,org11&N. De Marcoorg57&S.
De Pasqualeorg28&R.D. De Souzaorg122&H.F. Degenhardtorg121&A.
Deistingorg106,org103&A. Delofforg85&C. Deplanoorg91&P. Dhankherorg46&D. Di
Bariorg31&A. Di Mauroorg33&P. Di Nezzaorg49&B. Di Ruzzaorg55&T. Dietelorg99&P.
Dillensegerorg69&R. Diviàorg33&Ø. Djuvslandorg20&A. Dobrinorg33&D. Domenicis
Gimenezorg121&B. Dönigusorg69&O. Dordicorg19&L.V.R. Doremalenorg62&A.K.
Dubeyorg137&A. Dublaorg106&L. Ducrouxorg132&A.K. Duggalorg98&M.
Dukhishyamorg87&P. Dupieuxorg131&R.J. Ehlersorg141&D. Eliaorg51&E.
Endressorg111&H. Engelorg68&E. Eppleorg141&B. Erazmusorg114&F. Erhardtorg97&B.
Espagnonorg60&S. Esumiorg130&G. Eulisseorg33&J. Eumorg17&D. Evansorg110&S.
Evdokimovorg112&L. Fabbiettiorg104,org34&J. Faivreorg80&A. Fantoniorg49&M.
Faselorg94,org81&L. Feldkamporg70&A. Felicielloorg57&G. Feofilovorg136&A.
Fernández Téllezorg2&A. Ferrettiorg24&A. Festantiorg27,org33&V.J.G.
Feuillardorg74,org131&J. Figielorg118&M.A.S. Figueredoorg121&S.
Filchaginorg108&D. Finogeevorg61&F.M. Fiondaorg20,org22&M. Florisorg33&S.
Foertschorg75&P. Fokaorg106&S. Fokinorg89&E. Fragiacomoorg58&A.
Francesconorg33&A. Franciscoorg114&U. Frankenfeldorg106&G.G. Fronzeorg24&U.
Fuchsorg33&C. Furgetorg80&A. Fursorg61&M. Fusco Girardorg28&J.J.
Gaardhøjeorg90&M. Gagliardiorg24&A.M. Gagoorg111&K. Gajdosovaorg90&M.
Gallioorg24&C.D. Galvanorg120&P. Ganotiorg84&C. Garabatosorg106&E. Garcia-
Solisorg12&K. Gargorg26&C. Gargiuloorg33&P. Gasikorg104,org34&E.F.
Gaugerorg119&M.B. Gay Ducatiorg72&M. Germainorg114&J. Ghoshorg109&P.
Ghoshorg137&S.K. Ghoshorg4&P. Gianottiorg49&P. Giubellinoorg33,org106,org57&P.
Giubilatoorg27&E. Gladysz-Dziadusorg118&P. Glässelorg103&D.M. Goméz
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Gorbunovorg40&L. Görlichorg118&S. Gotovacorg117&V. Grabskiorg73&L.K.
Graczykowskiorg138&K.L. Grahamorg110&L. Greinerorg81&A. Grelliorg62&C.
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Hetlandorg35&H. Hillemannsorg33&C. Hillsorg126&B. Hippolyteorg133&J.
Hladkyorg65&B. Hohlwegerorg104&D. Horakorg37&S. Hornungorg106&R.
Hosokawaorg130,org80&P. Hristovorg33&C. Hughesorg127&T.J. Humanicorg16&N.
Hussainorg42&T. Hussainorg15&D. Hutterorg40&D.S. Hwangorg18&S.A. Iga
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Izucheevorg112&B. Jacakorg81&N. Jacazioorg25&P.M. Jacobsorg81&M.B.
Jadhavorg46&J. Jadlovskyorg116&S. Jaelaniorg62&C. Jahnkeorg34&M.J.
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Karorg137&A. Karasu Uysalorg79&O. Karavichevorg61&T. Karavichevaorg61&L.
Karayanorg103,org106&P. Karczmarczykorg33&E. Karpechevorg61&U.
Kebschullorg68&R. Keidelorg143&D.L.D. Keijdenerorg62&M. Keilorg33&B.
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Lapidusorg141&C. Laraorg68&A. Lardeuxorg74,org19&A. Lattucaorg24&E.
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Ohorg141&A. Ohlsonorg33,org103&T. Okuboorg45&L. Olahorg140&J.
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Poporg86&H. Poppenborgorg70&S. Porteboeuf-Houssaisorg131&V.
Pozdniakovorg76&S.K. Prasadorg4&R. Preghenellaorg52&F. Prinoorg57&C.A.
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Pujahariorg139&V. Puninorg108&J. Putschkeorg139&S. Rahaorg4&S. Rajputorg100&J.
Rakorg125&A. Rakotozafindrabeorg74&L. Ramelloorg30&F. Ramiorg133&D.B.
Ranaorg124&R. Raniwalaorg101&S. Raniwalaorg101&S.S. Räsänenorg44&B.T.
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Reidtorg33&X. Renorg7&R. Renfordtorg69&A.R. Reolonorg49&A. Reshetinorg61&K.
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Richterorg19&P. Riedlerorg33&W. Rieglerorg33&F. Riggiorg26&C. Risteaorg67&M.
Rodríguez Cahuantziorg2&K. Røedorg19&E. Rogochayaorg76&D. Rohrorg33,org40&D.
Röhrichorg20&P.S. Rokitaorg138&F. Ronchettiorg49&E.D. Rosasorg71&P.
Rosnetorg131&A. Rossiorg27,org55&A. Rotondiorg134&F. Roukoutakisorg84&A.
Royorg47&C. Royorg133&P. Royorg109&O.V. Ruedaorg71&R. Ruiorg23&B.
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Sandovalorg73&D. Sarkarorg137&N. Sarkarorg137&P. Sarmaorg42&M.H.P. Sasorg62&E.
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Schmidtorg106&H.R. Schmidtorg102&M.O. Schmidtorg103&M. Schmidtorg102&N.V.
Schmidtorg94,org69&J. Schukraftorg33&Y. Schutzorg33,org133&K. Schwarzorg106&K.
Schwedaorg106&G. Scioliorg25&E. Scomparinorg57&M. Šefčíkorg38&J.E.
Segerorg96&Y. Sekiguchiorg129&D. Sekihataorg45&I. Selyuzhenkovorg106,org82&K.
Senosiorg75&S. Senyukovorg3,org133,org33&E. Serradillaorg73&P. Settorg46&A.
Sevcencoorg67&A. Shabanovorg61&A. Shabetaiorg114&R. Shahoyanorg33&W.
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Sharmaorg100&M. Sharmaorg100&N. Sharmaorg98,org127&A.I. Sheikhorg137&K.
Shigakiorg45&Q. Shouorg7&K. Shtejerorg9,org24&Y. Sibiriakorg89&S.
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Singarajuorg137&R. Singhorg87&V. Singhalorg137&T. Sinhaorg109&B. Sitarorg36&M.
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Snellingsorg62&T.W. Snellmanorg125&J. Songorg17&M. Songorg142&F.
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Sputowskaorg118&B.K. Srivastavaorg105&J. Stachelorg103&I. Stanorg67&P.
Stankusorg94&E. Stenlundorg32&D. Stoccoorg114&M.M. Storetvedtorg35&P.
Strmenorg36&A.A.P. Suaideorg121&T. Sugitateorg45&C. Suireorg60&M.
Suleymanovorg14&M. Suljicorg23&R. Sultanovorg63&M. Šumberaorg93&S.
Sumowidagdoorg48&K. Suzukiorg113&S. Swainorg66&A. Szaboorg36&I. Szarkaorg36&U.
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Tarhiniorg60&M. Tariqorg15&M.G. Tarzilaorg86&A. Tauroorg33&G. Tejeda
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Teyssierorg132&D. Thakurorg47&S. Thakurorg137&D. Thomasorg119&F.
Thoresenorg90&R. Tieulentorg132&A. Tikhonovorg61&A.R. Timminsorg124&A.
Toiaorg69&S.R. Torresorg120&S. Tripathyorg47&S. Trogoloorg24&G.
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Tveterorg19&K. Ullalandorg20&E.N. Umakaorg124&A. Urasorg132&G.L. Usaiorg22&A.
Utrobicicorg97&M. Valaorg116,org64&J. Van Der Maarelorg62&J.W. Van
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Vargaorg140&A. Vargasorg2&M. Vargyasorg125&R. Varmaorg46&M. Vasileiouorg84&A.
Vasilievorg89&A. Vauthierorg80&O. Vázquez Doceorg104,org34&V.
Vecherninorg136&A.M. Veenorg62&A. Velureorg20&E. Vercellinorg24&S. Vergara
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Viinikainenorg125&Z. Vilakaziorg128&O. Villalobos Baillieorg110&A. Villatoro
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Vislaviciusorg32&A. Vodopyanovorg76&M.A. Völklorg103,org102&K.
Voloshinorg63&S.A. Voloshinorg139&G. Volpeorg31&B. von Hallerorg33&I.
Vorobyevorg104,org34&D. Voscekorg116&D. Vranicorg33,org106&J. Vrlákováorg38&B.
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Wenzelorg33&J.P. Wesselsorg70&U. Westerhofforg70&A.M. Whiteheadorg99&J.
Wiechulaorg69&J. Wikneorg19&G. Wilkorg85&J. Wilkinsonorg103,org52&G.A.
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Zaviyalovorg108&H. Zbroszczykorg138&M. Zhalovorg95&H. Zhangorg20,org7&X.
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Zichichiorg25,org11&A. Zimmermannorg103&M.B. Zimmermannorg33&G.
Zinovjevorg3&J. Zmeskalorg113&S. Zouorg7&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIGeorgia State University, Atlanta, Georgia, United States

orgIIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIVDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgVInstitute of Theoretical Physics, University of Wroclaw, Poland

## 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, Lyon, France

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

org10Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org11Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org12Chicago State University, Chicago, Illinois, United States

org13China Institute of Atomic Energy, Beijing, China

org14COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org15Department of Physics, Aligarh Muslim University, Aligarh, India

org16Department of Physics, Ohio State University, Columbus, Ohio, United
States

org17Department of Physics, Pusan National University, Pusan, Republic of
Korea

org18Department of Physics, Sejong University, Seoul, Republic of Korea

org19Department of Physics, University of Oslo, Oslo, Norway

org20Department of Physics and Technology, University of Bergen, Bergen,
Norway

org21Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org22Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org23Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

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

org25Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

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

org28Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org29Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org30Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org31Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org32Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org33European Organization for Nuclear Research (CERN), Geneva, Switzerland

org34Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org35Faculty of Engineering, Bergen University College, Bergen, Norway

org36Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org37Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org38Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org39Faculty of Technology, Buskerud and Vestfold University College,
Tonsberg, Norway

org40Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org41Gangneung-Wonju National University, Gangneung, Republic of Korea

org42Gauhati University, Department of Physics, Guwahati, India

org43Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org44Helsinki Institute of Physics (HIP), Helsinki, Finland

org45Hiroshima University, Hiroshima, Japan

org46Indian Institute of Technology Bombay (IIT), Mumbai, India

org47Indian Institute of Technology Indore, Indore, India

org48Indonesian Institute of Sciences, Jakarta, Indonesia

org49INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org50INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy

org51INFN, Sezione di Bari, Bari, Italy

org52INFN, Sezione di Bologna, Bologna, Italy

org53INFN, Sezione di Cagliari, Cagliari, Italy

org54INFN, Sezione di Catania, Catania, Italy

org55INFN, Sezione di Padova, Padova, Italy

org56INFN, Sezione di Roma, Rome, Italy

org57INFN, Sezione di Torino, Turin, Italy

org58INFN, Sezione di Trieste, Trieste, Italy

org59Inha University, Incheon, Republic of Korea

org60Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org61Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org62Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org63Institute for Theoretical and Experimental Physics, Moscow, Russia

org64Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org65Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org66Institute of Physics, Bhubaneswar, India

org67Institute of Space Science (ISS), Bucharest, Romania

org68Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org71Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org72Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org73Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org74IRFU, CEA, Université Paris-Saclay, Saclay, France

org75iThemba LABS, National Research Foundation, Somerset West, South Africa

org76Joint Institute for Nuclear Research (JINR), Dubna, Russia

org77Konkuk University, Seoul, Republic of Korea

org78Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org79KTO Karatay University, Konya, Turkey

org80Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org81Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org82Moscow Engineering Physics Institute, Moscow, Russia

org83Nagasaki Institute of Applied Science, Nagasaki, Japan

org84National and Kapodistrian University of Athens, Physics Department,
Athens, Greece

org85National Centre for Nuclear Studies, Warsaw, Poland

org86National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org87National Institute of Science Education and Research, HBNI, Jatni, India

org88National Nuclear Research Center, Baku, Azerbaijan

org89National Research Centre Kurchatov Institute, Moscow, Russia

org90Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org91Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org92Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org93Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org94Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org95Petersburg Nuclear Physics Institute, Gatchina, Russia

org96Physics Department, Creighton University, Omaha, Nebraska, United States

org97Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Cape Town, Cape Town, South Africa