2015 326 18 December

K∗(892)0 and $\phi$(1020) in p–Pb at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV

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

The production of K∗(892)0 and $\phi$(1020) mesons has been measured in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. K∗0 and $\phi$ are
reconstructed via their decay into charged hadrons with the ALICE detector in
the rapidity range –0.5 < $y$ < 0\. The transverse momentum spectra, measured
as a function of the multiplicity, have pT range from 0 to 15 GeV/$c$ for K∗0
and from 0.3 to 21 GeV/$c$ for $\phi$. Integrated yields, mean transverse
momenta and particle ratios are reported and compared with results in pp
collisions at $\sqrt{s}$ = 7 TeV and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. In Pb–Pb and p–Pb collisions, K∗0 and
$\phi$ probe the hadronic phase of the system and contribute to the study of
particle formation mechanisms by comparison with other identified hadrons. For
this purpose, the mean transverse momenta and the differential proton-
to-$\phi$ ratio are discussed as a function of the multiplicity of the event.
The short-lived K∗0 is measured to investigate re-scattering effects, believed
to be related to the size of the system and to the lifetime of the hadronic
phase.

##  1 Introduction

The phase transition predicted by QCD from ordinary matter to a deconfined
Quark-Gluon Plasma (QGP) has been studied in high-energy heavy-ion collision
(AA) experiments at the Super Proton Synchrotron (SPS) [1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11], the Relativistic Heavy Ion Collider (RHIC) [12, 13, 14, 15] and
the Large Hadron Collider (LHC) [16, 17, 18, 19, 20, 21, 22]. In this context,
hadronic resonances provide an important contribution to the study of particle
production mechanisms and the characterisation of the dynamic evolution of the
system formed in heavy-ion collisions, during the late hadronic phase. Results
on resonance production in different collision systems at RHIC have been
reported in [23, 24, 25, 26, 27, 28, 29]. At the LHC, K∗(892)0 and
$\phi$(1020) production have been measured in pp collisions at
$\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ by ALICE [30], ATLAS [31] and LHCb [32], and
in pp and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=2.76\,\mathrm{~{}TeV}$ by ALICE [33, 34]. Results
obtained in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$ with the ALICE detector are
presented in this paper.

Measurements in smaller collision systems such as proton-proton (pp) and
proton-nucleus (pA) constitute a reference for the interpretation of the
heavy-ion results. In addition, proton-nucleus collisions have proven to be
interesting in their own right, as several measurements [35, 36, 37, 38, 39]
indicate that they cannot be explained by an incoherent superposition of
$\mathrm{p\kern-0.50003ptp}$ collisions, but suggest instead the presence of
collective effects [40, 41]. In heavy-ion collisions, the presence of a strong
collective radial flow reveals itself in the evolution with centrality of the
transverse momentum spectra of identified hadrons [42]. The spectral shapes of
of ${\rm K}^{*0}$ and $\phi$ follow the common behaviour found for all the
other particles and exhibit an increase of the mean transverse momentum,
dominated by the low $p_{\mathrm{T}}$ region of the spectra where particle
production is more abundant, with centrality [33]. In central Pb–Pb events,
particles with similar mass such as the $\phi$ meson and the proton have
similar $\langle p_{\mathrm{T}}\rangle$ and, in addition, the $\phi$/p ratio
as a function of $p_{\mathrm{T}}$ is flat for $p_{\mathrm{T}}$ < 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. Both observations are
consistent with expectations from hydrodynamic models, where the mass of the
particle drives the particle spectral shapes at low momenta [43]. On the other
hand, in most peripheral Pb–Pb collisions, as well as in
$\mathrm{p\kern-0.50003ptp}$, the $\phi$/p ratio exhibits a strong
$p_{\mathrm{T}}$ dependence, suggesting that the production of low and
intermediate momentum baryons and mesons occurs by means of other mechanisms
such as fragmentation or recombination [44, 45].

Similarly to Pb–Pb, one is interested in searching for collective effects in
p–Pb collisions and in studying particle production as a function of the
hadron multiplicity, which strongly depends on the geometry of the collision.
In this respect, p–Pb collisions provide us with a system whose size in terms
of average charged-particle density and number of participating nucleons is
intermediate between pp and peripheral Pb–Pb collisions [46, 47, 18, 48, 49].
Measurements in an intermediate-size system as p–Pb can provide information on
the onset of the collective behaviour leading to the presence of radial flow.
The $\phi$ meson, with similar mass as that of the proton and rather long
lifetime ($\tau_{\phi}$ = 46.3 $\pm$ 0.4 fm/$c$ [50]) compared to that of the
fireball, is an ideal candidate for such study. The yields of short-lived
resonances such as the ${\rm K}^{*0}$ ($\tau_{{\rm K}^{*0}}$ = 4.16 $\pm$ 0.05
fm/$c$ [50]) instead, may be influenced by interactions during the hadronic
phase: the re-scattering of the decay products in the fireball may prevent the
detection of a fraction of the resonances, whereas pseudo-elastic hadron
scattering can regenerate them. The effects of re-scattering and regeneration
depend on the scattering cross section, the particle density, the particle
lifetime and the timespan between chemical and kinetic freeze-out, namely the
lifetime of the hadronic phase. Therefore, the observation of re-scattering
effects would imply the presence of an extended hadronic phase. The latter can
be studied by comparing particles with different lifetimes, such as the ${\rm
K}^{*0}$ resonance and the $\phi$ meson, which has a ten times longer
lifetime. ALICE has observed [33] that in most central Pb–Pb collisions at the
LHC the ${\rm K}^{*0}$/K ratio is significantly suppressed with respect to
peripheral Pb–Pb collisions, pp collisions and the value predicted by a
statistical hadronisation model [51]. This is interpreted as a scenario where
re-scattering during the hadronic phase, dominating for low-momentum
resonances ($p_{\mathrm{T}}$ < 2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) [52, 53], reduces the
measurable yield of ${\rm K}^{*0}$. No suppression is observed instead for the
ten times longer-lived $\phi$, since it decays mainly after kinetic freeze-
out. Based on these observations, a lower limit of 2 fm/$c$ on the lifetime of
the hadronic phase in 0–20$\%$ most central Pb–Pb events could be estimated
[33]. The ${\rm K}^{*0}$ suppression exhibits a monotonic trend with
centrality, suggesting a dependence on the volume of the particle source at
the kinetic freeze-out. A similar measurement of resonance production as a
function of the system size in p–Pb can provide information about the lifetime
of the hadronic fireball produced in such a smaller system.

The ${\rm K}^{*0}$ and $\phi$ mesons are reconstructed using the ALICE
detector in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$. Their yields, mean
transverse momenta and ratios to identified long-lived hadrons in p–Pb
collisions are studied as a function of the system size or the multiplicity of
the event, and compared with pp and Pb–Pb. The experimental conditions are
briefly presented in Sec. 2. Section 3 illustrates the analysis procedure,
including event and track selection, signal extraction, efficiency correction
and systematic uncertainties. The results are presented in Sec. 4 and in Sec.
5 the conclusions are summarised.

##  2 Experimental setup

A complete description of the ALICE detector and its performance during the
LHC Run I are reported in [54] and [55], respectively.
The analyses presented in this paper have been carried out on a sample of p–Pb
collision events at $\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$
collected in 2013. The LHC configuration was such that the lead beam, with
energy of 1.58 TeV per nucleon, was circulating in the counter-clockwise
direction, namely towards the ALICE “A” side (positive rapidity direction),
while the 4 TeV proton beam was circulating in the clockwise direction,
towards the ALICE muon spectrometer, or “C” side. According to this convention
for the sign of the coordinates, the nucleon-nucleon center-of-mass system was
moving in the laboratory frame with a rapidity of $y$NN = -0.465 in the
direction of the proton beam. In the following, $y$lab ($\eta_{\mathrm{lab}}$)
are used to indicate the (pseudo) rapidity in the laboratory reference frame,
whereas $y$ ($\eta$) denotes the (pseudo) rapidity in the nucleon-nucleon
center-of-mass reference system.
For the results presented in this paper, a low-luminosity data sample has been
analysed, consisting of events collected at an hadronic interaction rate of
about 10 kHz. The interaction region had a root mean square of 6.3 cm along
the beam direction and of about 60 $\mathrm{\mu}$m in the direction transverse
to the beam. The event pile-up rate has been estimated to have negligible
effects on the results of this analysis. In particular, pile-up of collisions
from different bunch crossings is negligible due to the 200 ns bunch-crossing
spacing, larger than the integration time of the Zero-Degree Calorimeter
(ZDC), while a small fraction of in-bunch pile-up events is removed by the
offline analysis, as described in the next section.
Small acceptance forward detectors (V0, T0, and ZDC) are used for triggering,
event characterisation, and multiplicity studies. The trigger is provided by
two arrays of 32 scintillator detectors, V0A and V0C, that cover the full
azimuthal angle in the pseudo-rapidity regions 2.8 < $\eta_{\mathrm{lab}}$ <
5.1 (Pb-going direction) and $-$3.7 < $\eta_{\mathrm{lab}}$ < $-$1.7 (p-going
direction), respectively. V0 information is also used to classify events in
multiplicity classes (see Sec. 2.1). The two quartz Cherenkov detectors T0A
(4.6 < $\eta_{\mathrm{lab}}$ < 4.9) and T0C ($-$3.3 < $\eta_{\mathrm{lab}}$ <
$-$3) deliver the time and the longitudinal position of the interaction. The
Zero-Degree Calorimeters (ZDC), consisting of two tungsten-quartz neutron and
two brass-quartz proton calorimeters placed symmetrically at a distance of 113
m from the interaction point, on both sides, are used to reject background and
to count spectator nucleons.
The reconstruction of the primary vertex of the collision and the tracking of
particles in the ALICE central barrel is provided by the Inner Tracking System
(ITS) and the Time-Projection Chamber (TPC), in the pseudo-rapidity range
$|\eta_{lab}|$ < 0.9 and the full azimuthal angle. The ITS is a silicon-based
detector, constituted by two innermost pixels layers (SPD), two intermediate
drift (SDD) and two outer strip layers (SSD), with radii between 3.9 and 43 cm
from the beam axis. The ALICE main tracker, the TPC, is a 90 m3 cylindrical
drift chamber filled with Ne-CO2 gas and divided in two parts by a central
cathode. The end plates are equipped with multi-wire proportional chambers
whose readout cathode pads allow to sample particle tracks up to 159 points
(clusters). In addition to tracking, the TPC allows particle identification
via the specific ionization energy loss $\mathrm{d}E/\mathrm{d}x$ in the gas.
The Time-Of-Flight (TOF) detector, a large Multigap Resistive Plate Chamber
(MRPC) array covering $|\eta|$<0.9 and the full azimuthal angle, allows for
particle identification at intermediate momenta and has been exploited
together with the TPC for the analysis presented in this paper (see Sec. 3.1).

###  2.1 Event selection

The minimum bias trigger during p–Pb data taking was configured to select
hadronic events with high efficiency, by requiring a signal in either V0A or
V0C. The resulting sample contains single-diffractive (SD), non-single
diffractive (NSD) and electromagnetic (EM) events. Diffractive interactions
are described in Regge theory by the exchange of a colour singlet object with
the quantum numbers of the vacuum (pomeron). In SD events one of the two
nucleons breaks up producing particles in a limited rapidity interval. NSD
events include double-diffractive interactions, where both nucleons break up
by producing particles separated by a large rapidity gap, and other inelastic
interactions. The offline analysis selects events having a coincidence of
signals in both V0A and V0C in order to reduce the contamination from SD and
EM events to a negligible amount. The trigger and event selection efficiency
for NSD events is estimated as $\epsilon_{\mathrm{NSD}}$ = 99.2$\%$ using a
combination of Monte-Carlo event generators, as described in [48, 49]. The
arrival time of signals on the V0 and the ZDC is required to be compatible
with a nominal p-Pb collision occurring close to the nominal interaction
point, to ensure the rejection of beam-gas and other machine-induced
background collisions.
The primary vertex of the collision is determined using tracks reconstructed
in the TPC and ITS. In case of low multiplicity events only the information
from the SPD is used to reconstruct the vertex, as described in detail in
[55]. 98.5$\%$ of all events have a primary vertex. Minimum bias events with
the primary vertex positioned along the beam axis within 10 cm from the center
of the ALICE detector are selected offline. A small fraction (0.2$\%$) of
pile-up events from the same bunch crossing has been removed from the sample
by rejecting events with multiple vertices. Events are accepted if the
vertices separately measured by the SPD and using tracks are within 0.5 cm,
and if the SPD vertex is determined by at least five track segments defined by
one hit in each one of the two layers of the detector.

After the trigger and offline event-selection criteria, the sample used for
this analysis counts about 108 events, corresponding to an integrated
luminosity of about 50 $\mu$b-1. The minimum bias sample has been further
divided in several event classes based on the charged-particle multiplicity,
estimated using the total charge deposited in the V0A detector positioned
along the direction of the Pb beam.
The yield of ${\rm K}^{*0}$ is measured in five multiplicity classes, namely
0–20$\%$, 20–40$\%$, 40–60$\%$, 60–80$\%$ and 80–100$\%$. In case of $\phi$
seven classes, namely 0–5$\%$, 5–10$\%$, 10–20$\%$, 20–40$\%$, 40–60$\%$,
60–80$\%$ and 80–100$\%$ are used. In addition, minimum bias spectra
normalised to the fraction of NSD events are measured for both particles.

In order to study the dependence of particle production on the geometry of the
collision, the V0A estimator for the charged particle multiplicity has been
used to determine centrality, by following the approach based on the Glauber
Monte Carlo model combined with a simple model for particle production [56,
57], a strategy customarily employed in heavy-ion collisions [58]. The average
number of binary collisions $\langle\mathrm{N_{coll}}\rangle$ (related to the
number of participant nucleons $N_{\mathrm{part}}$ by the simple relation
$N_{\mathrm{coll}}$ = $N_{\mathrm{part}}$ -1), obtained with this method for
each centrality class, are listed in Tab. 1 for future reference, together
with the mean charged particle multiplicity density, $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle_{|\eta|<0.5}$ [48, 47], here
corrected for trigger and vertex-reconstruction inefficiency, which is about
5.5$\%$ in the lowest multiplicity event class. In addition, the average
$N_{\mathrm{coll}}$ has been determined with an hybrid method that uses the
ZDC to classify the events according to the energy deposited by the neutrons
emitted in the Pb-going direction (by evaporation or fragmentation) or the
energy measured with the ZDC in the Pb-going direction and the assumption that
the charged-particle multiplicity measured at mid-rapidity is proportional to
the number of participant nucleons. This method was shown [49] to avoid
possible bias in the event sample related to the fact that the range of
multiplicities used to select a given class in p–Pb collisions is of similar
magnitude as the fluctuations on the same quantity. The variations of the
average $N_{\mathrm{coll}}$ for a given multiplicity class, obtained with
different methods are found not to exceed 6$\%$ in any of the used classes.

Multiplicity class ($\%$) | $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle_{|\eta|<0.5}$ | $\langle\mathrm{N_{coll}}\rangle$
---|---|---
0–5 | 45 $\pm$ 1 | 14.8 $\pm$ 1.5
5–10 | 36.2 $\pm$ 0.8 | 13.0 $\pm$ 1.3
10–20 | 30.5 $\pm$ 0.7 | 11.7 $\pm$ 1.2
0–20 | 35.6 $\pm$ 0.8 | 12.8 $\pm$ 1.3
20–40 | 23.2 $\pm$ 0.5 | 9.36 $\pm$ 0.84
40–60 | 16.1 $\pm$ 0.4 | 6.42 $\pm$ 0.46
60–80 | 9.8 $\pm$ 0.2 | 3.81 $\pm$ 0.76
80–100 | 4.16 $\pm$ 0.09 | 1.94 $\pm$ 0.45
Table 1: Average charged particle pseudo-rapidity density,
$\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle_{|\eta|<0.5}$, measured at mid-
rapidity in visible cross section event classes and average number of
colliding nucleons, $\langle\mathrm{N_{coll}}\rangle$. Multiplicity classes
are defined using the V0A estimator [48, 49], as described in the text. Total
systematic uncertainties are reported, see [49] for details, that do not
include the difference with respect to the other methods used to estimate the
average $N_{\mathrm{coll}}$. For minimum bias collisions,
$\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle$ = 16.81
$\pm$ 0.71 and $\langle\mathrm{N_{coll}}\rangle$ = 6.87 $\pm$ 0.5.

##  3 Resonance signal reconstruction

K∗(892)0 and $\phi$(1020) mesons are reconstructed through their decay into
charged hadrons, ${\rm K}^{*0}$ $\rightarrow$ ${\rm K}^{+}$$\pi^{-}$ and
$\overline{{\rm K}^{*0}}$ $\rightarrow$ ${\rm K}^{-}$$\pi^{+}$, B.R. = 0.666,
and $\phi$ $\rightarrow$ ${\rm K}^{+}$${\rm K}^{-}$, B.R. = 0.489 [50]. Since
K∗(892)0 and $\overline{\mathrm{K}^{*}}$(892)0 are expected to be produced in
equal amounts, as measured in lower energy experiments [59], for this
measurement the yields of particle and anti-particle are combined in order to
improve statistics. The average (K∗(892)0 \+
$\overline{\mathrm{K}^{*}}$(892)0)/2 is indicated as ${\rm K}^{*0}$ in the
following. The $\phi$(1020) meson is indicated as $\phi$.
For these measurements, the reconstructed ${\rm K}^{*0}$ and $\phi$ are
selected in the rapidity range $-$0.5 < $y$ < 0, in order to ensure the best
detector acceptance as the center of mass of the nucleon-nucleon system was
moving with respect to the beam interaction point.

###  3.1 Track selection and particle identification

The charged tracks coming from the primary vertex of the collision (“primary”
tracks) with $p_{\mathrm{T}}$ > 0.15
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $|\eta_{\mathrm{lab}}|$ <
0.8 are considered for the invariant mass reconstruction of ${\rm K}^{*0}$ and
$\phi$ in this analysis. The selection of primary tracks imposes that they
satisfy good reconstruction quality criteria. It is required that tracks have
left a signal in at least one of the layers of the SPD and that the distance
of closest approach to the primary vertex of the collisions is lower than
7$\sigma_{xy}$ in the transverse plane and within 2 cm along the longitudinal
direction. The resolution on the distance of closest approach in the
transverse plane, $\sigma_{xy}$, is strongly $p_{\mathrm{T}}$-dependent and
lower than 100 $\mu$m for $p_{\mathrm{T}}$ > 0.5
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ [55]. In addition tracks are
required to cross at least 70 out of maximum 159 horizontal segments (or
“rows”) along the transverse readout plane of the TPC.

Primary tracks have been identified as $\pi$ or K based on the information of
the TPC and TOF detectors. In the TPC, charged hadrons are identified by
measuring the specific ionisation energy loss ($\mathrm{d}E/\mathrm{d}x$) in
the detector gas. With a resolution ($\sigma_{\mathrm{TPC}}$) on
$\mathrm{d}E/\mathrm{d}x$ of 6$\%$, the TPC allows a 2$\sigma_{\mathrm{TPC}}$
separation between $\pi$ and K up to $p_{\mathrm{T}}$$\sim$0.8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and above 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, in the relativistic rise
region of the $\mathrm{d}E/\mathrm{d}x$. The TOF contributes to particle
identification with the measurement of the time-of-flight of the particle,
with the start time of the event measured by the T0 detector or using an
algorithm which combines the particle arrival times at the TOF surface. In
p-Pb collisions, when the event time is determined by the TOF algorithm
(available for 100 $\%$ of the events which have more than three tracks) the
resolution is 80 < $\sigma_{\mathrm{TOF}}$ < 100 ps. TOF allows a
2$\sigma_{\mathrm{TOF}}$ separation between identified $\pi$ and K in the
momentum range 0.7–3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, and
between K and protons up to 5 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
[60].

For the combined “TPC-TOF PID” approach, particles with a signal in the TOF
are identified by requiring that the measured time-of-flight and energy loss
do not deviate from the expected values for each given mass hypothesis by more
than 2$\sigma_{\mathrm{TOF}}$ and 5$\sigma_{\mathrm{TPC}}$, respectively. For
tracks which do not hit the TOF active region, a 2$\sigma_{\mathrm{TPC}}$
selection on the $\mathrm{d}E/\mathrm{d}x$ is applied. Variations of these
cuts have been used for systematic studies, as described in Sec. 3.4. Besides
the TPC-TOF, the measurement of $\phi$ has been performed following two
alternative strategies, one which exploits a 2$\sigma_{TPC}$ separation on the
particle energy loss in the TPC for the K identification, and the second for
which no PID cuts are applied. In the no-PID scheme all positively charged
hadrons are considered as ${\rm K}^{+}$ whereas all negatively charged hadrons
are considered as ${\rm K}^{-}$. The no-PID approach extends the measurement
of the yields from $p_{\mathrm{T}}$ = 10
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the upper limit reached by the
PID analysis, to 16 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
(multiplicity dependent) or 21 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
(minimum bias). At low $p_{\mathrm{T}}$, the TPC-TOF selection leads to a
better separation between signal and background with respect to TPC-only and
no-PID, therefore it is used until $p_{\mathrm{T}}$($\phi$)cutoff = 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. At high momentum, K and $\pi$
cannot be efficiently separated by TPC-TOF, therefore no-PID is used for
$p_{\mathrm{T}}$($\phi$) > 3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ to
maximise the total reconstruction efficiency. The multiplicity-integrated
yields of $\phi$ (see Sec. 4) obtained with the no-PID, TPC only, and TPC-TOF
approaches are compared in Fig. 1a in the common transverse momentum interval.
Details on the signal extraction procedure and efficiency correction are given
respectively in Sec. 3.2 and 3.3. The ratio of the data to the Lèvy-Tsallis
function (see Sec. 4.1) used to fit the TPC-TOF spectrum in the 0.3 <
$p_{\mathrm{T}}$ < 10 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ range
(Fig. 1b) further shows a good agreement among the three analyses, within
uncertainties. In the case of ${\rm K}^{*0}$, which is a wide resonance, PID
is necessary also at high momentum to reduce the background and therefore the
TPC-TOF strategy has been applied in the full kinematic range.

Figure 1: (a) Comparison of the transverse momentum spectrum
$\mathrm{d}^{2}N/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)$ of $\phi$-meson in
non-single diffractive (NSD) p–Pb events, reconstructed via the decay channel
into ${\rm K}^{+}$${\rm K}^{-}$ by exploiting three different strategies for K
identification: TPC only, TPC-TOF and no-PID. The reader can refer to Sec. 3.1
for details on the PID selection and to Sec. 3.2 for a description of the
signal extraction procedure. The uncertainties are the sum in quadrature of
statistical and systematic. A Lèvy-Tsallis function (see Eq. 1) is used to fit
the TPC-TOF spectrum in 0.3 < $p_{\mathrm{T}}$ < 10
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. (b) Ratio of each spectrum to
the fit function, showing good agreement of the three PID strategies within
uncertainties.

###  3.2 Signal extraction

Figure 2: Invariant-mass distributions for ${\rm K}^{*0}$ (a, b) and $\phi$
(c, d) in the transverse momentum range 1.2 $\leq$ $p_{\mathrm{T}}$ < 1.4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and multiplicity classes
0–20$\%$ and 0–5$\%$, respectively. Upper panels, (a) and (c), report the
unlike-sign invariant-mass distribution and the mixed event background (MEB)
normalised as described in the text. In lower panels, (b) and (c), the
distributions after background subtraction are shown. The ${\rm K}^{*0}$ peak
is fitted with a Breit-Wigner function whereas the $\phi$ meson peak is
described by a Voigtian function. A second order polynomial function is used
to describe the residual background.

${\rm K}^{*0}$ and $\phi$ signals are reconstructed in each multiplicity class
and transverse momentum interval, as described in [30, 33]. For each event,
the invariant-mass distribution of the ${\rm K}^{*0}$ ($\phi$) is constructed
using all unlike-sign combinations of charged K candidates with $\pi$ (K)
candidates. For ${\rm K}^{*0}$ in the full momentum range and for $\phi$ up to
3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ the TPC-TOF approach has been
used for particle identification. $\phi$ mesons with $p_{\mathrm{T}}$ > 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ have been reconstructed by
applying no PID. In the following the K+ and $\pi^{+}$ candidates are labelled
as $h^{+}$, the K- and $\pi^{-}$ are labelled as $h^{-}$. The combinatorial
background due to the uncorrelated pairs has been estimated in two ways, by
the mixed-event technique and from the invariant-mass distribution of like-
sign pairs from the same event. In the event-mixing method the shape of the
uncorrelated background is estimated from the invariant-mass distribution of
$h^{+}h^{-}$ combinations from five different events. Effects from
multiplicity fluctuations are minimised by dividing the sample into ten
multiplicity classes and by performing event mixing within the same
multiplicity class. In order to minimise distortions due to acceptance effects
within each multiplicity class, the events are further sub-divided into twenty
bins according to the relative vertex position along the $z$-axis
($\Delta{z_{\mathrm{v}}}$ = 1 cm). The final mixed-event distribution for each
multiplicity class is found by adding up the $M_{\mathrm{inv}}$ distributions
from each vertex $\Delta{z_{v}}$ interval. For the ${\rm K}^{*0}$ analysis,
the mixed-event distribution for each $p_{\mathrm{T}}$ bin is normalised by
the smallest factor that leads to a positive-defined unlike-sign distribution
after subtraction, within the statistical error in all invariant-mass bins.
The mixed-event distribution for $\phi$ is normalised in the mass region 1.04
< $M_{\mathrm{KK}}$ < 1.06 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$.
The normalisation range for ${\rm K}^{*0}$ and $\phi$ is varied for systematic
studies. In the like-sign technique, the invariant-mass distribution for the
uncorrelated background is obtained by combining the $h^{+}h^{+}$ and
$h^{-}h^{-}$ pairs from the same event according to a geometric mean
(2$\sqrt{(h^{+}h^{+})\cdot(h^{-}h^{-})}$), in order to reduce statistical
fluctuations in the resulting distribution. The like-sign background is
subtracted without normalisation from the unlike-sign pairs distribution. The
mixed-event method has been preferred for ${\rm K}^{*0}$ ($\phi$) signal
extraction in the range 0.4 < $p_{\mathrm{T}}$ < 15
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ (0.3 < $p_{\mathrm{T}}$ < 16
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$), given the smaller statistical
uncertainties on the invariant-mass distribution. At very low momentum,
$p_{\mathrm{T}}$ < 0.4 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the
like-sign distribution is found to reproduce better the background of the
${\rm K}^{*0}$ and not to be affected by the choice of the normalisation
range, therefore it has been preferred over the mixed-event. Figure 2 shows
the $M_{\mathrm{K\pi}}$ and $M_{\mathrm{KK}}$ invariant-mass distributions
before and after background subtraction in the transverse momentum interval
1.2 $\leq$ $p_{\mathrm{T}}$ < 1.4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, for the 0–20$\%$ and 0–5$\%$
V0A multiplicity classes, for ${\rm K}^{*0}$ and $\phi$, respectively.
After background subtraction, the resulting distributions exhibit a
characteristic peak on top of a residual background (lower panels of Fig. 2).
The latter is only partly due to imperfections in the description of the
combinatorial background and mainly due to correlated pairs from jets, multi-
body decay of heavier particles or correlated pairs contribution to the
background from real resonance decays where the daughter particles are
misidentified as K or $\pi$ by the TPC-TOF PID. A dedicated study in Monte
Carlo simulations has been performed to ensure that the shape of the
correlated background is a smooth function of mass and to verify that a
second-order polynomial provides a good description of it.
As in [30], the signal peaks for ${\rm K}^{*0}$ and $\phi$ are fitted
respectively with a (non-relativistic) Breit-Wigner and a Voigtian function
(convolution of Breit-Wigner and Gaussian) superimposed to a second order
polynomial function to shape the residual background. Examples are reported in
the lower panels of Fig. 2, where fits are performed in the intervals 0.76 <
$M_{\mathrm{K\pi}}$ < 1.04 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$
and 1.0 < $M_{\mathrm{KK}}$ < 1.05
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$. The fitting range is
optimised for each $p_{\mathrm{T}}$ bin across all multiplicity event classes.
The mass and width of ${\rm K}^{*0}$ and $\phi$ are found to be compatible
with the measurements in Pb–Pb collisions [33]. For the measurement of the
yields, the width of ${\rm K}^{*0}$ and $\phi$ have been fixed to their
natural values, $\Gamma$(${\rm K}^{*0}$) = 47.4 $\pm$ 0.6
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$, $\Gamma$($\phi$) = 4.26
$\pm$ 0.04 $\mathrm{MeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$ [50], whereas
the resolution parameter of the Voigtian function for $\phi$ has been kept as
a free parameter. The measured $p_{\mathrm{T}}$-dependent resolution on the
$\phi$ mass (sigma of Gaussian) varies between 0.9 and 1.5
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$, and it is consistent with
the values extracted from Monte Carlo simulation. The sensitivity to the
choice of the normalisation interval, the fitting range, the shape of the
background function, the fitting range and the constraints on mass, width and
resolution parameters has been studied by varying the default settings, as
described in Sec. 3.4.
In minimum bias collisions the sample of reconstructed particles includes
about 3.4$\times$106 ${\rm K}^{*0}$ and 8.6$\times$105 $\phi$ in the
transverse momentum range 0 < $p_{\mathrm{T}}$(${\rm K}^{*0}$) < 15
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and 0.3 <
$p_{\mathrm{T}}$($\phi$) < 21 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
respectively. With the available statistics, the ${\rm K}^{*0}$ production in
the 80–100$\%$ V0A multiplicity event class has been measured up to
$p_{\mathrm{T}}$ = 6 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, while the
$\phi$ spectra extend up to 16 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
in the 0-60$\%$ multiplicity percentile interval and up to 13
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in 60–80$\%$ and 80–100$\%$.

###  3.3 Detector acceptance and efficiency

Figure 3: Detector acceptance and signal reconstruction efficiency for ${\rm
K}^{*0}$ and $\phi$ mesons, which includes reconstruction, track selection and
particle identification efficiency. For ${\rm K}^{*0}$ and $\phi$ production
below $p_{\mathrm{T}}$ < 3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the
PID efficiency is relative to the TPC-TOF approach, whereas for $\phi$
production with $p_{\mathrm{T}}$ > 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ no PID contribution is
included, as no particle identification is applied in the analysis.

In order to evaluate the detector acceptance and reconstruction efficiency, a
sample of about 108 Monte Carlo simulated p–Pb events, based on the DPMJET
3.05 event generator [61], with the detector geometry and material budget
modeled by GEANT 3.21 [62], has been analysed. The acceptance and efficiency
correction is determined as the fraction of generated resonances in the
rapidity interval $-$0.5 < $y$ < 0 that have been reconstructed. The
reconstructed signal pairs are obtained upon combination of primary $\pi$ and
K selected by applying the same kinematics cuts and track cuts as in the data
(see Sec. 3.1), including TPC-TOF PID cuts for ${\rm K}^{*0}$, and $\phi$ with
$p_{\mathrm{T}}$ < 3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. For
$\phi$ with $p_{\mathrm{T}}$ > 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ no PID cuts are applied. The
acceptance and efficiency corrections, $\mathrm{Acc}\times\epsilon$, for ${\rm
K}^{*0}$ and $\phi$ are reported in Fig. 3 as a function of $p_{\mathrm{T}}$
for minimum bias events. Since only events with reconstructed primary vertex
have been considered in the computation of
($\mathrm{Acc}\times\epsilon$)($p_{\mathrm{T}}$), a correction factor has to
be applied to the total number of accepted events in each V0A multiplicity
event class, to account for vertex reconstruction inefficiency. The correction
is about 0.995 for 60-80$\%$ class and 0.945 for the lowest multiplicity
events 80-100$\%$, and it is applied as discussed in Sec. 4.1.

###  3.4 Systematic uncertainties

The measurement of ${\rm K}^{*0}$ and $\phi$ production in p–Pb collisions
have been tested for systematic effects due to global tracking efficiency,
track selection cuts, PID, signal extraction, knowledge of the material budget
and of the hadronic interaction cross section in the detector material, as
summarised in Tab. 2. The approach is similar to the one adopted for the study
of ${\rm K}^{*0}$ and $\phi$ in Pb–Pb collisions [33], but the total average
uncertainty evaluated in the p–Pb case is significantly lower (about half of
the relative uncertainty in the Pb–Pb), mainly due to lower contributions from
global tracking efficiency and the signal extraction procedure. No
multiplicity dependence of systematic effects has been observed, therefore the
uncertainties presented in Sec. 2 have been averaged among all multiplicity
event classes. For each particle, they are quoted for two separate momentum
intervals: for ${\rm K}^{*0}$, one can distinguish a low-$p_{\mathrm{T}}$
range (0 < $p_{\mathrm{T}}({\rm K}^{*0})$ < 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) where the knowledge of the
material budget and hadronic interaction cross section in the detector
material enter in the systematic uncertainty, as opposite to the
high-$p_{\mathrm{T}}$ range (4 < $p_{\mathrm{T}}({\rm K}^{*0})$ < 15
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) where these contributions are
negligible (< 0.5$\%$). In the $\phi$ case, two $p_{\mathrm{T}}$ intervals are
considered, according to the particle identification approach used to identify
the decay products, namely the “TPC-TOF” and “No PID” strategies described in
Sec. 3.1. The $p_{\mathrm{T}}$ region where the TPC-TOF PID is applied
($p_{\mathrm{T}}$ < 3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$),
coincides also with the range where effects of material budget and hadronic
interaction cross section are relevant for the measurement of $\phi$
production.
The main source of uncertainty, common to ${\rm K}^{*0}$ and $\phi$, comes
from the determination of the global tracking efficiency. In p–Pb collisions
this contribution has been estimated to be a $p_{\mathrm{T}}$-independent
effect of 3$\%$ for charged particles [48], which results in a 6$\%$ effect
when any two tracks are combined in the invariant-mass analysis of ${\rm
K}^{*0}$ and $\phi$.
The track selection was varied to study systematic effects: the analyses are
sensitive to variations of the cuts on the number of crossed rows in the TPC
and the distance of closest approach to the primary vertex of the collision.
Track selection enters in the total uncertainty with a relative contribution
of 2.5 $\%$ for ${\rm K}^{*0}$ and about 1.9 to 2.2$\%$ for the $\phi$ case.
At high transverse momentum, namely for $p_{\mathrm{T}}({\rm K}^{*0})$ > 8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and $p_{\mathrm{T}}(\phi)$ > 12
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the systematic uncertainties
are dominated by the raw yield extraction procedure. This contribution is
labelled as “Signal extraction” in Tab. 2 and it includes the background
normalisation region, the choice of the fitting range, the residual background
shape and variations of the constraints on the fit parameters. In addition to
the default strategy described in Sec. 3.2, the mixed-event background
distributions for ${\rm K}^{*0}$ and $\phi$ have been normalised in different
invariant mass regions that surround, but exclude the signal peaks. The
sensitivity of the ${\rm K}^{*0}$ ($\phi$) yield extraction to the fit range
has been studied by varying each interval boundary within $\pm$50
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$($\pm$5
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$). As alternative to the
second order polynomial, a third and first order polynomial functions have
been used to fit the residual background. The measurements for both ${\rm
K}^{*0}$ and $\phi$ turned out to be independent on the mass parameters, but
not on the constraints on the ${\rm K}^{*0}$ width and $\phi$ mass resolution.
Therefore, the ${\rm K}^{*0}$ width has been varied by $\pm$50$\%$ for
systematic studies, while the $\phi$ resolution has been varied within the
range of values observed in the simulation. Due to the lower particle
multiplicity and the improved PID strategy that has led to a lower residual
background after mixed-event background subtraction, the contribution of
signal extraction for ${\rm K}^{*0}$ is reduced by half in p–Pb with respect
to the Pb–Pb case, where the uncertainty associated to the choice of the
fitting range was larger than 9$\%$ [33].
In order to study the effect of the PID selection on signal extraction, the
cuts on TOF and TPC have been varied to 3$\sigma$ and 4$\sigma$ with respect
to the default settings described in Sec. 3.1, resulting in the average
contribution to the systematic uncertainty reported in Tab. 2 as “particle
identification”. For ${\rm K}^{*0}$ the average contribution from PID is
1.1$\%$ in the low-$p_{\mathrm{T}}$ range, and 2.7$\%$ at high transverse
momenta. The contribution to the $\phi$ uncertainty is 0.9$\%$ on average in
the transverse momentum range where TPC-TOF PID is applied.
The knowledge of the material budget contributes for ${\rm K}^{*0}$ ($\phi$)
with an average of 1.2$\%$ (2.2$\%$) at low transverse momentum, and a maximum
of 3.5$\%$ (5.4$\%$), reached for 0 < $p_{\mathrm{T}}$ <0.2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ (0.8 < $p_{\mathrm{T}}$ <0.9
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$). In both cases, it is
negligible for $p_{\mathrm{T}}$ > 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The contribution from the
estimate of the hadronic interaction cross section in the detector material is
1.9$\%$ (2.4$\%$) for ${\rm K}^{*0}$ ($\phi$) at low $p_{\mathrm{T}}$,
negligible for $p_{\mathrm{T}}$ > 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ ($p_{\mathrm{T}}$ > 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$). These effects were evaluated
by combining the uncertainties for a $\pi$ and a K (for ${\rm K}^{*0}$), and
for two K (in case of $\phi$), determined as in [47, 42], according to the
kinematics of the decay.
The systematics were studied independently for all event classes, in order to
separate the sources which are multiplicity-dependent and uncorrelated across
multiplicity bins. In particular, signal extraction and PID are fully
uncorrelated sources, whereas global tracking, track cuts, material budget and
hadronic cross section are correlated among different event classes.

|  ${\rm K}^{*0}$ |  $\phi$
---|---|---
$p_{\mathrm{T}}$ ($\mathrm{GeV}\kern-0.45003pt/\kern-0.18004ptc$) |  0 – 4.0 |  4.0 – 15.0 |  0.3 – 3.0 |  3.0 – 21.0
PID technique |  TPC-TOF |  TPC-TOF |  No PID
Global tracking efficiency |  6$\%$ |  6$\%$
Track selection cuts |  2.5$\%$ |  1.9$\%$ |  2.2$\%$
Material budget |  1.2$\%$ |  <0.5$\%$ |  2.2$\%$ |  <0.5$\%$
Hadronic interaction cross section |  1.9$\%$ |  <0.5$\%$ |  2.4$\%$ |  <1$\%$
Particle identification |  1.1$\%$ |  2.7$\%$ |  0.9$\%$ |  –
Signal extraction |  3.8$\%$ |  4.6$\%$ |  1.8$\%$ |  4.3$\%$
Total |  7.9$\%$ |  8.4$\%$ |  7.4$\%$ |  7.7$\%$
Table 2: Sources of systematic uncertainties for ${\rm K}^{*0}$ and $\phi$
yields ($\mathrm{d}^{2}N/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)$). For each
source and transverse momentum range (see text for details), the average
relative uncertainty over all multiplicity classes is listed. For each
$p_{\mathrm{T}}$ range, the particle identification (“PID technique”) used for
the analysis is also indicated. The contributions have been summed in
quadrature to estimate the total relative systematic uncertainty.

##  4 Results and discussion

###  4.1 Transverse momentum spectra

The multiplicity-dependent transverse momentum spectra of ${\rm K}^{*0}$ and
$\phi$ mesons measured in the rapidity range $-$0.5 < $y$ < 0 are reported in
Fig. 4. Measured yields are corrected for acceptance, efficiency and branching
ratio, and normalised to the visible cross section in each V0A multiplicity
event class, as discussed in Sec. 3.3. The minimum bias spectra for ${\rm
K}^{*0}$ and $\phi$ are also reported in Fig. 4 and have been normalised to
the number of NSD events after applying the correction for trigger efficiency
and event selection ($\epsilon_{NSD}$), vertex reconstruction
($\epsilon_{vtx}$) and vertex selection described in Sec. 2, resulting in a
total scaling factor of 0.964.

Figure 4: Transverse momentum spectra
$\mathrm{d}^{2}N/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)$ of ${\rm K}^{*0}$ (a)
and $\phi$ (b) for different multiplicity classes (V0A estimator), measured in
the rapidity range $-$0.5 < $y$ < 0\. ${\rm K}^{*0}$ and $\overline{{\rm
K}^{*0}}$ are averaged. The multiplicity-dependent spectra are normalised to
the visible cross section, whereas the minimum bias spectrum is normalised to
the fraction of NSD events (see text). Statistical (bars) and systematic
(boxes) uncertainties are indicated. Dashed lines represent Lévy-Tsallis fits,
see text for details.

The $p_{\mathrm{T}}$-integrated particle yields, $\mathrm{d}N/\mathrm{d}y$,
and mean transverse momentum, $\langle p_{\mathrm{T}}\rangle$, are determined
by using the transverse momentum spectra in the measured range and by using a
fit function to extrapolate the yield in the $p_{\mathrm{T}}$ range where no
measurement is available. The same procedure is applied to the spectra of
${\rm K}^{*0}$ and $\phi$ for each event class. The Lévy-Tsallis
parameterization [63] has been chosen to fit the corrected
$\mathrm{d}^{2}N/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)$ spectra, as it has
successfully been adopted to fit the particle spectra in pp collisions at RHIC
and at LHC [30, 64, 65, 66]. The Lévy-Tsallis functional form describes the
shape of the exponential spectra at low transverse momentum and the power law
distributions at large $p_{\mathrm{T}}$ with an inverse slope parameter $C$
and an exponent parameter $n$

$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{T}\mathrm{d}y}=p_{T}\frac{\mathrm{d}N}{\mathrm{d}y}\frac{(n-1)(n-2)}{nC[nC+m_{0}(n-2)]}\left[1+\frac{\sqrt{p_{T}^{2}+m_{0}^{2}}-m_{0}}{nC}\right]^{-n},$
(1)

where $m_{0}$ is the mass of the particle, $n$, $C$ and the integrated yields
$\mathrm{d}N/\mathrm{d}y$ are the free parameters. The fits are performed in
the $p_{\mathrm{T}}$ range where the Lévy-Tsallis function provides a
satisfactory description of each spectrum, namely in the interval 0–10
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for ${\rm K}^{*0}$ and 0.3–10.0
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for $\phi$. The values of the
fit parameters $C$ and $n$, as well as the reduced $\chi^{2}$ are reported in
Tab. 3, together with the $\mathrm{d}N/\mathrm{d}y$ and $\langle
p_{\mathrm{T}}\rangle$ obtained using the data and the fit function in the
extrapolation region.

${\rm K}^{*0}$
---
Multiplicity ($\%$) |  $C$ (GeV) | $n$ |  $\chi^{2}$/ndf | Extr. |  $\mathrm{d}N/\mathrm{d}y$ (data + extr.) |  $\langle p_{\mathrm{T}}\rangle$ ($\mathrm{GeV}\kern-0.40002pt/\kern-0.16003ptc$)
0–20 |  0.440 $\pm$ 0.010 |  11.1 $\pm$ 0.5 | 1.7 |  < 10-4 |  0.616 $\pm$ 0.008 $\pm$ 0.037 $\pm$ 0.037 |  1.379 $\pm$ 0.011 $\pm$ 0.020
20–40 |  0.430 $\pm$ 0.009 |  9.7 $\pm$ 0.4 | 1.7 |  < 10-4 |  0.426 $\pm$ 0.006 $\pm$ 0.026 $\pm$ 0.026 |  1.300 $\pm$ 0.010 $\pm$ 0.019
40–60 |  0.359 $\pm$ 0.008 |  8.8 $\pm$ 0.3 | 0.5 |  < 10-4 |  0.302 $\pm$ 0.004 $\pm$ 0.019 $\pm$ 0.018 |  1.211 $\pm$ 0.009 $\pm$ 0.017
60–80 |  0.309 $\pm$ 0.008 |  7.8 $\pm$ 0.3 | 0.6 |  < 10-4 |  0.185 $\pm$ 0.003 $\pm$ 0.013 $\pm$ 0.011 |  1.108 $\pm$ 0.009 $\pm$ 0.021
80–100 |  0.224 $\pm$ 0.008 |  6.2 $\pm$ 0.3 | 0.4 | 0.002 |  0.083 $\pm$ 0.001 $\pm$ 0.005 $\pm$ 0.005 |  0.943 $\pm$ 0.009 $\pm$ 0.016
NSD |  0.388 $\pm$ 0.003 |  9.4 $\pm$ 0.1 | 1.8 |  < 10-4 |  0.315 $\pm$ 0.002 $\pm$ 0.018 $\pm$ 0.018 |  1.270 $\pm$ 0.005 $\pm$ 0.017
$\phi$
Multiplicity ($\%$) |  $C$ (GeV) | $n$ |  $\chi^{2}$/ndf | Extr. |  $\mathrm{d}N/\mathrm{d}y$ (data + extr.) |  $\langle p_{\mathrm{T}}\rangle$ ($\mathrm{GeV}\kern-0.40002pt/\kern-0.16003ptc$)
0–5 |  0.472 $\pm$ 0.010 |  12.5 $\pm$ 0.9 | 1.5 | 0.094 |  0.377 $\pm$ 0.004 $\pm$ 0.020 $\pm$ 0.023 |  1.437 $\pm$ 0.009 $\pm$ 0.028
5–10 |  0.469 $\pm$ 0.010 |  12.0 $\pm$ 0.8 | 1.1 | 0.094 |  0.288 $\pm$ 0.003 $\pm$ 0.014 $\pm$ 0.017 |  1.442 $\pm$ 0.009 $\pm$ 0.025
10–20 |  0.453 $\pm$ 0.010 |  11.3 $\pm$ 0.6 | 1.2 | 0.097 |  0.244 $\pm$ 0.002 $\pm$ 0.012 $\pm$ 0.014 |  1.421 $\pm$ 0.008 $\pm$ 0.024
20–40 |  0.413 $\pm$ 0.009 |  9.8 $\pm$ 0.4 | 1.1 | 0.105 |  0.185 $\pm$ 0.001 $\pm$ 0.009 $\pm$ 0.011 |  1.357 $\pm$ 0.006 $\pm$ 0.025
40–60 |  0.382 $\pm$ 0.009 |  8.8 $\pm$ 0.4 | 0.6 | 0.115 |  0.1229 $\pm$ 0.0008 $\pm$ 0.0064 $\pm$ 0.0073 |  1.310 $\pm$ 0.006 $\pm$ 0.031
60–80 |  0.349 $\pm$ 0.009 |  8.3 $\pm$ 0.4 | 0.5 | 0.115 |  0.0695 $\pm$ 0.0006 $\pm$ 0.0037 $\pm$ 0.0041 |  1.242 $\pm$ 0.008 $\pm$ 0.024
80–100 |  0.260 $\pm$ 0.010 |  6.7 $\pm$ 0.3 | 0.4 | 0.163 |  0.0297 $\pm$ 0.0004 $\pm$ 0.0023 $\pm$ 0.0018 |  1.055 $\pm$ 0.010 $\pm$ 0.030
NSD |  0.412 $\pm$ 0.014 |  10.0 $\pm$ 0.5 | 0.8 | 0.106 |  0.1344 $\pm$ 0.0005 $\pm$ 0.0069 $\pm$ 0.0081 |  1.355 $\pm$ 0.003 $\pm$ 0.030
Table 3: Parameters of the Lévy-Tsallis fit function and values of $\phi$ and
${\rm K}^{*0}$ $\mathrm{d}N/\mathrm{d}y$ and $\langle p_{\mathrm{T}}\rangle$
for different multiplicity classes. The $C$ and $n$ parameters with their
statistical uncertainty, the reduced $\chi^{2}$ of the fit and the fraction of
the total yield obtained by extrapolation (“Extr.”) are reported. The yields
and $\langle p_{\mathrm{T}}\rangle$ are obtained considering data in the
measured range and using the result of the fit in the extrapolation region,
and are listed as (value $\pm$ stat. $\pm$ uncorr. $\pm$ corr.), where the
errors are the statistical uncertainty, the uncorrelated and correlated
contributions to the systematic uncertainty, respectively. In the $\langle
p_{\mathrm{T}}\rangle$ case, the contribution to the systematic uncertainty
correlated across multiplicity classes is negligible. The minimum bias
spectrum has been normalised to the fraction of non-single diffractive events
(NSD) and an additional 3.1 $\%$ relative contribution from the normalisation
to NSD has to be considered in the systematic uncertainty on
$\mathrm{d}N/\mathrm{d}y$.

For ${\rm K}^{*0}$ the extrapolation, necessary only at high $p_{\mathrm{T}}$,
covers a fraction of the total yield lower than 0.1$\%$. For $\phi$ the
extrapolated yield is dominated by the fraction of signal in the low
transverse momentum region, which constitutes about 10.6$\%$ of the total in
the minimum bias case. For all multiplicity classes this fraction is reported
in Tab. 3. It can be noticed that the inverse slope parameter $C$ and the
exponent parameter $n$ increase with multiplicity, reflecting the flattening
of the spectra from peripheral to most central events.
The uncertainty on $\mathrm{d}N/\mathrm{d}y$ and $\langle
p_{\mathrm{T}}\rangle$ is dominated by systematics, which include the
contribution of the $p_{\mathrm{T}}$-uncorrelated systematic uncertainty on
the measured spectrum (in average about 6.3$\%$ for ${\rm K}^{*0}$, 3.6$\%$
for $\phi$), the $p_{\mathrm{T}}$-correlated contributions from global
tracking efficiency (6$\%$ for ${\rm K}^{*0}$ and $\phi$, only on
$\mathrm{d}N/\mathrm{d}y$), and the extrapolation of the yield. The first
contribution has been estimated by repeating the Lévy-Tsallis fits moving the
measured points within their systematic uncertainties, whereas in order to
evaluate the latter, a Blast-Wave function [67] has been used alternatively to
fit the spectra. The relative systematic uncertainty on
$\mathrm{d}N/\mathrm{d}y$ due to the choice of the fit function varies between
1.5$\%$ and 3$\%$ for $\phi$, going from high to low multiplicity. Such a
contribution is negligible in the case of ${\rm K}^{*0}$, due to the fact that
its production is measured down to zero transverse momentum.

###  4.2 Mean transverse momentum

In a hydrodynamically evolving system the spectral shapes are driven by the
expansion velocity, thus by the mass of the particle and they are expected to
follow “mass ordering”. Viceversa, the observation of mass ordering of
particle spectra may be suggestive of the presence of collective
(hydrodynamic) behaviour of the system. Although the presence of a strong
radial flow is established in Pb–Pb collisions [42], the measurements in p–Pb
are not conclusive [47], as the comparison between data and models for pp
collisions that incorporate final-state effects (such as color-reconnection),
shows that the latter could mimic the presence of radial flow. The
measurements of ${\rm K}^{*0}$ and $\phi$ can further probe the presence of
“mass ordering”, since they have similar mass as the proton.

The transverse momentum spectra of ${\rm K}^{*0}$ and $\phi$, reported in Fig.
4, become flatter, thus harder, going from the most peripheral to the most
central p–Pb events. In other words, the mean transverse momentum increases
with multiplicity. This is also shown in Fig. 5, where the $\langle
p_{\mathrm{T}}\rangle$ of ${\rm K}^{*0}$ and $\phi$ as a function of the
average charged particle multiplicity density ($\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle_{|\eta|<0.5}$) is compared to that of
other identified hadrons, including $\pi$±, K±, K${}^{0}_{S}$, p, $\Lambda$,
$\Xi^{-}$ and $\Omega^{-}$, in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$ [47, 68].

Figure 5: Mean transverse momentum of ${\rm K}^{*0}$ and $\phi$ compared to
that of identified $\pi$±, K±, K${}^{0}_{S}$, p, $\Lambda$, $\Xi^{-}$ and
$\Omega^{-}$ previously measured by ALICE in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$ [47, 68] as a function of
the charged particle density measured in the pseudo-rapidity range
$|\eta_{\mathrm{lab}}|$ < 0.5 ($\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle_{|\eta|<0.5}$). The K${}^{0}_{S}$,
$\Lambda$ and $\Xi^{-}$ points are slightly displaced along the x-axis to
avoid superposition with other points. Statistical uncertainties are
represented as bars, whereas boxes indicate systematic uncertainties.

Going from the lowest to the highest multiplicity events, the relative
increase of $\langle p_{\mathrm{T}}\rangle$ for ${\rm K}^{*0}$ and $\phi$
mesons is about 40$\%$, common to a wide variety of particles, including K±,
K${}^{0}_{S}$, $\Lambda$, $\Xi^{\pm}$ and $\Omega^{\pm}$. The relative
increase is smaller for $\pi$ (about 26$\%$) but larger for protons (about
52$\%$). The $\langle p_{\mathrm{T}}\rangle$ of ${\rm K}^{*0}$ is about 10$\%$
larger than that of proton in all event classes and compatible with $\langle
p_{\mathrm{T}}\rangle$ of $\Lambda$. The $\langle p_{\mathrm{T}}\rangle$ of
$\phi$ is instead about 20$\%$ larger than proton and between 4$\%$ (0–5$\%$)
and 8$\%$ (80–100$\%$) larger than $\Lambda$. A similar hierarchy is also
observed in pp collisions and peripheral Pb–Pb collisions, but not in central
Pb–Pb collisions, where, as expected from hydrodynamics, particles with
similar mass have similar $\langle p_{\mathrm{T}}\rangle$.

Figure 6: System size dependence of the mean transverse momentum of ${\rm
K}^{*0}$ compared to that of the proton (left panel) and $\langle
p_{\mathrm{T}}\rangle$ of $\phi$ compared to that of the proton (right panel).
The system size is defined as the cubic root of the average charged particle
multiplicity density ($\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$) measured in the ALICE central
barrel ($|\eta_{\mathrm{lab}}|$ < 0.5) in $\mathrm{p\kern-0.50003ptp}$ at
$\sqrt{s}$ = 7 TeV (green) [30, 64], p–Pb at $\sqrt{s_{\mathrm{NN}}}$ = 5.02
TeV (blue) [47, 68] and Pb–Pb at
$\sqrt{s_{\mathrm{NN}}}~{}=2.76\,\mathrm{~{}TeV}$(red) [33, 42]. Statistical
uncertainties are represented as bars, boxes indicate total systematic
uncertainties. Figure 7: Mass dependence of the mean transverse momentum of
identified particles measured by ALICE in minimum bias pp collisions at
$\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ [64, 30, 66] and 0–20$\%$ p–Pb collisions
[47, 68]. Statistical uncertainties are represented as bars, boxes indicate
total systematic uncertainties.

In Fig. 6 the $\langle p_{\mathrm{T}}\rangle$ of ${\rm K}^{*0}$, proton and
$\phi$ are compared in the three collision systems as a function of the cubic
root of the average charged particle multiplicity density,
$\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$.
Based on the observation that the femtoscopic radii scale approximately
linearly with $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$ [20], this observable is used
as a proxy for the system size, associated with the radius of the fireball at
freeze-out. In p–Pb, where no extended hadronic medium is expected to be
formed, the system size can be associated to the width of the distribution of
the particle emission points. The argument holding for Pb–Pb has been extended
in this paper also to the proton-nucleus case, based on the linear trend of
the measured radii with $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$ in p–Pb collisions [69]. From
Fig. 6 one can see that at similar event multiplicity, the $\langle
p_{\mathrm{T}}\rangle$ is larger in p–Pb than in Pb–Pb and the increase with
multiplicity is steeper. An analogous observation for unidentified charged
particles has been reported in [70], where it is shown that in models of pp
collisions, the strong increase in $\langle p_{\mathrm{T}}\rangle$ with
$\langle N_{\mathrm{ch}}\rangle$ can be understood as the effect of color
reconnection between strings produced in multi-parton interactions.
Considering that for a given multiplicity class in p–Pb and peripheral Pb–Pb
events the geometry of the collision and the dynamics of the systems are
different but the production of ${\rm K}^{*0}$ and $\phi$ mesons relative to
long-lived hadrons is comparable (see Sec. 4.4), one can conclude that the
sample of p–Pb collisions is dominated by events with a larger fraction of
quadri-momentum transferred, thus “harder”.
In central Pb–Pb collisions, $\langle p_{\mathrm{T}}\rangle$ of ${\rm
K}^{*0}$, proton and $\phi$ are consistent within uncertainties (Fig. 6), and
follow “mass ordering”. This is consistent with the hypothesis that particle
boost in the hadronic phase is driven by radial flow [42, 33]. This mass
ordering seems to weaken going towards peripheral Pb–Pb collisions, where it
is only approximate. In p–Pb and minimum bias $\mathrm{p\kern-0.50003ptp}$
collisions $\langle p_{\mathrm{T}}\rangle(\phi)$ > $\langle
p_{\mathrm{T}}\rangle({\rm K}^{*0})$ > $\langle p_{\mathrm{T}}\rangle(p)$.

The $\langle p_{\mathrm{T}}\rangle$ for several particles as a function of
their mass for 0-20$\%$ p–Pb at
$\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$ and minimum bias
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$
[64, 30, 66] are illustrated in Fig. 7. In p–Pb, the $\langle
p_{\mathrm{T}}\rangle$ of all particles but ${\rm K}^{*0}$ has been obtained
as the average between the available measured values weighted by the particle
integrated yields in 0-5$\%$, 5-10$\%$ and 10-20$\%$ [47, 68]. For ${\rm
K}^{*0}$, the direct measurement of $\langle p_{\mathrm{T}}\rangle$ in
0-20$\%$ is available (see Tab. 3). For the $\mathrm{p\kern-0.50003ptp}$ case,
also the recent measurements on the short-lived baryonic resonances
$\Sigma$(1385)± and $\Xi$(1530)0 (indicated as $\Sigma^{*\pm}$ and $\Xi^{*0}$)
have been included in the comparison. The mean transverse momentum is larger
for larger masses, but Fig. 7 shows that in $\mathrm{p\kern-0.50003ptp}$ and
p–Pb collisions the $\langle p_{\mathrm{T}}\rangle$ values for ${\rm K}^{*0}$
and $\phi$ mesons are systematically larger with respect to a linear trend
which includes protons and $\Lambda$ instead. These results seem to suggest
that a different type of scaling holds in $\mathrm{p\kern-0.50003ptp}$ and
p–Pb collisions and prepare the way for a more detailed investigation, which
is however outside of the scope of this paper.

Figure 8: The $(\mathrm{p}+\bar{\mathrm{p}})/\phi$ ratio measured in p–Pb in
0–5$\%$ and 80–100$\%$ V0A multiplicity classes, compared to the same ratio
measured in minimum bias $\mathrm{p\kern-0.50003ptp}$ collision at
$\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ [30, 64], 0–10$\%$ central and 60-80$\%$
peripheral Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=2.76\,\mathrm{~{}TeV}$ [33].

###  4.3 Differential (p+$\overline{\mathrm{p}}$)/$\phi$ ratio

The multiplicity dependence of the (p+$\rm\overline{p}$)/$\phi$ ratio as a
function of transverse momentum is studied to compare the spectral shapes of
$\phi$ mesons and protons [47]. The differential ratios for the 0–5$\%$ and
80–100$\%$ V0A multiplicity event classes in p–Pb collisions are reported in
Fig. 8 together with the ratios in minimum bias pp collisions, 0–10$\%$
central and 60-80$\%$ peripheral Pb–Pb. In peripheral p–Pb the
$(\mathrm{p}+\bar{\mathrm{p}})/\phi$ ratio exhibits a qualitatively similar
steep decrease as in $\mathrm{p\kern-0.50003ptp}$ collisions, and it is
consistent with the ratio measured in 80-90$\%$ peripheral Pb–Pb collisions
([33], not shown in Fig. 8). The flat behaviour of
$(\mathrm{p}+\bar{\mathrm{p}})/\phi$ for $p_{\mathrm{T}}$ < 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in 0–10$\%$ central Pb–Pb
collisions has been previously discussed in [33] and found to be consistent
with the expectations of hydrodynamic models. In the 0–5$\%$ p–Pb, a hint of
flattening is observed for $p_{\mathrm{T}}$ < 1.5
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, but systematic uncertainties
are such that no conclusive evidence can be derived. Despite being about
10–20$\%$ larger but compatible within uncertainties, the best qualitative
agreement of $(\mathrm{p}+\bar{\mathrm{p}})/\phi$ in high-multiplicity p–Pb
(0–5$\%$ V0A multiplicity event class) is achieved with respect to the
60–80$\%$ peripheral Pb–Pb collisions, which has also a similar particle
multiplicity.

###  4.4 Integrated particle ratios

Particle ratios are useful observables to study particle production mechanisms
by comparing particles with similar or different strangeness content, mass and
lifetime. Short-lived particles such as ${\rm K}^{*0}$ and $\phi$ are used in
heavy-ion collisions to derive information on the lifetime of the hadronic
phase and on the mechanisms which take place before the kinetic freeze-out,
such as re-scattering and regeneration. If dominant over regeneration, re-
scattering is expected to reduce the observed yield of resonances, especially
at low momentum and in high particle density environments [52]. For the ${\rm
K}^{*0}$ resonance re-scattering is the dominant effect at play in most
central Pb–Pb collisions (and at low transverse momentum, $p_{\mathrm{T}}$ < 2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$). This observation comes from
the strong centrality dependence of the ${\rm K}^{*0}$/K ratio (see Fig. 9)
and its direct comparison with the ratio of the longer-lived $\phi$ meson
relative to K [33].
For p–Pb collisions, the ratios of ${\rm K}^{*0}$ and $\phi$-meson production
to that of long-lived hadrons have been computed starting from the integrated
yields of $\pi$, K and proton measured by ALICE with the same data sample
[47], and are reported for each multiplicity class in Tab. 4.

${\rm K}^{*0}$
---
Multiplicity ($\%$) |  (${\rm K}^{*0}$+$\overline{{\rm K}^{*0}}$)/($\pi^{+}$+$\pi^{-}$) |  (${\rm K}^{*0}$+$\overline{{\rm K}^{*0}}$)/(${\rm K}^{+}$+${\rm K}^{-}$) |  (${\rm K}^{*0}$+$\overline{{\rm K}^{*0}}$)/(p+$\rm\overline{p}$)
0–20 |  0.0379 $\pm$ 0.0006 $\pm$ 0.0028 (0.0026) |  0.270 $\pm$ 0.004 $\pm$ 0.027 (0.026) |  0.676 $\pm$ 0.009 $\pm$ 0.062 (0.059)
20–40 |  0.0392 $\pm$ 0.0006 $\pm$ 0.0029 (0.0027) |  0.289 $\pm$ 0.004 $\pm$ 0.027 (0.026) |  0.698 $\pm$ 0.009 $\pm$ 0.063 (0.060)
40–60 |  0.0395 $\pm$ 0.0006 $\pm$ 0.0030 (0.0028) |  0.298 $\pm$ 0.004 $\pm$ 0.028 (0.026) |  0.700 $\pm$ 0.009 $\pm$ 0.064 (0.060)
60–80 |  0.0393 $\pm$ 0.0006 $\pm$ 0.0032 (0.0029) |  0.308 $\pm$ 0.004 $\pm$ 0.028 (0.026) |  0.696 $\pm$ 0.009 $\pm$ 0.065 (0.061)
80–100 |  0.0399 $\pm$ 0.0006 $\pm$ 0.0030 (0.0028) |  0.325 $\pm$ 0.005 $\pm$ 0.028 (0.026) |  0.745 $\pm$ 0.011 $\pm$ 0.067 (0.063)
$\phi$
Multiplicity ($\%$) |  2$\phi$/($\pi^{+}$+$\pi^{-}$) |  2$\phi$/(${\rm K}^{+}$+${\rm K}^{-}$) |  2$\phi$/(p+$\rm\overline{p}$)
0–5 |  0.0185 $\pm$ 0.0002 $\pm$ 0.0014 (0.0009) |  0.1290 $\pm$ 0.0013 $\pm$ 0.0126 (0.0076) |  0.331 $\pm$ 0.003 $\pm$ 0.030 (0.016)
5–10 |  0.0174 $\pm$ 0.0002 $\pm$ 0.0013 (0.0006) |  0.1241 $\pm$ 0.0013 $\pm$ 0.0112 (0.0057) |  0.311 $\pm$ 0.003 $\pm$ 0.028 (0.012)
10–20 |  0.0174 $\pm$ 0.0001 $\pm$ 0.0012 (0.0006) |  0.1254 $\pm$ 0.0010 $\pm$ 0.0110 (0.0053) |  0.310 $\pm$ 0.003 $\pm$ 0.027 (0.011)
20–40 |  0.0170 $\pm$ 0.0001 $\pm$ 0.0012 (0.0006) |  0.1250 $\pm$ 0.0008 $\pm$ 0.0107 (0.0053) |  0.303 $\pm$ 0.002 $\pm$ 0.026 (0.011)
40–60 |  0.0161 $\pm$ 0.0001 $\pm$ 0.0012 (0.0006) |  0.1213 $\pm$ 0.0009 $\pm$ 0.0102 (0.0052) |  0.286 $\pm$ 0.002 $\pm$ 0.025 (0.011)
60–80 |  0.0147 $\pm$ 0.0001 $\pm$ 0.0011 (0.0006) |  0.1143 $\pm$ 0.0012 $\pm$ 0.0089 (0.0046) |  0.261 $\pm$ 0.003 $\pm$ 0.022 (0.010)
80–100 |  0.0143 $\pm$ 0.0002 $\pm$ 0.0013 (0.0009) |  0.1160 $\pm$ 0.0018 $\pm$ 0.0110 (0.0078) |  0.267 $\pm$ 0.004 $\pm$ 0.028 (0.018)
Table 4: Ratio of ${\rm K}^{*0}$ resonance and $\phi$-meson yields to long-
lived hadrons [47], for different multiplicity classes in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$. The results are reported as
value $\pm$ stat. $\pm$ sys. (uncorr.), where the first error is the
statistical uncertainty, the second is the total systematic uncertainty and
the value in parentheses indicates the component of uncertainty uncorrelated
across multiplicity classes.

The systematic uncertainty on tracking, track selection, material budget and
hadronic interaction cross section are correlated among each particle and its
decay products, thus they partially cancel out in the propagation of the error
to the final ratio. The residual uncertainties after cancellation are
correlated across the event classes. Systematic uncertainties derived from
signal extraction and PID selection are uncorrelated.
Based on the results reported in Tab. 4, one can conclude that no significant
multiplicity dependence is observed in the ${\rm K}^{*0}$/$\pi$ and the ${\rm
K}^{*0}$/p ratios. The 2$\phi$/($\pi^{+}$+$\pi^{-}$) ratio exhibits instead an
increasing trend with multiplicity, going from 0.0143 $\pm$ 0.001 in the
lowest multiplicity bin to 0.0185 $\pm$ 0.001 in the highest multiplicity
class, for a total increase of 29$\%$ with a 2.6$\sigma$ significance. A
similar trend with multiplicity is also observed for the
2$\phi$/(p+$\rm\overline{p}$) ratio, which increases by about 24$\%$ with a
significance of 1.3$\sigma$ going from 80–100$\%$ to 0–5$\%$.
The increase of the 2$\phi$/($\pi^{+}$+$\pi^{-}$) ratio with multiplicity can
be interpreted in the context of strangeness enhancement. The enhancement of
$\phi$-meson (s$\overline{\mathrm{s}}$) production relative to pion has been
observed in Pb–Pb to follow the enhancement observed for other strange and
multi-strange baryons [33]. In p–Pb the results are in general agreement with
the results on $\Xi$/$\pi$ and $\Omega$/$\pi$ ratio [68], that seem to
indicate that the strangeness content may control the rate of increase with
multiplicity.

Figure 9: Ratio of ${\rm K}^{*0}$ and $\phi$ to charged K measured in the
three collision systems, as a function of the cube root of the average charged
particle density ($\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$) measured at mid-rapidity,
used as a proxy for the system size. Squares represent ${\rm K}^{*0}$/K,
circles refer to $\phi$/K. Statistical uncertainties (bars) are shown together
with total (hollow boxes) and multiplicity-uncorrelated (shaded boxes)
systematic uncertainties. Measurements in pp at
$\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=2.76\,\mathrm{~{}TeV}$ are taken from [30] and
[33], respectively.

Most interesting are the ratios of ${\rm K}^{*0}$ and $\phi$ to charged K,
which have been compared to similar measurements in
$\mathrm{p\kern-0.50003ptp}$ at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ [30] and
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}~{}=2.76\,\mathrm{~{}TeV}$ [33],
looking for indications of the presence of re-scattering effects in central
p–Pb collisions. ${\rm K}^{*0}$/K and $\phi$/K in the three collision systems
are reported in Fig. 9 as a function of $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$. While spanning a smaller
range of particle multiplicities, the ${\rm K}^{*0}$/K and $\phi$/K ratios in
p–Pb cover within uncertainties the range of values measured in peripheral
(40–60$\%$ and 60–80$\%$) Pb–Pb and pp collisions.
In order to quantify the evolution of the p–Pb ratios with multiplicity class,
the ratios ($y$) have been fitted with a first order polynomial, $y=ax+b$,
where $x$ = $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta_{\mathrm{lab}}\rangle^{1/3}$. Only the statistical and
-uncorrelated systematic uncertainties, added in quadrature, have been
considered for the purpose of the fit. In p–Pb collisions the $\phi$/K ratio
follows the trend from minimum bias pp to peripheral Pb–Pb collisions. The
linear fit to the p–Pb data returns a positive but small slope parameter, aϕ =
0.008 $\pm$ 0.004. A similar fit to the ${\rm K}^{*0}$/K ratio in p–Pb
instead, results into a negative slope, a${}_{{\rm K}^{*0}}$ = -0.030 $\pm$
0.018. The pp value for the ${\rm K}^{*0}$/K ratio is consistent with the
ratio in the lowest multiplicity p–Pb events. The slope obtained fitting the
Pb–Pb data, a’${}_{{\rm K}^{*0}}$ = -0.016 $\pm$ 0.006, is interpreted as due
to re-scattering effects in central collisions [33]. The slopes in Pb–Pb and
p–Pb are compatible within the uncertainties (about 60$\%$ in p–Pb and 27$\%$
for Pb–Pb), and the decreasing trend in ${\rm K}^{*0}$/K may be a hint of the
presence of re-scattering effects in high-multiplicity p–Pb events and
indicative for a finite lifetime of the hadronic phase in p–Pb collisions.
Further comparisons with models of p–Pb collisions which include resonances
and re-scattering effects would be useful to distinguish between the different
scenarios.

##  5 Conclusions

The production of ${\rm K}^{*0}$ resonances and $\phi$ mesons in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=5.02\,\mathrm{~{}TeV}$ has been
measured with the ALICE detector, including multiplicity-dependent transverse
momentum spectra, mean transverse momentum and particle ratios to long-lived
light-flavoured hadron production. The system size dependence of these
observables has been studied by comparing the p–Pb results with previous
measurements in Pb–Pb and $\mathrm{p\kern-0.50003ptp}$ collisions. In all
collision systems, the mean transverse momentum increases with multiplicity
for all particle species. The mass ordering observed in central Pb–Pb
collisions, where particle with similar mass have similar $\langle
p_{\mathrm{T}}\rangle$, can be attributed to the presence of radial flow. In
p–Pb as well as in $\mathrm{p\kern-0.50003ptp}$ collisions $\langle
p_{\mathrm{T}}\rangle$ mass ordering is not observed. The measurement of
$\langle p_{\mathrm{T}}\rangle$ for other hadronic species could shed more
light on whether the observed effect is due to the mesonic (baryonic) nature
of the particles, or instead, this behaviour is common to resonances rather
than long-lived hadrons. Ratios of ${\rm K}^{*0}$ and $\phi$ production to
charged K are found to be in agreement with the ratios measured at similar
multiplicities in pp and Pb–Pb collisions. The measurements in p–Pb follow the
trend observed in Pb–Pb within the accessible multiplicity range and the
uncertainties. The ${\rm K}^{*0}$/K ratio exhibits a finite negative slope
from the lowest to the highest multiplicity p–Pb events, suggestive of a
finite lifetime of the hadronic phase in the small p–Pb system.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

J. Adam40, D. Adamová84, M.M. Aggarwal88, G. Aglieri Rinella36, M. Agnello110,
N. Agrawal48, Z. Ahammed132, S. Ahmad19, S.U. Ahn68, S. Aiola136, A.
Akindinov58, S.N. Alam132, D. Aleksandrov80, B. Alessandro110, D.
Alexandre101, R. Alfaro Molina64, A. Alici104,12, A. Alkin3, J.R.M.
Almaraz119, J. Alme38, T. Alt43, S. Altinpinar18, I. Altsybeev131, C. Alves
Garcia Prado120, C. Andrei78, A. Andronic97, V. Anguelov94, T. Antičić98, F.
Antinori107, P. Antonioli104, L. Aphecetche113, H. Appelshäuser53, S.
Arcelli28, R. Arnaldi110, O.W. Arnold37,93, I.C. Arsene22, M. Arslandok53, B.
Audurier113, A. Augustinus36, R. Averbeck97, M.D. Azmi19, A. Badalà106, Y.W.
Baek67, S. Bagnasco110, R. Bailhache53, R. Bala91, S. Balasubramanian136, A.
Baldisseri15, R.C. Baral61, A.M. Barbano27, R. Barbera29, F. Barile33, G.G.
Barnaföldi135, L.S. Barnby101, V. Barret70, P. Bartalini7, K. Barth36, J.
Bartke117, E. Bartsch53, M. Basile28, N. Bastid70, S. Basu132, B. Bathen54, G.
Batigne113, A. Batista Camejo70, B. Batyunya66, P.C. Batzing22, I.G.
Bearden81, H. Beck53, C. Bedda110, N.K. Behera50, I. Belikov55, F. Bellini28,
H. Bello Martinez2, R. Bellwied122, R. Belmont134, E. Belmont-Moreno64, V.
Belyaev75, P. Benacek84, G. Bencedi135, S. Beole27, I. Berceanu78, A.
Bercuci78, Y. Berdnikov86, D. Berenyi135, R.A. Bertens57, D. Berzano36, L.
Betev36, A. Bhasin91, I.R. Bhat91, A.K. Bhati88, B. Bhattacharjee45, J.
Bhom128, L. Bianchi122, N. Bianchi72, C. Bianchin134,57, J. Bielčík40, J.
Bielčíková84, A. Bilandzic81,37,93, G. Biro135, R. Biswas4, S. Biswas4,79, S.
Bjelogrlic57, J.T. Blair118, D. Blau80, C. Blume53, F. Bock74,94, A.
Bogdanov75, H. Bøggild81, L. Boldizsár135, M. Bombara41, J. Book53, H.
Borel15, A. Borissov96, M. Borri83,124, F. Bossú65, E. Botta27, C. Bourjau81,
P. Braun-Munzinger97, M. Bregant120, T. Breitner52, T.A. Broker53, T.A.
Browning95, M. Broz40, E.J. Brucken46, E. Bruna110, G.E. Bruno33, D.
Budnikov99, H. Buesching53, S. Bufalino36,27, P. Buncic36, O. Busch94,128, Z.
Buthelezi65, J.B. Butt16, J.T. Buxton20, D. Caffarri36, X. Cai7, H. Caines136,
L. Calero Diaz72, A. Caliva57, E. Calvo Villar102, P. Camerini26, F. Carena36,
W. Carena36, F. Carnesecchi28, J. Castillo Castellanos15, A.J. Castro125,
E.A.R. Casula25, C. Ceballos Sanchez9, P. Cerello110, J. Cerkala115, B.
Chang123, S. Chapeland36, M. Chartier124, J.L. Charvet15, S. Chattopadhyay132,
S. Chattopadhyay100, A. Chauvin93,37, V. Chelnokov3, M. Cherney87, C.
Cheshkov130, B. Cheynis130, V. Chibante Barroso36, D.D. Chinellato121, S.
Cho50, P. Chochula36, K. Choi96, M. Chojnacki81, S. Choudhury132, P.
Christakoglou82, C.H. Christensen81, P. Christiansen34, T. Chujo128, S.U.
Chung96, C. Cicalo105, L. Cifarelli12,28, F. Cindolo104, J. Cleymans90, F.
Colamaria33, D. Colella59,36, A. Collu74,25, M. Colocci28, G. Conesa
Balbastre71, Z. Conesa del Valle51, M.E. ConnorsII,136, J.G. Contreras40, T.M.
Cormier85, Y. Corrales Morales110, I. Cortés Maldonado2, P. Cortese32, M.R.
Cosentino120, F. Costa36, P. Crochet70, R. Cruz Albino11, E. Cuautle63, L.
Cunqueiro54,36, T. Dahms93,37, A. Dainese107, M.C. Danisch94, A. Danu62, D.
Das100, I. Das51,100, S. Das4, A. Dash121,79, S. Dash48, S. De120, A. De
Caro31,12, G. de Cataldo103, C. de Conti120, J. de Cuveland43, A. De Falco25,
D. De Gruttola12,31, N. De Marco110, S. De Pasquale31, A. Deisting97,94, A.
Deloff77, E. DénesI,135, C. Deplano82, P. Dhankher48, D. Di Bari33, A. Di
Mauro36, P. Di Nezza72, M.A. Diaz Corchero10, T. Dietel90, P. Dillenseger53,
R. Divià36, Ø. Djuvsland18, A. Dobrin82,62, D. Domenicis Gimenez120, B.
Dönigus53, O. Dordic22, T. Drozhzhova53, A.K. Dubey132, A. Dubla57, L.
Ducroux130, P. Dupieux70, R.J. Ehlers136, D. Elia103, E. Endress102, H.
Engel52, E. Epple136, B. Erazmus113, I. Erdemir53, F. Erhardt129, B.
Espagnon51, M. Estienne113, S. Esumi128, J. Eum96, D. Evans101, S.
Evdokimov111, G. Eyyubova40, L. Fabbietti93,37, D. Fabris107, J. Faivre71, A.
Fantoni72, M. Fasel74, L. Feldkamp54, A. Feliciello110, G. Feofilov131, J.
Ferencei84, A. Fernández Téllez2, E.G. Ferreiro17, A. Ferretti27, A.
Festanti30, V.J.G. Feuillard15,70, J. Figiel117, M.A.S. Figueredo124,120, S.
Filchagin99, D. Finogeev56, F.M. Fionda25, E.M. Fiore33, M.G. Fleck94, M.
Floris36, S. Foertsch65, P. Foka97, S. Fokin80, E. Fragiacomo109, A.
Francescon36,30, U. Frankenfeld97, G.G. Fronze27, U. Fuchs36, C. Furget71, A.
Furs56, M. Fusco Girard31, J.J. Gaardhøje81, M. Gagliardi27, A.M. Gago102, M.
Gallio27, D.R. Gangadharan74, P. Ganoti89, C. Gao7, C. Garabatos97, E. Garcia-
Solis13, C. Gargiulo36, P. Gasik93,37, E.F. Gauger118, M. Germain113, A.
Gheata36, M. Gheata36,62, P. Ghosh132, S.K. Ghosh4, P. Gianotti72, P.
Giubellino110,36, P. Giubilato30, E. Gladysz-Dziadus117, P. Glässel94, D.M.
Goméz Coral64, A. Gomez Ramirez52, V. Gonzalez10, P. González-Zamora10, S.
Gorbunov43, L. Görlich117, S. Gotovac116, V. Grabski64, O.A. Grachov136, L.K.
Graczykowski133, K.L. Graham101, A. Grelli57, A. Grigoras36, C. Grigoras36, V.
Grigoriev75, A. Grigoryan1, S. Grigoryan66, B. Grinyov3, N. Grion109, J.M.
Gronefeld97, J.F. Grosse-Oetringhaus36, J.-Y. Grossiord130, R. Grosso97, F.
Guber56, R. Guernane71, B. Guerzoni28, K. Gulbrandsen81, T. Gunji127, A.
Gupta91, R. Gupta91, R. Haake54, Ø. Haaland18, C. Hadjidakis51, M. Haiduc62,
H. Hamagaki127, G. Hamar135, J.C. Hamon55, J.W. Harris136, A. Harton13, D.
Hatzifotiadou104, S. Hayashi127, S.T. Heckel53, E. Hellbär53, H. Helstrup38,
A. Herghelegiu78, G. Herrera Corral11, B.A. Hess35, K.F. Hetland38, H.
Hillemanns36, B. Hippolyte55, D. Horak40, R. Hosokawa128, P. Hristov36, M.
Huang18, T.J. Humanic20, N. Hussain45, T. Hussain19, D. Hutter43, D.S.
Hwang21, R. Ilkaev99, M. Inaba128, E. Incani25, M. Ippolitov75,80, M. Irfan19,
M. Ivanov97, V. Ivanov86, V. Izucheev111, N. Jacazio28, P.M. Jacobs74, M.B.
Jadhav48, S. Jadlovska115, J. Jadlovsky115,59, C. Jahnke120, M.J.
Jakubowska133, H.J. Jang68, M.A. Janik133, P.H.S.Y. Jayarathna122, C. Jena30,
S. Jena122, R.T. Jimenez Bustamante97, P.G. Jones101, A. Jusko101, P.
Kalinak59, A. Kalweit36, J. Kamin53, J.H. Kang137, V. Kaplin75, S. Kar132, A.
Karasu Uysal69, O. Karavichev56, T. Karavicheva56, L. Karayan97,94, E.
Karpechev56, U. Kebschull52, R. Keidel138, D.L.D. Keijdener57, M. Keil36, M.
Mohisin KhanIII,19, P. Khan100, S.A. Khan132, A. Khanzadeev86, Y. Kharlov111,
B. Kileng38, D.W. Kim44, D.J. Kim123, D. Kim137, H. Kim137, J.S. Kim44, M.
Kim137, S. Kim21, T. Kim137, S. Kirsch43, I. Kisel43, S. Kiselev58, A.
Kisiel133, G. Kiss135, J.L. Klay6, C. Klein53, J. Klein36, C. Klein-Bösing54,
S. Klewin94, A. Kluge36, M.L. Knichel94, A.G. Knospe118,122, C. Kobdaj114, M.
Kofarago36, T. Kollegger97, A. Kolojvari131, V. Kondratiev131, N.
Kondratyeva75, E. Kondratyuk111, A. Konevskikh56, M. Kopcik115, P.
Kostarakis89, M. Kour91, C. Kouzinopoulos36, O. Kovalenko77, V. Kovalenko131,
M. Kowalski117, G. Koyithatta Meethaleveedu48, I. Králik59, A. Kravčáková41,
M. Kretz43, M. Krivda59,101, F. Krizek84, E. Kryshen86,36, M. Krzewicki43,
A.M. Kubera20, V. Kučera84, C. Kuhn55, P.G. Kuijer82, A. Kumar91, J. Kumar48,
L. Kumar88, S. Kumar48, P. Kurashvili77, A. Kurepin56, A.B. Kurepin56, A.
Kuryakin99, M.J. Kweon50, Y. Kwon137, S.L. La Pointe110, P. La Rocca29, P.
Ladron de Guevara11, C. Lagana Fernandes120, I. Lakomov36, R. Langoy42, C.
Lara52, A. Lardeux15, A. Lattuca27, E. Laudi36, R. Lea26, L. Leardini94, G.R.
Lee101, S. Lee137, F. Lehas82, R.C. Lemmon83, V. Lenti103, E. Leogrande57, I.
León Monzón119, H. León Vargas64, M. Leoncino27, P. Lévai135, S. Li7,70, X.
Li14, J. Lien42, R. Lietava101, S. Lindal22, V. Lindenstruth43, C. Lippmann97,
M.A. Lisa20, H.M. Ljunggren34, D.F. Lodato57, P.I. Loenne18, V. Loginov75, C.
Loizides74, X. Lopez70, E. López Torres9, A. Lowe135, P. Luettig53, M.
Lunardon30, G. Luparello26, T.H. Lutz136, A. Maevskaya56, M. Mager36, S.
Mahajan91, S.M. Mahmood22, A. Maire55, R.D. Majka136, M. Malaev86, I.
Maldonado Cervantes63, L. MalininaIV,66, D. Mal’Kevich58, P. Malzacher97, A.
Mamonov99, V. Manko80, F. Manso70, V. Manzari36,103, M. Marchisone27,65,126,
J. Mareš60, G.V. Margagliotti26, A. Margotti104, J. Margutti57, A. Marín97, C.
Markert118, M. Marquard53, N.A. Martin97, J. Martin Blanco113, P.
Martinengo36, M.I. Martínez2, G. Martínez García113, M. Martinez Pedreira36,
A. Mas120, S. Masciocchi97, M. Masera27, A. Masoni105, L. Massacrier113, A.
Mastroserio33, A. Matyja117, C. Mayer117,36, J. Mazer125, M.A. Mazzoni108, D.
Mcdonald122, F. Meddi24, Y. Melikyan75, A. Menchaca-Rocha64, E. Meninno31, J.
Mercado Pérez94, M. Meres39, Y. Miake128, M.M. Mieskolainen46, K.
Mikhaylov66,58, L. Milano74,36, J. Milosevic22, L.M. Minervini103,23, A.
Mischke57, A.N. Mishra49, D. Miśkowiec97, J. Mitra132, C.M. Mitu62, N.
Mohammadi57, B. Mohanty79,132, L. Molnar55,113, L. Montaño Zetina11, E.
Montes10, D.A. Moreira De Godoy113,54, L.A.P. Moreno2, S. Moretto30, A.
Morreale113, A. Morsch36, V. Muccifora72, E. Mudnic116, D. Mühlheim54, S.
Muhuri132, M. Mukherjee132, J.D. Mulligan136, M.G. Munhoz120, R.H.
Munzer37,93, H. Murakami127, S. Murray65, L. Musa36, J. Musinsky59, B. Naik48,
R. Nair77, B.K. Nandi48, R. Nania104, E. Nappi103, M.U. Naru16, H. Natal da
Luz120, C. Nattrass125, S.R. Navarro2, K. Nayak79, R. Nayak48, T.K. Nayak132,
S. Nazarenko99, A. Nedosekin58, L. Nellen63, F. Ng122, M. Nicassio97, M.
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Ozdemir53, Y. Pachmayer94, P. Pagano31, G. Paić63, S.K. Pal132, J. Pan134,
A.K. Pandey48, V. Papikyan1, G.S. Pappalardo106, P. Pareek49, W.J. Park97, S.
Parmar88, A. Passfeld54, V. Paticchio103, R.N. Patra132, B. Paul100, H. Pei7,
T. Peitzmann57, H. Pereira Da Costa15, D. Peresunko80,75, C.E. Pérez Lara82,
E. Perez Lezama53, V. Peskov53, Y. Pestov5, V. Petráček40, V. Petrov111, M.
Petrovici78, C. Petta29, S. Piano109, M. Pikna39, P. Pillot113, L.O.D.L.
Pimentel81, O. Pinazza36,104, L. Pinsky122, D.B. Piyarathna122, M. Płoskoń74,
M. Planinic129, J. Pluta133, S. Pochybova135, P.L.M. Podesta-Lerma119, M.G.
Poghosyan85,87, B. Polichtchouk111, N. Poljak129, W. Poonsawat114, A. Pop78,
S. Porteboeuf-Houssais70, J. Porter74, J. Pospisil84, S.K. Prasad4, R.
Preghenella104,36, F. Prino110, C.A. Pruneau134, I. Pshenichnov56, M.
Puccio27, G. Puddu25, P. Pujahari134, V. Punin99, J. Putschke134, H.
Qvigstad22, A. Rachevski109, S. Raha4, S. Rajput91, J. Rak123, A.
Rakotozafindrabe15, L. Ramello32, F. Rami55, R. Raniwala92, S. Raniwala92,
S.S. Räsänen46, B.T. Rascanu53, D. Rathee88, K.F. Read85,125, K. Redlich77,
R.J. Reed134, A. Rehman18, P. Reichelt53, F. Reidt94,36, X. Ren7, R.
Renfordt53, A.R. Reolon72, A. Reshetin56, J.-P. Revol12, K. Reygers94, V.
Riabov86, R.A. Ricci73, T. Richert34, M. Richter22, P. Riedler36, W.
Riegler36, F. Riggi29, C. Ristea62, E. Rocco57, M. Rodríguez Cahuantzi11,2, A.
Rodriguez Manso82, K. Røed22, E. Rogochaya66, D. Rohr43, D. Röhrich18, R.
Romita124, F. Ronchetti72,36, L. Ronflette113, P. Rosnet70, A. Rossi36,30, F.
Roukoutakis89, A. Roy49, C. Roy55, P. Roy100, A.J. Rubio Montero10, R. Rui26,
R. Russo27, E. Ryabinkin80, Y. Ryabov86, A. Rybicki117, S. Sadovsky111, K.
Šafařík36, B. Sahlmuller53, P. Sahoo49, R. Sahoo49, S. Sahoo61, P.K. Sahu61,
J. Saini132, S. Sakai74, M.A. Saleh134, J. Salzwedel20, S. Sambyal91, V.
Samsonov86, L. Šándor59, A. Sandoval64, M. Sano128, D. Sarkar132, P. Sarma45,
E. Scapparone104, F. Scarlassara30, C. Schiaua78, R. Schicker94, C. Schmidt97,
H.R. Schmidt35, S. Schuchmann53, J. Schukraft36, M. Schulc40, T. Schuster136,
Y. Schutz36,113, K. Schwarz97, K. Schweda97, G. Scioli28, E. Scomparin110, R.
Scott125, M. Šefčík41, J.E. Seger87, Y. Sekiguchi127, D. Sekihata47, I.
Selyuzhenkov97, K. Senosi65, S. Senyukov3,36, E. Serradilla10,64, A.
Sevcenco62, A. Shabanov56, A. Shabetai113, O. Shadura3, R. Shahoyan36, A.
Shangaraev111, A. Sharma91, M. Sharma91, M. Sharma91, N. Sharma125, K.
Shigaki47, K. Shtejer9,27, Y. Sibiriak80, S. Siddhanta105, K.M. Sielewicz36,
T. Siemiarczuk77, D. Silvermyr34, C. Silvestre71, G. Simatovic129, G.
Simonetti36, R. Singaraju132, R. Singh79, S. Singha132,79, V. Singhal132, B.C.
Sinha132, T. Sinha100, B. Sitar39, M. Sitta32, T.B. Skaali22, M. Slupecki123,
N. Smirnov136, R.J.M. Snellings57, T.W. Snellman123, C. Søgaard34, J. Song96,
M. Song137, Z. Song7, F. Soramel30, S. Sorensen125, R.D.de Souza121, F.
Sozzi97, M. Spacek40, E. Spiriti72, I. Sputowska117, M. Spyropoulou-
Stassinaki89, J. Stachel94, I. Stan62, P. Stankus85, G. Stefanek77, E.
Stenlund34, G. Steyn65, J.H. Stiller94, D. Stocco113, P. Strmen39, A.A.P.
Suaide120, T. Sugitate47, C. Suire51, M. Suleymanov16, M. SuljicI,26, R.
Sultanov58, M. Šumbera84, A. Szabo39, A. Szanto de ToledoI,120, I. Szarka39,
A. Szczepankiewicz36, M. Szymanski133, U. Tabassam16, J. Takahashi121, G.J.
Tambave18, N. Tanaka128, M.A. Tangaro33, M. Tarhini51, M. Tariq19, M.G.
Tarzila78, A. Tauro36, G. Tejeda Muñoz2, A. Telesca36, K. Terasaki127, C.
Terrevoli30, B. Teyssier130, J. Thäder74, D. Thomas118, R. Tieulent130, A.R.
Timmins122, A. Toia53, S. Trogolo27, G. Trombetta33, V. Trubnikov3, W.H.
Trzaska123, T. Tsuji127, A. Tumkin99, R. Turrisi107, T.S. Tveter22, K.
Ullaland18, A. Uras130, G.L. Usai25, A. Utrobicic129, M. Vajzer84, M. Vala59,
L. Valencia Palomo70, S. Vallero27, J. Van Der Maarel57, J.W. Van Hoorne36, M.
van Leeuwen57, T. Vanat84, P. Vande Vyvre36, D. Varga135, A. Vargas2, M.
Vargyas123, R. Varma48, M. Vasileiou89, A. Vasiliev80, A. Vauthier71, V.
Vechernin131, A.M. Veen57, M. Veldhoen57, A. Velure18, M. Venaruzzo73, E.
Vercellin27, S. Vergara Limón2, R. Vernet8, M. Verweij134, L. Vickovic116, G.
ViestiI,30, J. Viinikainen123, Z. Vilakazi126, O. Villalobos Baillie101, A.
Villatoro Tello2, A. Vinogradov80, L. Vinogradov131, Y. VinogradovI,99, T.
Virgili31, V. Vislavicius34, Y.P. Viyogi132, A. Vodopyanov66, M.A. Völkl94, K.
Voloshin58, S.A. Voloshin134, G. Volpe33, B. von Haller36, I. Vorobyev37,93,
D. Vranic97,36, J. Vrláková41, B. Vulpescu70, B. Wagner18, J. Wagner97, H.
Wang57, M. Wang7,113, D. Watanabe128, Y. Watanabe127, M. Weber36,112, S.G.
Weber97, D.F. Weiser94, J.P. Wessels54, U. Westerhoff54, A.M. Whitehead90, J.
Wiechula35, J. Wikne22, G. Wilk77, J. Wilkinson94, M.C.S. Williams104, B.
Windelband94, M. Winn94, H. Yang57, P. Yang7, S. Yano47, C. Yasar69, Z. Yin7,
H. Yokoyama128, I.-K. Yoo96, J.H. Yoon50, V. Yurchenko3, I. Yushmanov80, A.
Zaborowska133, V. Zaccolo81, A. Zaman16, C. Zampolli36,104, H.J.C. Zanoli120,
S. Zaporozhets66, N. Zardoshti101, A. Zarochentsev131, P. Závada60, N.
Zaviyalov99, H. Zbroszczyk133, I.S. Zgura62, M. Zhalov86, H. Zhang18, X.
Zhang74, Y. Zhang7, C. Zhang57, Z. Zhang7, C. Zhao22, N. Zhigareva58, D.
Zhou7, Y. Zhou81, Z. Zhou18, H. Zhu18, J. Zhu113,7, A. Zichichi28,12, A.
Zimmermann94, M.B. Zimmermann54,36, G. Zinovjev3, M. Zyzak43

Affiliation Notes

I Deceased
II Also at: Georgia State University, Atlanta, Georgia, United States
III Also at Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
3 Bogolyubov Institute for Theoretical Physics, 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 Centre de Calcul de l’IN2P3, Villeurbanne, France
9 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
10 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain
11 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico
12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico
Fermi”, Rome, Italy
13 Chicago State University, Chicago, Illinois, USA
14 China Institute of Atomic Energy, Beijing, China
15 Commissariat à l’Energie Atomique, IRFU, Saclay, France
16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan
17 Departamento de Física de Partículas and IGFAE, Universidad de Santiago de
Compostela, Santiago de Compostela, Spain
18 Department of Physics and Technology, University of Bergen, Bergen, Norway
19 Department of Physics, Aligarh Muslim University, Aligarh, India
20 Department of Physics, Ohio State University, Columbus, Ohio, United States
21 Department of Physics, Sejong University, Seoul, South Korea
22 Department of Physics, University of Oslo, Oslo, Norway
23 Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari, Italy
24 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN Rome,
Italy
25 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
26 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
27 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
29 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
30 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
31 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy
33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
34 Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden
35 Eberhard Karls Universität Tübingen, Tübingen, Germany
36 European Organization for Nuclear Research (CERN), Geneva, Switzerland
37 Excellence Cluster Universe, Technische Universität München, Munich,
Germany
38 Faculty of Engineering, Bergen University College, Bergen, Norway
39 Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia
40 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
41 Faculty of Science, P.J. Šafárik University, Košice, Slovakia
42 Faculty of Technology, Buskerud and Vestfold University College, Vestfold,
Norway
43 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
44 Gangneung-Wonju National University, Gangneung, South Korea
45 Gauhati University, Department of Physics, Guwahati, India
46 Helsinki Institute of Physics (HIP), Helsinki, Finland
47 Hiroshima University, Hiroshima, Japan
48 Indian Institute of Technology Bombay (IIT), Mumbai, India
49 Indian Institute of Technology Indore, Indore (IITI), India
50 Inha University, Incheon, South Korea
51 Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-
IN2P3, Orsay, France
52 Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
53 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
54 Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany
55 Institut Pluridisciplinaire Hubert Curien (IPHC), Université de Strasbourg,
CNRS-IN2P3, Strasbourg, France
56 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
57 Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands
58 Institute for Theoretical and Experimental Physics, Moscow, Russia
59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia
60 Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic
61 Institute of Physics, Bhubaneswar, India
62 Institute of Space Science (ISS), Bucharest, Romania
63 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
64 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
65 iThemba LABS, National Research Foundation, Somerset West, South Africa
66 Joint Institute for Nuclear Research (JINR), Dubna, Russia
67 Konkuk University, Seoul, South Korea
68 Korea Institute of Science and Technology Information, Daejeon, South Korea
69 KTO Karatay University, Konya, Turkey
70 Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France
71 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
72 Laboratori Nazionali di Frascati, INFN, Frascati, Italy
73 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Moscow Engineering Physics Institute, Moscow, Russia
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 National Centre for Nuclear Studies, Warsaw, Poland
78 National Institute for Physics and Nuclear Engineering, Bucharest, Romania
79 National Institute of Science Education and Research, Bhubaneswar, India
80 National Research Centre Kurchatov Institute, Moscow, Russia
81 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
82 Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands
83 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
84 Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u
Prahy, Czech Republic
85 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
86 Petersburg Nuclear Physics Institute, Gatchina, Russia
87 Physics Department, Creighton University, Omaha, Nebraska, United States
88 Physics Department, Panjab University, Chandigarh, India
89 Physics Department, University of Athens, Athens, Greece
90 Physics Department, University of Cape Town, Cape Town, South Africa
91 Physics Department, University of Jammu, Jammu, India
92 Physics Department, University of Rajasthan, Jaipur, India
93 Physik Department, Technische Universität München, Munich, Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Purdue University, West Lafayette, Indiana, United States
96 Pusan National University, Pusan, South Korea
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany
98 Rudjer Bošković Institute, Zagreb, Croatia
99 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
100 Saha Institute of Nuclear Physics, Kolkata, India
101 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
102 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
103 Sezione INFN, Bari, Italy
104 Sezione INFN, Bologna, Italy
105 Sezione INFN, Cagliari, Italy
106 Sezione INFN, Catania, Italy
107 Sezione INFN, Padova, Italy
108 Sezione INFN, Rome, Italy
109 Sezione INFN, Trieste, Italy
110 Sezione INFN, Turin, Italy
111 SSC IHEP of NRC Kurchatov institute, Protvino, Russia
112 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
113 SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France
114 Suranaree University of Technology, Nakhon Ratchasima, Thailand
115 Technical University of Košice, Košice, Slovakia
116 Technical University of Split FESB, Split, Croatia
117 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
118 The University of Texas at Austin, Physics Department, Austin, Texas, USA
119 Universidad Autónoma de Sinaloa, Culiacán, Mexico
120 Universidade de São Paulo (USP), São Paulo, Brazil
121 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
122 University of Houston, Houston, Texas, United States
123 University of Jyväskylä, Jyväskylä, Finland
124 University of Liverpool, Liverpool, United Kingdom
125 University of Tennessee, Knoxville, Tennessee, United States
126 University of the Witwatersrand, Johannesburg, South Africa
127 University of Tokyo, Tokyo, Japan
128 University of Tsukuba, Tsukuba, Japan
129 University of Zagreb, Zagreb, Croatia
130 Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne,
France
131 V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia
132 Variable Energy Cyclotron Centre, Kolkata, India
133 Warsaw University of Technology, Warsaw, Poland
134 Wayne State University, Detroit, Michigan, United States
135 Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary
136 Yale University, New Haven, Connecticut, United States
137 Yonsei University, Seoul, South Korea
138 Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany