2021 086 10 May

Measurement of $\mathrm{K}$∗(892)± production

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

The first results on $\mathrm{K}$∗(892)± resonance production in inelastic pp
collisions at LHC energies of $\sqrt{s}$ = 5.02, 8, and 13 TeV are presented.
The $\mathrm{K}$∗(892)± has been reconstructed via its hadronic decay channel
$\mathrm{K}$∗(892)±$\rightarrow$
$\mathrm{K^{0}_{S}}$$~{}+~{}\mbox{$\mathrm{\pi}$}^{\pm}$ with the ALICE
detector. Measurements of transverse momentum distributions,
$p_{\mathrm{T}}$-integrated yields, and mean transverse momenta for charged
$\mathrm{K}$∗(892) are found to be consistent with previous ALICE measurements
for neutral $\mathrm{K}$∗(892) within uncertainties. For $p_{\mathrm{T}}$ $>$
1 GeV/$c$ the $\mathrm{K}$∗(892)± transverse momentum spectra become harder
with increasing centre-of-mass energy from 5.02 to 13 TeV, similar to what
previously observed for charged kaons and pions. For $p_{\mathrm{T}}$ $<$ 1
GeV/$c$ the $\mathrm{K}$∗(892)± yield does not evolve significantly and the
abundance of $\mathrm{K}$∗(892)± relative to $\mathrm{K}$ is rather
independent of the collision energy. The transverse momentum spectra, measured
for $\mathrm{K}$∗(892)± at midrapidity in the interval 0 $<$ $p_{\mathrm{T}}$
$<$ 15 GeV/$c$, are not well described by predictions of different versions of
PYTHIA 6, PYTHIA 8 and EPOS-LHC event generators. These generators reproduce
the measured $p_{\mathrm{T}}$-integrated $\mathrm{K}$∗±/$\mathrm{K}$ ratios
and describe well the momentum dependence for $p_{\mathrm{T}}$ $<$ 2 GeV/$c$.

##  1 Introduction

Measurements of identified hadron production in high-energy proton-proton
interactions provide key observables to characterize the global properties of
the collisions. Particle production at high collider energies originates from
the interplay of perturbative (hard) and non-perturbative (soft) Quantum
Chromodynamic (QCD) processes. Soft scattering processes and parton shower
hadronization dominate the bulk of particle production at low transverse
momenta and can only be modeled phenomenologically.

At the Large Hadron Collider (LHC) [1], the small Bjorken $x$ regime is probed
and contributions from hard-scattering processes are more relevant with
increasing centre-of-mass energy. This produces a hardening of the transverse
momentum spectra, as already observed in Refs. [2, 3]. Measurements of strange
hadrons such as the $\mathrm{K}$∗(892) vector meson at different collision
energies allow for testing and tuning perturbative QCD and low-transverse
momentum phenomenological calculations [4, 5, 6], including strangeness
production.

In the following, $\mathrm{K}$∗0 denotes $\mathrm{K}$∗(892)0 and
$\overline{\mbox{$\mathrm{K}$}^{*}(892)^{\mathrm{0}}}$, $\mathrm{K}$∗± stands
for $\mathrm{K}$∗(892)+ and $\mathrm{K}$∗(892)-, while $\mathrm{K}$∗ indicates
$\mathrm{K}$∗0 and $\mathrm{K}$∗±.

In heavy-ion collisions, due to their short lifetimes comparable with the
lifetime of the hadronic phase of the system [7], resonances such as
$\mathrm{K}$∗ ($\tau\approx$ 4 fm/$c$) are sensitive probes of the dynamical
evolution of the fireball. Re-scattering and regeneration in the hadron gas
may change the number of resonances reconstructed via the hadronic decay
channels compared to those predicted by thermal models at the chemical freeze-
out, i.e. when the inelastic interactions stop. The $\mathrm{K}$∗ vector meson
and its corresponding ground state, the $\mathrm{K}$, have an identical quark
content. They differ only in mass, lifetime and relative orientation of their
quark spins. Therefore, the $\mathrm{K}$∗$/$$\mathrm{K}$ ratio is an ideal
observable to study the $\mathrm{K}$∗ properties and the freeze-out conditions
in relativistic heavy-ion collisions. The integrated yield ratio
$\mathrm{K}$∗0/$\mathrm{K}$ exhibits a suppression with respect to pp
collisions, which increases with the centrality of the collisions [8, 9, 10,
11]. This could be explained as due to the dominance of re-scattering effects
of $\mathrm{K}$∗0 decay products over regeneration processes in the hadronic
phase of the collisions.

Hints of the suppression of $\mathrm{K}$∗0/$\mathrm{K}$ were observed also in
high-multiplicity p–Pb and pp collisions [12, 13, 14] at LHC energies,
suggesting the possible presence of re-scattering effects and thus of a
hadronic phase with a short but finite lifetime in small collision systems.
The observed multiplicity-dependent suppression should therefore be validated
by measurements with an increased precision. This is particularly important
for small systems such as pp and p–Pb because the $\mathrm{K}$∗0/$\mathrm{K}$
ratios, measured in the highest and lowest multiplicity event classes differ
by less than 2$\sigma$ [12, 13, 14], with the largest uncertainty in the ratio
being relative to the $\mathrm{K}$∗0 yield measurement. In this work, the
$\mathrm{K}$∗/$\mathrm{K}$ ratio is studied with increased precision by
measuring the production yield of $\mathrm{K}$∗± in pp collisions with the
ALICE detector [15]. The production of charged and neutral $\mathrm{K}$∗
vector mesons is expected to be comparable. Indeed, they have a similar quark
composition, $\mathrm{K}$∗(892)+ = (u$\overline{\mathrm{s}}$),
$\mathrm{K}$∗(892)0 = (d$\overline{\mathrm{s}}$), $\mathrm{K}$∗(892)- =
($\overline{\mathrm{u}}$s) and
$\overline{\mbox{$\mathrm{K}$}^{*}(892)^{\mathrm{0}}}$ =
($\overline{\mathrm{d}}$s), and their masses differ by about 0.004
GeV/$c^{\mathrm{2}}$, being M($\mathrm{K}$∗±) = 0.89166 $\pm$ 0.0026
GeV/$c^{\mathrm{2}}$ [16] and M($\mathrm{K}$∗0) = 0.89581 $\pm$ 0.0019
GeV/$c^{\mathrm{2}}$ [16]. At LHC energies, the measurement of the
$\mathrm{K}$∗± and $\mathrm{K}$∗0 strange vector mesons is quite challenging.
These are reconstructed via their hadronic decay into a charged pion and a
kaon: a neutral kaon for $\mathrm{K}$∗± and a charged kaon for $\mathrm{K}$∗0.
Because of the different strategies used for their identification in ALICE,
$\mathrm{K^{0}_{S}}$ are measured with a lower systematic uncertainty than
charged kaons [13, 3].

In this paper, transverse momentum ($p_{\mathrm{T}}$) distributions of
$\mathrm{K}$∗± resonances at midrapidity ($\left|y\right|$ $<$ 0.5) are
presented for the first time for inelastic pp collisions at the LHC. The
evolution of the $p_{\mathrm{T}}$ distributions with the energy was
investigated by studying pp collisions at the centre-of-mass energies of
$\sqrt{s}$ $=$ 5.02, 8, and 13 TeV. The similarity of the charged and neutral
$\mathrm{K}$∗ production was checked by comparing $\mathrm{K}$∗± results with
existing $\mathrm{K}$∗0 measurements at the same collision energy [11, 17, 3].
These measurements are a useful probe of strangeness production and provide
input to tune Monte Carlo event generators such as PYTHIA and EPOS-LHC [4, 5,
6] as a function of collision energy. Furthermore, the measurements in
inelastic pp collisions at $\sqrt{s}$ $=$ 5.02, 8, and 13 TeV reported in this
paper serve as reference data to study nuclear effects in p–Pb and Pb–Pb
collisions.

The paper is organized as follows. In Sec. 2 the ALICE experimental setup is
described, focusing on the detectors employed in the analysis presented here.
Details on the event, track and particle identification as well as on the
corrections applied to the measured raw yields and estimation of systematic
uncertainties are discussed in Sec. 3. In Sec. 4, the results on the
production of $\mathrm{K}$∗± resonances are shown. These include the
transverse momentum spectra, the mean transverse momenta, the per-event
$p_{\mathrm{T}}$-integrated particle yields and the
$\mathrm{K}$∗±/$\mathrm{K}$ = ($\mathrm{K}$∗+ \+
$\mathrm{K}$∗-)/($\mathrm{K}$+ \+ $\mathrm{K}$-) ratio as a function of the
collision energy. All these observables are compared with similar results for
$\mathrm{K}$∗0. The comparison of the $p_{\mathrm{T}}$ spectra with different
event generator (PYTHIA6, PYTHIA8 and EPOS-LHC) predictions is also presented.
In Sec. 5 results are summarized and conclusions are drawn.

##  2 Experimental setup

A detailed description of the ALICE detector and its performance can be found
in Refs. [15, 18]. The sub-detectors used for the analysis presented in this
paper are the Inner Tracking System (ITS) [15], the Time Projection Chamber
(TPC) [19], and the V0 detectors [20]. All tracking detectors are positioned
in a solenoidal magnetic field B = 0.5 T parallel to the LHC beam axis.

Charged particle tracks are reconstructed by the ITS and the TPC. The ITS is
the innermost barrel detector consisting of six cylindrical layers of high-
resolution silicon tracking detectors. The innermost layers consist of two
arrays of hybrid Silicon Pixel Detectors (SPD) located at an average radial
distance $r$ of 3.9 and 7.6 cm from the beam axis and covering
$\left|\eta\right|$ $<$ 2.0 and $\left|\eta\right|$ $<$ 1.4, respectively. The
SPD is used to reconstruct the primary vertex (PV) of the collisions, which is
found as a space point to which the maximum number of tracklets (track
segments defined by pairs of points, one point in each SPD layer) converges.
The outer layers of the ITS are composed of two layers of silicon drift and
two layers of silicon strip detectors, with the outermost layer positioned at
$r$ = 43 cm. The TPC is the main tracking device of ALICE. It is a large
volume (90 m3) cylindrical drift chamber with radial and longitudinal
dimension of about 85 $<~{}r~{}<$ 250 cm and $-250$ $<~{}z~{}<~{}$250 cm,
respectively, covering for full-length tracks a pseudorapidity range of
$\left|\eta\right|$ $<$ 0.9 over the full azimuth. The end-caps of the TPC are
equipped with multiwire proportional chambers segmented radially into pad
rows. Together with the measurement of the drift time, the TPC provides three
dimensional space point information, with up to 159 samples per track. The
resolution on the position is 1100-800 $\mu$m on the transverse plane and
1250-1100 $\mu$m along $z$. Charged tracks originating from the primary vertex
can be reconstructed down to $p_{\mathrm{T}}$ $\approx$ 0.1 GeV/$c$ [18]. The
TPC enables charged particle identification (PID) via the measurement of the
specific ionization energy loss (d$E$/d$x$) with a resolution of about 5.2%
[18] at low transverse momentum. A separation between
$\mathrm{\pi}$-$\mathrm{K}$ and $\mathrm{K}$-p at the level of two standard
deviations is possible for $p_{\mathrm{T}}$ $<$ 0.8 GeV/$c$ and 1.6 GeV/$c$,
respectively.

The V0 detectors are two forward scintillator hodoscopes employed for
triggering and beam background suppression. They are placed along the beam
axis on each side of the nominal interaction point (IP) at $z$ = 340 cm and
$z=~{}-90$ cm, covering the pseudorapidity regions 2.8 $<~{}\eta~{}<$ 5.1
(V0A) and $-3.7~{}<~{}\eta~{}<~{}-1.7$ (V0C), respectively.

The pp data at $\sqrt{s}$ = 5.02 and 13 TeV used in this paper were collected
in 2015 while data at $\sqrt{s}$ = 8 TeV were collected in 2012. The data were
collected with a minimum bias trigger requiring a hit in both V0 detectors, in
coincidence with the arrival of proton bunches from both beam directions.

The analysed data are low pile-up samples in which the average number of
interactions per bunch crossing are $\mu~{}=$ 0.019 $\pm$ 0.009, 0.02 $\pm$
0.01 and 0.068 $\pm$ 0.003 for collisions at $\sqrt{s}$ = 5.02, 8, and 13 TeV,
respectively. Contamination from beam-gas events is removed offline by using
timing information from the V0 detector, which has a time resolution better
than 1 ns. The events in which pile-up or beam-gas interaction occurred are
also rejected by exploiting the correlation between the number of SPD hits and
the number of SPD tracklets, as discussed in detail in Ref. [18].

The events selected from the analysis are required to have a reconstructed
primary vertex with its position along the beam axis being within 10 cm with
respect to the nominal interaction point (the centre of the ALICE barrel). The
events containing more than one reconstructed vertex are tagged as pile-up
occurring within the same bunch crossing and discarded for the analysis.

The size of the analyzed samples after selection and the corresponding pp
integrated luminosities are given in Tab. 1. In the same table, the primary
vertex reconstruction efficiency $\epsilon_{\mathrm{vertex}}$ and the trigger
selection efficiency $\epsilon_{\mathrm{trig}}$ are also reported. For each
energy, the $\epsilon_{\mathrm{trig}}$ value, mainly defined by the charged
particle multiplicity of the collision, is the ratio between the V0-triggered
cross section [21, 22, 23] and the inelastic cross section [24] and the
$\epsilon_{\mathrm{vertex}}$ is the fraction of V0-triggered events for which
a primary vertex is reconstructed.

Table 1: Number of minimum bias events after event selection (NMB), integrated luminosity ($\mathcal{L}_{\mathrm{int}}$), the trigger selection efficiency ($\epsilon_{\mathrm{trig}}$), and the primary vertex reconstruction efficiency ($\epsilon_{\mathrm{vertex}}$) for the analyzed data sets. The uncertainty on $\epsilon_{\mathrm{vertex}}$ is lower than 0.1$\%$. $\sqrt{s}$ (TeV) | NMB (107) |  $\mathcal{L}_{\mathrm{int}}$ (nb-1) | $\epsilon_{\mathrm{trig}}$ | $\epsilon_{\mathrm{vertex}}$
---|---|---|---|---
5.02 | 10.87 | 2.12 $\pm$ 0.05 | 0.757 $\pm$ 0.019 | 0.958
8.0 | 6.99 | 1.25 $\pm$ 0.03 | 0.772 $\pm$ 0.021 | 0.972
13.0 | 5.32 | 0.92 $\pm$ 0.02 | 0.745 $\pm$ 0.019 | 0.931

##  3 Data analysis

The $\mathrm{K}$∗(892)± is a short-lived particle and its decay vertex cannot
be distinguished from the primary collision vertex. It is reconstructed in
ALICE via its main decay channel $\mathrm{K}$∗±$\rightarrow$
$\mathrm{K^{0}_{S}}$\+ $\pi^{\pm}$, which has a branching ratio (B.R.) of
(33.3 $\pm$ 0.003)% [16], taking into account the B.R. of $\mathrm{K}$∗±
$\rightarrow$ $\mathrm{K^{0}}$\+ $\pi^{\pm}$ decay and the probability of
$\mathrm{K^{0}}$ to be into a $\mathrm{K^{0}_{S}}$ state. The
$\mathrm{K^{0}_{S}}$ is reconstructed by exploiting its characteristic weak
decay topology ($\mathrm{K^{0}_{S}}$$\rightarrow$ $\mathrm{\pi}$+ \+
$\mathrm{\pi}$-) into two oppositely charged particles (V0 topology) with
branching ratio (69.2 $\pm$ 0.05)% [16].

###  3.1 Pion and $\mathrm{\bf{K^{0}_{S}}}$ selection

Particle identification for charged pions originating from the primary and
secondary vertices (“primary and secondary pions”) is applied on a sample of
high-quality tracks reconstructed with the TPC and the ITS. Informations from
ITS are required only for primary tracks. The primary and secondary tracks
reconstructed with the TPC are required to have crossed at least 70 readout
rows out of a maximum 159. They are also requested to avoid large gaps in the
number of expected tracking points in the radial direction. This is achieved
by ensuring that the number of clusters expected, based on the reconstructed
trajectory and the measurements in neighbouring TPC pad rows, do not differ by
more than 20%. Particles are required to have $p_{\mathrm{T}}$ $>$ 0.15
GeV/$c$ and to be located in the pseudorapidity range $\left|\eta\right|$ $<$
0.8 to avoid edge effects in the TPC acceptance. Furthermore, tracks of
particles possibly originating from weak decays of pions and kaons are
rejected when a kink in the track is observed [18]. Primary tracks are
required to be associated with at least one cluster in the SPD and the
goodness-of-fit values $\chi^{2}$ per cluster of the track fit in the ITS and
in TPC are restricted in order to select high-quality tracks. Primary tracks
are required to have a distance of closest approach (DCA) to the primary
vertex lower than 2 cm along the beam axis and 7$\sigma$ in the transverse
plane, where $\sigma$ = (0.0015+0.0050 $p_{\mathrm{T}}$-1.1) cm with
$p_{\mathrm{T}}$ in units of GeV/$c$. Secondary tracks are required to have a
DCA to the primary vertex larger than 0.06 cm. Selected pion candidates are
identified by requiring that the specific ionization energy loss d$E$/d$x$
measured in the TPC lies within $n$ standard deviations ($\sigma_{TPC}$) from
the specific energy loss expected for pions, with $n$ equal to 3 or 5 for
primary and secondary pions, respectively.

The selection criteria used for the $\mathrm{K^{0}_{S}}$ reconstruction are
listed in Tab. 2. Candidates $\mathrm{K^{0}_{S}}$ are in the rapidity range
$\left|y\right|$ $<$ 0.8. The distance of closest approach between positively
and negatively charged tracks is required to be smaller than one standard
deviation with respect to the ideal value of zero and the cosine of the
pointing angle ($\theta_{\mathrm{PA}}$), which corresponds to the angle
between the V0 momentum and the line connecting the secondary to the primary
vertex, is required to be larger than 0.97. Only those V0 candidates located
at a radial distance larger than 0.5 cm (V0 radius) are used in this analysis.
Competing V0 rejection is also applied: the V0 mass is recalculated assuming
that one of the pions is a (anti-)proton, and the V0 candidates (about 2%) are
rejected if their mass is compatible with the $\mathrm{\Lambda}$ mass within
$\pm$ 0.0043 GeV/$c^{\mathrm{2}}$, which is about three times the typical mass
resolution for the reconstructed $\mathrm{\Lambda}$ in ALICE [25]. In
addition, $\mathrm{K^{0}_{S}}$ candidates with a proper lifetime larger than
20 cm$/c$ are rejected to remove combinatorial background from interactions
with the detector material. The proper lifetime is estimated as
$Lm_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}/p$, where $L$ is the linear (3D)
distance between the primary vertex and the V0 decay vertex, $p$ is the total
momentum of $\mathrm{K^{0}_{S}}$, and
$m_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}$ = 0.497611 GeV/$c^{\mathrm{2}}$ is
the nominal $\mathrm{K^{0}_{S}}$ mass [16]. Finally, the invariant mass of
$\pi^{+}$$\pi^{-}$ pairs is required to be compatible with the nominal
$\mathrm{K^{0}_{S}}$ rest mass within $\pm
4\sigma_{m\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}$, with the
$\mathrm{K^{0}_{S}}$ mass resolution value increasing smoothly with the
transverse momentum, from $\approx$ 3.5$\times$10-3 GeV/$c^{\mathrm{2}}$ at
$p_{\mathrm{T}}$ $\approx$ 0 to $\approx$ 6.2$\times$10-3 GeV/$c^{\mathrm{2}}$
at $p_{\mathrm{T}}$ = 10 GeV/$c$.

ALICE has measured $\mathrm{K}$∗0 exploiting its decay into $\mathrm{K}$± \+
$\pi^{\mp}$ [11, 17, 3, 26, 9, 12, 10], with pions and kaons reconstructed as
primary particles and identified using energy loss and time-of-flight
measurements. The crucial difference in the $\mathrm{K}$∗± and $\mathrm{K}$∗0
reconstruction is the charged and neutral kaon identification. In particular,
the neutral kaon reconstruction efficiency is larger for $p_{\mathrm{T}}$ $<$
0.2 GeV/$c$ and for $p_{\mathrm{T}}$ $>$ 2 GeV/$c$. At low $p_{\mathrm{T}}$,
primary charged kaon detection depends on the tracking efficiency with a
threshold of about 0.1 GeV/$c$, whereas at high $p_{\mathrm{T}}$ the larger
efficiency in neutral kaon reconstruction is mainly connected to a loose
charged particle selection based on the expected specific energy loss.

Table 2: The selection criteria parameters for $\mathrm{K^{0}_{S}}$ candidates. DCA stands for distance of closest approach, PV means primary vertex, $\theta_{\mathrm{PA}}$ is the pointing angle, $Lm_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}/p$ is the proper lifetime. The competing V0 rejection window is 1.1157 $\pm$ 0.0043 GeV/$c^{\mathrm{2}}$ while for the mass of the $\pi^{+}$$\pi^{-}$ pairs the window is $\left|m_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}-m_{\textrm{$\pi^{+}$$\pi^{-}$}}\right|<4\sigma_{m\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}$. $\mathrm{K^{0}_{S}}$ selection criteria | Value
---|---
Pion d$E$/d$x$ ($\sigma$) |  $<$ 5
DCA of daughter to PV (cm$/c$) |  $>$ 0.06
DCA between daughters ($\sigma$) |  $<$ 1
Cosine of $\theta_{\mathrm{PA}}$ |  $>$ 0.97
V0 radius (cm) |  $>$ 0.5
Proper lifetime $Lm_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}/p$ (cm) |  $<$ 20
Competing V0 rejection window (GeV/$c^{\mathrm{2}}$) |  $\pm$0.0043
Mass $\mathrm{K^{0}_{S}}$ window ($\sigma$) |  $\pm$4
Rapidity $\left|y\right|$ |  $<$ 0.8

Figure 1: (Left panels) The $\mathrm{K^{0}_{S}}$$\pi^{\pm}$ invariant mass
distributions at $\left|y\right|$ $<$ 0.5 in pp collisions at $\sqrt{s}$ =
5.02, 8, and 13 TeV. The background shape estimated by the event-mixing
technique is shown with empty red circles. Statistical uncertainties are shown
with error bars. (Right panels) The $\mathrm{K^{0}_{S}}$$\pi^{\pm}$ invariant
mass distributions in pp collisions at $\sqrt{s}$ = 5.02, 8, and 13 TeV after
background subtraction. The solid red curve is the result of the fit with Eq.
1; the dashed red line describes the residual background distribution given by
Eq. 2. Statistical uncertainties are shown with error bars.

###  3.2 Signal extraction

The raw yield of the $\mathrm{K}$∗± is extracted from the same-event
$\mathrm{K^{0}_{S}}$$\pi^{\pm}$ invariant mass distribution in different
$p_{\mathrm{T}}$ intervals between 0 and 15 GeV/$c$. The nominal mass value
[16] is assigned to the $\mathrm{K^{0}_{S}}$ when the
$\mathrm{K^{0}_{S}}$$\pi^{\pm}$ invariant mass is estimated. The shape of the
uncorrelated background is estimated using the invariant mass distribution of
$\mathrm{K^{0}_{S}}$$\pi^{\pm}$ pairs selected from different events (event
mixing method). To avoid any mismatch due to different acceptances and to
ensure a similar event structure, particles from events with similar vertex
positions along $z$ ($\Delta z$ $<$ 1 cm) and track multiplicities $n$
($\Delta n$ $<$ 5) are mixed. To reduce statistical uncertainties each event
is mixed with 9 others. The mixed-event distribution is then normalized to the
same-event distribution in the mass region 1.1
$<M_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}<$ 1.2
GeV/$c^{\mathrm{2}}$ and subtracted from the same-event distribution in each
$p_{\mathrm{T}}$ bin. The mixed-event background normalization range is varied
for the study of systematic uncertainties.

The $\mathrm{K^{0}_{S}}$$\pi^{\pm}$ invariant mass distributions in different
$p_{\mathrm{T}}$ ranges obtained for the different collision energies are
shown in the left panels of Fig. 1. Similar to previous $\mathrm{K}$∗0
analyses [11, 17, 3, 26, 9, 12, 10] the uncorrelated mixed-event background is
subtracted from the same-event invariant mass distribution. The resulting
distributions exhibit a characteristic peak on top of a residual background,
as reported in the right panels of Fig. 1. The latter is due to the presence
of correlated pairs from jets, multi-body decays of heavier particles and
misreconstructed resonance decays. The resulting distribution is fitted with a
combination of the non-relativistic Breit-Wigner function to describe the
signal peak and a $F_{BG}$ function to describe the residual background.

The fit, based on the minimization of the $\chi^{\textrm{2}}$, was performed
according to the following expression:

$\displaystyle\frac{dN}{dM_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}}=\frac{C}{2\pi}\frac{\Gamma_{\textrm{0}}}{\left(M_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}-M_{\textrm{0}}\right)^{2}+\frac{\Gamma_{\textrm{0}}^{2}}{4}}+F_{BG}\left(M_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}\right)$
(1)

where $M_{\textrm{0}}$ and $\Gamma_{\textrm{0}}$ are the mass and the width of
the $\mathrm{K}$∗± [16]. The $C$ parameter is the integral of the peak
function from 0 to $\infty$. The detector mass resolution for the
reconstruction of $\mathrm{K}$∗± is negligible compared to its natural width,
$\Gamma_{\textrm{0}}$ = (0.0508 $\pm$ 0.0009) GeV/$c^{\mathrm{2}}$ [16], and
it is therefore not included in the peak model. The mass and width of
$\mathrm{K}$∗± were found to be compatible with the values reported in [16].
For the measurement of the yields, the width of $\mathrm{K}$∗± was fixed to
its natural value. Fits were performed with the width kept as a free parameter
or fixed at 0.0517 or 0.0499 GeV/$c^{\mathrm{2}}$ to estimate the systematic
uncertainty.

The shape of the correlated background in the invariant mass distribution of
$\mathrm{K^{0}_{S}}$$\pi^{\pm}$ pairs is studied using the same samples of
simulated events described in Sect. 3.3 that were used to estimate the
Acceptance$\times$Efficiency corrections. The produced particles and their
decay products are propagated through the ALICE detector using GEANT3 [27].
Invariant mass distributions for $\mathrm{K^{0}_{S}}$$\mathrm{\pi}$+ and
$\mathrm{K^{0}_{S}}$$\mathrm{\pi}$- pairs are accumulated after applying the
same event, track and particle identification selections as in data. The study
shows that after subtracting the combinatorial background, the remaining
background has a smooth dependence on mass. It is well described by the
following function, already used in Refs. [28, 29]:

$\displaystyle
F_{BG}\left(M_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}\right)=\left[M_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}-\left(m_{\textrm{$\pi^{\pm}$}}+m_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}\right)\right]^{n}\exp\left(a+bM_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}+cM_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}^{2}\right)$
(2)

where $n$, $a$, $b$, and $c$ are fit parameters and $m_{\textrm{$\pi^{\pm}$}}$
and $m_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}$ are the pion and
$\mathrm{K^{0}_{S}}$ masses [16]. Examples of these fits for different
$p_{\mathrm{T}}$ intervals and different pp collision energies are shown in
the right panels of Fig. 1. The typical fitting interval was 0.66
$<M_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}$\pi^{\pm}$}}<$ 1.1
GeV/$c^{\mathrm{2}}$.

The $\mathrm{K}$∗± raw yield ($N_{\mathrm{raw}}$) is determined by integrating
the combinatorial background-subtracted invariant mass distribution over the
interval 0.79$-$0.99 GeV/$c^{\mathrm{2}}$, subtracting the integral of the
residual background fit function over the same range, and correcting the
result to account for the yield outside that range. The yield in the tails is
estimated by integrating the non-relativistic Breit-Wigner function from
$m_{\textrm{$\pi^{\pm}$}}+m_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}}$ to 0.79
GeV/$c^{\mathrm{2}}$ and from 0.99 GeV/$c^{\mathrm{2}}$ to infinity. This
correction to the total yield is about 13%. As an alternative used to estimate
the systematic uncertainties, the $\mathrm{K}$∗± yield is also obtained by
integrating the peak fitting function in the allowed region
($m_{\textrm{$\pi^{\pm}$}}+m_{\textrm{\mbox{$\mathrm{K^{0}_{S}}$}}},\infty$).

Figure 2: Acceptance$\times$Efficiency as a function of $p_{\mathrm{T}}$ for
$\mathrm{K}$∗± mesons, detected by their decay to $\mathrm{K^{0}_{S}}$ \+
$\pi^{\pm}$, with $\mathrm{K^{0}_{S}}$ reconstructed by their decay to
$\pi^{+}$ \+ $\pi^{-}$. The $\mathrm{K^{0}_{S}}$ $\rightarrow$ $\pi^{+}$ \+
$\pi^{-}$branching ratio is included in the efficiency estimation. Statistical
uncertainties are shown with error bars.

###  3.3 Efficiency and acceptance

To obtain the corrected resonance yields, the convolution between the
geometrical acceptance ($A$) and the resonance reconstruction efficiency
($\epsilon_{\mathrm{rec}}$), which takes into account the criteria used to
select primary charged pions and $\mathrm{K^{0}_{S}}$, is determined. The
$A\times\epsilon_{\mathrm{rec}}$ product takes into account also the branching
ratio of $\mathrm{K^{0}_{S}}$ $\rightarrow$ $\pi^{+}$ \+ $\pi^{-}$. For each
collision energy, $A\times\epsilon_{\mathrm{rec}}$ is determined using samples
of about 50 million pp events simulated with different Monte Carlo event
generators (PYTHIA6-Perugia 2011 tune [4, 30], PYTHIA8-Monash 2013 tune [5,
31], EPOS-LHC [6]) and a GEANT3-based simulation [27] of the ALICE detector
response. The actual positions of the detectors (alignment), maps of dead or
noisy elements, and time and amplitude calibrations are used in the
reconstruction of real and simulated data. All the parameters taken into
account for a careful calibration of the ALICE detector are listed in [18].
The residual differences between data and the sample of Monte Carlo simulation
previously described are considered in the systematic uncertainty.

For each $p_{\mathrm{T}}$ interval, the $A\times\epsilon_{\mathrm{rec}}$ is
calculated as the ratio $N_{\mathrm{rec}}/N_{\mathrm{gen}}$, where
$N_{\mathrm{rec}}$ is the number of particles reconstructed in the
$\mathrm{K^{0}_{S}}$ \+ $\pi^{\pm}$ channel after all event and particle
selections, while $N_{\mathrm{gen}}$ is the number of generated mesons
decaying in the same channel. Both generated and reconstructed mesons have the
rapidity in the range $\left|y\right|$ $<$ 0.5. In general, the efficiency
depends on the shape of the generated particle $p_{\mathrm{T}}$ spectrum.
Therefore, at the different collision energies, the efficiency for
$\mathrm{K}$∗± is estimated re-weighting iteratively the shape of the
generated $p_{\mathrm{T}}$ spectrum to measured shape. As an example the
transverse momentum dependence of $A\times\epsilon_{\mathrm{rec}}$ is reported
in Fig. 2 for the $\sqrt{s}$ = 5.02 TeV sample.

###  3.4 Yield corrections

The differential transverse momentum yield for inelastic pp collisions was
calculated as

$\displaystyle\frac{1}{N_{\mathrm{INEL}}}\frac{d^{2}N}{dp_{T}dy}=\frac{N_{\mathrm{raw}}}{N_{\mathrm{MB}}\times{\mathrm{B.R.}}\times\Delta
p_{\mathrm{T}}\times\Delta
y}\frac{f_{\mathrm{SL}}}{(A\times\epsilon_{\mathrm{rec}})}\times\epsilon_{\mathrm{trig}}\times\epsilon_{\mathrm{vertex}}.$
(3)

The raw yields are corrected for the resonance branching ratio (B.R. =
33.3$\%$) and $A\times\epsilon_{\mathrm{rec}}$ in the $\mathrm{K^{0}_{S}}$ \+
$\pi^{\pm}$ channel. Furthermore, these yields were normalized to the number
of minimum bias events $N_{\mathrm{MB}}$ and corrected for the vertex
reconstruction efficiency $\epsilon_{\mathrm{vertex}}$ as well as for the
trigger selection efficiency $\epsilon_{\mathrm{trig}}$. Values of
$N_{\mathrm{MB}}$, $\epsilon_{\mathrm{vertex}}$, and
$\epsilon_{\mathrm{trig}}$ for all collision energies are reported in Tab. 1.
The signal-loss correction $f_{\mathrm{SL}}$ takes into account the fraction
of $\mathrm{K}$∗± mesons in non-triggered inelastic events and it is estimated
by Monte Carlo simulations. The latter is a $p_{\mathrm{T}}$-dependent
correction factor which has its maximum at low $p_{\mathrm{T}}$
($f_{\mathrm{SL}}\approx$ 1.04 for $p_{\mathrm{T}}$ $<$ 1 GeV/$c$ and
$f_{\mathrm{SL}}~{}\approx$ 1.01 for $p_{\mathrm{T}}$ $>$ 1 GeV/$c$).

###  3.5 Systematic uncertainties

The measurement of $\mathrm{K}$∗± production in pp collisions was tested for
systematic effects due to uncertainties in signal extraction, track selection
criteria and particle identification for primary pions, $\mathrm{K^{0}_{S}}$
reconstruction, global tracking efficiency for primary pions, primary vertex
selection window, knowledge of the ALICE material budget and hadronic
interaction cross section used in simulations and signal loss correction, as
summarized in Tab. 3. The yield-weighted mean values are quoted for three
separate transverse momentum intervals: low (0 $<$ $p_{\mathrm{T}}$ $<$ 1.2
GeV/$c$), intermediate (1.2 $<$ $p_{\mathrm{T}}$ $<$ 4 GeV/$c$), and
high-$p_{\mathrm{T}}$ (4 $<$ $p_{\mathrm{T}}$ $<$ 15 GeV/$c$).

The systematic uncertainties are dominated by the raw yield extraction,
labeled as “Signal extraction" in Tab. 3 and amount to about 3-6%. This
includes the sensitivity in the choice of the normalization interval, the
fitting range, the shape of the residual background function, the bin counting
range and the constraints on the resonance width imposed in the fitting
procedure. In addition to the default strategy described in Sec 3.2, the
combinatorial background was normalized in different invariant mass regions.
The sensitivity of the $\mathrm{K}$∗± yield extraction to the fit range was
studied by varying each interval boundary by $\pm$ 0.005 GeV/$c^{\mathrm{2}}$.
As an alternative to the function used to describe the shape of the residual
background (Eq.2), a third- and a second-order polynomial function was used.
In this last case, the fitting range was restricted to the region 0.74-1.1
GeV/$c^{\mathrm{2}}$, where the background is reasonably approximated by a
second order polynomial shape. The integration limits were varied by $\pm$
0.01 GeV/$c^{\mathrm{2}}$. The sensitivity of the fit to the constraint on the
$\mathrm{K}$∗± signal width was estimated by using width values that take into
account the current uncertainty on the PDG average value (0.0009
GeV/$c^{\mathrm{2}}$ [16]) or by fitting the signal without any constraint.

The contribution to the uncertainty related to the primary charged pion
reconstruction, reported in Tab. 3, was estimated by varying simultaneously in
the data and Monte Carlo events the track and the PID selections. This
uncertainty ranges from 1 to 2$\%$. In particular, the sensitivity of the
track selection on the number of crossed rows, the number of reconstructed TPC
space points and the distance of closest approach to the primary vertex was
tested. To study the effect of PID on the signal extraction, the selection
criteria based on the TPC energy loss were varied with respect to the default
setting described in Sec. 3.1. PID criteria of 2.5$\sigma_{TPC}$ and
4$\sigma_{TPC}$ were used.

Systematic uncertainties due to the V0 topological and $\mathrm{K^{0}_{S}}$
secondary track selections are reported in Tab. 3 under label
“$\mathrm{K^{0}_{S}}$ reconstruction". These uncertainties were estimated by
varying simultaneously in the data and Monte Carlo events the track and the
PID selection criteria for the secondary tracks, and by varying all the
topological selection criteria (DCA of decay products to PV and between decay
products, cosine of pointing angle and V0 radius). The sensitivity of the
measurement to the competing V0 rejection, the mass selection, the
$\mathrm{K^{0}_{S}}$ rapidity range and lifetime was also studied by varying
the interval selections. Relative uncertainties in the range 0.7-2.9$\%$ were
estimated for the three energies in all the $p_{\mathrm{T}}$ intervals. The
total systematic uncertainties associated with the $\mathrm{K^{0}_{S}}$
measurement are lower than those for the charged ones [13, 3]. In particular,
by exploiting the topological identification of $\mathrm{K^{0}_{S}}$, the
large uncertainties (amounting to about 6$\%$) originating from track
selection and the PID procedure for $\mathrm{K}$± are avoided.

In ALICE, the track reconstruction proceeds from the outermost to the
innermost radius of the TPC. To have a high-quality track for a particle
originating from the primary vertex, the segment of track reconstructed in the
TPC should be matched to reconstructed points in the ITS. This is not
necessary for secondary tracks that originate from weak decay vertices. The
differences in matching probabilities of TPC tracks with reconstructed points
in the ITS between data and Monte Carlo simulations define the global tracking
efficiency uncertainty. This uncertainty is in the range 1-1.4$\%$ for the
5.02 TeV data set, while a constant value of 1$\%$ and 3$\%$ was estimated for
the 13 and 8 TeV data, respectively. These uncertainties are correlated across
$p_{\mathrm{T}}$ for the inspected data sets. Variations in the selection
window around the primary vertex position can modify the yield by about
0.6-2$\%$. The uncertainty related to the knowledge of the ALICE material
budget ranges from 3.1$\%$ to 1.7$\%$ for $p_{\mathrm{T}}$ $<$ 4 GeV/$c$ and
is about 0.7$\%$ at higher $p_{\mathrm{T}}$. The uncertainty connected to the
knowledge of the hadronic interaction cross section in the detector material
is about 1$\%$ for $p_{\mathrm{T}}$ $<$ 4 GeV/$c$. These effects are evaluated
combining the uncertainties for a $\pi$ and a $\mathrm{K^{0}_{S}}$, determined
as in [3, 32], according to the kinematics of the decay. For the signal loss
correction an uncertainty of about 1.5$\%$ was estimated for $p_{\mathrm{T}}$
$<$ 1.2 GeV/$c$ for 5.02 and 13 TeV collisions, while a slightly lower value
was estimated for the 8 TeV collisions. This, for each $p_{\mathrm{T}}$
interval, is the largest value between one half of ($f_{\mathrm{SL}}$ \- 1)
and the difference of signal-loss correction values estimated with different
event generators.

The total systematic uncertainty is 4 - 8$\%$ for all the considered
$p_{\mathrm{T}}$ intervals whereas the systematic uncertainties assigned to
the $\mathrm{K}$∗0 measurements performed to date range from 9$\%$ to 18$\%$
depending on energy and $p_{\mathrm{T}}$ [11, 17, 3]. This confirms that the
systematic uncertainty on the $\mathrm{K}$${}^{*}/$$\mathrm{K}$ ratio can be
reduced by studying the charged resonant state.

Table 3: Sources and yield-weighted mean values of the relative systematic
uncertainties (expressed in $\%$) on the differential yields of the
$\mathrm{K}$∗± resonance at the three centre-of-mass energies under study for
low, intermediate and high-$p_{\mathrm{T}}$ ranges.

$\sqrt{s}$ (TeV) |  5.02 |  8.0 |  13.0
---|---|---|---

$p_{\mathrm{T}}$ (GeV/$c$) | 0 – 1.2 | 1.2 – 4 | 4 – 15 | 0 – 1.2 | 1.2 – 4 | 4 – 15 | 0 – 1.2 | 1.2 – 4 | 4 – 15
---|---|---|---|---|---|---|---|---|---
Signal extraction ($\%$) | 5.4 | 2.8 | 3.4 | 5.8 | 5.5 | 5.4 | 4.4 | 3.7 | 4.5
Primary pion reconstruction ($\%$) | 1.2 | 1.0 | 1.0 | 1.2 | 1.1 | 1.5 | 2.1 | 1.4 | 1.3
$\mathrm{K^{0}_{S}}$ reconstruction ($\%$) | 0.8 | 0.7 | 1.0 | 2.9 | 0.9 | 0.9 | 2.2 | 1.3 | 1.2
Global tracking efficiency ($\%$) | 1.0 | 1.0 | 1.4 | 3.0 | 3.0 | 3.0 | 1.0 | 1.0 | 1.0
Primary vertex ($\%$) | 2.3 | 0.7 | 1.4 | 1.5 | 0.6 | 1.5 | 1.0 | 0.6 | 0.7
Material budget ($\%$) | 3.1 | 1.7 | 0.7 | 3.1 | 1.7 | 0.7 | 3.0 | 1.6 | 0.7
Hadronic interaction ($\%$) | 1.1 | 1.1 | 0.5 | 1.1 | 1.1 | 0.5 | 1.1 | 1.1 | 0.5
Signal Loss ($\%$) | 1.4 | 0.6 | 0.4 | 0.9 | 0.4 | 0.1 | 1.6 | 0.7 | 0.5
Total ($\%$) | 7.1 | 3.9 | 4.3 | 8.1 | 6.8 | 6.6 | 6.6 | 4.8 | 5.1

Figure 3: (Colour online) The $p_{\mathrm{T}}$ spectra of $\mathrm{K}$∗± in
inelastic pp collisions at $\sqrt{s}$ = 5.02, 8, and 13 TeV (full symbols) are
compared to the $p_{\mathrm{T}}$ spectra of $\mathrm{K}$∗0 mesons (open
symbols) at the same energies [11, 17, 3]. Statistical and systematic
uncertainties are reported as error bars and boxes, respectively. The
normalization uncertainties (2.51%, 2.72%, and 2.55% for 5.02, 8, and 13 TeV,
respectively, see Tab. 1) are indicated as coloured boxes and are not included
in the point-to-point uncertainties. The ratio of each measured
$p_{\mathrm{T}}$ distribution for $\mathrm{K}$∗± mesons at $\sqrt{s}$ = 5.02
(red points), 8 (blue points) and 13 TeV (black points) to the $\mathrm{K}$∗0
spectrum at the same collision energy is reported in the bottom panels. The
systematic uncertainty due to global tracking, material budget and hadronic
interaction cross section of primary pions are equal for charged and neutral
$\mathrm{K}$∗, thus they cancel out in the propagation of the uncertainty to
the final ratio. Figure 4: (Colour online) The $\mathrm{K}$∗± $p_{\mathrm{T}}$
spectra (black dots) measured in inelastic pp collisions at (a)$\sqrt{s}$ =
5.02 TeV, (b) 8 TeV, and (c) 13 TeV are compared to the distributions
predicted by PYTHIA8-Monash 2013 [31] (blue lines), PYTHIA6-Perugia 2011 [30]
(red lines), and EPOS-LHC [6] (black lines). Statistical and systematic
uncertainties are shown with error bars and empty boxes, respectively. The
ratios of the rebinned predictions to the measured distributions are reported
in the bottom panels. The shaded bands represent the fractional uncertainties
of the data points.

Figure 5: (Left panel) Ratios of transverse momentum spectra of $\mathrm{K}$∗±
in inelastic pp events at $\sqrt{s}$ = 8 and 13 TeV to corresponding spectra
at 5.02 TeV. Statistical and systematic uncertainties are shown with error
bars and empty boxes, respectively. The normalization uncertainties are shown
as coloured boxes around 1 and they are not included in the point-to-point
uncertainties. Blue and red histograms represent the predictions for the same
ratios from PYTHIA6 Perugia 2011, PYTHIA8 Monash 2013, and EPOS-LHC. (Right
panel) Ratios of transverse momentum spectra of $\mathrm{K}$∗±,
$\mbox{$\mathrm{K}^{+}$}+\mbox{$\mathrm{K}^{-}$}$ and
$\mbox{$\mathrm{\pi}^{+}$}+\mbox{$\mathrm{\pi}^{-}$}$ in inelastic pp events
at $\sqrt{s}$ = 13 TeV [3] to corresponding spectra at 5.02 TeV [33].
Statistical and systematic uncertainties are shown with error bars and empty
boxes, respectively. Figure 6: (Colour online) Particle ratios
$\mathrm{K}$∗±/K and $\mathrm{K}$∗0/K, depicted as $\mathrm{K}$∗/K, in pp [9,
26, 10, 34, 11, 17, 3, 33, 8, 35], central d–Au [36], central p–Pb [12] and
central A–A [9, 10, 37, 8, 35] collisions as a function of
$\sqrt{s_{\mathrm{NN}}}$. For the d–Au data, the numerator yield is derived
from a combination of $\mathrm{K}$∗0 and $\mathrm{K}$∗± states. Bars represent
the statistical uncertainties and boxes represent the systematic
uncertainties. The points for $\mathrm{K}$∗0 for d–Au, Cu–Cu and p–Pb
collisions and for $\mathrm{K}$∗± for pp collisions have been shifted
horizontally for visibility. Red, blue and black lines represent the
$\mathrm{K}$∗±/K ratio predicted with PYTHIA6-Perugia 2011 [30],
PYTHIA8-Monash 2013 [31] and EPOS-LHC [6], respectively.

##  4 Results and discussion

###  4.1 Energy dependence of $\bf{p}_{\mathrm{\bf{T}}}$ spectra and model
comparison

The first measurement of $\mathrm{K}$∗± meson production in inelastic pp
collisions at $\sqrt{s}$ $=$ 5.02, 8, and 13 TeV up to $p_{\mathrm{T}}$ = 15
GeV/$c$ is presented in Fig. 3. The $p_{\mathrm{T}}$-differential yields of
$\mathrm{K}$∗± are compared to those previously measured for $\mathrm{K}$∗0 in
the same collision systems [11, 17, 3]. The spectra of the charged and neutral
mesons are consistent within the uncertainties, as expected considering the
similarity of their quark content and mass.

A comparison between the measured $p_{\mathrm{T}}$ spectra and predictions
based on QCD-inspired event generators such as PYTHIA6 [4], PYTHIA8 [5] and
EPOS-LHC [6] provides useful information on the hadron production mechanisms.

Event generators such as PYTHIA combine a perturbative formalism of hard
processes with a non-perturbative description of hadronization that is
simulated using the Lund string fragmentation model [38]. In the PYTHIA tunes
considered here, multiple parton-parton interactions in the same event and the
colour reconnection mechanism are taken into account. These effects are
important in hadron-hadron interactions at the high LHC energies. In
particular, colour string formation between final-state partons may mimic
effects similar to those induced by collective flow in heavy-ion collisions
[39].

The PYTHIA6-Perugia 2011 tune takes into account some of the lessons learnt
from the early LHC data from inelastic pp collisions at 0.9 and 7 TeV. For
instance, it takes into account the observed increase in baryon production in
the strangeness sector by tuning the $\Lambda/\mbox{$\mathrm{K}$}$ ratio on
the ALICE [40, 41] and CMS [42] data. On the other hand, the
$\mathrm{K}$∗0/$\mathrm{K}$ ratio is tuned on the LEP measurements [30].
Monash 2013 is an updated set of parameters for the PYTHIA8 event generator,
with particular attention to heavy-quark fragmentation and strangeness
production. For all studied LHC collision energies the PYTHIA predictions
overestimate by a factor of 1.5–2 the $\mathrm{K}$∗0 production at transverse
momenta below 0.5 GeV/$c$ and underestimate its production by about 10-20% at
$p_{\mathrm{T}}$ $>$ 1 GeV/$c$ [17, 3, 26].

The EPOS-LHC event generator differs significantly from PYTHIA in its modeling
of both the hadronization and the underlying event. It is a microscopic model
that relies on parton-based Gribov-Regge theory with an improved flow
parameterization which takes into account the case of a very dense system in a
small volume. This high density core is produced by the overlap of string
segments due to multiple parton interactions in pp or multiple nucleon
interactions dominating in nucleus–nucleus collisions. EPOS-LHC reproduces the
increased baryon-to-meson ratios at intermediate $p_{\mathrm{T}}$ as a
consequence of radial flow in high-multiplicity pp events [13]. Both PYTHIA8
and EPOS-LHC are tuned to reproduce the charged particle multiplicity and the
production of identified hadrons (such as $\mathrm{\pi}$, $\mathrm{K}$, p,
$\mathrm{\Lambda}$, $\mathrm{\Xi^{-}}$) measured in pp collisions at
$\sqrt{s}$ = 7 TeV [6].

Figure 4 shows the comparison of the measured $\mathrm{K}$∗± $p_{\mathrm{T}}$
spectra at $\sqrt{s}$ = 5.02, 8, and 13 TeV with the PYTHIA6 (Perugia 2011
tune) [30] and the PYTHIA8 (Monash 2013 tune) generators [31], and EPOS-LHC
[6]. The bottom panels show the ratios of the model predictions to the
measured distributions for $\mathrm{K}$∗± mesons. The agreement with data
improves with the collision energy. The best agreement is reached with
PYTHIA6-Perugia 2011 and PYTHIA8-Monash 2013 for 13 TeV collisions. None of
the models considered for comparison is able to fully reproduce the data. For
all three energies the models overestimate by a factor of 1.5–2 the yield for
$p_{\mathrm{T}}$ $<$ 0.5 GeV/$c$ and underestimate it in the intermediate
$p_{\mathrm{T}}$ region. EPOS-LHC predictions largely overestimate the data in
the high-$p_{\mathrm{T}}$ region, whereas an agreement within the
uncertainties is observed for PYTHIA6 and also for PYTHIA8 at
$\sqrt{s}~{}=~{}13$ TeV. Agreement is also observed with PYTHIA6 for
$p_{\mathrm{T}}$ $>$ 4 GeV/$c$ at $\sqrt{s}~{}=~{}8$ TeV. These results
complement the observation reported in Ref. [3] confirming that a more
accurate tuning of the models is needed to reproduce the phase-space
distribution of strange hadrons.

An evolution of the transverse momentum spectra with the collision energy is
clearly observed in the left panel of Fig. 5, where the ratios of the
$\mathrm{K}$∗± transverse-momentum spectra at $\sqrt{s}$ $=$ 8 and 13 TeV to
the one at $\sqrt{s}$ $=$ 5.02 TeV are reported. The systematic uncertainties
associated with the estimate of the material budget of the ALICE detector and
the hadronic interaction cross section used in the simulations are the same
for the different collision energies. Hence, they cancel out in the
propagation of the uncertainties to the ratio. For $p_{\mathrm{T}}$ $>$ 1
GeV/$c$, a hardening of the $\mathrm{K}$∗± $p_{\mathrm{T}}$ spectrum is
observed from 5.02 to 13 TeV, which is indicative of an increasing
contribution of hard scattering processes in particle production with the
collision energy. In the right panel of Fig. 5 the ratios of the
$\mathrm{K}^{+}$ \+ $\mathrm{K}^{-}$and $\mathrm{\pi}^{+}$ \+
$\mathrm{\pi}^{-}$ $p_{\mathrm{T}}$ distributions at $\sqrt{s}$ $=$ 13 TeV [3]
to the ones at $\sqrt{s}$ $=$ 5.02 TeV [33] are compared to the same ratio for
$\mathrm{K}$∗±. Distributions of these ratios are similar for the different
particle species as shown in ref. [3] for ratios of $p_{\mathrm{T}}$
distributions at $\sqrt{s}$ $=$ 13 TeV to the one at $\sqrt{s}$ $=$ 7 TeV.
These distributions, like the ones for $\mathrm{K}$∗±, show a progressive and
significant evolution of the spectral shape at high $p_{\mathrm{T}}$ with
increasing collision energy and the shape independent of $p_{\mathrm{T}}$
within uncertainties in the soft regime, $p_{\mathrm{T}}$ $<$ 1 GeV/$c$.

In the left panel of Fig. 5 the ratios of the $\mathrm{K}$∗± transverse-
momentum spectra at $\sqrt{s}$ $=$ 8 and 13 TeV to the one at $\sqrt{s}$ $=$
5.02 TeV predicted by PYTHIA6, PYTHIA8 and EPOS-LHC are also shown. PYTHIA6
and PYTHIA8 predict a larger hardening with the energy, while EPOS-LHC is
consistent with data.

###  4.2 Energy dependence of d$\bf{N}$/d$\bf{y}$,
$\langle$$\bf{p}_{\mathrm{\bf{T}}}$$\rangle$ and K∗±/K ratio

The measurements of particle production and particle ratios in pp collisions
are important, also as a baseline for comparison with heavy-ion reactions. The
per-event $p_{\mathrm{T}}$-integrated $\mathrm{K}$∗± yields (corresponding to
$1/{N_{\mathrm{INEL}}}\times$ d$N$/d$y$, hereby denoted as d$N$/d$y$ for
brevity) for inelastic collisions and the mean transverse momenta
$\langle$$p_{\mathrm{T}}$$\rangle$ are determined by integrating and averaging
the transverse momentum spectra over the measured range and are listed in Tab.
4. For per-event $p_{\mathrm{T}}$-integrated yields and
$\langle$$p_{\mathrm{T}}$$\rangle$ statistical uncertainties are estimated
varying the data randomly inside the estimated uncertainties of each bin. The
systematic uncertainties are computed assuming a full correlation across
$p_{\mathrm{T}}$. The uncertainty on d$N$/d$y$ is estimated from the highest
and lowest spectra allowed by the bin-by-bin systematic uncertainties whereas
in the case of the $\langle$$p_{\mathrm{T}}$$\rangle$ the allowed hardest and
the softer $p_{\mathrm{T}}$ distribution are considered.

Table 4: The per-event $p_{\mathrm{T}}$-integrated ($\mathrm{K}$∗+ \+ $\mathrm{K}$∗-)/2 yield for inelastic events in the interval 0 $<$ $p_{\mathrm{T}}$ $<$ 15 GeV/$c$ at midrapidity, d$N$/d$y$, the mean transverse momentum, $\langle$$p_{\mathrm{T}}$$\rangle$, and $\mathrm{K}$∗±/$\mathrm{K}$ for inelastic pp collisions at $\sqrt{s}$ = 5.02, 8 and 13 TeV. The kaon yield is ($\mathrm{K}$+ \+ $\mathrm{K}$-)/2 [33, 17, 3]. The first uncertainty is statistical and the second one is the systematic uncertainty. The systematic uncertainty on d$N$/d$y$ due to the normalization to inelastic collisions (2.51%, 2.72% and 2.55% for 5.02, 8, and 13 TeV, respectively) is not included. $\sqrt{s}$ (TeV) | d$N$/d$y$ |  $\langle$$p_{\mathrm{T}}$$\rangle$ (GeV/$c$) |  $\mathrm{K}$∗±/$\mathrm{K}$
---|---|---|---
5.02 | 0.095 $\pm$ 0.001 $\pm$ 0.006 | 1.04 $\pm$ 0.01 $\pm$ 0.02 | 0.35 $\pm$ 0.01 $\pm$ 0.02
8 | 0.106 $\pm$ 0.002 $\pm$ 0.008 | 1.08 $\pm$ 0.02 $\pm$ 0.02 | 0.34 $\pm$ 0.01 $\pm$ 0.03
13 | 0.108 $\pm$ 0.002 $\pm$ 0.007 | 1.15 $\pm$ 0.02 $\pm$ 0.02 | 0.35 $\pm$ 0.01 $\pm$ 0.03

The per-event $p_{\mathrm{T}}$-integrated yield of the $\mathrm{K}$∗± in
inelastic pp collisions increases from $\sqrt{s}$ = 5.02 TeV to 13 TeV by 13.5
$\pm$ 1.2$\%$. The hardening of the $\mathrm{K}$∗± transverse momentum spectra
reported in Fig. 5 manifests itself in the increasing mean transverse
momentum. In pp collisions, the measured $\langle$$p_{\mathrm{T}}$$\rangle$ at
$\sqrt{s}~{}=$ 13 TeV is 11.1 $\pm$ 0.3$\%$ larger than at
$\sqrt{s}~{}=~{}5.02$ TeV. Similar increasing trend of per-event
$p_{\mathrm{T}}$-integrated yields and mean $p_{\mathrm{T}}$ are observed for
$\mathrm{K}$∗0 across the same collisions energies [11, 17, 3].

Using the $\mathrm{K}$∗± yields presented in this paper and the long-lived
$\mathrm{K}$± production measured by ALICE at the same pp collision energies
[33, 17, 3], the values of the $\mathrm{K}$∗±/$\mathrm{K}$ ratio were
estimated and reported in Tab. 4. The value of d$N$/d$y$ for
($\mathrm{K}$++$\mathrm{K}$-) in $\mathrm{p\kern-0.50003ptp}$ collisions at
$\sqrt{s}$ $=$ 8 TeV was estimated by fitting the data points at $\sqrt{s}$ =
0.9, 2.76 and 7 TeV [17] with the polynomial function $A(\sqrt{s})^{n}+B$,
where $A$, $n$ and $B$ are the fit parameters and by extrapolating the value
for $\sqrt{s}$ = 8 TeV. Due to the fact that the same data samples were
analyzed to extract both resonance and kaon yields, the uncertainties due to
the absolute normalization cancel and therefore they are not included in the
systematic uncertainties of these ratios. Consistent values are obtained for
the ratio at the three collision energies. These ratios are presented in Fig.
6 together with the results obtained for $\mathrm{K}$∗0/$\mathrm{K}$ in
different collisions at RHIC [8, 35, 36] and LHC [9, 26, 12, 10, 34, 37, 11,
17, 3, 33] energies. The $\mathrm{K}$∗±/K ratios predicted by PYTHIA6-Perugia
2011 [30], PYTHIA8-Monash 2013 [31] and EPOS-LHC [6] at 5.02, 8 and 13 TeV are
reported in Fig. 6 with dashed lines. The predicted ratios do not change
varying the collision energy and are in agreement with the measured values
within uncertainties. In pp, p–A and d–A collisions at RHIC and the LHC, the
$\mathrm{K}$∗/$\mathrm{K}$ ratio do not exhibit a strong dependence on the
colliding system size or the centre-of-mass energy. A lower value is reported
for $\mathrm{K}$∗0/$\mathrm{K}$ ratio in central A–A collisions both at RHIC
and LHC energies. The observed suppression of the $\mathrm{K}$∗0/$\mathrm{K}$
ratio is currently understood as the result of re-scattering and regeneration
effects in the hadronic phase of heavy-ion collisions, with the former
dominating over the latter [9, 10, 11].

In the upper panel of Fig. 7 the $\mathrm{K}$∗± and $\mathrm{K}^{\pm}$ [33, 3]
$p_{\mathrm{T}}$ spectra at $\sqrt{s}$ = 5.02 and 13 TeV are compared. At both
energies the $\mathrm{K}^{\pm}$ and the $\mathrm{K}$∗± spectra exhibit the
same slopes and consistent yields for $p_{\mathrm{T}}$ $>$ 3 GeV/$c$. For
$p_{\mathrm{T}}$ $<$ 2 GeV/$c$ a larger yield for $\mathrm{K}^{\pm}$ is
measured with respect to $\mathrm{K}$∗±. In the same figure the
$\mathrm{K}^{\pm}$ $p_{\mathrm{T}}$ spectra are compared with the PYTHIA6
(Perugia 2011 tune) [30], PYTHIA8 (Monash 2013 tune) [31] and EPOS-LHC [6]
generators. The ratios of the rebinned predictions to the measured
$p_{\mathrm{T}}$ distributions for $\mathrm{K}^{\pm}$ are reported in the two
middle panels. Likewise $\mathrm{K}$∗±, for $\mathrm{K}^{\pm}$ the agreement
with data improves at higher collision energies. The best agreement is reached
for 13 TeV collisions. For both energies PYTHIA8 and EPOS-LHC overestimate by
a factor of 1.3–1.4 the $\mathrm{K}$ yield for $p_{\mathrm{T}}$ $<$ 0.5
GeV/$c$ while PYTHIA6-Perugia 2011 reproduces or slightly underestimates the
spectra in the same region. At 5.02 TeV all the models underestimate the
spectra in the 1 $<$ $p_{\mathrm{T}}$ $<$ 6 GeV/$c$ region. For
$p_{\mathrm{T}}$ larger than 5 GeV/$c$ PYTHIA6-Perugia2011 model at 13 TeV is
not able to reproduce the $\mathrm{K}$ data by a factor 1.2.

The $p_{\mathrm{T}}$ dependence of the $\mathrm{K}$∗±/$\mathrm{K}$ ratios for
pp collisions at $\sqrt{s}$ = 5.02 and 13 TeV is shown in the bottom panels of
Fig. 7. These ratios increase at low $p_{\mathrm{T}}$ and saturate for
$p_{\mathrm{T}}$ $>$ 3.0 GeV/$c$. The $\mathrm{K}$∗±/$\mathrm{K}$ ratios
predicted by PYTHIA6, PYTHIA8 and EPOS-LHC are also shown for comparison.
While PYTHIA6 and PYTHIA8 slightly underestimate the ratios for
$p_{\mathrm{T}}$ larger than 2 GeV/$c$, EPOS-LHC predictions largely
overestimate the data in the high-$p_{\mathrm{T}}$ region. All the generators
describe rather well the distributions at low transverse momentum.

Figure 7: (Colour online) (Upper panel) The $p_{\mathrm{T}}$ spectra of
$\mathrm{K}$∗± in inelastic pp collisions at $\sqrt{s}$ = 5.02 and 13 TeV
(full symbols) are compared to the $p_{\mathrm{T}}$ spectra of
$\mathrm{K}^{\pm}$ mesons (open symbols) at the same energies [33, 3].
Statistical and systematic uncertainties are reported as error bars and boxes,
respectively. Red, blue and black lines represent the $\mathrm{K}$ spectra
predicted with PYTHIA6-Perugia 2011 [30], PYTHIA8-Monash 2013 [31] and EPOS-
LHC [6], respectively. (Middle panels) The ratios of the rebinned predictions
to the measured $p_{\mathrm{T}}$ distributions for $\mathrm{K}^{\pm}$ are
reported in the two middle panels. The shaded bands represent the fractional
uncertainties of the data points. (Bottom panels) The ratio of each measured
$p_{\mathrm{T}}$ distribution for $\mathrm{K}$∗± mesons at $\sqrt{s}$ = 5.02
(red points) and 13 TeV (black points) to the $\mathrm{K}$ spectrum at the
same collision energy is reported in the bottom panels. Red, blue and black
lines represent the $\mathrm{K}$∗±/K ratio predicted with PYTHIA6-Perugia 2011
[30], PYTHIA8-Monash 2013 [31] and EPOS-LHC [6], respectively.

##  5 Summary

The first measurements of the $\mathrm{K}$∗± resonance in inelastic pp
collisions at different (5.02, 8, and 13 TeV) LHC energies were presented. The
transverse momentum spectra were measured at midrapidity in the range 0 $<$
$p_{\mathrm{T}}$ $<$ 15 GeV/$c$ and $p_{\mathrm{T}}$-integrated yields as well
as $\langle$$p_{\mathrm{T}}$$\rangle$ were calculated. These measurements
complement and confirm the previous results for $\mathrm{K}$∗0 although with
smaller systematic uncertainties.

The ratios of the $\mathrm{K}$∗± $p_{\mathrm{T}}$ distributions at $\sqrt{s}$
= 8 TeV and 13 TeV to those at 5.02 TeV reveal a hardening of the spectra with
increasing collision energy for $p_{\mathrm{T}}$ $>$ 1 GeV/$c$. An increase in
$\langle$$p_{\mathrm{T}}$$\rangle$ by about 11% is observed going from
$\sqrt{s}$ = 5.02 to 13 TeV. This is consistent with the expectation that the
contribution of hard processes to particle production increases with the
collision energy. The weak energy dependence of the spectra below 1 GeV/$c$ is
consistent with the relatively small increase of the yields, since the
$p_{\mathrm{T}}$-integrated yields are dominated by the low-$p_{\mathrm{T}}$
part of the spectrum. A similar evolution of the ratios of the
$p_{\mathrm{T}}$ distributions at $\sqrt{s}$ $=$ 13 TeV to the one at
$\sqrt{s}$ $=$ 5.02 TeV is observed for $\mathrm{K}^{+}$ \+ $\mathrm{K}^{-}$
and $\mathrm{\pi}^{+}$ \+ $\mathrm{\pi}^{-}$. This confirms the independence
of the evolution of the spectral shape from particle species as observed in
[3].

At $\sqrt{s}$ = 5.02 and 13 TeV the $\mathrm{K}^{\pm}$ and the $\mathrm{K}$∗±
spectra exhibit the same slopes and consistent yields for $p_{\mathrm{T}}$ $>$
3 GeV/$c$. This indicates that production mechanisms as gluon fragmentation
should have the same importance in the generation of ground and excitated
status of $\mathrm{K}$. Moreover the $\mathrm{K}$∗±/$\mathrm{K}$
$p_{\mathrm{T}}$-integrated yield ratios for the three reported energies are
equal within uncertainties. This confirms, with a smaller uncertainty, the
independence of $\mathrm{K}$∗/$\mathrm{K}$ ratio in pp collisions at LHC
energies and the weak dependence on the colliding system size or the centre-
of-mass energy in pp, p–A and d–A collisions at RHIC and the LHC.

Predictions of QCD-inspired (PYTHIA6, PYTHIA8) and hybrid (EPOS-LHC) event
generators are not able to fully describe the $\mathrm{K}$∗± transverse
momentum spectra. The ability of the models to both qualitatively and
quantitatively describe the data improves with the collision energy. The best
agreement is obtained with PYTHIA6-Perugia 2011 and PYTHIA8-Monash 2013 for 13
TeV. However, EPOS-LHC better reproduces the relative hardening of the
$p_{\mathrm{T}}$ spectrum with increasing collision energy. The
$\mathrm{K}$∗±/$\mathrm{K}$ ratios predicted from the event generators are in
agreement with the measured ones and, like in data, are independent from the
collision energy. All the generators describe reasonably well the
$\mathrm{K}$∗±/$\mathrm{K}$ ratio measured at low $p_{\mathrm{T}}$ while they
fail for $p_{\mathrm{T}}$ larger than 2 GeV/$c$.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: 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; 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 Education and Science, 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 Energy, Nuclear and Mineral Research Agency (TENMAK), 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] L. Evans and P. Bryant, “LHC Machine”, JINST 3 (2008) S08001.
  * [2] ALICE Collaboration, J. Adam et al., “Pseudorapidity and transverse momentum distributions of charged particles in proton-proton collisions at $\sqrt{s}$ = 13 TeV”, Phys. Lett. B753 (2016) 319–329, arXiv:1509.08734.
  * [3] ALICE Collaboration, S. Acharya et al., “Production of light-flavor hadrons in pp collisions at $\sqrt{s}$ = 7 and $\sqrt{s}$ = 13 TeV”, Eur. Phys. J. C81 (2021) 256, arXiv:2005.11120.
  * [4] T. Sjöstrand, S. Mrenna, and P. Z. Skands, “PYTHIA 6.4 Physics and Manual”, JHEP 05 (2006) 026, arXiv:hep-ph/0603175 [hep-ph].
  * [5] T. Sjöstrand, S. Mrenna, and P. Z. Skands, “A Brief Introduction to PYTHIA 8.1”, Comput. Phys. Commun. 178 (2008) 852–867, arXiv:0710.3820 [hep-ph].
  * [6] T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, and K. Werner, “EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider”, Phys. Rev. C92 no. 3, (2015) 034906, arXiv:1306.0121 [hep-ph].
  * [7] ALICE Collaboration, A. Aamodt et al., “Two-pion Bose-Einstain correlations in central Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV”, Phys. Lett. B696 (2011) 328–337, arXiv:1012.4035.
  * [8] STAR Collaboration, J. Adams et al., “K(892)* resonance production in Au+Au and p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV at STAR”, Phys. Rev. C71 (2005) 064902, arXiv:nucl-ex/0412019 [nucl-ex].
  * [9] ALICE Collaboration, B. Abelev et al., “${K}^{*}{(892)}^{0}$ and $\phi(1020)$ production in Pb-Pb collisions at $\sqrt{{s}_{NN}}$ = 2.76 TeV”, Phys. Rev. C91 (2015) 024609, arXiv:1404.0495 [nucl-ex].
  * [10] ALICE Collaboration, J. Adam et al., “K${}^{*}(892)^{0}$ and $\phi(1020)$ meson production at high transverse momentum in pp and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV”, Phys. Rev. C95 no. 6, (2017) 064606, arXiv:1702.00555 [nucl-ex].
  * [11] ALICE Collaboration, S. Acharya et al., “Evidence of rescattering effect in Pb–Pb collisions at the LHC through production of $K^{*0}$ and $\phi(1020)$ mesons”, Phys. Lett. B802 (2020) 135225, arXiv:1910.14419 [nucl-ex].
  * [12] ALICE Collaboration, J. Adam et al., “Production of K∗(892)0 and $\phi$(1020) in p-Pb collisions at $\sqrt{s_{{\text{NN}}}}$ = 5.02 TeV”, Eur. Phys. J. C76 no. 5, (2016) 245, arXiv:1601.07868 [nucl-ex].
  * [13] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s}$ = 7 TeV”, Phys. Rev. C99 (2019) 024906, arXiv:1807.11321.
  * [14] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of $K^{*}(892)^{0}$ and $\phi$(1020) production in pp collisions at 13 TeV”, Phys. Lett. B807 (2020) 135501, arXiv:1910.14397 [nucl-ex].
  * [15] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC”, JINST 3 (2008) S08002.
  * [16] Particle Data Group Collaboration, C. Patrignani et al., “Review of Particle Physics”, Chin. Phys. C40 no. 10, (2016) 100001.
  * [17] ALICE Collaboration, S. Acharya et al., “$K^{*}(892)^{0}$ and $\phi$(1020) production at mid-rapidity in pp collisions at $\sqrt{s}$ = 8 TeV”, Phys. Rev. C (2020) 024912, arXiv:1910.14410 [nucl-ex].
  * [18] ALICE Collaboration, 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].
  * [19] 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, arXiv:1001.1950 [physics.ins-det].
  * [20] ALICE Collaboration, E. Abbas et al., “Performance of the ALICE VZERO system”, J. Instr. 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].
  * [21] ALICE Collaboration, “ALICE luminosity determination for pp collisions at $\sqrt{s}$ = 5.02 TeV”, ALICE-PUBLIC-2016-005 (2016) . https://cds.cern.ch/record/2202638?ln=it.
  * [22] ALICE Collaboration, “ALICE luminosity determination for pp collisions at $\sqrt{s}$ = 8 TeV”, ALICE-PUBLIC-2017-002 (2017) . https://cds.cern.ch/record/2255216?ln=it.
  * [23] ALICE Collaboration, “ALICE luminosity determination for pp collisions at $\sqrt{s}$ = 13 TeV”, ALICE-PUBLIC-2016-002 (2016) . https://cds.cern.ch/record/2160174?ln=it.
  * [24] C. Loizides, J. Kamin, and D. d’Enterria, “Improved Monte Carlo Glauber predictions at present and future nuclear colliders”, Phys. Rev. C97 (May, 2018) 054910. https://link.aps.org/doi/10.1103/PhysRevC.97.054910.
  * [25] ALICE Collaboration, B. Abelev et al., “Multiplicity dependence of pion, kaon, proton and lambda production in p-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV”, Phys. Lett. B728 (2014) 25, arXiv:1307.6796 [nucl-ex].
  * [26] ALICE Collaboration, B. Abelev et al., “Production of $K^{*}(892)^{0}$ and $\phi(1020)$ in pp collisions at $\sqrt{s}$ = 7 TeV”, Eur. Phys. J. C72 (2012) 2183, arXiv:1208.5717 [hep-ex].
  * [27] R. Brun, F. Bruyant, F. Carminati, S. Giani, M. Maire, A. McPherson, G. Patrick, and L. Urban, “GEANT Detector Description and Simulation Tool”, tech. rep., 1993.  CERN Program Library, Long Writeup:W5013.  cds.cern.ch/record/1082634.
  * [28] DELPHI Collaboration, P. Abreu et al., “Production characteristics of K0 and light meson resonances in hadronic decays of the Z0”, Z. Phys. C65 (1995) 587–602.
  * [29] OPAL Collaboration, K. Ackerstaff et al., “Photon and light meson production in hadronic Z0 decays”, Eur. Phys. J. C5 (1998) 411–437, arXiv:hep-ex/9805011 [hep-ex].
  * [30] P. Z. Skands, “Tuning Monte Carlo Generators: The Perugia Tunes”, Phys. Rev. D82 (2010) 074018, arXiv:1005.3457 [hep-ph].
  * [31] P. Skands, S. Carrazza, and J. Rojo, “Tuning PYTHIA 8.1: the Monash 2013 Tune”, Eur. Phys. J. C74 no. 8, (2014) 3024, arXiv:1404.5630 [hep-ph].
  * [32] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV”, Eur. Phys. J. C80 (2020) 167, arXiv:1908.01861 [nucl-ex].
  * [33] ALICE Collaboration, S. Acharya et al., “Production of charged pions, kaons and (anti)protons in Pb-Pb and inelastic pp collisions at $\sqrt{s_{NN}}$ = 5.02 TeV”, Phys. Rev. C101 (2020) 044907, arXiv:1910.07678 [nucl-ex].
  * [34] 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 no. 5, (2015) 226, arXiv:1504.00024 [nucl-ex].
  * [35] STAR Collaboration, M. M. Aggarwal et al., “$K^{*0}$ production in Cu+Cu and Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV”, Phys. Rev. C84 (2011) 034909, arXiv:1006.1961 [nucl-ex].
  * [36] STAR Collaboration, B. I. Abelev et al., “Hadronic resonance production in d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at RHIC”, Phys. Rev. C78 (2008) 044906, arXiv:0801.0450 [nucl-ex].
  * [37] ALICE Collaboration, B. Abelev et al., “Centrality dependence of $\pi$, K, p production in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV”, Phys. Rev. C88 (2013) 044910, arXiv:1303.0737 [hep-ex].
  * [38] B. Andersson et al., “Parton fragmentation and string dynamics”, Phys. Rep. 97 (1983) 31.
  * [39] A. Ortiz Velasquez et al., “Color reconnection and flow-like patterns in pp collisions”, Phys. Rev. Lett. 111 no. 4, (2013) 042001, arXiv:1303.6326 [hep-ph].
  * [40] 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].
  * [41] ALICE Collaboration, K. Aamodt et al., “Production of pions, kaons and protons in pp collisions at $\sqrt{s}$ = 900 GeV with ALICE at the LHC”, Eur. Phys. J. C71 (2011) 1655, arXiv:1101.4110 [hep-ex].
  * [42] CMS Collaboration, V. Khachatryan et al., “Strange particle production in pp collisions at $\sqrt{s}$ = 0.9 and 7 TeV”, JHEP 05 (2011) 064, arXiv:1102.4282 [hep-ex].

##  Appendix A The ALICE Collaboration

S. Acharya143, D. Adamová98, A. Adler76, J. Adolfsson83, G. Aglieri Rinella35,
M. Agnello31, N. Agrawal55, Z. Ahammed143, S. Ahmad16, S.U. Ahn78, I. Ahuja39,
Z. Akbar52, A. Akindinov95, M. Al-Turany110, S.N. Alam41, D. Aleksandrov91, B.
Alessandro61, H.M. Alfanda7, R. Alfaro Molina73, B. Ali16, Y. Ali14, A.
Alici26, N. Alizadehvandchali127, A. Alkin35, J. Alme21, T. Alt70, L.
Altenkamper21, I. Altsybeev115, M.N. Anaam7, C. Andrei49, D. Andreou93, A.
Andronic146, M. Angeletti35, V. Anguelov107, F. Antinori58, P. Antonioli55, C.
Anuj16, N. Apadula82, L. Aphecetche117, H. Appelshäuser70, S. Arcelli26, R.
Arnaldi61, I.C. Arsene20, M. Arslandok148,107, A. Augustinus35, R.
Averbeck110, S. Aziz80, M.D. Azmi16, A. Badalà57, Y.W. Baek42, X. Bai131,110,
R. Bailhache70, Y. Bailung51, R. Bala104, A. Balbino31, A. Baldisseri140, B.
Balis2, M. Ball44, D. Banerjee4, R. Barbera27, L. Barioglio108,25, M.
Barlou87, G.G. Barnaföldi147, L.S. Barnby97, V. Barret137, C. Bartels130, K.
Barth35, E. Bartsch70, F. Baruffaldi28, N. Bastid137, S. Basu83, G.
Batigne117, B. Batyunya77, D. Bauri50, J.L. Bazo Alba114, I.G. Bearden92, C.
Beattie148, I. Belikov139, A.D.C. Bell Hechavarria146, F. Bellini26,35, R.
Bellwied127, S. Belokurova115, V. Belyaev96, G. Bencedi71, S. Beole25, A.
Bercuci49, Y. Berdnikov101, A. Berdnikova107, D. Berenyi147, L. Bergmann107,
M.G. Besoiu69, L. Betev35, P.P. Bhaduri143, A. Bhasin104, I.R. Bhat104, M.A.
Bhat4, B. Bhattacharjee43, P. Bhattacharya23, L. Bianchi25, N. Bianchi53, J.
Bielčík38, J. Bielčíková98, J. Biernat120, A. Bilandzic108, G. Biro147, S.
Biswas4, J.T. Blair121, D. Blau91, M.B. Blidaru110, C. Blume70, G. Boca29,59,
F. Bock99, A. Bogdanov96, S. Boi23, J. Bok63, L. Boldizsár147, A.
Bolozdynya96, M. Bombara39, P.M. Bond35, G. Bonomi142,59, H. Borel140, A.
Borissov84, H. Bossi148, E. Botta25, L. Bratrud70, P. Braun-Munzinger110, M.
Bregant123, M. Broz38, G.E. Bruno109,34, M.D. Buckland130, D. Budnikov111, H.
Buesching70, S. Bufalino31, O. Bugnon117, P. Buhler116, Z. Buthelezi74,134,
J.B. Butt14, S.A. Bysiak120, D. Caffarri93, M. Cai28,7, H. Caines148, A.
Caliva110, E. Calvo Villar114, J.M.M. Camacho122, R.S. Camacho46, P.
Camerini24, F.D.M. Canedo123, F. Carnesecchi35,26, R. Caron140, J. Castillo
Castellanos140, E.A.R. Casula23, F. Catalano31, C. Ceballos Sanchez77, P.
Chakraborty50, S. Chandra143, S. Chapeland35, M. Chartier130, S.
Chattopadhyay143, S. Chattopadhyay112, A. Chauvin23, T.G. Chavez46, C.
Cheshkov138, B. Cheynis138, V. Chibante Barroso35, D.D. Chinellato124, S.
Cho63, P. Chochula35, P. Christakoglou93, C.H. Christensen92, P.
Christiansen83, T. Chujo136, C. Cicalo56, L. Cifarelli26, F. Cindolo55, M.R.
Ciupek110, G. ClaiII,55, J. CleymansI,126, F. Colamaria54, J.S. Colburn113, D.
Colella109,54,34,147, A. Collu82, M. Colocci35,26, M. ConcasIII,61, G. Conesa
Balbastre81, Z. Conesa del Valle80, G. Contin24, J.G. Contreras38, M.L.
Coquet140, T.M. Cormier99, P. Cortese32, M.R. Cosentino125, F. Costa35, S.
Costanza29,59, P. Crochet137, R. Cruz-Torres82, E. Cuautle71, P. Cui7, L.
Cunqueiro99, A. Dainese58, F.P.A. Damas117,140, M.C. Danisch107, A. Danu69, I.
Das112, P. Das89, P. Das4, S. Das4, S. Dash50, S. De89, A. De Caro30, G. de
Cataldo54, L. De Cilladi25, J. de Cuveland40, A. De Falco23, D. De Gruttola30,
N. De Marco61, C. De Martin24, S. De Pasquale30, S. Deb51, H.F. Degenhardt123,
K.R. Deja144, L. Dello Stritto30, S. Delsanto25, W. Deng7, P. Dhankher19, D.
Di Bari34, A. Di Mauro35, R.A. Diaz8, T. Dietel126, Y. Ding138,7, R. Divià35,
D.U. Dixit19, Ø. Djuvsland21, U. Dmitrieva65, J. Do63, A. Dobrin69, B.
Dönigus70, O. Dordic20, A.K. Dubey143, A. Dubla110,93, S. Dudi103, M.
Dukhishyam89, P. Dupieux137, N. Dzalaiova13, T.M. Eder146, R.J. Ehlers99, V.N.
Eikeland21, D. Elia54, B. Erazmus117, F. Ercolessi26, F. Erhardt102, A.
Erokhin115, M.R. Ersdal21, B. Espagnon80, G. Eulisse35, D. Evans113, S.
Evdokimov94, L. Fabbietti108, M. Faggin28, J. Faivre81, F. Fan7, A. Fantoni53,
M. Fasel99, P. Fecchio31, A. Feliciello61, G. Feofilov115, A. Fernández
Téllez46, A. Ferrero140, A. Ferretti25, V.J.G. Feuillard107, J. Figiel120, S.
Filchagin111, D. Finogeev65, F.M. Fionda56,21, G. Fiorenza35,109, F. Flor127,
A.N. Flores121, S. Foertsch74, P. Foka110, S. Fokin91, E. Fragiacomo62, E.
Frajna147, U. Fuchs35, N. Funicello30, C. Furget81, A. Furs65, J.J.
Gaardhøje92, M. Gagliardi25, A.M. Gago114, A. Gal139, C.D. Galvan122, P.
Ganoti87, C. Garabatos110, J.R.A. Garcia46, E. Garcia-Solis10, K. Garg117, C.
Gargiulo35, A. Garibli90, K. Garner146, P. Gasik110, E.F. Gauger121, A.
Gautam129, M.B. Gay Ducati72, M. Germain117, J. Ghosh112, P. Ghosh143, S.K.
Ghosh4, M. Giacalone26, P. Gianotti53, P. Giubellino110,61, P. Giubilato28,
A.M.C. Glaenzer140, P. Glässel107, D.J.Q. Goh85, V. Gonzalez145, L.H.
González-Trueba73, S. Gorbunov40, M. Gorgon2, L. Görlich120, S. Gotovac36, V.
Grabski73, L.K. Graczykowski144, L. Greiner82, A. Grelli64, C. Grigoras35, V.
Grigoriev96, A. GrigoryanI,1, S. Grigoryan77,1, O.S. Groettvik21, F.
Grosa35,61, J.F. Grosse-Oetringhaus35, R. Grosso110, G.G. Guardiano124, R.
Guernane81, M. Guilbaud117, K. Gulbrandsen92, T. Gunji135, A. Gupta104, R.
Gupta104, I.B. Guzman46, S.P. Guzman46, L. Gyulai147, M.K. Habib110, C.
Hadjidakis80, G. Halimoglu70, H. Hamagaki85, G. Hamar147, M. Hamid7, R.
Hannigan121, M.R. Haque144,89, A. Harlenderova110, J.W. Harris148, A.
Harton10, J.A. Hasenbichler35, H. Hassan99, D. Hatzifotiadou55, P. Hauer44,
L.B. Havener148, S. Hayashi135, S.T. Heckel108, E. Hellbär70, H. Helstrup37,
T. Herman38, E.G. Hernandez46, G. Herrera Corral9, F. Herrmann146, K.F.
Hetland37, H. Hillemanns35, C. Hills130, B. Hippolyte139, B. Hofman64, B.
Hohlweger93,108, J. Honermann146, G.H. Hong149, D. Horak38, S. Hornung110, A.
Horzyk2, R. Hosokawa15, P. Hristov35, C. Huang80, C. Hughes133, P. Huhn70,
T.J. Humanic100, H. Hushnud112, L.A. Husova146, A. Hutson127, D. Hutter40,
J.P. Iddon35,130, R. Ilkaev111, H. Ilyas14, M. Inaba136, G.M. Innocenti35, M.
Ippolitov91, A. Isakov38,98, M.S. Islam112, M. Ivanov110, V. Ivanov101, V.
Izucheev94, M. Jablonski2, B. Jacak82, N. Jacazio35, P.M. Jacobs82, S.
Jadlovska119, J. Jadlovsky119, S. Jaelani64, C. Jahnke124,123, M.J.
Jakubowska144, M.A. Janik144, T. Janson76, M. Jercic102, O. Jevons113, F.
Jonas99,146, P.G. Jones113, J.M. Jowett 35,110, J. Jung70, M. Jung70, A.
Junique35, A. Jusko113, J. Kaewjai118, P. Kalinak66, A. Kalweit35, V.
Kaplin96, S. Kar7, A. Karasu Uysal79, D. Karatovic102, O. Karavichev65, T.
Karavicheva65, P. Karczmarczyk144, E. Karpechev65, A. Kazantsev91, U.
Kebschull76, R. Keidel48, D.L.D. Keijdener64, M. Keil35, B. Ketzer44, Z.
Khabanova93, A.M. Khan7, S. Khan16, A. Khanzadeev101, Y. Kharlov94, A.
Khatun16, A. Khuntia120, B. Kileng37, B. Kim17,63, D. Kim149, D.J. Kim128,
E.J. Kim75, J. Kim149, J.S. Kim42, J. Kim107, J. Kim149, J. Kim75, M. Kim107,
S. Kim18, T. Kim149, S. Kirsch70, I. Kisel40, S. Kiselev95, A. Kisiel144, J.P.
Kitowski2, J.L. Klay6, J. Klein35, S. Klein82, C. Klein-Bösing146, M.
Kleiner70, T. Klemenz108, A. Kluge35, A.G. Knospe127, C. Kobdaj118, M.K.
Köhler107, T. Kollegger110, A. Kondratyev77, N. Kondratyeva96, E.
Kondratyuk94, J. Konig70, S.A. Konigstorfer108, P.J. Konopka35,2, G.
Kornakov144, S.D. Koryciak2, L. Koska119, A. Kotliarov98, O. Kovalenko88, V.
Kovalenko115, M. Kowalski120, I. Králik66, A. Kravčáková39, L. Kreis110, M.
Krivda113,66, F. Krizek98, K. Krizkova Gajdosova38, M. Kroesen107, M.
Krüger70, E. Kryshen101, M. Krzewicki40, V. Kučera35, C. Kuhn139, P.G.
Kuijer93, T. Kumaoka136, D. Kumar143, L. Kumar103, N. Kumar103, S. Kundu35,89,
P. Kurashvili88, A. Kurepin65, A.B. Kurepin65, A. Kuryakin111, S. Kushpil98,
J. Kvapil113, M.J. Kweon63, J.Y. Kwon63, Y. Kwon149, S.L. La Pointe40, P. La
Rocca27, Y.S. Lai82, A. Lakrathok118, M. Lamanna35, R. Langoy132, K.
Lapidus35, P. Larionov53, E. Laudi35, L. Lautner35,108, R. Lavicka38, T.
Lazareva115, R. Lea142,24,59, J. Lee136, J. Lehrbach40, R.C. Lemmon97, I. León
Monzón122, E.D. Lesser19, M. Lettrich35,108, P. Lévai147, X. Li11, X.L. Li7,
J. Lien132, R. Lietava113, B. Lim17, S.H. Lim17, V. Lindenstruth40, A.
Lindner49, C. Lippmann110, A. Liu19, J. Liu130, I.M. Lofnes21, V. Loginov96,
C. Loizides99, P. Loncar36, J.A. Lopez107, X. Lopez137, E. López Torres8, J.R.
Luhder146, M. Lunardon28, G. Luparello62, Y.G. Ma41, A. Maevskaya65, M.
Mager35, T. Mahmoud44, A. Maire139, M. Malaev101, Q.W. Malik20, L.
MalininaIV,77, D. Mal’Kevich95, N. Mallick51, P. Malzacher110, G.
Mandaglio33,57, V. Manko91, F. Manso137, V. Manzari54, Y. Mao7, J. Mareš68,
G.V. Margagliotti24, A. Margotti55, A. Marín110, C. Markert121, M. Marquard70,
N.A. Martin107, P. Martinengo35, J.L. Martinez127, M.I. Martínez46, G.
Martínez García117, S. Masciocchi110, M. Masera25, A. Masoni56, L.
Massacrier80, A. Mastroserio141,54, A.M. Mathis108, O. Matonoha83, P.F.T.
Matuoka123, A. Matyja120, C. Mayer120, A.L. Mazuecos35, F. Mazzaschi25, M.
Mazzilli35, M.A. Mazzoni60, J.E. Mdhluli134, A.F. Mechler70, F. Meddi22, Y.
Melikyan65, A. Menchaca-Rocha73, E. Meninno116,30, A.S. Menon127, M. Meres13,
S. Mhlanga126,74, Y. Miake136, L. Micheletti61,25, L.C. Migliorin138, D.L.
Mihaylov108, K. Mikhaylov77,95, A.N. Mishra147, D. Miśkowiec110, A. Modak4,
A.P. Mohanty64, B. Mohanty89, M. Mohisin Khan16, Z. Moravcova92, C.
Mordasini108, D.A. Moreira De Godoy146, L.A.P. Moreno46, I. Morozov65, A.
Morsch35, T. Mrnjavac35, V. Muccifora53, E. Mudnic36, D. Mühlheim146, S.
Muhuri143, J.D. Mulligan82, A. Mulliri23, M.G. Munhoz123, R.H. Munzer70, H.
Murakami135, S. Murray126, L. Musa35, J. Musinsky66, C.J. Myers127, J.W.
Myrcha144, B. Naik134,50, R. Nair88, B.K. Nandi50, R. Nania55, E. Nappi54,
M.U. Naru14, A.F. Nassirpour83, A. Nath107, C. Nattrass133, A. Neagu20, L.
Nellen71, S.V. Nesbo37, G. Neskovic40, D. Nesterov115, B.S. Nielsen92, S.
Nikolaev91, S. Nikulin91, V. Nikulin101, F. Noferini55, S. Noh12, P.
Nomokonov77, J. Norman130, N. Novitzky136, P. Nowakowski144, A. Nyanin91, J.
Nystrand21, M. Ogino85, A. Ohlson83, V.A. Okorokov96, J. Oleniacz144, A.C.
Oliveira Da Silva133, M.H. Oliver148, A. Onnerstad128, C. Oppedisano61, A.
Ortiz Velasquez71, T. Osako47, A. Oskarsson83, J. Otwinowski120, K. Oyama85,
Y. Pachmayer107, S. Padhan50, D. Pagano142,59, G. Paić71, A. Palasciano54, J.
Pan145, S. Panebianco140, P. Pareek143, J. Park63, J.E. Parkkila128, S.P.
Pathak127, R.N. Patra104,35, B. Paul23, J. Pazzini142,59, H. Pei7, T.
Peitzmann64, X. Peng7, L.G. Pereira72, H. Pereira Da Costa140, D. Peresunko91,
G.M. Perez8, S. Perrin140, Y. Pestov5, V. Petráček38, M. Petrovici49, R.P.
Pezzi72, S. Piano62, M. Pikna13, P. Pillot117, O. Pinazza55,35, L. Pinsky127,
C. Pinto27, S. Pisano53, M. Płoskoń82, M. Planinic102, F. Pliquett70, M.G.
Poghosyan99, B. Polichtchouk94, S. Politano31, N. Poljak102, A. Pop49, S.
Porteboeuf-Houssais137, J. Porter82, V. Pozdniakov77, S.K. Prasad4, R.
Preghenella55, F. Prino61, C.A. Pruneau145, I. Pshenichnov65, M. Puccio35, S.
Qiu93, L. Quaglia25, R.E. Quishpe127, S. Ragoni113, A. Rakotozafindrabe140, L.
Ramello32, F. Rami139, S.A.R. Ramirez46, A.G.T. Ramos34, T.A. Rancien81, R.
Raniwala105, S. Raniwala105, S.S. Räsänen45, R. Rath51, I. Ravasenga93, K.F.
Read99,133, A.R. Redelbach40, K. RedlichV,88, A. Rehman21, P. Reichelt70, F.
Reidt35, H.A. Reme-ness37, R. Renfordt70, Z. Rescakova39, K. Reygers107, A.
Riabov101, V. Riabov101, T. Richert83,92, M. Richter20, W. Riegler35, F.
Riggi27, C. Ristea69, S.P. Rode51, M. Rodríguez Cahuantzi46, K. Røed20, R.
Rogalev94, E. Rogochaya77, T.S. Rogoschinski70, D. Rohr35, D. Röhrich21, P.F.
Rojas46, P.S. Rokita144, F. Ronchetti53, A. Rosano33,57, E.D. Rosas71, A.
Rossi58, A. Rotondi29,59, A. Roy51, P. Roy112, S. Roy50, N. Rubini26, O.V.
Rueda83, R. Rui24, B. Rumyantsev77, P.G. Russek2, A. Rustamov90, E.
Ryabinkin91, Y. Ryabov101, A. Rybicki120, H. Rytkonen128, W. Rzesa144, O.A.M.
Saarimaki45, R. Sadek117, S. Sadovsky94, J. Saetre21, K. Šafařík38, S.K.
Saha143, S. Saha89, B. Sahoo50, P. Sahoo50, R. Sahoo51, S. Sahoo67, D. Sahu51,
P.K. Sahu67, J. Saini143, S. Sakai136, S. Sambyal104, V. SamsonovI,101,96, D.
Sarkar145, N. Sarkar143, P. Sarma43, V.M. Sarti108, M.H.P. Sas148, J.
Schambach99,121, H.S. Scheid70, C. Schiaua49, R. Schicker107, A. Schmah107, C.
Schmidt110, H.R. Schmidt106, M.O. Schmidt107, M. Schmidt106, N.V.
Schmidt99,70, A.R. Schmier133, R. Schotter139, J. Schukraft35, Y. Schutz139,
K. Schwarz110, K. Schweda110, G. Scioli26, E. Scomparin61, J.E. Seger15, Y.
Sekiguchi135, D. Sekihata135, I. Selyuzhenkov110,96, S. Senyukov139, J.J.
Seo63, D. Serebryakov65, L. Šerkšnytė108, A. Sevcenco69, T.J. Shaba74, A.
Shabanov65, A. Shabetai117, R. Shahoyan35, W. Shaikh112, A. Shangaraev94, A.
Sharma103, H. Sharma120, M. Sharma104, N. Sharma103, S. Sharma104, O.
Sheibani127, K. Shigaki47, M. Shimomura86, S. Shirinkin95, Q. Shou41, Y.
Sibiriak91, S. Siddhanta56, T. Siemiarczuk88, T.F. Silva123, D. Silvermyr83,
G. Simonetti35, B. Singh108, R. Singh89, R. Singh104, R. Singh51, V.K.
Singh143, V. Singhal143, T. Sinha112, B. Sitar13, M. Sitta32, T.B. Skaali20,
G. Skorodumovs107, M. Slupecki45, N. Smirnov148, R.J.M. Snellings64, C.
Soncco114, J. Song127, A. Songmoolnak118, F. Soramel28, S. Sorensen133, I.
Sputowska120, J. Stachel107, I. Stan69, P.J. Steffanic133, S.F.
Stiefelmaier107, D. Stocco117, I. Storehaug20, M.M. Storetvedt37, C.P.
Stylianidis93, A.A.P. Suaide123, T. Sugitate47, C. Suire80, M. Suljic35, R.
Sultanov95, M. Šumbera98, V. Sumberia104, S. Sumowidagdo52, S. Swain67, A.
Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi108, G. Taillepied137, J.
Takahashi124, G.J. Tambave21, S. Tang137,7, Z. Tang131, M. Tarhini117, M.G.
Tarzila49, A. Tauro35, G. Tejeda Muñoz46, A. Telesca35, L. Terlizzi25, C.
Terrevoli127, G. Tersimonov3, S. Thakur143, D. Thomas121, R. Tieulent138, A.
Tikhonov65, A.R. Timmins127, M. Tkacik119, A. Toia70, N. Topilskaya65, M.
Toppi53, F. Torales-Acosta19, T. Tork80, S.R. Torres38, A. Trifiró33,57, S.
Tripathy55,71, T. Tripathy50, S. Trogolo35,28, G. Trombetta34, V. Trubnikov3,
W.H. Trzaska128, T.P. Trzcinski144, B.A. Trzeciak38, A. Tumkin111, R.
Turrisi58, T.S. Tveter20, K. Ullaland21, A. Uras138, M. Urioni59,142, G.L.
Usai23, M. Vala39, N. Valle59,29, S. Vallero61, N. van der Kolk64, L.V.R. van
Doremalen64, M. van Leeuwen93, P. Vande Vyvre35, D. Varga147, Z. Varga147, M.
Varga-Kofarago147, A. Vargas46, M. Vasileiou87, A. Vasiliev91, O. Vázquez
Doce108, V. Vechernin115, E. Vercellin25, S. Vergara Limón46, L. Vermunt64, R.
Vértesi147, M. Verweij64, L. Vickovic36, Z. Vilakazi134, O. Villalobos
Baillie113, G. Vino54, A. Vinogradov91, T. Virgili30, V. Vislavicius92, A.
Vodopyanov77, B. Volkel35, M.A. Völkl107, K. Voloshin95, S.A. Voloshin145, G.
Volpe34, B. von Haller35, I. Vorobyev108, D. Voscek119, J. Vrláková39, B.
Wagner21, C. Wang41, D. Wang41, M. Weber116, R.J.G.V. Weelden93, A.
Wegrzynek35, S.C. Wenzel35, J.P. Wessels146, J. Wiechula70, J. Wikne20, G.
Wilk88, J. Wilkinson110, G.A. Willems146, B. Windelband107, M. Winn140, W.E.
Witt133, J.R. Wright121, W. Wu41, Y. Wu131, R. Xu7, S. Yalcin79, Y.
Yamaguchi47, K. Yamakawa47, S. Yang21, S. Yano47,140, Z. Yin7, H. Yokoyama64,
I.-K. Yoo17, J.H. Yoon63, S. Yuan21, A. Yuncu107, V. Zaccolo24, A. Zaman14, C.
Zampolli35, H.J.C. Zanoli64, N. Zardoshti35, A. Zarochentsev115, P. Závada68,
N. Zaviyalov111, H. Zbroszczyk144, M. Zhalov101, S. Zhang41, X. Zhang7, Y.
Zhang131, V. Zherebchevskii115, Y. Zhi11, D. Zhou7, Y. Zhou92, J. Zhu7,110, Y.
Zhu7, A. Zichichi26, G. Zinovjev3, N. Zurlo142,59

## Affiliation notes

I Deceased
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Science and Technology, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 Budker Institute for Nuclear Physics, Novosibirsk, Russia
6 California Polytechnic State University, San Luis Obispo, California, United
States
7 Central China Normal University, Wuhan, China
8 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
9 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
10 Chicago State University, Chicago, Illinois, United States
11 China Institute of Atomic Energy, Beijing, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia
14 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
29 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia,
Italy
30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
31 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy
33 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
34 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
35 European Organization for Nuclear Research (CERN), Geneva, Switzerland
36 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
37 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
38 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
39 Faculty of Science, P.J. Šafárik University, Košice, Slovakia
40 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
41 Fudan University, Shanghai, China
42 Gangneung-Wonju National University, Gangneung, Republic of Korea
43 Gauhati University, Department of Physics, Guwahati, India
44 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
45 Helsinki Institute of Physics (HIP), Helsinki, Finland
46 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
47 Hiroshima University, Hiroshima, Japan
48 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany
49 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
50 Indian Institute of Technology Bombay (IIT), Mumbai, India
51 Indian Institute of Technology Indore, Indore, India
52 Indonesian Institute of Sciences, Jakarta, Indonesia
53 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
54 INFN, Sezione di Bari, Bari, Italy
55 INFN, Sezione di Bologna, Bologna, Italy
56 INFN, Sezione di Cagliari, Cagliari, Italy
57 INFN, Sezione di Catania, Catania, Italy
58 INFN, Sezione di Padova, Padova, Italy
59 INFN, Sezione di Pavia, Pavia, Italy
60 INFN, Sezione di Roma, Rome, Italy
61 INFN, Sezione di Torino, Turin, Italy
62 INFN, Sezione di Trieste, Trieste, Italy
63 Inha University, Incheon, Republic of Korea
64 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
65 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
66 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia
67 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
68 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
69 Institute of Space Science (ISS), Bucharest, Romania
70 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
71 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
72 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
73 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
74 iThemba LABS, National Research Foundation, Somerset West, South Africa
75 Jeonbuk National University, Jeonju, Republic of Korea
76 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
77 Joint Institute for Nuclear Research (JINR), Dubna, Russia
78 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
79 KTO Karatay University, Konya, Turkey
80 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France
81 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
82 Lawrence Berkeley National Laboratory, Berkeley, California, United States
83 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
84 Moscow Institute for Physics and Technology, Moscow, Russia
85 Nagasaki Institute of Applied Science, Nagasaki, Japan
86 Nara Women’s University (NWU), Nara, Japan
87 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
88 National Centre for Nuclear Research, Warsaw, Poland
89 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
90 National Nuclear Research Center, Baku, Azerbaijan
91 National Research Centre Kurchatov Institute, Moscow, Russia
92 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
93 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
94 NRC Kurchatov Institute IHEP, Protvino, Russia
95 NRC «Kurchatov»Institute - ITEP, Moscow, Russia
96 NRNU Moscow Engineering Physics Institute, Moscow, Russia
97 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
98 Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic
99 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
100 Ohio State University, Columbus, Ohio, United States
101 Petersburg Nuclear Physics Institute, Gatchina, Russia
102 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
103 Physics Department, Panjab University, Chandigarh, India
104 Physics Department, University of Jammu, Jammu, India
105 Physics Department, University of Rajasthan, Jaipur, India
106 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
107 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany
108 Physik Department, Technische Universität München, Munich, Germany
109 Politecnico di Bari and Sezione INFN, Bari, Italy
110 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
111 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
112 Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India
113 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
114 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
115 St. Petersburg State University, St. Petersburg, Russia
116 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
117 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France
118 Suranaree University of Technology, Nakhon Ratchasima, Thailand
119 Technical University of Košice, Košice, Slovakia
120 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
121 The University of Texas at Austin, Austin, Texas, United States
122 Universidad Autónoma de Sinaloa, Culiacán, Mexico
123 Universidade de São Paulo (USP), São Paulo, Brazil
124 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
125 Universidade Federal do ABC, Santo Andre, Brazil
126 University of Cape Town, Cape Town, South Africa
127 University of Houston, Houston, Texas, United States
128 University of Jyväskylä, Jyväskylä, Finland
129 University of Kansas, Lawrence, Kansas, United States
130 University of Liverpool, Liverpool, United Kingdom
131 University of Science and Technology of China, Hefei, China
132 University of South-Eastern Norway, Tonsberg, Norway
133 University of Tennessee, Knoxville, Tennessee, United States
134 University of the Witwatersrand, Johannesburg, South Africa
135 University of Tokyo, Tokyo, Japan
136 University of Tsukuba, Tsukuba, Japan
137 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
138 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon
, Lyon, France
139 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
140 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
141 Università degli Studi di Foggia, Foggia, Italy
142 Università di Brescia, Brescia, Italy
143 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
144 Warsaw University of Technology, Warsaw, Poland
145 Wayne State University, Detroit, Michigan, United States
146 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
147 Wigner Research Centre for Physics, Budapest, Hungary
148 Yale University, New Haven, Connecticut, United States
149 Yonsei University, Seoul, Republic of Korea