[chapter]warnswrnList of Todos

2019 168 02 August

Multiplicity dependence of strangeness in pp at $\sqrt{s}$ = 13 TeV

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

The production rates and the transverse momentum distribution of strange
hadrons at mid-rapidity ($\left|y\right|<0.5$) are measured in proton-proton
collisions at $\sqrt{s}$ = 13 TeV as a function of the charged particle
multiplicity, using the ALICE detector at the LHC. The production rates of
${\rm K}^{0}_{S}$, $\Lambda$, $\Xi$, and $\Omega$ increase with the
multiplicity faster than what is reported for inclusive charged particles. The
increase is found to be more pronounced for hadrons with a larger strangeness
content. Possible auto-correlations between the charged particles and the
strange hadrons are evaluated by measuring the event-activity with charged
particle multiplicity estimators covering different pseudorapidity regions.
When comparing to lower energy results, the yields of strange hadrons are
found to depend only on the mid-rapidity charged particle multiplicity.
Several features of the data are reproduced qualitatively by general purpose
QCD Monte Carlo models that take into account the effect of densely-packed QCD
strings in high multiplicity collisions. However, none of the tested models
reproduce the data quantitatively. This work corroborates and extends the
ALICE findings on strangeness production in proton-proton collisions at 7 TeV.

##  1 Introduction

The production rates of strange and multi-strange hadrons in high-energy
hadronic interactions are important observables for the study of the
properties of Quantum Chromodynamics (QCD) in the non-perturbative regime. In
the simplest case, strange quarks ($s$) in proton-proton (pp) collisions can
be produced from the excitation of the sea partons. Indeed, in the past
decades a significant effort has been dedicated to the study of the actual
strangeness content of the nuclear wave function [1]. In QCD-inspired Monte
Carlo generators based on Parton Showers (PS) [2] the hard (perturbative)
interactions are typically described at the Leading Order (LO). In this
picture the $s$ quark can be produced in the hard partonic scattering via
flavour creation and flavour excitation processes as well as in the subsequent
shower evolution via gluon splitting. At low transverse momentum, $s\bar{s}$
pairs can be produced via non-perturbative processes, as described for
instance in string fragmentation models, where the production of strangeness
is suppressed with respect to light quark production due to the larger strange
quark mass [3]. However, these models fail to quantitatively describe
strangeness production in hadronic collisions [4, 5, 6].

An enhanced production of strange hadrons in heavy-ion collisions was
suggested as a signature for the creation of a Quark-Gluon Plasma (QGP) [7,
8]. The main argument in these early studies was that the mass of the strange
quark is of the order of the QCD deconfinement temperature, allowing for
thermal production in the deconfined medium. The lifetime of the QGP was then
estimated to be comparable to the strangeness relaxation time in the plasma,
leading to full equilibration. Strangeness enhancement in heavy-ion collisions
was indeed observed at the SPS [9] and higher energies [10, 11]. However,
strangeness enhancement is no longer considered an unambiguous signature for
deconfinement (see e.g. [12]). Strange hadron production in heavy-ion
collisions is currently usually described in the framework of statistical-
hadronisation (or thermal) models [13, 14]. In central heavy-ion collisions,
the yields of strange hadrons turn out to be consistent with the expectation
from a grand-canonical ensemble, i.e. the production of strange hadrons is
compatible with thermal equilibrium, characterised by a common temperature. On
the other hand, the strange hadron yields in elementary collisions are
suppressed with respect to the predictions of the (grand-canonical) thermal
models. The suppression of the relative abundance of strange hadrons with
respect to lighter flavours was suggested to be, at least partially, a
consequence of the finite volume, which makes the application of a grand-
canonical ensemble not valid in hadron-hadron and hadron-nucleus interactions
(canonical suppression) [15, 16, 17]. However, this approach cannot explain
the observed particle abundances if the same volume is assumed for both
strange and non-strange hadrons [18] and does not describe the system size
dependence of the $\phi$ meson, a hidden-strange hadron [19, 20].

The ALICE Collaboration recently reported an enhancement in the relative
production of (multi-) strange hadrons as a function of multiplicity in pp
collisions at $\sqrt{s}$ = 7 TeV [21] and in p–Pb collisions at $\sqrt{s_{\rm
NN}}$ = 5.02 TeV [22, 23]. In the case of p-Pb collisions, the yields of
strange hadrons relative to pions reach values close to those observed in
Pb–Pb collisions at full equilibrium. These are surprising observations,
because thermal strangeness production was considered to be a defining feature
of heavy-ion collisions, and because none of the commonly-used pp Monte Carlo
models reproduced the existing data [21, 3]. The mechanisms at the origin of
this effect need to be understood, and then implemented in the state-of-the-
art Monte Carlo generators [3].

In this paper, strangeness production in pp interactions is studied at the
highest energy reached at the LHC, $\sqrt{s}$ = 13 TeV. We present the
measurement of the yields and transverse momentum ($p_{\rm T}$) distributions
of single-strange (${\rm K}^{0}_{S}$, $\Lambda$, $\overline{\Lambda}$) and
multi-strange ($\Xi^{-}$, $\overline{\Xi}^{+}$, $\Omega^{-}$,
$\overline{\Omega}^{+}$) particles at mid-rapidity, $\left|y\right|<0.5$, with
the ALICE detector [24]. The comparison of the present results with the former
ones for pp and p–Pb interactions allows the investigation of the energy,
multiplicity and system size dependence of strangeness production.
Schematically, the multiplicity of a given pp event depends on i) the number
of Multiple Parton Interactions (MPI), ii) the momentum transfer of those
interactions, iii) fluctuations in the fragmentation process. A systematic
study of the biases induced by the choice of the multiplicity estimator along
with the specific connections to the underlying MPI are also discussed in this
paper.

The paper is organised as follows. In Sec. 2 we discuss the data set and
detectors used for the measurement; in Sec. 3 we describe the analysis
techniques; in Sec. 4 we cover the evaluation of the systematic uncertainties;
in Sec. 5 we present and discuss the results; in Sec. 6 we report our
conclusions.

##  2 Experimental setup and data selection

A detailed description of the ALICE detector and its performance can be found
in [24, 25]. In this section, we briefly outline the main detectors used for
the measurements presented in this paper. The ALICE apparatus comprises a
central barrel used for vertex reconstruction, track reconstruction and
charged-hadron identification, complemented by specialised forward detectors.
The central barrel covers the pseudorapidity region $\left|\eta\right|<0.9$.
The main central-barrel tracking devices used for this analysis are the Inner
Tracking System (ITS) and the Time-Projection Chamber (TPC), which are located
inside a solenoidal magnet providing a 0.5 T magnetic field. The ITS is
composed 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 also used to reconstruct
tracklets, short two-point track segments covering the pseudorapidity region
$\left|\eta\right|<1.4$. The outer layers of the ITS are composed of silicon
strips and drift detectors, with the outermost layer having a radius
$r~{}=~{}43~{}\mathrm{cm}$. The TPC is a large cylindrical drift detector of
radial and longitudinal sizes of about $85~{}<~{}r~{}<~{}250$ cm and
$-250~{}<~{}z~{}<~{}250$ cm, respectively. It is segmented in radial “pad
rows”, providing up to 159 tracking points. It also provides charged-hadron
identification information via specific ionisation energy loss in the gas
filling the detector volume. The measurement of strange hadrons is based on
“global tracks”, reconstructed using information from the TPC as well as from
the ITS, if the latter is available. Further outwards in radial direction from
the beam-pipe and located at a radius of approximately 4 m, the Time of Flight
(TOF) detector measures the time-of-flight of the particles. It is a large-
area array of multigap resistive plate chambers with an intrinsic time
resolution of 50 ps. The V0 detectors are two forward scintillator hodoscopes
employed for triggering, background suppression and event-class determination.
They are placed on either side of the interaction region at $z~{}=~{}-0.9$ m
and $z~{}=~{}3.3$ m, covering the pseudorapidity regions
$-3.7~{}<~{}\eta~{}<~{}-1.7$ and $2.8~{}<~{}\eta~{}<~{}5.1$, respectively.

The data considered in the analysis presented in this paper were collected in
2015, at the beginning of Run 2 operations of the LHC at $\sqrt{s}$ = 13 TeV.
The sample consists of 50 M events collected with a minimum bias trigger
requiring a hit in both V0 scintillators in coincidence with the arrival of
proton bunches from both directions. The interaction probability per single
bunch crossing ranges between 2% and 14%.

The contamination from beam-induced background is removed offline by using the
timing information in the V0 detectors and taking into account the correlation
between tracklets and clusters in the SPD detector, as discussed in detail in
[25]. The contamination from in-bunch pile-up events is removed offline
excluding events with multiple vertices reconstructed in the SPD. Part of the
data used in this paper were collected in periods in which the LHC collided
“trains” of bunches each separated by 50 ns from its neighbours. In these beam
conditions most of the ALICE detectors have a readout window wider than a
single bunch spacing and are therefore sensitive to events produced in bunch
crossings different from those triggering the collision. In particular, the
SPD has a readout window of 300 ns. The drift speed in the TPC is about 2.5
cm$/{\mu}$s, which implies that events produced less than about 0.5 ${\mu}$s
apart cannot be resolved. Pile-up events produced in different bunch crossings
are removed exploiting multiplicity correlations in detectors having different
readout windows.

##  3 Analysis details

The results are presented for primary strange hadrons111A primary particle
[26] is defined as a particle with a mean proper decay length $c\tau$ larger
than 1 cm, which is either a) produced directly in the interaction, or b) from
decays of particles with $c\tau$ smaller than 1 cm, excluding particles
produced in interactions with material.. The measurements reported here have
been obtained for events having at least one charged particle produced with
$p_{\rm T}$ $>$ 0 in the pseudorapidity interval $\left|\eta\right|<1$
($\mathrm{INEL}>0$), corresponding to about 75% of the total inelastic cross-
section. In order to study the multiplicity dependence of strange and multi-
strange hadrons, for each multiplicity estimator the sample is divided into
event classes based on the total charge deposited in the V0 detectors (V0M
amplitude) or on the number of tracklets in two pseudorapidity regions:
$\left|\eta\right|<0.8$ and $0.8<\left|\eta\right|<1.5$. The event classes are
summarised in Table 1. Since the measurement of strange hadrons is performed
in the region $\left|y\right|<0.5$, the usage of these three estimators allows
one to evaluate potential biases on particle production, arising from
measuring the multiplicity in a pseudorapidity region partially overlapping
with the one of the reconstructed strange hadrons ($N_{\rm
tracklets}^{\left|\eta\right|<0.8}$), or disjoint from it (V0M and $N_{\rm
tracklets}^{0.8<\left|\eta\right|<1.5}$). In particular, the effect of
fluctuations can be expected to be stronger if the multiplicity estimator and
the observable of interest are measured in the same pseudorapidity region. The
usage of two different non-overlapping estimators allows the study of the
effect of a rapidity gap between the multiplicity estimator and the
measurement of interest.

The events used for the data analysis are required to have a reconstructed
vertex in the fiducial region $\left|z\right|~{}<$ 10 cm. As mentioned in the
previous section, events containing more than one distinct vertex are tagged
as pile-up and discarded. For each event class and each multiplicity
estimator, the average pseudorapidity density of primary charged-particles
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ is measured at mid-rapidity
($\left|\eta\right|<0.5$) using the technique described in [27]. The
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ values, corrected for acceptance
and efficiency as well as for contamination from secondary particles and
combinatorial background, are listed in Table 1. When multiplicity event
classes are selected outside the $\left|\eta\right|<0.8$ region, the
corresponding charged particle multiplicity at mid-rapidity is characterized
by large a variance. In the case of the V0M estimator, the variance ranges
between 30% and 70% of the mean $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ for
the highest and lowest multiplicity classes, respectively.

Table 1: Event classes selected according to different multiplicity estimators (see text for details). For each estimator, the second column summarises the relative multiplicity w.r.t. the INEL $>$ 0 event class and the third column represents the corresponding fraction of the INEL $>$ 0 cross-section. The average charged particle multiplicity density is reported in the last column for all event classes. For all the multiplicity estimators, the charged particle multiplicity density is quoted in $\left|\eta\right|<0.5$. |  |  |  | $\sigma/\sigma_{\mathrm{I}NEL>0}$ | $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$
---|---|---|---|---|---
Event Class | $\frac{\langle\mathrm{V0M}\rangle_{\mathrm{mult}}}{\langle\mathrm{V0M}\rangle_{\mathrm{INEL>0}}}$ | $\frac{\langle N_{\rm tracklets}^{\left|\eta\right|<0.8}\rangle_{\mathrm{mult}}}{\langle N_{\rm tracklets}^{\left|\eta\right|<0.8}\rangle_{\mathrm{INEL>0}}}$ | $\frac{\langle N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}\rangle_{\mathrm{mult}}}{\langle N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}\rangle_{\mathrm{INEL>0}}}$ | V0M | $N_{\rm tracklets}^{\left|\eta\right|<0.8}$ | $N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}$ | V0M | $N_{\rm tracklets}^{\left|\eta\right|<0.8}$ | $N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}$
INEL$>$0 | Not Applicable | Not Applicable | 6.89$\pm$0.11
I | 3.7 | 4.7 | 3.8 | 0.0-0.90% | 0.0-0.91% | 0.0-0.91% | 25.75$\pm$0.40 | 32.49$\pm$0.50 | 26.32$\pm$0.40
II | 2.9 | 3.4 | 2.8 | 0.90-4.5% | 0.91-4.6% | 0.91-4.6% | 19.83$\pm$0.30 | 23.42$\pm$0.35 | 19.51$\pm$0.29
III | 2.3 | 2.7 | 2.2 | 4.5-8.9% | 4.6-9.1% | 4.6-9.1% | 16.12$\pm$0.24 | 18.29$\pm$0.28 | 15.45$\pm$0.23
IV | 2.0 | 2.2 | 1.9 | 8.9-13.5% | 9.1-13.7% | 9.1-13.7% | 13.76$\pm$0.21 | 14.90$\pm$0.23 | 13.14$\pm$0.20
V | 1.8 | 1.9 | 1.7 | 13.5-18.0% | 13.7-18.3% | 13.7-18.2% | 12.06$\pm$0.18 | 12.90$\pm$0.19 | 11.63$\pm$0.17
VI | 1.5 | 1.6 | 1.4 | 18.0-27.0% | 18.3-27.4% | 18.2-27.4% | 10.11$\pm$0.15 | 10.72$\pm$0.16 | 9.50$\pm$0.14
VII | 1.2 | 1.2 | 1.1 | 27.0-36.1% | 27.4-36.6% | 27.4-36.6% | 8.07$\pm$0.12 | 8.14$\pm$0.12 | 7.68$\pm$0.11
VIII | 0.95 | 0.85 | 0.91 | 36.1-45.3% | 36.6-45.9% | 36.6-45.9% | 6.48$\pm$0.10 | 5.95$\pm$0.09 | 6.35$\pm$0.10
IX | 0.68 | 0.55 | 0.62 | 45.3-64.5% | 45.9-65.0% | 45.9-65.6% | 4.64$\pm$0.07 | 3.82$\pm$0.06 | 4.36$\pm$0.06
X | 0.37 | 0.25 | 0.38 | 64.5-100.0% | 65.0-100.0% | 65.6-100% | 2.52$\pm$0.04 | 1.76$\pm$0.03 | 2.67$\pm$0.04

The strange hadrons ${\rm K}^{0}_{S}$, $\Lambda$, $\overline{\Lambda}$,
$\Xi^{-}$, $\overline{\Xi}^{+}$, $\Omega^{-}$ and $\overline{\Omega}^{+}$ are
reconstructed at mid-rapidity ($\left|y\right|<0.5$) with an invariant mass
analysis, exploiting their specific weak decay topology. The following decay
channels are studied [28]:

${\rm K}^{0}_{S}$ | $\to$ |  ${\pi}^{+}$ \+ ${\pi}^{-}$ | B.R. = (69.20 $\pm$ 0.05) %
---|---|---|---
$\Lambda$ ($\overline{\Lambda}$) | $\to$ |  $\rm p$ ($\overline{\rm p}$) + ${\pi}^{-}$ (${\pi}^{+}$) | B.R. = (63.9 $\pm$ 0.5) %
$\Xi^{-}$ ($\overline{\Xi}^{+}$) | $\to$ |  $\Lambda$ ($\overline{\Lambda}$) + ${\pi}^{-}$ (${\pi}^{+}$) | B.R. = (99.887 $\pm$ 0.035) %
$\Omega^{-}$ ($\overline{\Omega}^{+}$) | $\to$ |  $\Lambda$ ($\overline{\Lambda}$) + ${\rm K}^{-}$ (${\rm K}^{+}$) | B.R. = (67.8 $\pm$ 0.7) %

In the following, we refer to the sum of particles and anti-particles,
$\Lambda+\overline{\Lambda}$, $\Xi^{-}+\overline{\Xi}^{+}$ and
$\Omega^{-}+\overline{\Omega}^{+}$, simply as $\Lambda$, $\Xi$ and $\Omega$.

The details of the analysis have been discussed in earlier ALICE publications
[22, 6, 5, 18]. The tracks retained in the analysis are required to cross at
least 70 TPC readout pads out of a maximum of 159. Tracks are also required
not to have large gaps in the number of expected tracking points in the radial
direction. This is achieved by checking 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%.

Table 2: Track, topological and candidate selection criteria applied to ${\rm K}^{0}_{S}$, $\Lambda$ and $\overline{\Lambda}$ candidates. DCA stands for “distance of closest approach”, PV represents the “primary event vertex” and $\theta$ is the angle between the momentum vector of the reconstructed $V^{0}$ and the displacement vector between the decay and primary vertices. The selection on DCA between $V^{0}$ daughter tracks takes into account the corresponding experimental resolution.  Toplogical Variable |  ${\rm K}^{0}_{S}$ ($\Lambda$ and $\overline{\Lambda}$) Selection criteria
---|---
$V^{0}$ transverse decay radius |  $>$ 0.50 cm
DCA (Negative / Positive Track - PV) |  $>$ 0.06 cm
Cosine of $V^{0}$ Pointing Angle ($\theta_{V^{0}}$) |  $>$ 0.97 (0.995)
DCA between $V^{0}$ daughter tracks |  $<$ 1.0 standard deviations
Track selection |  ${\rm K}^{0}_{S}$ ($\Lambda$ and $\overline{\Lambda}$) Selection criteria
Daughter Track Pseudorapidity Interval | $|\eta|<0.8$
Daughter Track $N_{crossedrows}$ |  $\geq$ 70
Daughter Track $N_{crossed}/N_{findable}$ |  $\geq$ 0.8
p inner wall TPC (proton only) |  $>$ 0.3 $\mathrm{GeV}/c$
TPC d$E$/d$x$ |  $<$ $5\sigma$
out-of-bunch pile-up track rejection | requested for at least one daughter
Candidate selection |  ${\rm K}^{0}_{S}$ ($\Lambda$ and $\overline{\Lambda}$) Selection criteria
Rapidity Interval | $|y|<0.5$
Proper Lifetime ($mL/p$) |  $<$ 20 cm (30 cm)
Competing $V^{0}$ Rejection | 5 $\mathrm{MeV}/c^{2}$ (10 $\mathrm{MeV}/c^{2}$)
MC Association (MC Only) | identity assumption for $V^{0}$ and for daughter tracks
Table 3: Track, topological and candidate selection criteria applied to charged $\Xi^{-}$, $\overline{\Xi}^{+}$, $\Omega^{-}$ and $\overline{\Omega}^{+}$ candidates. DCA stands for “distance of closest approach”, PV represents the “primary event vertex” and $\theta$ is the angle between the momentum vector of the reconstructed $V^{0}$ or cascade and the displacement vector between the decay and primary vertices. The selection on DCA between $V^{0}$ daughter tracks takes into account the corresponding experimental resolution. Topological Variable |  $\Xi$ ($\Omega$) Selection criteria
---|---
Cascade transverse decay radius R2D |  $>$ 0.6 (0.5) cm
$V^{0}$ transverse decay radius |  $>$ 1.2 (1.1) cm
DCA (bachelor - PV) |  $>$ 0.04 cm
DCA ($V^{0}$ \- PV) |  $>$ 0.06 cm
DCA (meson $V^{0}$ track - PV) |  $>$ 0.04 cm
DCA (baryon $V^{0}$ track - PV) |  $>$ 0.03 cm
DCA between $V^{0}$ daughter tracks |  $<$ 1.5 standard deviations
DCA (bachelor - $V^{0}$) |  $<$ 1.3 cm
Cosine of Cascade Pointing Angle ($\theta_{\rm casc}$) |  $>$ 0.97
Cosine of $V^{0}$ Pointing Angle ($\theta_{V^{0}}$) |  $>$ 0.97
$V^{0}$ invariant mass window |  $\pm$ 0.008 $\mathrm{GeV}/c^{2}$
Track selection |  $\Xi$ ($\Omega$) Selection criteria
Daughter Track Pseudorapidity Interval | $|\eta|<0.8$
Daughter Track $N_{TPCclusters}$ |  $\geq$ 70
TPC d$E$/d$x$ |  $<$ $5\sigma$
out-of-bunch pile-up track rejection | requested for at least one daughter
Candidate selection |  $\Xi$ ($\Omega$) Selection criteria
Rapidity Interval | $|y|<0.5$
Proper Lifetime ($mL/p$) | $<3\times c\tau$
Competing Cascade Rejection (only $\Omega$) | $|M(\Lambda\pi)-1321|>8~{}\mathrm{MeV}/c^{2}$
MC Association (MC Only) | identity assumption for cascades and for daughter tracks

Each decay product arising from $V^{0}$ (${\rm K}^{0}_{S}$, $\Lambda$,
$\overline{\Lambda}$) and cascade ($\Xi^{-}$, $\overline{\Xi}^{+}$,
$\Omega^{-}$, $\overline{\Omega}^{+}$) candidates is verified to lie within
the fiducial tracking region $\left|\eta\right|<0.8$. The specific energy loss
(${\rm d}E/{\rm d}x$) measured in the TPC, used for the particle
identification (PID) of the decay products, is also requested to be compatible
within 5$\sigma$ with the one expected for the corresponding particle species’
hypothesis. The ${\rm d}E/{\rm d}x$ is evaluated as a truncated mean using the
lowest 60% of the values out of a possible total of 159. This leads to a
resolution of about 6%. A set of “geometrical” selections is applied in order
to identify specific decay topologies (topological selection), improving the
signal/background ratio. The topological variables used for $V^{0}$s and
cascades are described in detail in [6]. In addition, in order to reject the
residual out-of-bunch pile-up background on the measured yields, it is
requested that at least one of the tracks from the decay products of the
(multi-)strange hadron under study is matched in either the ITS or the TOF
detector. The selections used in this paper are summarised in Table 2 for the
$V^{0}$s and in Table 3 for the cascades.

Strange hadron candidates are required to be in the rapidity window
$\left|y\right|<0.5$. ${\rm K}^{0}_{S}$ ($\Lambda$) candidates compatible with
the alternative $V^{0}$ hypothesis are rejected if they lie within $\pm$5
$\mathrm{MeV}/c^{2}$ ($\pm$10 $\mathrm{MeV}/c^{2}$) of the nominal $\Lambda$
(${\rm K}^{0}_{S}$) mass. A similar selection is applied to the $\Omega$,
where candidates compatible within $\pm$8 $\mathrm{MeV}/c^{2}$ of the nominal
$\Xi$ mass are rejected. The width of the rejected region was determined
according to the invariant mass resolution of the corresponding competing
signal. Furthermore, candidates whose proper lifetimes are unusually large for
their expected species are also rejected to avoid combinatorial background
from interactions with the detector material. The signal extraction is
performed as a function of $p_{\rm T}$. A preliminary fit is performed on the
invariant mass distribution using a Gaussian plus a linear function describing
the background. This allows for the extraction of the mean ($\mu$) and width
($\sigma_{\rm G}$) of the peak. A “peak” region is defined within $\pm
6(4)\sigma_{\rm G}$ for $V^{0}$s (cascades) with respect to $\mu$ for any
measured $p_{\rm T}$ bin. Adjacent background bands, covering a combined mass
interval as wide as the peak region, are defined on both sides of that central
region. The signal is then extracted with a bin counting procedure,
subtracting counts in the background region from those of the signal region.
Alternatively, the signal is extracted by fitting the background with a linear
function extrapolated under the signal region. This procedure is used to
compute the systematic uncertainty due to the signal extraction. Examples of
the invariant mass peaks for all particles are shown in Fig. 1.

Figure 1:  Invariant mass distributions for ${\rm K}^{0}_{S}$, $\Lambda$,
$\Xi^{-}$, $\Omega^{-}$ in different V0M multiplicity and $p_{\rm T}$
intervals. The candidates are reconstructed in $\left|y\right|<0.5$. The grey
areas delimited by the short-dashed lines are used for signal extraction in
the bin counting procedure. The red dashed lines represent the fit to the
invariant mass distributions, shown for drawing purpose only.

Only the $\Lambda$ turns out to be affected by a significant contamination
from secondary particles, coming from the decay of charged and neutral $\Xi$.
In order to estimate this contribution we use the measured $\Xi^{-}$ and
$\overline{\Xi}^{+}$ spectra, folded with a $p_{\rm T}$-binned 2D matrix
describing the decay kinematics and secondary $\Lambda$ reconstruction
efficiencies. The $\Xi\to\Lambda\pi$ decay matrix is extracted from Monte
Carlo (see below for the details on the generator settings). The fraction of
secondary $\Lambda$ particles in the measured spectrum varies between 10% and
20%, depending on $p_{\rm T}$ and multiplicity. Further details on the
uncertainties characterising the feed-down contributions are provided in the
next section.

The raw $p_{\rm T}$ distributions are corrected for acceptance and efficiency
using Monte Carlo simulated data. Events are generated using the PYTHIA 6.425,
(Tune Perugia 2011) [29, 30] event generator, and transported through a GEANT
3 [31] (v2-01-1) model of the detector. With respect to previous GEANT 3
versions, the adopted one contains a more realistic description of
(anti)proton interactions. The quality of this description was cross-checked
comparing to the results obtained with the state-of-the-art transport codes
FLUKA [32, 33] and GEANT 4.9.5 [34]. It was found that a correction factor
$<5\%$ is needed for the efficiency of $\overline{\Lambda}$,
$\overline{\Xi}^{+}$, $\overline{\Omega}^{+}$ for $p_{\rm T}<1~{}{\rm GeV}/c$,
while the effect is negligible at higher $p_{\rm T}$. Events generated using
PYTHIA 8.210 (tune Monash 2013) [35, 36] and EPOS-LHC (CRMC package 1.5.4)
[37] and transported in the same way are used for systematic studies, namely
to compute the systematic uncertainties arising from the normalisation and
from the closure of the correction procedure (details provided in the next
sections).

The acceptance-times-efficiency changes with $p_{\rm T}$, saturating at a
value of about 40%, 30%, 30% and 20% at $p_{\rm T}$ $\simeq$ 2, 3, 3 and 4
${\rm GeV}/c$ for ${\rm K}^{0}_{S}$, $\Lambda$, $\Xi$ and $\Omega$,
respectively. These values include the losses due to the branching ratio. They
are found to be independent of the multiplicity class within 2%, limited by
the available Monte Carlo simulated data. The dependence of the efficiency on
the generated $p_{\rm T}$ distributions was checked for all particle species.
It is found to be relevant only in the case of the $\Omega$, where large
$p_{\rm T}$ bins are used. This effect is removed by reweighting the Monte
Carlo $p_{\rm T}$ distribution with the measured one using an iterative
procedure.

In order to compute $\langle p_{\rm T}\rangle$ and the $p_{\rm T}$-integrated
production yields, the spectra are fitted with a Tsallis-Lévy [38]
distribution to extrapolate in the unmeasured $p_{\rm T}$ region. The
systematic uncertainties on this extrapolation procedure are evaluated using
other fit functions, as discussed in Sec. 4.

##  4 Systematic uncertainties

Several sources of systematic effects on the evaluation of the $p_{\rm T}$
distributions were investigated. The main contributions for three
representative $p_{\rm T}$ values are summarised in Table 4 for the INEL $>$ 0
data sample.

The stability of the signal extraction method was checked by varying the
widths used to define the “signal” and “background” regions, expressed in
terms of number of $\sigma_{G}$ as defined in Sec. 3. The raw counts were also
extracted with a fitting procedure and compared to the standard ones computed
by the bin counting technique. An uncertainty ranging between 0.2% and 3.5%
depending on $p_{\rm T}$ is assigned to the signal extraction of the $V^{0}$s
and cascades based on these checks.

The stability of the acceptance and efficiency corrections was verified by
varying all track, candidate and topological selection criteria within ranges
leading to a maximum variation of $\pm 10\%$ in the raw signal yield. The
results were compared to those obtained with the default selection criteria
(Sec. 3). Variations not compatible with statistical fluctuations (following
the prescription in [39] with a 2$\sigma$ threshold) are added to the
systematic uncertainty.

The resulting uncertainty from topological and track selections (except TPC
d$E$/d$x$) depends on $p_{\rm T}$ and amounts at most to 4%, 5%, 4% and 6% for
${\rm K}^{0}_{S}$, $\Lambda$, $\Xi$ and $\Omega$, respectively.

The TPC d$E$/d$x$ selection is used to reduce the combinatorial background in
the strange baryon invariant mass distribution. The uncertainty was evaluated
varying the TPC d$E$/d$x$ selection requirements between 4 and 7$\sigma$ and
was found to be at most 1% (3%) for $\Lambda$ ($\Xi$ and $\Omega$). For the
${\rm K}^{0}_{S}$ the uncertainty due to the TPC d$E$/d$x$ usage was evaluated
by comparing results obtained adopting the default loose PID requirements
($5~{}\sigma$) with those obtained without applying any PID selection. The
difference is found to be negligible ($<1\%$).

The systematic uncertainty for the competing decay rejection was investigated
by removing entirely this condition for $\Lambda$ and $\Omega$. It resulted in
a deviation on the $p_{\rm T}$ spectra of at most 4% and 6%, respectively. For
the ${\rm K}^{0}_{S}$ the systematic uncertainty was evaluated by changing the
width of the competing rejected mass window between 3 and 5.5
$\mathrm{MeV}/c^{2}$ and the corresponding deviation was found to be at most
1%.

For the strange baryons, the systematic uncertainty related to the proper
lifetime was computed by varying the selection requirements between 2.5 and 5
$c\tau$. The variation range for the ${\rm K}^{0}_{S}$ was set to 5-15
$c\tau$. The statistically significant deviations were found to be at most 3%
for the $\Lambda$ and negligible ($<1$%) for all other particles.

An uncertainty related to the absorption in the detector material was assigned
to the anti-baryons, mostly due to the interactions of anti-proton daughters.
It was estimated on the basis of the comparison of the different transport
codes mentioned in Sec. 3. The uncertainty on the absorption cross section for
baryons and ${\rm K}^{0}_{S}$ was found to be negligible.

Furthermore an additional 2% uncertainty is added to account for possible
variations of the tracking efficiency with multiplicity (Sec. 3).

The uncertainty due to approximations in the description of the detector
material was estimated with a Monte Carlo simulation where the material budget
was varied within its uncertainty [25]. The assigned systematic uncertainty
ranges between 8% at low $p_{\rm T}$ to about 1% at high $p_{\rm T}$.

The $\Lambda$ $p_{\rm T}$ spectrum is affected by an uncertainty coming from
the feed-down correction, due to the uncertainties on the measured $\Xi$
spectrum and on the multiplicity dependence of the feed-down fraction.
Furthermore the contribution from neutral $\Xi^{0}$ was taken into account by
assuming $\Xi^{\pm}/\Xi^{0}=1$ or using the ratio provided by the Monte Carlo
(using the reference Pythia 6 sample described in the previous section). The
difference between these two estimates was taken into account in the
calculation of the total uncertainty due to the feed-down correction, which
ranges from 2% to 4% depending on $p_{\rm T}$ and multiplicity.

The systematic uncertainty due to the out-of-bunch pile-up rejection was
evaluated by changing the matching scheme with the relevant detectors,
considering the following configurations: matching of at least one decay track
with the ITS (TOF) detector below (above) 2 GeV/$c$ of the reconstructed
(multi-) strange hadron; ITS matching of at least one decay track in the full
$p_{\rm T}$ range. Half of the maximum difference between these configurations
and the standard selection was taken as the systematic uncertainty, which was
found to increase with transverse momentum and to saturate at high $p_{\rm
T}$, reaching a maximum value of 2.4% (3%) for $V^{0}$s (cascades).

The effect of a possible residual contamination from in-bunch pile-up events
was estimated varying the pile-up rejection criteria and dividing the data
sample in three groups with an average interaction probability per bunch
crossing of 3%, 6%, 13%, respectively. The resulting uncertainty is larger at
low multiplicity, and ranges between 1% (3%) for the ${\rm K}^{0}_{S}$ to 2%
(3%) for the baryons in high-(low-)multiplicity events.

Table 4: Main sources and values of the relative systematic uncertainties
(expressed in %) of the $p_{\rm T}$-differential yields. These values are
reported for low, intermediate and high $p_{\rm T}$. The values for the
$\mathrm{INEL}>0$ data sample are shown in the table. Results as a function of
multiplicity are further affected by an uncertainty originating from the
multiplicity dependence of the efficiency (2%) and, in the case of the
$\Lambda$, of the feed-down contributions (2%).

Hadron | ${\rm K}^{0}_{S}$ |  $\Lambda$ \+ $\overline{\Lambda}$ |  $\Xi^{-}$ \+ $\overline{\Xi}^{+}$ |  $\Omega^{-}$ \+ $\overline{\Omega}^{+}$
---|---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  $\simeq$0.95 |  $\simeq$4.8 |  $\simeq$9.0 |  $\simeq$0.50 |  $\simeq$4.5 |  $\simeq$7.3 |  $\simeq$0.80 |  $\simeq$3.2 |  $\simeq$5.8 |  $\simeq$1.3 |  $\simeq$2.8 |  $\simeq$4.7
Signal extraction | 0.6 | 0.6 | 1.6 | 1.1 | 2.4 | 1.1 | 0.6 | 0.4 | negl. | 2.1 | 2.1 | 3.3
Topological and track | 0.7 | 2.7 | 2.5 | 2.9 | 2.6 | 2.3 | 4.8 | 2.6 | 2.0 | 5.6 | 6.0 | 5.5
selection (but TPC d$E$/d$x$)
TPC d$E$/d$x$ selection | 0.1 | negl. | negl. | 0.7 | 0.3 | 1.7 | 0.4 | 0.3 | 0.3 | 1.7 | 2.2 | 1.6
Competing decay rejection | 0.1 | 0.2 | 1.0 | negl. | 0.9 | 5.7 | not applied | 1.2 | 3.1 | 5.6
Proper lifetime | 0.1 | negl. | negl. | 1.1 | negl. | negl. | 0.5 | 0.8 | 0.8 | 3.1 | 1.8 | 1.0
Transport code (for anti-particles) | not applied | 1.8 | negl. | negl. | 1.1 | negl. | negl. | 0.6 | negl. | negl.
Material budget | 1.1 | 0.5 | 0.5 | 8.3 | 0.8 | 0.8 | 5.1 | 1.2 | 0.6 | 3.3 | 1.5 | 1.5
Feed-down correction | not applied | 2.2 | 1.3 | 2.1 | not applied | not applied
out-of-bunch pile-up track rejection | 1.1 | 1.5 | 1.5 | 1.2 | 2.4 | 2.4 | 1.0 | 2.5 | 2.5 | 3.0 | 3.0 | 3.0
Residual in-bunch pile-up | 1.6 | 2.5 | 2.5 | 2.0 | 2.9 | 2.9 | 2.0 | 2.0 | 2.9 | 2.0 | 2.0 | 2.0
Total | 2.4 | 4.1 | 4.3 | 9.6 | 5.5 | 7.8 | 7.5 | 4.4 | 4.4 | 8.6 | 8.6 | 9.6
Common ($N_{\rm ch}$-independent) | 2.3 | 4.0 | 3.8 | 9.2 | 5.3 | 7.0 | 6.8 | 4.2 | 4.2 | 7.7 | 8.4 | 7.5

Several additional consistency checks have been performed which are described
in the following. The analysis has been repeated separately for events with
positive and negative $z$-vertex position, as well as considering candidates
reconstructed in positive and negative rapidity windows. The resulting $p_{\rm
T}$-spectra were found to be statistically compatible with the standard
analysis.

In order to ensure that the estimated systematic uncertainties are not
affected by statistical fluctuations, two checks were performed. First of all,
the threshold used to consider a variation statistically significant was
varied between one and three standard deviations. Then, the analysis was
repeated with wider $p_{\rm T}$ bins. These checks showed that statistical
fluctuations in the systematic uncertainty analysis are well under control.

The results related to the $\langle p_{\rm T}\rangle$ and $p_{\rm
T}$-integrated yields for all particles but the ${\rm K}^{0}_{S}$ are further
affected by an uncertainty coming from the extrapolation to zero $p_{\rm T}$.
The default extrapolation is performed using a Lévy-Tsallis distribution. As
confirmed by a $\chi^{2}$ analysis, this function describes the $p_{\rm T}$
spectra well for all the examined strange hadrons over the measured $p_{\rm
T}$ range.

The uncertainty on the extrapolated fraction was estimated repeating the fit
to the spectra with five alternative functions (Blast-Wave, Boltzmann, Bose-
Einstein, $m_{\rm T}$-exponential, Fermi-Dirac). Since these alternative
functions do not, in general, describe the full $p_{\rm T}$-distribution, the
fit range was limited to a small number of data points in order to obtain a
good description of the fitted part of the spectrum. This procedure was
repeated separately for the low and for the high $p_{\rm T}$ extrapolation,
with the final uncertainties being dominated by the low $p_{\rm T}$
contribution. The reliability of the extrapolation uncertainty estimate was
checked using a simple linear extrapolation to $p_{\rm T}$ $=0$ as an extreme
case and in a full Monte Carlo closure test where the EPOS model was used with
data and PYTHIA was used to estimate the corrections. The resulting
uncertainty on the integrated yields is around 2.5% for the $\Lambda$ and
ranges between 3% (4%) at high multiplicity to 19% (12%) at low multiplicity
for the $\Xi$ ($\Omega$). The extrapolation uncertainty on $\langle p_{\rm
T}\rangle$ is $\sim$2% for the $\Lambda$ and ranges between 2% (3%) at high
multiplicity to 12% (7%) at low multiplicity for the $\Xi$ ($\Omega$).

The main focus of this paper is the study of the multiplicity dependence of
strangeness production. In this light, the different systematic uncertainties
can be categorised in the following way:

  1. 1.

Fully uncorrelated uncertainties: the change in the data is completely
uncorrelated across multiplicity classes. These sources are rare, as most
systematic effects have a smooth evolution with multiplicity.

  2. 2.

Fully correlated uncertainties: lead to a correlated shift of the data in the
same direction, independently of the multiplicity class being studied. The
common part of this shift has to be considered separately, since it does not
affect the shape of the multiplicity-dependent observable.

  3. 3.

Anti-correlated uncertainties: the effect is opposite in low and high
multiplicity events.

In the following we quote separately uncertainties that affect the trends as a
function of multiplicity and those that lead to a constant fractional shift
across all multiplicity classes. The effect of every systematic variation was
evaluated simultaneously in each multiplicity class and in minimum bias events
to separate the fully correlated part of the uncertainty. Sources leading to a
global, fully-correlated shift in the spectra were subtracted from the total
uncertainty while the remaining contribution could in principle belong to any
of the three aforementioned categories. However, since different (independent)
sources are combined in the final uncertainties, it is a reasonable assumption
to consider them as uncorrelated. For the figures shown in Sec. 5, total
uncertainties are shown as boxes, while shadowed boxes represent uncertainties
uncorrelated across different multiplicity classes. Statistical uncertainties
are depicted as error bars.

##  5 Results and discussion

Particles and anti-particles turn out to have compatible transverse momentum
distributions within uncertainties, consistently with previous results at the
LHC. In the following, unless specified otherwise, we present results for
their sum. The $p_{\rm T}$ distributions of strange hadrons, measured in
$\left|y\right|<0.5$, are shown in Figs. 2–4 for the different multiplicity
classes, selected using the estimators V0M, tracklets in
$\left|\eta\right|<0.8$ and tracklets in $0.8<\left|\eta\right|<1.5$, as
summarised in Table 1. The Lévy-Tsallis fit to the $p_{\rm T}$ distributions,
used for the extrapolation, are also displayed. The bottom panels depict the
ratio to the minimum bias ($\mathrm{INEL}>0$) $p_{\rm T}$ distribution. The
$p_{\rm T}$ spectra become harder as the multiplicity increases, as also shown
in Fig. 5, which shows the average $p_{\rm T}$ ($\left<p_{\rm T}\right>$) as a
function of the mid-rapidity charged particle multiplicity. While the V0M and
$N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}$ results show the same trend,
the spectra obtained with the $N_{\rm tracklets}^{\left|\eta\right|<0.8}$
estimator are systematically softer for comparable
$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ values (though still compatible
within uncertainty in the case of the strange baryons).

The increase of the $\left<p_{\rm T}\right>$ as a function of the charged-
particle multiplicity (Fig. 5) is compatible, within uncertainties, for all
particle species. The hardening of $p_{\rm T}$ spectra with the charged-
particle multiplicity was already reported for pp [40] and p–Pb collisions
[22] at lower energies.

It is interesting to notice that the ratio of the measured $p_{\rm T}$ spectra
to the minimum bias one, shown in the bottom panel of Figs. 2–4, reaches a
plateau for $p_{\rm T}\gtrsim 4~{}{\rm GeV}/c$. This applies to all particle
species and to all multiplicity estimators. The trend at high-$p_{\rm T}$ is
highlighted in Fig. 6, which shows the integrated yields for $p_{\rm
T}~{}>~{}4~{}{\rm GeV}/c$ as a function of the mid-rapidity multiplicity. Both
the yields of strange hadrons and the charged particle multiplicity are self-
normalised, i.e. they are divided by their average quoted on the
$\mathrm{INEL}>0$ sample. The high-$p_{\rm T}$ yields of strange hadrons
increase faster than the charged particle multiplicity. Despite the large
uncertainties, the data also hint at the increase being non-linear. The self-
normalised yields of strange hadrons reach, at high multiplicity, larger
values for the $N_{\rm tracklets}^{\left|\eta\right|<0.8}$ multiplicity
selection as compared to the other estimators. For all multiplicity selections
the self-normalised yields of baryons are higher than those of ${\rm
K}^{0}_{S}$ mesons. The Monte Carlo models EPOS-LHC, PYTHIA 8 and PYTHIA 6,
also shown in Fig. 6, reproduce the overall trend of strange hadrons seen in
the data, with EPOS-LHC showing a clear difference between the ${\rm
K}^{0}_{S}$ and the baryons, as observed in the data. Indeed, a non-linear
increase can be explained by the combined effect of multiplicity fluctuations
and interactions between different MPIs, which produces a collective boost
[41]. Both colour reconnection effects implemented in PYTHIA and a collective
hydrodynamic expansion can account for the non-linear increase pattern.

Figure 2: Transverse momentum distribution of ${\rm K}^{0}_{S}$, $\Lambda$,
$\Xi$, and $\Omega$, for multiplicity classes selected using the V0 detector.
Statistical and total systematic uncertainties are shown by error bars and
boxes, respectively. In the bottom panels ratios of multiplicity dependent
spectra to INEL $>$ 0 are shown. The systematic uncertainties on the ratios
are obtained by considering only contributions uncorrelated across
multiplicity. The spectra are scaled by different factors to improve the
visibility. The dashed curves represent Tsallis-Lévy fits to the measured
spectra.

Figure 3: Transverse momentum distribution of ${\rm K}^{0}_{S}$, $\Lambda$,
$\Xi$, and $\Omega$, for multiplicity classes selected using the tracklets in
$\left|\eta\right|<0.8$. Statistical and total systematic uncertainties are
shown by error bars and boxes, respectively. In the bottom panels ratios of
multiplicity dependent spectra to INEL $>$ 0 are shown. The systematic
uncertainties on the ratios are obtained by considering only contributions
uncorrelated across multiplicity. The spectra are scaled by different factors
to improve the visibility. The dashed curves represent Tsallis-Lévy fits to
the measured spectra.

Figure 4: Transverse momentum distribution of ${\rm K}^{0}_{S}$, $\Lambda$,
$\Xi$, and $\Omega$, for multiplicity classes selected using the tracklets in
$0.8<\left|\eta\right|<1.5$. Statistical and total systematic uncertainties
are shown by error bars and boxes, respectively. In the bottom panels ratios
of multiplicity dependent spectra to INEL $>$ 0 are shown. The systematic
uncertainties on the ratios are obtained by considering only contributions
uncorrelated across multiplicity. The spectra are scaled by different factors
to improve the visibility. The dashed curves represent Tsallis-Lévy fits to
the measured spectra.  Figure 5: $\left<p_{\rm T}\right>$ of ${\rm
K}^{0}_{S}$, $\Lambda$, $\Xi$, and $\Omega$ in multiplicity event classes
selected according to different estimators (see text for details). Statistical
and systematic uncertainties are shown by error bars and empty boxes,
respectively. Shadowed boxes represent uncertainties uncorrelated across
multiplicity.

Figure 6:  Self-normalised yields of strange hadrons integrated for $p_{\rm
T}$ $>4$ ${\rm GeV}/c$ (3.8 ${\rm GeV}/c$ for the $\Omega$) versus the self-
normalised charged particle multiplicity quoted using different multiplicity
estimators (see text for details). Statistical and systematic uncertainties
are shown by error bars and empty boxes, respectively. Shadowed boxes
represent uncertainties uncorrelated across multiplicity. Strange particle
yields are compared to expectations from Monte Carlo models.

The left (right) panel of Fig. 7 shows the ratio of the $p_{\rm T}$ spectra
obtained with different estimators for multiplicity classes with comparable
average $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ value
($\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle\simeq 26$); the
numerator refers to the $N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}$
($N_{\rm tracklets}^{\left|\eta\right|<0.8}$) estimator while the denominator
refers to the V0M estimator. These selections correspond to the highest
multiplicity class studied for the V0M and $N_{\rm
tracklets}^{0.8<\left|\eta\right|<1.5}$ estimators. The $N_{\rm
tracklets}^{\left|\eta\right|<0.8}$estimator, on the other hand, was re-
adjusted to lead to the same $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ value.
These classes correspond to approximately 1%, 1% and 4% of the
$\mathrm{INEL}>0$ cross section for V0M, $N_{\rm
tracklets}^{\left|\eta\right|<0.8}$ and $N_{\rm
tracklets}^{0.8<\left|\eta\right|<1.5}$, respectively. It is seen that the
spectra are identical within uncertainties for the V0M and $N_{\rm
tracklets}^{0.8<\left|\eta\right|<1.5}$ estimators. The comparison between the
V0M and $N_{\rm tracklets}^{\left|\eta\right|<0.8}$ estimators shows that the
bias introduced by the latter estimator does not depend on the particle
species and is more pronounced at low and intermediate $p_{\rm T}$, although
the uncertainties are large.

The $p_{\rm T}$-integrated yields of strange hadrons are shown in Fig. 8 for
the three estimators considered in this paper. For reference, Fig. 9 shows the
results integrated in the measured $p_{\rm T}$ range with no extrapolation.
These are characterised by a smaller uncertainty and can be useful for Monte
Carlo tuning. In the rest of this section, we focus on the discussion of the
fully extrapolated yields. The results obtained with the V0M and $N_{\rm
tracklets}^{0.8<\left|\eta\right|<1.5}$estimators follow a similar linear
trend, while the results obtained with $N_{\rm
tracklets}^{\left|\eta\right|<0.8}$ tend to saturate, showing a lower
$\mathrm{d}N/\mathrm{d}y$ for a similar high-multiplicity class. In order to
gain insight on this difference, a generator-level PYTHIA (tune Perugia 2011)
simulation study was performed. The abundance of strange hadrons in
$\left|y\right|<0.5$ was studied as a function of the estimated mid-rapidity
charged particle multiplicity for several event classes, selected using
charged primary particles measured in the $\eta$ ranges corresponding to the
experimental estimators presented in this paper: this generator level study
confirms the trend observed in the data, which can be understood in terms of a
selection bias sensitive to fluctuations in particles yields. Indeed, an
estimator based on charged tracks enhances charged primary particles over
neutral particles or secondaries. If the multiplicity estimator and the
observable under study are measured in the same $\eta$ region one expects
primary charged-particles to be enhanced with respect to strange hadrons,
which explains the saturation of yields observed in Fig. 8 for the $N_{\rm
tracklets}^{\left|\eta\right|<0.8}$ estimator. As a further check of this
interpretation, Fig. 10 shows the correlations between the yields of different
strange hadrons for the multiplicity estimators studied in this paper. The
trend is linear, and similar for all estimators, confirming that the selection
bias on primary charged-particles is stronger than that on strange hadrons.

Figure 7:  Ratio of $p_{\rm T}$ spectra of ${\rm K}^{0}_{S}$, $\Lambda$ and
$\Xi$ obtained with two different estimators for multiplicity classes with
comparable average $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ value
($\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle\simeq 26$); the
numerator does refer to the $N_{\rm tracklets}^{0.8<\left|\eta\right|<1.5}$
($N_{\rm tracklets}^{\left|\eta\right|<0.8}$) estimator while the denominator
refers to the V0M estimator. Statistical and systematic uncertainties are
shown by error bars and empty boxes, respectively. Shadowed boxes represent
uncertainties uncorrelated across multiplicity.

Figure 8: d$N$/d$y$ (integrated over the full $p_{\rm T}$ range) as a function
of multiplicity for different strange particle species reported for different
multiplicity classes (see text for details). Error bars and boxes represent
statistical and total systematic uncertainties, respectively. The bin-to-bin
systematic uncertainties are shown by shadowed boxes.

Figure 9: d$N$/d$y$ (integrated over the measured $p_{\rm T}$ ranges 0-12,
0.4-8, 0.6-6.5 and 0.9-5.5 ${\rm GeV}/c$ for ${\rm K}^{0}_{S}$, $\Lambda$,
$\Xi^{-}$ and $\Omega^{-}$, respectively) as a function of multiplicity for
different strange particle species reported for different multiplicity classes
(see text for details). Error bars and boxes represent statistical and total
systematic uncertainties, respectively. The bin-to-bin systematic
uncertainties are shown by shadowed boxes.

Figure 10:  Correlations between integrated yield of different strange hadrons
in multiplicity classes selected according to different estimators (see text
for details). Statistical and systematic uncertainties are shown by error bars
and empty boxes, respectively. Shadowed boxes represent uncertainties
uncorrelated across multiplicity.

The energy dependence of the strangeness yields and $\left<p_{\rm T}\right>$
versus the charged particle multiplicity at mid-rapidity is studied in Figs.
11 and 12, where our results are compared to the previous pp measurements at
$\sqrt{s}$ = 7 TeV [21]. The minimum bias results in the $\mathrm{INEL}>0$
event class at $\sqrt{s}$ = 7 and 13 TeV [5] are also shown.

As can be seen in Fig. 11, the yields of strange hadrons increase with the
charged particle multiplicity following a power law behaviour, and the trend
is the same at $\sqrt{s}$ = 7 and 13 TeV. The $\mathrm{INEL}>0$ results also
follow the same trend at all the tested centre-of-mass energies. This result
indicates that the abundance of strange hadrons depends on the local charged
particle density and turns out to be invariant with the collision energy, i.e.
an energy scaling property applies for the multiplicity-dependent yields of
strange hadrons. It should also be noted that the yields of particles with
larger strange quark content increase faster as a function of multiplicity as
already reported in [21]. Figure 13 shows the $\Lambda$/${\rm K}^{0}_{S}$ (no
$\overline{\Lambda}$ contribution considered here), $\Xi$/${\rm K}^{0}_{S}$
and $\Omega$/${\rm K}^{0}_{S}$ ratios compared to calculations from grand-
canonical thermal models [13, 14], which were found to satisfactorily describe
central Pb-Pb data at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. In the context of a
canonical thermal model for a gas of hadrons, an increase of the relative
strangeness abundance depending on the strange quark content can be
interpreted as a consequence of a change in the system volume, called
canonical suppression. Indeed, it was recently shown in [18] that the existing
ALICE data can be described within this framework, introducing an additional
parameter to quantify the rapidity window over which strangeness is
effectively correlated. It was also suggested that strangeness follows a
universal scaling behaviour in all colliding systems, when the transverse
energy density [42] or the multiplicity per transverse area [43] are used as a
scaling variable. While there are some caveats in the observation reported in
these papers (due to the uncertainties on the transverse size of the system)
this is a very intriguing observation, that could help to clarify the origin
of strangeness enhancement.

The $\left<p_{\rm T}\right>$ is seen in Fig. 12 to be harder at 13 TeV than at
7 TeV for event classes with a similar
$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$. All the tested Monte Carlo models
describe in a qualitative way the observed smooth rise of the $\left<p_{\rm
T}\right>$ with $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$; from a
quantitative point of view, EPOS-LHC provides a slightly better description of
the $\left<p_{\rm T}\right>$ multiplicity evolution, especially for what
concerns the strange baryons.

Figure 11: Integrated yields of ${\rm K}^{0}_{S}$, $\Lambda$, $\Xi$, and
$\Omega$ as a function of $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ in V0M
multiplicity event classes at $\sqrt{s}$ = 7 and 13 TeV. Statistical and
systematic uncertainties are shown by error bars and empty boxes,
respectively. Shadowed boxes represent uncertainties uncorrelated across
multiplicity. The corresponding results obtained for $\mathrm{INEL}>0$ event
class are also shown.

Figure 12: $\left<p_{\rm T}\right>$ of ${\rm K}^{0}_{S}$, $\Lambda$, $\Xi$,
and $\Omega$ as a function of $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ in
V0M multiplicity event classes at $\sqrt{s}$ = 7 and 13 TeV. Statistical and
systematic uncertainties are shown by error bars and empty boxes,
respectively. Shadowed boxes represent uncertainties uncorrelated across
multiplicity. The results are compared to predictions from several Monte Carlo
models. Figure 13: Ratios of integrated yields of $\Lambda$ (no
$\overline{\Lambda}$ contribution considered here), $\Xi$, and $\Omega$ to
${\rm K}^{0}_{S}$ as a function of $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$
for different multiplicity estimators (see text for details) in pp collisions
at $\sqrt{s}$ = 13 TeV. Statistical and systematic uncertainties are shown by
error bars and empty boxes, respectively. Shadowed boxes represent
uncertainties uncorrelated across multiplicity. The corresponding calculations
from grand-canonical thermal models, which refer to most central Pb-Pb
collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV, are shown.

In Fig. 14 the results on the strange hadron yields as a function of the
charged particle multiplicity at mid-rapidity are compared with some commonly-
used general purpose QCD inspired models, focusing on the multiplicity classes
defined by the V0M estimator. The yields of all measured strange hadrons show
an almost linear increase with multiplicity: a linear fit to the baryon trends
would intercept the $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ axis at
positive values. Alternatively one may regard such qualitative observation as
the trend of the points to have an enhanced (more than linear) increase for
the hadrons with larger strangeness content.

The PYTHIA 8.210 event generator (tune Monash 2013) gives a reasonable
description of the ${\rm K}^{0}_{S}$ results, however it shows a less
pronounced increase of the strange baryons yields versus the charged particle
multiplicity than what is observed in the data. The description worsens with
increasing strangeness content. Recent attempts to improve the PYTHIA colour-
reconnection scheme to account for the observed strangeness enhancement are
discussed in [3], however they cannot explain the reported experimental
observations.

The DIPSY Monte Carlo [44, 45] is based on a BFKL inspired initial state
dipole evolution model [46] interfaced to the Ariadne model [47] for final
state dipole evolution and to the PYTHIA hadronisation scheme, where the
latter has been modified to take into account the high density of strings that
occurs in events with several MPI. More specifically, depending on their
transverse density, the strings are allowed to form “colour-ropes” leading to
increased string tension, which leads to an increase of strangeness production
stronger than in default PYTHIA [48]. However, despite a qualitative
improvement in the description of the data, the discrepancy for the $\Omega$
distributions remains large. Moreover, as discussed in [21], DIPSY also
predicts an increase of protons normalised to pions as a function of
multiplicity, which is not observed in our $\sqrt{s}$ = 7 TeV data.

The Monte Carlo generators based on EPOS [49] rely on the Parton Based Gribov
Regge Theory (PBGRT) [50]. A common feature of all the EPOS versions is a
collective evolution of matter in the secondary scattering stage in all
reactions, from pp to AA, with a core-corona separation mechanism [51] which
defines the initial conditions of the secondary interactions. In EPOS, the
initial parton scatterings create “flux tubes” that either escape the medium
and hadronise as jets or contribute to the core, described in terms of
hydrodynamics. The core is then hadronised in terms of a grand-canonical
statistical model. The relative amount of multi-hadron production arising from
the core grows with the number of MPIs. The EPOS-LHC model adopted in this
analysis (distributed with the CRMC package 1.5.4) shows a pronounced increase
of the strangeness yields as a function of the charged particle multiplicity
at mid-rapidity. Despite the differences in the underlying physics, the
comparison to data leads to a similar conclusion for EPOS-LHC and DIPSY.

The comparison of the Monte Carlo model predictions to the data indicates that
the origin of the strangeness enhancement in hadronic collisions and its
relation to the QCD deconfinement phase transition are still open problems for
models. While the current versions of these models do not reproduce the data
quantitatively, it is possible that the agreement can be improved with further
tuning or with new implementations. A quantitative description of strangeness
production and enhancement in a microscopic Monte Carlo model would represent
a major step to understand flavour production in hadronic collisions at high
energy.

Figure 14: Integrated yields of ${\rm K}^{0}_{S}$, $\Lambda$, $\Xi$, and
$\Omega$ as a function of $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ in V0M
multiplicity event classes at $\sqrt{s}$ = 7 and 13 TeV. Statistical and
systematic uncertainties are shown by error bars and empty boxes,
respectively. Shadowed boxes represent uncertainties uncorrelated across
multiplicity. The results are compared to predictions from several Monte Carlo
models.

##  6 Summary

We studied the production of primary strange and multi-strange hadrons at mid-
rapidity in pp collisions at $\sqrt{s}$ = 13 TeV, focusing on the multiplicity
dependence. The main feature of this analysis is the usage of multiplicity
estimators defined in different pseudorapidity regions, providing a different
sensitivity to the fragmentation and MPI components of particle production and
allowing for a detailed study of the selection biases due to fluctuations.

Hardening of the $p_{\rm T}$ spectra with the increase of the multiplicity is
observed, as already reported for pp [40] and p–Pb collisions [22] at lower
energies.

The $p_{\rm T}$-integrated yields of strange hadrons increase as a function of
multiplicity faster than the ones of unidentified charged-particles. This
behaviour is even more pronounced for particles with higher strangeness
content, confirming the earlier observations in pp collisions at $\sqrt{s}$ =
7 TeV [21]. This leads to a multiplicity-dependent increase of the ratio of
the strange baryons $\Xi$ and $\Omega$ over ${\rm K}^{0}_{S}$, while the
$\Lambda$ over ${\rm K}^{0}_{S}$ ratio turns out to be constant within
uncertainties. In the context of a canonical thermal model, an increase of the
relative strangeness abundance depending on the strange quark content can be
understood as a consequence of an increase in the system volume leading to a
progressive removal of canonical suppression.

Comparing the 13 TeV results to the 7 TeV ones, the data exhibit an
interesting scaling property: for multiplicity estimators selected in the
forward region, the strange hadron yields turn out to be independent of the
centre of mass energy, the $\sqrt{s}$ increase resulting just in harder
$p_{\rm T}$ spectra.

The use of high-multiplicity triggered data collected during the full Run 2
period will allow us to test these scaling ansatzes extending the measurement
to higher multiplicities, comparable to peripheral Pb-Pb collisions at the LHC
($\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\sim 40-50$).

The colour reconnection effects implemented in PYTHIA 8 and DIPSY as well as
the collective hydrodynamic expansion implemented in EPOS-LHC could not
account quantitatively for all the reported results. Some of the qualitative
features of the data are described by these models, including the indication
of a non-linear increase of the yields of strange hadrons at high $p_{\rm T}$,
similar to what was previously reported in [52] for $\rm J/\psi$ and $D$ meson
production. Although none of the tested models can reproduce the data from a
quantitative point of view, EPOS-LHC and DIPSY do provide a better qualitative
description of the strangeness enhancement.

## 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), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China; Croatian Science Foundation and Ministry of Science and Education, 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 Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA), Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and 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; National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg73&J.
Adolfssonorg79&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10,org48,org53&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg75&A.
Akindinovorg90&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg86&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org27,org53&A. Alkinorg2&J. Almeorg22&T.
Altorg68&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg125&N. Apadulaorg78&L.
Aphecetcheorg114&H. Appelshäuserorg68&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg78&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg68&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&S. Balouzaorg103&R.C. Baralorg84&R.
Barberaorg28&L. Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V.
Barretorg134&P. Bartaliniorg6&K. Barthorg34&E. Bartschorg68&F.
Baruffaldiorg29&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg74&P.C. Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G.
Beardenorg87&C. Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F.
Belliniorg34&R. Bellwiedorg125&V. Belyaevorg91&G. Bencediorg145&S.
Beoleorg26&A. Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg58&M.G. Besoiuorg67&L. Betevorg34&A.
Bhasinorg99&I.R. Bhatorg99&M.A. Bhatorg3&H. Bhattorg48&B.
Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg26&N. Bianchiorg51&J.
Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg103,org117&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg86&C. Blumeorg68&G.
Bocaorg139&F. Bockorg34,org94&A. Bogdanovorg91&L. Boldizsárorg145&A.
Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H. Borelorg137&A.
Borissovorg91,org144&M. Borriorg127&H. Bossiorg146&E. Bottaorg26&L.
Bratrudorg68&P. Braun-Munzingerorg105&M. Bregantorg121&T.A. Brokerorg68&M.
Brozorg37&E.J. Bruckenorg43&E. Brunaorg58&G.E. Brunoorg33,org104&M.D.
Bucklandorg127&D. Budnikovorg107&H. Bueschingorg68&S. Bufalinoorg31&O.
Bugnonorg114&P. Buhlerorg113&P. Buncicorg34&Z. Butheleziorg72&J.B.
Buttorg15&J.T. Buxtonorg95&S.A. Bysiakorg118&D. Caffarriorg88&A.
Calivaorg105&E. Calvo Villarorg110&R.S. Camachoorg44&P. Cameriniorg25&A.A.
Caponorg113&F. Carnesecchiorg10,org27&J. Castillo Castellanosorg137&A.J.
Castroorg130&E.A.R. Casulaorg54&F. Catalanoorg31&C. Ceballos Sanchezorg52&P.
Chakrabortyorg48&S. Chandraorg141&B. Changorg126&W. Changorg6&S.
Chapelandorg34&M. Chartierorg127&S. Chattopadhyayorg141&S.
Chattopadhyayorg108&A. Chauvinorg24&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg34&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg34&T.
Chowdhuryorg134&P. Christakoglouorg88&C.H. Christensenorg87&P.
Christiansenorg79&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org27&F.
Cindoloorg53&J. Cleymansorg124&F. Colamariaorg52&D. Colellaorg52&A.
Colluorg78&M. Colocciorg27&M. Concasorg58orgI&G. Conesa Balbastreorg77&Z.
Conesa del Valleorg61&G. Continorg59,org127&J.G. Contrerasorg37&T.M.
Cormierorg94&Y. Corrales Moralesorg26,org58&P. Corteseorg32&M.R.
Cosentinoorg123&F. Costaorg34&S. Costanzaorg139&P. Crochetorg134&E.
Cuautleorg69&P. Cuiorg6&L. Cunqueiroorg94&D. Dabrowskiorg142&T.
Dahmsorg103,org117&A. Daineseorg56&F.P.A. Damasorg114,org137&S. Daniorg65&M.C.
Danischorg102&A. Danuorg67&D. Dasorg108&I. Dasorg108&P. Dasorg3&S. Dasorg3&A.
Dashorg84&S. Dashorg48&A. Dashiorg103&S. Deorg49,org84&A. De Caroorg30&G. de
Cataldoorg52&C. de Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De
Gruttolaorg10&N. De Marcoorg58&S. De Pasqualeorg30&R. Derradi de
Souzaorg122&S. Deborg49&H.F. Degenhardtorg121&K.R. Dejaorg142&A.
Delofforg83&S. Delsantoorg26,org131&D. Devetakorg105&P. Dhankherorg48&D. Di
Bariorg33&A. Di Mauroorg34&R.A. Diazorg8&T. Dietelorg124&P.
Dillensegerorg68&Y. Dingorg6&R. Diviàorg34&Ø. Djuvslandorg22&U.
Dmitrievaorg62&A. Dobrinorg34,org67&B. Dönigusorg68&O. Dordicorg21&A.K.
Dubeyorg141&A. Dublaorg105&S. Dudiorg98&M. Dukhishyamorg84&P.
Dupieuxorg134&R.J. Ehlersorg146&V.N. Eikelandorg22&D. Eliaorg52&H.
Engelorg73&E. Eppleorg146&B. Erazmusorg114&F. Erhardtorg97&A.
Erokhinorg112&M.R. Ersdalorg22&B. Espagnonorg61&G. Eulisseorg34&J. Eumorg18&D.
Evansorg109&S. Evdokimovorg89&L. Fabbiettiorg103,org117&M. Fagginorg29&J.
Faivreorg77&F. Fanorg6&A. Fantoniorg51&M. Faselorg94&P. Fecchioorg31&A.
Felicielloorg58&G. Feofilovorg112&A. Fernández Téllezorg44&A. Ferreroorg137&A.
Ferrettiorg26&A. Festantiorg34&V.J.G. Feuillardorg102&J. Figielorg118&S.
Filchaginorg107&D. Finogeevorg62&F.M. Fiondaorg22&G. Fiorenzaorg52&F.
Flororg125&M. Florisorg34&S. Foertschorg72&P. Fokaorg105&S. Fokinorg86&E.
Fragiacomoorg59&U. Frankenfeldorg105&G.G. Fronzeorg26&U. Fuchsorg34&C.
Furgetorg77&A. Fursorg62&M. Fusco Girardorg30&J.J. Gaardhøjeorg87&M.
Gagliardiorg26&A.M. Gagoorg110&A. Galorg136&C.D. Galvanorg120&P.
Ganotiorg82&C. Garabatosorg105&E. Garcia-Solisorg11&K. Gargorg28&C.
Gargiuloorg34&A. Garibliorg85&K. Garnerorg144&P. Gasikorg103,org117&E.F.
Gaugerorg119&M.B. Gay Ducatiorg70&M. Germainorg114&J. Ghoshorg108&P.
Ghoshorg141&S.K. Ghoshorg3&P. Gianottiorg51&P. Giubellinoorg58,org105&P.
Giubilatoorg29&P. Glässelorg102&D.M. Goméz Coralorg71&A. Gomez Ramirezorg73&V.
Gonzalezorg105&P. González-Zamoraorg44&S. Gorbunovorg39&L. Görlichorg118&S.
Gotovacorg35&V. Grabskiorg71&L.K. Graczykowskiorg142&K.L. Grahamorg109&L.
Greinerorg78&A. Grelliorg63&C. Grigorasorg34&V. Grigorievorg91&A.
Grigoryanorg1&S. Grigoryanorg74&O.S. Groettvikorg22&F. Grosaorg31&J.F. Grosse-
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Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

org14Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Pusan National University, Pusan, Republic of
Korea

org19Department of Physics, Sejong University, Seoul, Republic of Korea

org20Department of Physics, University of California, Berkeley, California,
United States

org21Department of Physics, University of Oslo, Oslo, Norway

org22Department of Physics and Technology, University of Bergen, Bergen,
Norway

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

org42Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

org44High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org45Hiroshima University, Hiroshima, Japan

org46Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org47Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

org61Institut de Physique Nucléaire d’Orsay (IPNO), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3/CNRS), Université de
Paris-Sud, Université Paris-Saclay, Orsay, France

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

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

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

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

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

org67Institute of Space Science (ISS), Bucharest, Romania

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

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

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

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

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

org73Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org74Joint Institute for Nuclear Research (JINR), Dubna, Russia

org75Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org76KTO Karatay University, Konya, Turkey

org77Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org78Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org79Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org80Nagasaki Institute of Applied Science, Nagasaki, Japan

org81Nara Women’s University (NWU), Nara, Japan

org82National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org83National Centre for Nuclear Research, Warsaw, Poland

org84National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org85National Nuclear Research Center, Baku, Azerbaijan

org86National Research Centre Kurchatov Institute, Moscow, Russia

org87Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org88Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org89NRC Kurchatov Institute IHEP, Protvino, Russia

org90NRC «Kurchatov Institute» - ITEP, Moscow, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

org101Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org102Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

org105Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org108Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org109School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org110Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

org113Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org114SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

org117Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Techonology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

org145Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea