2020 122 16 June Production of $\omega$ mesons in pp collisions at
$\sqrt{s}=$7\text{\text{ }}\mathrm{T}\mathrm{e}\mathrm{V}$$ ALICE
Collaboration††thanks: See Appendix A for the list of collaboration members
ALICE Collaboration

The invariant differential cross section of inclusive $\omega(782)$ meson
production at midrapidity ($|y|<0.5$) in pp collisions at
$\sqrt{s}=$7\text{\text{ }}\mathrm{T}\mathrm{e}\mathrm{V}$$ was measured with
the ALICE detector at the LHC over a transverse momentum range of
$2<p_{\mathrm{T}}<$17\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$. The
$\omega$ meson was reconstructed via its
$\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}$ decay channel. The measured $\omega$
production cross section is compared to various calculations: PYTHIA 8.2
Monash 2013 describes the data, while PYTHIA 8.2 Tune 4C overestimates the
data by about 50%. A recent NLO calculation, which includes a model describing
the fragmentation of the whole vector-meson nonet, describes the data within
uncertainties below $$6\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$,
while it overestimates the data by up to 50% for higher $p_{\mathrm{T}}$. The
$\omega/\pi^{0}$ ratio is in agreement with previous measurements at lower
collision energies and the PYTHIA calculations. In addition, the measurement
is compatible with transverse mass scaling within the measured
$p_{\mathrm{T}}$ range and the ratio is constant with
$C^{\omega/\pi^{0}}=0.67\pm 0.03\text{~{}(stat)~{}}\pm 0.04\text{~{}(sys)~{}}$
above a transverse momentum of $$2.5\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$.

##  1 Introduction

Measurements of hadron production cross sections in proton-proton (pp)
collisions at high energies are important to test our understanding of strong
interaction and its underlying theory of Quantum Chromodynamics (QCD) [1]. Its
perturbative treatment (pQCD) becomes feasible for predictions of particle
production in hard scattering processes that have a sufficiently high momentum
transfer $Q^{2}$. This is possible by factorizing [2] the scattering process
into three contributions: a QCD matrix element describing the scattering of
partons, a parton distribution function (PDF) [3] describing the probability
to find a scattering parton within each colliding hadron, and a fragmentation
function (FF) [4] that relates the final-state parton momentum to the momentum
of an observed hadron. While the QCD matrix element can be calculated in pQCD
for sufficiently hard scales, the FFs and PDFs are obtained by global fits of
experimental data at various collision energies [5]. However, most particles
are produced in soft scattering processes that involve small momentum
transfers and therefore can not be calculated within pQCD. In this regime,
calculations rely on phenomenological models that also require experimental
verification.

Comparison of measured particle spectra with calculations is essential to test
their underlying assumptions and provide constraints for the FFs and the PDFs.
For example, recent measurements of $\pi^{0}$ and $\eta$ mesons [6, 7, 8] at
several LHC collision energies constrained gluon fragmentation [9] in a regime
not accessible by measurements at lower collision energies. Like the $\pi^{0}$
and $\eta$ mesons, the $\omega$ meson is comprised mainly of light valence
quarks and hence has similar flavor content. However, it has spin 1 and is
heavier than the $\pi^{0}$ and $\eta$ with a mass of $$782\text{\text{
}}\mathrm{M}\mathrm{e}\mathrm{V}$/c^{2}$ [10]. These differences make the
$\omega$ meson an interesting complementary probe to improve our understanding
of hadron production in high-energy collisions. Even though there have been
several theoretical efforts to describe the fragmentation into pseudoscalar
mesons and baryons such as $\pi$, K, $\eta$ and protons [11, 12], only a few
theoretical models exist to describe the fragmentation into vector mesons, due
to a lack of experimental data. Nonetheless, recent efforts [13, 14] have been
made to describe the fragmentation into the entire vector meson nonet using a
model with broken SU(3) symmetry by analysing RHIC (pp) and LEP ($e^{+}e^{-}$)
data.

This article presents the invariant differential cross section of inclusive
$\omega$ meson production at mid-rapidity ($|y|<0.5$) in pp collisions at
$\sqrt{s}=$7\text{\text{ }}\mathrm{T}\mathrm{e}\mathrm{V}$$. The cross section
of $\omega$ production in hadronic interactions has been measured at collision
energies of $\sqrt{s}=$62\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$$ [15]
and $\sqrt{s}=$200\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$$ [16, 17, 18]
at ISR and RHIC respectively. At LHC energies, $\omega$ production has only
been measured by ALICE at forward rapidities ($2.5<y<4.0$) in pp collision at
$7\text{\text{ }}\mathrm{T}\mathrm{e}\mathrm{V}$ [19] in a transverse momentum
($p_{\mathrm{T}}$) range of $1<$ $p_{\mathrm{T}}$ $<$5\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$. The results reported here provide the
first measurement of $\omega$ production at mid-rapidity at LHC energies, and
in a wide $p_{\mathrm{T}}$ range of $2<p_{\mathrm{T}}<$17\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$, which tests existing calculations in
this regime and provides input for future theoretical studies of vector meson
fragmentation functions. In addition, the $\omega/\pi^{0}$ production ratio as
a function of $p_{\mathrm{T}}$ is compared to results of measurements at lower
collision energies. This ratio also tests the validity of transverse mass
($m_{\mathrm{T}}$) scaling [20] for $\omega$ mesons at LHC energies, which is
typically applied to estimate hadronic backgrounds in direct photon or di-
electron measurements in situations where no measured hadron spectra are
available. The empirical scaling rule, which was established in measurements
of identified particle spectra at lower collision energies at ISR and RHIC
[21], states that the $p_{\mathrm{T}}$-differential yields of most particles
can be described as $E\derivative*[3]{\sigma}{p}=C^{h}f(m_{\mathrm{T}})$,
where $f(m_{\mathrm{T}})$ is a universal function for all hadron species and
$C^{h}$ is a constant normalisation factor.

The article is structured as follows:

##  2 sec:alicedetector

briefly describes the ALICE sub-detectors, with a focus on those relevant for
the measurement. Details on the event selection and signal extraction are
given in Secs. 4 to 6. Sources of systematic uncertainties are discussed in
Sec. 7. The data and comparisons to model predictions are presented in Sec. 8.
Finally, conclusions are provided in Sec. 9.

##  3 ALICE detector

The $\omega$ meson was reconstructed via its decay to $\pi^{+}\pi^{-}\pi^{0}$,
where in turn the $\pi^{0}$ decays to two photons. This strategy required the
reconstruction of charged tracks in the ALICE central tracking system,
composed of the Inner Tracking System (ITS) [22] and the Time Projection
Chamber (TPC) [23], and the reconstruction of photons using the
ElectroMagnetic Calorimeter (EMCal) [24, 25] and the Photon Spectrometer
(PHOS) [26]. In addition, photons were reconstructed using the Photon
Conversion Method (PCM) [27], which exploits the capability of the central
tracking system to reconstruct photons from electron-positron track pairs. A
detailed description of the ALICE detector system and its performance can be
found in Refs. [28] and [27], respectively. Below, a brief overview of the
previously mentioned detectors and the V0 detector [29], used for the minimum
bias trigger, is given.

The ITS is positioned closest to the nominal interaction point and consists of
two layers of Silicon Pixel Detectors (SPD), two layers of Silicon Drift
Detectors (SDD) and two outermost layers of Silicon Strip Detectors (SSD). The
layers are positioned between $3.9\text{\text{ }}\mathrm{c}\mathrm{m}$ and
$43.0\text{\text{ }}\mathrm{c}\mathrm{m}$ radial distance from the beamline,
where the two SPD layers cover a pseudorapidity range of $|\eta|<2$ and
$|\eta|<1.4$, respectively. The SDD and SSD have a pseudorapidity coverage of
$|\eta|<0.9$ and $|\eta|<1.0$, respectively. The ITS is used for the tracking
of charged particles and the reconstruction of the primary vertex.

The TPC is a large ($90\text{\text{ }}\mathrm{m}^{3}$) cylindrical drift
detector, which allows for the measurement of charged particles and their
identification via specific energy loss ($\derivative*{E}{x}$) measurements.
The TPC covers a pseudorapidity range of $|\eta|<0.9$ over the full azimuth
and enables the measurement of up to 159 space points per track. A large
solenoidal magnet surrounding the central barrel detectors provides a magnetic
field of $B=$0.5\text{\text{ }}\mathrm{T}$$, which allows one to reconstruct
tracks down to $p_{\mathrm{T}}\approx$100\text{\text{
}}\mathrm{M}\mathrm{e}\mathrm{V}$/c$. For the reconstruction of charged
particles in the ITS and TPC, a transverse momentum resolution of about $1\%$
at $$1\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$ is achieved, which
decreases to about $3\%$ at $$10\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$ [23].

The EMCal is a Pb-scintillator sampling calorimeter, which covered an
azimuthal range of $\Delta\varphi=$40\text{\text{
}}\mathrm{\SIUnitSymbolDegree}$$ and $|\eta|<0.67$ in pseudorapidity during
2010 data taking. In that period, it was comprised of 4 super modules, each
consisting of 288 modules. The module consists of four towers with a size of
$\approx 6\times$6\text{\text{ }}\mathrm{c}\mathrm{m}^{2}$$, corresponding to
approximately twice the Molière radius. Each tower is made up of 140
alternating lead and scintillator layers, where the latter are connected to
Avalanche Photo Diodes (APDs) that measure the scintillation light of the
electromagnetic showers produced by particles traversing the lead absorber.
The energy resolution is given by $\sigma_{E}/E=4.8\%/E\oplus
11.3\%/\sqrt{E}\oplus 1.7\%$ with energy $E$ in units of GeV [25].

The PHOS is an electromagnetic calorimeter with high granularity based on
lead-tungstate (Pb$\text{WO}_{4}$) scintillation crystals. At the time these
data were collected, it had an acceptance of $\Delta\varphi=$60\text{\text{
}}\mathrm{\SIUnitSymbolDegree}$$ and $|\eta|<0.12$, divided into three
modules, each consisting of 3584 crystals that are connected to APDs. A high
granularity is achieved by small crystal size of $\approx
2.2\times$2.2\text{\text{ }}\mathrm{c}\mathrm{m}^{2}$$, where the lateral
dimensions of the cells are only slightly larger than the Pb$\text{WO}_{4}$
Molière radius of $2\text{\text{ }}\mathrm{c}\mathrm{m}$. The high light yield
of the Pb$\text{WO}_{4}$ crystals operated at $-25\text{\text{
}}\mathrm{\SIUnitSymbolCelsius}$ results in an energy resolution of
$\sigma_{E}/E=1.3\%/E\oplus 3.6\%/\sqrt{E}\oplus 1.1\%$ with energy $E$ in
units of GeV [30].

The V0 detector provides the minimum bias triggers and is employed to reduce
background events, such as beam-gas interactions and out-of-bunch pileup. It
consists of two scintillator arrays located in the forward and backward
rapidity regions of the ALICE apparatus, covering a pseudorapidity of
$2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively.

##  4 Event and track selection

The pp collision data used for the $\omega$ meson measurement were recorded by
the ALICE experiment in 2010 at a centre-of-mass energy of
$\sqrt{s}=$7\text{\text{ }}\mathrm{T}\mathrm{e}\mathrm{V}$$. In 2010, a
minimum bias trigger $\text{MB}_{\text{OR}}$, which required a signal either
in the SPD or in one of the V0 scintillator arrays, was used. The total
inelastic pp collision cross section was determined on the basis of the van
der Meer scan and was found to be
$\sigma_{\text{inel}}=73.2^{+2.0}_{-4.6}\text{(model)}\pm
2.6\text{(lumi)}\,$\mathrm{mb}$$ [31]. The corresponding cross section of the
$\text{MB}_{\text{OR}}$ trigger was $\sigma_{\text{MB}_{\text{OR}}}=$62.4\pm
2.2\text{\text{ }}\mathrm{mb}$$. Beam-induced background events, such as beam-
gas interactions or out-of-bunch pileup, are rejected offline by using the
timing information from the V0 detectors and the number of reconstructed hit
points and track segments in the SPD, which are expected to be uncorrelated
for background events. The rejection of in-bunch pileup events, where multiple
interactions occur per bunch crossing, was achieved by requiring that only a
single primary vertex is reconstructed with the SPD per event. Moreover,
collision events with a reconstructed vertex more than $10\text{\text{
}}\mathrm{c}\mathrm{m}$ away from the nominal interaction point along the beam
axis were rejected. The integrated luminosities
$\mathcal{L}_{\text{int}}=N_{\text{evt}}/\sigma_{\text{MB}_{\text{OR}}}$ were
determined to be $\mathcal{L}_{\text{int}}^{\text{EMCal}}=$6.4\pm
0.2\text{\text{ }}\mathrm{n}\mathrm{b}^{-1}$$ and
$\mathcal{L}_{\text{int}}^{\text{PHOS}}=$6.0\pm 0.2\text{\text{
}}\mathrm{n}\mathrm{b}^{-1}$$ for the measurement involving the EMCal and
PHOS, respectively. The integrated luminosity of the sample using only the PCM
for photon reconstruction amounts to
$\mathcal{L}_{\text{int}}^{\text{PCM}}=$7.4\pm 0.3\text{\text{
}}\mathrm{n}\mathrm{b}^{-1}$$.

Charged pion trajectories (tracks) with $|\eta|<0.9$ were reconstructed in the
ITS and TPC, requiring at least 70 crossed cathode pad rows in the TPC and at
least one hit in any of the layers of the ITS. Furthermore, the $\chi^{2}$ of
the track refit procedure per TPC space point was required to be below 4 and
tracks with a momentum below $$100\text{\text{
}}\mathrm{M}\mathrm{e}\mathrm{V}$/c$ were rejected. The tracks were loosely
constrained to the collision vertex by requiring a maximum distance of closest
approach of a few centimeters to the collision vertex in beam direction and
transverse plane. The resolution of the transverse distance to the primary
vertex for ITS and TPC charged particle tracks is below $150\text{\text{
}}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ for
$p_{\mathrm{T}}$$\gtrsim$0.5\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$
[27]. Furthermore, charged pions can be identified using the specific energy
loss $\derivative*{E}{x}$ along the track in the TPC [32].

##  5 Photon measurement

To enhance the probability of the reconstruction of $\pi^{0}$ mesons, all
methods to measure photons and $\pi^{0}$s at midrapidity with ALICE were
exploited. The EMCal and the PHOS allow for the measurement of photons via
their electromagnetic shower deposits above $\sim 0.5\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$, while the PCM enables the measurement of
photons down to lower $p_{\mathrm{T}}$ by exploiting the $e^{+}e^{-}$ pair
creation by a photon within the inner detector material. Looser photon
selection criteria as in previous publications, see e.g. Ref. [33], were
applied to increase the $\omega$ reconstruction efficiency.

The electromagnetic shower produced in the EMCal or PHOS by an incoming
particle usually spreads over multiple adjacent towers, requiring the
combination of the individual energy depositions to so-called clusters, which
is achieved by clusterisation algorithms [27]. Each reconstructed cluster in
the EMCal and PHOS was required to have a total energy of
$E_{\text{clus}}>$0.7\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$$ and
$0.3\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$ respectively to suppress
contributions from minimum-ionising particles and noise. Additionally, in case
of the EMCal, it ensures a good timing resolution. Detector noise in a single
tower was removed by only selecting clusters with at least $2$ (EMCal) or $3$
(PHOS) towers for analysis. In order to remove clusters from pileup events
originating from subsequent bunch crossings, which occur in
$\approx$150\text{\text{ }}\mathrm{n}\mathrm{s}$$ intervals, a cut on the
timing of the leading tower for EMCal clusters of $-$100\text{\text{
}}\mathrm{n}\mathrm{s}$<t_{\text{cluster}}<$100\text{\text{
}}\mathrm{n}\mathrm{s}$$ with respect to the collision time was applied.
Photon clusters were selected according to their cluster shape and,
additionally, a track-matching procedure was applied to suppress clusters
originating from charged particles reconstructed in the tracking system. The
EMCal cluster shape is parametrised by the larger eigenvalue
$\sigma_{\text{long}}^{2}$ of the dispersion matrix of the shower shape
ellipse [33, 34]. A requirement of $0.1\leq\sigma_{\text{long}}^{2}\leq 0.5$
was imposed, where the lower threshold removes contamination from non-physical
background. The upper threshold suppresses elongated clusters originating from
low-$p_{\mathrm{T}}$ electron and hadron tracks that hit the calorimeter
surface not perpendicularly and merged clusters. The latter mostly originate
from high-$p_{\mathrm{T}}$ neutral pions that decay with a small opening
angle, resulting in both decay photons to be reconstructed as a single
cluster.

Photons traversing the detector material of ALICE convert to an electron-
positron pair with a probability of about 8.5% [27] within a radial distance
of $180\text{\text{ }}\mathrm{c}\mathrm{m}$ from the beam axis. Such photons
can be reconstructed using the PCM, which allows for the measurement of
photons converting in the ITS and TPC within the fiducial acceptance of
$|\eta|<0.9$. First, secondary vertices ($\text{V}^{0}$s) were reconstructed
by an algorithm [35] exploiting the distinct topology of two tracks with
opposite curvature that originate from a common point within the tracking
detectors. Good reconstruction quality of the tracks associated with a
secondary vertex was assured by requiring $p_{\mathrm{T}}>$50\text{\text{
}}\mathrm{M}\mathrm{e}\mathrm{V}$/c$ and for the track to be comprised of at
least 60% of the findable TPC clusters. Tracks originating from electrons were
identified via their specific energy loss $\derivative*{E}{x}$ in the TPC,
which was required to be within $-3$ to $5$ $\sigma_{e}$ of the expected
energy loss of electrons, where $\sigma_{e}$ is the standard deviation of the
measured $\derivative*{E}{x}$ distribution of electrons. Contamination of
charged pion tracks was suppressed by rejecting tracks whose
$\derivative*{E}{x}$ was within $\pm 1\sigma_{\pi^{\pm}}$ of the expected
energy loss for pions. Several additional selection criteria were applied to
identify $\text{V}^{0}$ candidates originating from photon conversions,
exploiting the kinematics and topology of the conversion, as discussed in more
detail in Ref. [8]. These include, e.g. selections to assure that the momentum
vector of a conversion pair is pointing towards the primary vertex and a
selection based on the minimal distance between the conversion point and the
primary vertex, in order to remove contributions from Dalitz decays.
Furthermore, the quality of the obtained $\text{V}^{0}$ candidates was
improved by constraining the reduced $\chi^{2}$ of the Kalman-filter
hypothesis for the track pair. Remaining contamination from
$\mathrm{K}_{\text{S}}^{0}$, $\Lambda$ and $\bar{\Lambda}$ decays was reduced
by a selection based on the decay kinematics in an Armenteros-Podolanski plot
[36], where photon conversions contribute as symmetric decays of a particle
with vanishing rest mass. Compared to previous PCM measurements [8, 33], a
$p_{\mathrm{T}}$ dependence of the selection criteria was introduced to
further reduce the contamination from $\text{K}_{\text{S}}^{0}$ and $\Lambda$
decays.

Figure 1: Invariant mass of $\pi^{+}\pi^{-}\pi^{0}$ candidates shown in the
vicinity of the nominal mass of the $\omega$ meson for indicated
$p_{\mathrm{T}}$-ranges for $\pi^{0}$ reconstruction with PCM (left), EMC
(middle) and PHOS (right). The second order polynomial used for the background
description is shown with a band denoting the statistical uncertainties of the
fit. The points show the signal obtained after subtraction of the background
fit. The signal is fitted with a Gaussian, where the vertical lines indicate
the integration range used to obtain the raw yield by bin-by-bin counting, as
outlined in Sec. 6.

##  6 Meson reconstruction

In order to reconstruct the $\omega$ mesons via their $\pi^{+}\pi^{-}\pi^{0}$
decay channel, where the $\pi^{0}$ decays to two photons with a branching
ratio of $\approx 99\%$, a prior selection of $\pi^{0}$ candidates from pairs
of photon candidates was applied. For the photons that passed the selection
criteria, the two-photon invariant mass ($M_{\gamma\gamma}$) of all possible
photon pairs in a given event was calculated. Four different methods were used
for the $\pi^{0}$ candidate reconstruction, differing in how the photons
entering the $M_{\gamma\gamma}$ calculation were selected. These are referred
to as PCM, PHOS and EMC, when _both_ photons used for the $\pi^{0}$
reconstruction were measured with the respective method. In addition, a hybrid
method (PCM-EMC) was used, where one PCM photon was combined with a photon
measured with the EMCal. The resulting invariant mass distributions exhibit a
peak of photon pairs originating from $\pi^{0}$ decays on top of combinatorial
background. The peak was parametrised in $p_{\mathrm{T}}$ slices with a
Gaussian to characterize the mean and width ($\sigma_{\pi^{0}}$) of the
$\pi^{0}$ mass distribution. Photon pairs lying within about $\pm
2\sigma_{\pi^{0}}$ of the expected $\pi^{0}$ mass were selected as neutral
pion candidates for the $\omega$ meson reconstruction. For the PHOS
measurement [37], $\pi^{0}$ candidates were furthermore required to have both
photons in the same PHOS module and to have a minimum transverse momentum of
$$1.5\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$. Finally, the nominal
neutral pion mass was assigned to the mass of selected $\pi^{0}$ candidates in
order to improve the $\omega$ mass resolution. This was achieved by
subtracting the difference between the reconstructed $\pi^{0}$ mass and its
nominal mass from the reconstructed $\omega$ mass.

Analogously to the $\pi^{0}$ reconstruction, the invariant mass of all
$\pi^{+}\pi^{-}\pi^{0}$ combinations in a given event was determined by
summing the four-momentum vectors of the candidate decay products passing the
selection criteria. While charged pions were identified by requiring a
$\derivative*{E}{x}$ within $\pm 3\sigma$ of their expected energy loss, no
such selection was applied for the $\omega$ analysis with the $\pi^{0}$
reconstructed in PHOS to improve the $\omega$ reconstruction efficiency.

Figure 1 shows the invariant mass distribution in the vicinity of the $\omega$
nominal mass for indicated $p_{\mathrm{T}}$ intervals for the $\pi^{0}$
reconstructed with PCM, EMC and PHOS, where a peak originating from $\omega$
meson decays is clearly visible above the combinatorial background. The latter
can be described using a second order polynomial for
$p_{\mathrm{T}}<$10\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$. At
higher momenta, a first order polynomial was used for the PHOS measurement.
The signal obtained after background subtraction was fitted with a Gaussian
and the raw yield was obtained by adding counts within $\pm 2\sigma_{\omega}$
($\pm 3\sigma_{\omega}$ for PHOS) of the reconstructed $\omega$ mass, where
$\sigma_{\omega}$ denotes the standard deviation of the Gaussian $\omega$
signal fit. The $\omega$ mass resolution was found to be about
$$15\text{\text{ }}\mathrm{M}\mathrm{e}\mathrm{V}$/c^{2}$ with a slight
dependence on $p_{\mathrm{T}}$ and reconstruction technique. This is achieved
by the use of the previously mentioned nominal mass assignment for $\pi^{0}$
candidates, which improved the mass resolution by up to $30\%$.

Figure 2: Correction factors applied to the raw $\omega$ yields for each
indicated $\pi^{0}$ reconstruction method. The factors include the geometrical
acceptance $A$ and the reconstruction efficiency $\epsilon_{\text{rec.}}$. In
addition, a normalisation to unit rapidity and $2\pi$ azimuth angle is applied
to allow for a direct comparison between the different methods.

The obtained raw yields for each reconstruction method were corrected for
geometrical acceptance and reconstruction efficiency, which were evaluated
using Monte Carlo simulations. The event generator PYTHIA6.2 [38] was used to
simulate the minimum bias pp collisions, where the implemented kinematics of
the $\omega$ three-body decay are weighted assuming the experimentally
observed phase space density distributions [39, 40]. All final state particles
were propagated through the ALICE detector using GEANT 3 [41], taking into
account the operating conditions of the detector at the time of data taking.
For each calorimeter, PHOS and EMCal, the relative difference in the energy
scale and the non-linearity were tuned in the Monte Carlo to ensure agreement
between the $p_{\mathrm{T}}$-dependent reconstructed $\pi^{0}$ mass and width
in data. This agreement propagates to the $\omega$ candidates, where mass and
width in data and Monte Carlo are found to be consistent within the
statistical uncertainties. The full correction factors, $\varepsilon$, that
were applied to the raw yields for the four different methods are shown in
Fig. 2. These factors include the geometrical acceptance evaluated for each
method and the reconstruction efficiency, where the former is normalised to
unit rapidity and $2\pi$ azimuth angle to allow for a direct comparison
between the different methods. The use of the four reconstruction techniques
combines the strengths of the individual methods and maximizes the accessible
$p_{\mathrm{T}}$ reach. The reconstruction with PCM offers a low
$p_{\mathrm{T}}$-reach, however, the efficiency is limited due to the low
conversion probability of about 8.5%, while the reconstruction with the two
calorimeters complements the measurement at high $p_{\mathrm{T}}$.

##  7 Systematic uncertainties

The systematic and statistical uncertainties on the measured $\omega$ yield
for the four individual reconstruction techniques in exemplary
$p_{\mathrm{T}}$ intervals are summarised in Tab. 1. The uncertainties are
given as relative uncertainties of the measured values in percent.

Table 1: Overview of the relative uncertainties given in percent in exemplary
$p_{\mathrm{T}}$-intervals for the four individual reconstruction techniques
of the $\omega$ meson. The given categories summarise systematic uncertainties
arising from each analysis step. For each method the statistical and total
uncertainties are reported in addition, as well as the uncertainties of the
combined measurement. The uncertainty from the
$\sigma_{\text{MB}_{\text{OR}}}$ determination of 3.5% is independent from the
individual measurements and indicated separately in Fig. 3.

$p_{\mathrm{T}}$ interval |  $4-5$ GeV/$c$ |  $6-8$ GeV/$c$ |  $12-14$ GeV/$c$
---|---|---|---
Method | PCM | PCM- | EMC | PCM | PCM- | EMC | PHOS | EMC | PHOS
EMC | EMC
Signal extraction | $12.3$ | $12.6$ | $12.2$ | $13.5$ | $13.5$ | $12.3$ | $6.0$ | $18.9$ | $11.0$
Material | $9.0$ | $4.7$ | $3.0$ | $9.0$ | $4.7$ | $3.0$ | $3.5$ | $3.0$ | $3.5$
Charged pion rec. | $6.8$ | $6.8$ | $6.8$ | $6.8$ | $6.8$ | $6.8$ | $6.0$ | $6.8$ | $6.0$
Conv photon rec. | $4.1$ | $4.1$ | - | $4.1$ | $4.1$ | - | - | - | -
Calo photon rec. | - | $5.0$ | $6.9$ | - | $5.0$ | $6.9$ | $5.2$ | $6.9$ | $9.3$
Neutral pion rec. | $6.0$ | $6.0$ | $6.0$ | $6.0$ | $6.0$ | $6.0$ | $4.0$ | $6.0$ | $4.0$
Pileup | $0.5$ | $0.5$ | $0.5$ | $0.5$ | $0.5$ | $0.5$ | 0.5 | $0.5$ | $0.5$
Total syst. uncertainty | $18.1$ | $17.7$ | $17.0$ | $19.1$ | $18.3$ | $17.1$ | $11.0$ | $22.4$ | $16.0$
Statistical uncertainty | $14.5$ | $14.7$ | $9.8$ | $18.9$ | $22.0$ | $9.2$ | $13.0$ | $21.7$ | $32.0$
Combined stat. unc. | 7.4 | 7.2 | 18.0
Combined syst. unc. | 13.7 | 10.3 | 16.6

The signal extraction dominates the systematic uncertainties of the
measurement and includes uncertainties due to the yield extraction. For the
PCM, PCM-EMC and EMC techniques the yield extraction uncertainty was estimated
by varying simultaneously the bin-counting window used to obtain the raw yield
in data and Monte Carlo and the fit range used for the polynomial fit of the
combinatorial background. Additionally, for the PHOS analysis, the signal
region was excluded from the background fit and the signal was obtained by
Gaussian integral instead of bin-by-bin counting. The material budget
uncertainty accounts for a possible mismatch between the amount of material
present in the ALICE detector and its implementation in GEANT 3. The material
budget uncertainty for a conversion photon was studied in Ref. [6], and found
to be 4.5% per photon. For the measurements involving the EMCal or the PHOS
uncertainties of $3$ and $3.5$%, respectively, were assigned for the material
budget, which is dominated by the material of outer detectors positioned in
front of calorimeter modules during data taking in 2010, as outlined in Ref.
[33]. The material uncertainty of the inner detectors is negligible for
calorimeter photons due to the low conversion probability.

The conversion and calorimeter photon reconstruction uncertainties were
evaluated by independently varying the respective selection criteria given in
Sec. 5. The conversion photon reconstruction uncertainty was found to be
dominated by the reduced $\chi^{2}$ selection of the electron tracks and the
requirement on the number of space points in the TPC for each track. For EMCal
related measurements, the cluster energy selection and the cluster shape have
most influence on the uncertainty. For PHOS, the photon reconstruction
uncertainty was evaluated by variation of the track matching condition and
cluster shape selection. Uncertainties arising from the non-linearity and
cluster energy scale of the respective calorimeters was taken into account by
varying the scheme used to obtain the energy scale calibration and are
included in the overall calorimeter photon reconstruction uncertainty. Like
the photon reconstruction uncertainties, the systematic uncertainties arising
from the charged pion reconstruction were estimated by independent variation
of the selection criteria given in Sec. 4. To study the influence of in-bunch
pileup on the measurement, the rejection criterium was loosened, resulting in
a 0.5% systematic uncertainty. The systematic uncertainty due to the selection
of neutral pion candidates was estimated by varying the invariant mass
selection window. For the PHOS measurement, the selection was additionally
varied according to the $\pi^{0}$ candidates transverse momentum. A detailed
description of these sources of uncertainty is provided in Refs. [33] and
[37].

Table 1 also shows, for each method, the statistical uncertainty together with
the total systematic uncertainty, which is obtained by adding the individual
sources in quadrature. In addition, the statistical and systematic
uncertainties of the combined measurement are given, which were obtained taken
into account correlations across the measurements as elaborated in the
following section.

##  8 Results

The fully corrected invariant cross sections of $\omega$ production were
obtained for each reconstruction technique using

$E\derivative[3]{\sigma^{pp\rightarrow\omega+X}}{p}=\frac{1}{2\pi}\frac{1}{\text{$p_{\mathrm{T}}$}}\cdot\frac{1}{\mathcal{L}_{\text{int}}}\cdot\frac{1}{A\cdot\varepsilon_{\text{rec.}}}\cdot\frac{1}{\text{BR}_{\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}}}\cdot\frac{N^{\omega}}{\Delta
y\Delta\text{$p_{\mathrm{T}}$}}.$ (1)

Here, $\mathcal{L}_{\text{Int}}$ is the integrated luminosity given in Sec. 4,
$\varepsilon_{\text{rec.}}$ and $A$ are the reconstruction efficiency and
acceptance of the corresponding method and $\text{BR}=(89.3\pm 0.6)\%$ is the
branching ratio of the $\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}$ decay [10].
Moreover, $N^{\omega}$ denotes the number of reconstructed $\omega$ mesons in
the transverse momentum range $\Delta$$p_{\mathrm{T}}$ and the given rapidity
range $\Delta y$.

The production cross sections were measured individually for each
reconstruction method and then combined using $p_{\mathrm{T}}$-dependent
weights that are calculated according to the Best Linear Unbiased Estimate
(BLUE) algorithm [42], which uses concepts that are routinely applied in
statistical fields. The combination took into account statistical and
systematic uncertainties. For the systematic uncertainties, the individual
measurements are found to be correlated by about 30%, dominantly originating
from the charged-pion selection and the material budget uncertainties. These
correlations were taken into account in the combination procedure. The
statistical and systematic uncertainties of the combined measurement are given
in Tab. 1.

Figure 3: Invariant cross section of $\omega$ meson production in pp
collisions at $\sqrt{s}=$7\text{\text{ }}\mathrm{T}\mathrm{e}\mathrm{V}$$
compared to theoretical predictions. The statistical and systematic
uncertainties are represented by vertical bars and boxes, respectively. A
Levy-Tsallis function was used to parametrise the spectrum, where the obtained
fit parameters are given in Tab. 2. The predictions are obtained using PYTHIA
8.2 [43] with the Monash 2013 [44] and 4C [45] tunes. Furthermore, a NLO
calculation [14] incorporating a model dedicated to describe vector-meson
fragmentation is shown, where the band denotes the uncertainty of the scale
$\mu$, which was used for factorisation, renormalisation and fragmentation. In
the bottom panel, the ratios of the theoretical estimates to the Levy-Tsallis
fit of the measurement are shown; the ratio of the data to the Levy-Tsallis
fit is also presented.

The cross section of $\omega$ meson production for
$2<$$p_{\mathrm{T}}$$<$17\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$ at
midrapidity in pp collisions at $\sqrt{s}=$7\text{\text{
}}\mathrm{T}\mathrm{e}\mathrm{V}$$ is shown in Fig. 3. It was fitted using a
Levy-Tsallis function [46] given by

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

which describes the cross section over the whole measured transverse momentum
range, as demonstrated in the lower panel of the figure. The parameters $m$
and $m_{\text{\tiny T}}=\sqrt{m^{2}+p_{\text{\tiny T}}^{2}}$ correspond to the
particle mass and the transverse mass, respectively, while $C$, $T$ and $n$
are the free parameters of the Levy-Tsallis function.

Table 2: Parameters and $\chi^{2}$/NDF of the fit to the $\omega$ invariant
cross section using the Levy-Tsallis function [46] from Eq. 2.

Levy-Tsallis |  $C$ ($\times 10^{10}$ pb) |  $T$ (GeV) | $n$ |  $\chi^{2}$/NDF | NDF
---|---|---|---|---|---
$\omega$ | $4.01^{\pm 2.47~{}\text{(stat)}}_{\pm 3.41~{}\text{(tot)}}$ | $0.182^{\pm 0.042~{}\text{(stat)}}_{\pm 0.061~{}\text{(tot)}}$ | $6.46^{\pm 0.37~{}\text{(stat)}}_{\pm 0.55~{}\text{(tot)}}$ | $~{}^{0.45~{}\text{(stat)}}_{0.22~{}\text{(tot)}}$ | 7

The values of the fit parameters and the reduced $\chi^{2}$ of the fit are
given in Tab. 2, where the fit was obtained using only statistical
uncertainties, and using the systematic and statistical uncertainties of the
measurement added in quadrature. To account for finite
$p_{\mathrm{T}}$-interval width, the combined cross section points were
assigned to $p_{\mathrm{T}}$ values shifted from the bin centre of the
$p_{\mathrm{T}}$ intervals according to the underlying spectrum [47] described
by a Levy-Tsallis function. This correction resulted in a shift below 2% in
each $p_{\mathrm{T}}$ interval.

Figure 4, which shows the ratios of the cross sections for the individual
reconstruction methods to the Levy-Tsallis fit of the combined measurement,
demonstrates the agreement between all methods within the statistical and
systematic uncertainties, justifying the combination of the individual results
as discussed earlier.

Figure 4: Ratios of the fully corrected $\omega$ spectra obtained with the
individual reconstruction methods to the Levy-Tsallis fit of the combined
spectrum, where the fit parameters are shown in Tab. 2. The statistical and
systematic uncertainties are represented by vertical bars and boxes,
respectively.

The measured differential cross section of $\omega$ production is compared to
several calculations in Fig. 3. The ratio of each prediction to the Levy-
Tsallis fit of the measurement is shown in the bottom panel of the figure. Two
PYTHIA 8.2 [43] Monte Carlo event generator calculations were considered for
comparison, which are based on the Monash 2013 [44] and the 4C [45] tunes,
respectively. The Monash 2013 tune describes the measurement over the full
reported $p_{\mathrm{T}}$ range within the uncertainties, while the Tune 4C
overestimates the data by about 50%. The Monash 2013 tune includes more recent
experimental results than Tune 4C and thus a more refined set of parameters.
In particular, the rate of light flavor vector meson production used in
hadronisation process was revised and lowered, improving the description of
$\omega$ meson yields [44].

The measurement is also compared to a next-to-leading order (NLO) calculation
using a model with broken SU(3) symmetry to describe vector meson production
[14], where the model parameters have been constrained using $\omega$
production data measured by PHENIX in pp collisions at
$\sqrt{s}=$200\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$$ [16]. The same
scale $\mu=\text{$p_{\mathrm{T}}$}$ was used for factorisation,
renormalisation and fragmentation for the calculation and the shaded band
reported in Fig. 3 denotes the scale variation of
$\text{$p_{\mathrm{T}}$}^{2}/2\leq\mu^{2}\leq 2\text{$p_{\mathrm{T}}$}^{2}$.
The calculation describes the measurement within the uncertainties below
$$6\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$, and overestimates the
data by up to 50% for higher $p_{\mathrm{T}}$.

The ratio of $\omega$ relative to $\pi^{0}$ meson production is shown as a
function of $p_{\mathrm{T}}$ in Fig. 5, where data points for the $\pi^{0}$
measurement were taken from Ref. [6]. The ratio is observed to be constant
above $$2.5\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$ with a value of
$C^{\omega/\pi^{0}}=0.69\pm 0.03\text{~{}(stat)~{}}\pm 0.04\text{~{}(sys)}$.
Within the uncertainties, the $\omega/\pi^{0}$ ratio is described by the
PYTHIA predictions. Even though the Tune 4C overestimates the $\omega$
production, it describes the $\omega/\pi^{0}$ ratio due to a similar
overestimation of $\pi^{0}$ production, which was reported in Ref. [8].

The measured $\omega/\pi^{0}$ ratio at $\sqrt{s}=$7\text{\text{
}}\mathrm{T}\mathrm{e}\mathrm{V}$$ is compared to data from lower collision
energies at $\sqrt{s}=62$ [15] and $200\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$ [16, 17, 18]. The $\omega/\pi^{0}$ ratios
measured at the different collision energies agree within the uncertainties.
In order to test the validity of $m_{\mathrm{T}}$-scaling, the Levy-Tsallis
parametrisation $f_{\pi^{0}}(p_{\text{\tiny T,}\pi^{0}})$ of the $\pi^{0}$
spectrum reported in Ref. [6] was scaled using the ratio
$C^{\omega/\pi^{0}}=0.67$, following the procedure discussed in detail in Ref.
[20]. The scaled parametrisation $f_{\omega}(p_{\text{\tiny T,}\omega})$ was
used to calculate the $\omega/\pi^{0}$ ratio via $f_{\omega}(p_{\text{\tiny
T,}\omega})/f_{\pi^{0}}(p_{\text{\tiny T,}\omega})$, where the relation
$p_{\text{\tiny T,}\omega}^{2}+m_{0,\omega}^{2}=p_{\text{\tiny
T,}\pi^{0}}^{2}+m_{0,\pi^{0}}^{2}$ was used to ensure the evaluation of both
spectra at the same transverse mass. The obtained $m_{\mathrm{T}}$-scaling
prediction of the $\omega/\pi^{0}$ ratio is shown in Fig. 5 and found to be
consistent with the measurement. Unlike in the case of the $\eta/\pi^{0}$
ratio measured at $\sqrt{s}=2.76$, $7$ and $8\text{\text{
}}\mathrm{T}\mathrm{e}\mathrm{V}$ [6, 33, 8], where a violation of
$m_{\mathrm{T}}$-scaling was observed below $3.5\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$, no such violation is observed within the
uncertainties for the $\omega$ meson in the entire measured momentum range.
However, while the measurement is compatible with the $m_{\mathrm{T}}$-scaling
prediction at low-$p_{\mathrm{T}}$, the sensitivity of the measurement to a
possible $m_{\mathrm{T}}$-scaling violation is limited by the uncertainties
and $p_{\mathrm{T}}$ reach. Here, future studies with increased precision
could provide further insights and more stringent tests of
$m_{\mathrm{T}}$-scaling for low-$p_{\mathrm{T}}$ $\omega$ mesons.
Interestingly, the PYTHIA calculations and the $m_{\mathrm{T}}$-scaled
prediction both describe the $\omega/\pi^{0}$ ratio at lower collision
energies even below $p_{\mathrm{T}}=$2\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$, suggesting a universal feature of meson
production.

Figure 5: Ratio of $\omega/\pi^{0}$ production as a function of transverse
momentum $p_{\mathrm{T}}$ for pp collisions at $\sqrt{s}=$7\text{\text{
}}\mathrm{T}\mathrm{e}\mathrm{V}$$ (black) compared to various lower collision
energies ranging from $\sqrt{s}=62-$200\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$$ [15, 17, 16, 18] (gray). In addition,
PYTHIA predictions at $\sqrt{s}=$7\text{\text{
}}\mathrm{T}\mathrm{e}\mathrm{V}$$ and the $\omega/\pi^{0}$ ratio obtained
from $m_{\mathrm{T}}$-scaling are shown with lines.

##  9 Conclusion

The invariant differential cross section of $\omega$ meson production at
midrapidity in pp collisions $\sqrt{s}=$7\text{\text{
}}\mathrm{T}\mathrm{e}\mathrm{V}$$ was measured with the ALICE detector,
covering a transverse-momentum range of 2 to $$17\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$. Within the uncertainties, PYTHIA 8.2
predictions for the Monash 2013 tune describes the measurement over the whole
$p_{\mathrm{T}}$ range, while Tune 4C overestimates the data by about 50%. A
NLO calculation using a model dedicated to describing fragmentation into the
entire vector meson nonet describes the data below $$6\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$, while it overestimates the data by up to
50% at higher $p_{\mathrm{T}}$. Above $$2.5\text{\text{
}}\mathrm{G}\mathrm{e}\mathrm{V}$/c$ the $\omega/\pi^{0}$ ratio is found to be
constant with a value of $C^{\omega/\pi^{0}}=0.67\pm
0.03\text{~{}(stat)~{}}\pm 0.04\text{~{}(sys)}$ and agrees with measurements
at lower collision energies and with PYTHIA predictions over the whole
reported $p_{\mathrm{T}}$ range. Within the uncertainties, the
$m_{\mathrm{T}}$-scaling prediction for $\omega$ mesons is consistent with the
measured spectrum above $$2\text{\text{ }}\mathrm{G}\mathrm{e}\mathrm{V}$/c$.

## Acknowledgments

We thank D. Indumathi for providing the NLO 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, Austrian Science Fund (FWF): [M 2467-N36] 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), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN 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 und Forschung (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), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), 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), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, 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, National Science Centre and WUT ID-UB, 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 Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) 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.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg95&A. Adlerorg74&J. Adolfssonorg81&M.M.
Aggarwalorg100&S. Aghaorg14&G. Aglieri Rinellaorg34&M. Agnelloorg30&N.
Agrawalorg10,org54&Z. Ahammedorg141&S. Ahmadorg16&S.U. Ahnorg76&Z.
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Terlizziorg25&C. Terrevoliorg125&D. Thakurorg50&S. Thakurorg141&D.
Thomasorg119&F. Thoresenorg89&R. Tieulentorg135&A. Tikhonovorg62&A.R.
Timminsorg125&A. Toiaorg68&N. Topilskayaorg62&M. Toppiorg52&F. Torales-
Acostaorg19&S.R. Torresorg37&A. Trifiróorg32,org56&S. Tripathyorg50,org69&T.
Tripathyorg49&S. Trogoloorg28&G. Trombettaorg33&L. Tropporg38&V.
Trubnikovorg2&W.H. Trzaskaorg126&T.P. Trzcinskiorg142&B.A.
Trzeciakorg37,org63&A. Tumkinorg109&R. Turrisiorg57&T.S. Tveterorg20&K.
Ullalandorg21&E.N. Umakaorg125&A. Urasorg135&G.L. Usaiorg23&M. Valaorg38&N.
Valleorg139&S. Valleroorg59&N. van der Kolkorg63&L.V.R. van Doremalenorg63&M.
van Leeuwenorg63&P. Vande Vyvreorg34&D. Vargaorg145&Z. Vargaorg145&M. Varga-
Kofaragoorg145&A. Vargasorg45&M. Vasileiouorg84&A. Vasilievorg88&O. Vázquez
Doceorg105&V. Vecherninorg113&E. Vercellinorg25&S. Vergara Limónorg45&L.
Vermuntorg63&R. Vernetorg7&R. Vértesiorg145&M. Verweijorg63&L.
Vickovicorg35&Z. Vilakaziorg131&O. Villalobos Baillieorg111&G. Vinoorg53&A.
Vinogradovorg88&T. Virgiliorg29&V. Vislaviciusorg89&A. Vodopyanovorg75&B.
Volkelorg34&M.A. Völklorg103&K. Voloshinorg92&S.A. Voloshinorg143&G.
Volpeorg33&B. von Hallerorg34&I. Vorobyevorg105&D. Voscekorg117&J.
Vrlákováorg38&B. Wagnerorg21&M. Weberorg114&S.G. Weberorg144&A.
Wegrzynekorg34&S.C. Wenzelorg34&J.P. Wesselsorg144&J. Wiechulaorg68&J.
Wikneorg20&G. Wilkorg85&J. Wilkinsonorg10&G.A. Willemsorg144&E.
Willsherorg111&B. Windelbandorg104&M. Winnorg137&W.E. Wittorg130&J.R.
Wrightorg119&Y. Wuorg128&R. Xuorg6&S. Yalcinorg77&Y. Yamaguchiorg46&K.
Yamakawaorg46&S. Yangorg21&S. Yanoorg137&Z. Yinorg6&H. Yokoyamaorg63&I.-K.
Yooorg17&J.H. Yoonorg61&S. Yuanorg21&A. Yuncuorg104&V. Yurchenkoorg2&V.
Zaccoloorg24&A. Zamanorg14&C. Zampolliorg34&H.J.C. Zanoliorg63&N.
Zardoshtiorg34&A. Zarochentsevorg113&P. Závadaorg66&N. Zaviyalovorg109&H.
Zbroszczykorg142&M. Zhalovorg98&S. Zhangorg40&X. Zhangorg6&Z. Zhangorg6&V.
Zherebchevskiiorg113&Y. Zhiorg12&D. Zhouorg6&Y. Zhouorg89&Z. Zhouorg21&J.
Zhuorg6,org107&Y. Zhuorg6&A. Zichichiorg10,org26&G. Zinovjevorg2&N.
Zurloorg140&

## Affiliation notes

org*Deceased

orgIItalian National Agency for New Technologies, Energy and Sustainable
Economic Development (ENEA), Bologna, Italy

orgIIDipartimento DET del Politecnico di Torino, Turin, Italy

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

org2Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org3Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

org5California Polytechnic State University, San Luis Obispo, California,
United States

org6Central China Normal University, Wuhan, China

org7Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org10Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org14COMSATS University Islamabad, Islamabad, Pakistan

org15Creighton University, Omaha, Nebraska, United States

org16Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

org19Department of Physics, University of California, Berkeley, California,
United States

org20Department of Physics, University of Oslo, Oslo, Norway

org21Department of Physics and Technology, University of Bergen, Bergen,
Norway

org22Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

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

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

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

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

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

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

org29Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

org32Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34European Organization for Nuclear Research (CERN), Geneva, Switzerland

org35Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org36Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

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

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

org39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org40Fudan University, Shanghai, China

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

org45High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org46Hiroshima University, Hiroshima, Japan

org47Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org48Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org49Indian Institute of Technology Bombay (IIT), Mumbai, India

org50Indian Institute of Technology Indore, Indore, India

org51Indonesian Institute of Sciences, Jakarta, Indonesia

org52INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org53INFN, Sezione di Bari, Bari, Italy

org54INFN, Sezione di Bologna, Bologna, Italy

org55INFN, Sezione di Cagliari, Cagliari, Italy

org56INFN, Sezione di Catania, Catania, Italy

org57INFN, Sezione di Padova, Padova, Italy

org58INFN, Sezione di Roma, Rome, Italy

org59INFN, Sezione di Torino, Turin, Italy

org60INFN, Sezione di Trieste, Trieste, Italy

org61Inha University, Incheon, Republic of Korea

org62Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org63Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

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

org65Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org66Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org67Institute of Space Science (ISS), Bucharest, Romania

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

org69Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org70Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org71Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org72iThemba LABS, National Research Foundation, Somerset West, South Africa

org73Jeonbuk National University, Jeonju, Republic of Korea

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

org79Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org80Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org81Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org82Nagasaki Institute of Applied Science, Nagasaki, Japan

org83Nara Women’s University (NWU), Nara, Japan

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

org85National Centre for Nuclear Research, Warsaw, Poland

org86National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org87National Nuclear Research Center, Baku, Azerbaijan

org88National Research Centre Kurchatov Institute, Moscow, Russia

org89Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org90Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org91NRC Kurchatov Institute IHEP, Protvino, Russia

org92NRC «Kurchatov»Institute - ITEP, Moscow, Russia

org93NRNU Moscow Engineering Physics Institute, Moscow, Russia

org94Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org95Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org96Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org97Ohio State University, Columbus, Ohio, United States

org98Petersburg Nuclear Physics Institute, Gatchina, Russia

org99Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org100Physics Department, Panjab University, Chandigarh, India

org101Physics Department, University of Jammu, Jammu, India

org102Physics Department, University of Rajasthan, Jaipur, India

org103Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org104Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org105Physik Department, Technische Universität München, Munich, Germany

org106Politecnico di Bari, Bari, Italy

org107Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org108Rudjer Bošković Institute, Zagreb, Croatia

org109Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org110Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org111School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org112Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org113St. Petersburg State University, St. Petersburg, Russia

org114Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org115SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org116Suranaree University of Technology, Nakhon Ratchasima, Thailand

org117Technical University of Košice, Košice, Slovakia

org118The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org119The University of Texas at Austin, Austin, Texas, United States

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

org121Universidade de São Paulo (USP), São Paulo, Brazil

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Technology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

org134Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org135Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org136Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org137Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU,
Départment de Physique Nucléaire (DPhN), Saclay, France

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

org141Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

org144Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org145Wigner Research Centre for Physics, Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea