2022 067 24 March

$\mathrm{K}^{*}(\mathrm{{892}})^{0}$ and $\mathrm{\phi({1020})}$ in p–Pb at
$\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV ALICE Collaboration††thanks: See Appendix B
for the list of collaboration members ALICE Collaboration

The transverse-momentum ($p_{\rm T}$) spectra of K${}^{*}(892)^{0}~{}$and
$\mathrm{\phi(1020)}~{}$measured with the ALICE detector up to $p_{\rm T}$ =
16 GeV/$c$ in the rapidity range $-$1.2 $<$ $y$ $<$ 0.3, in p–Pb collisions at
the center-of-mass energy per nucleon–nucleon collision
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV are presented as a function of charged
particle multiplicity and rapidity. The measured $p_{\rm T}$ distributions
show a dependence on both multiplicity and rapidity at low $p_{\rm T}$ whereas
no significant dependence is observed at high $p_{\rm T}$. A rapidity
dependence is observed in the $p_{\rm T}$-integrated yield (d$N$/d$y$),
whereas the mean transverse momentum $\left(\langle p_{\rm T}\rangle\right)$
shows a flat behavior as a function of rapidity. The rapidity asymmetry
($Y_{\mathrm{asym}}$) at low $p_{\rm T}$ ( $<$ 5 GeV/$c$) is more significant
for higher multiplicity classes. At high $p_{\rm T}$, no significant rapidity
asymmetry is observed in any of the multiplicity classes. Both
K${}^{*}(892)^{0}~{}$and $\mathrm{\phi(1020)}~{}$show similar
$Y_{\mathrm{asym}}$. The nuclear modification factor ($Q_{\mathrm{CP}}$) as a
function of $p_{\rm T}$ shows a Cronin-like enhancement at intermediate
$p_{\rm T}$, which is more prominent at higher rapidities (Pb-going direction)
and in higher multiplicity classes. At high $p_{\rm T}$ ($>$ 5 GeV/$c$), the
$Q_{\mathrm{CP}}$ values are greater than unity and no significant rapidity
dependence is observed.

##  1 Introduction

The primary goals of high-energy heavy-ion (A–A) collisions are to create a
system of deconfined quarks and gluons known as quark–gluon plasma (QGP) and
to study its properties [1, 2, 3, 4]. Asymmetric collision systems like
proton-nucleus (p–A) and deuteron-nucleus (d–A) can be considered as control
experiments where the formation of an extended QGP phase is not expected.
These collision systems are used as baseline measurements to study the
possible effects of cold nuclear matter and disentangle the same from hot
dense matter effects produced in heavy-ion collisions [5, 6, 7, 8, 9, 10, 11,
12, 13, 14]. In addition, p–A collisions at Large Hadron Collider (LHC)
energies enable probing the parton distribution functions in nuclei at very
small values of the Bjorken $x$ variable, where gluon saturation effects may
occur [15, 16, 17]. Recent measurements in high-multiplicity pp, p–Pb, p–Au,
d–Au, and 3He–Au collisions at different energies have shown features such as
anisotropies in particle emission azimuthal angles, strangeness enhancement,
and long–range structures in two-particle angular correlations on the near and
away side, which previously have been observed in nucleus-nucleus collisions
[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. The origin of these
phenomena in small systems is not yet fully understood. A systematic study of
multiplicity and rapidity dependence of hadron production allows us to
investigate the mechanism of particle production and shed light on the physics
processes that contribute to the particle production [15]. Similar studies
have been reported by the experiments at the LHC [16, 17, 9, 10] and
Relativistic Heavy Ion Collider (RHIC) [19, 20, 6, 21, 7]. The mechanism of
hadron production may be influenced by different effects such as nuclear
modification of the parton distribution functions (nuclear shadowing) and
possible parton saturation, multiple scattering, and radial flow [30, 31, 32,
16]. These effects are expected to depend on the rapidity of the produced
particles. In p–Pb collisions, one can expect that the production mechanism
may be sensitive to different effects at forward (p-going) and backward (Pb-
going) rapidities [16, 17, 9, 10, 33, 32]. The partons of the incident proton
are expected to undergo multiple scattering while traversing the Pb-nucleus.
It is thus interesting to study the ratio of particle yields between Pb- and
p-going directions, represented by the rapidity asymmetry
($Y_{\mathrm{asym}}$) defined as:

$Y_{\mathrm{asym}}(p_{\mathrm{T}})=\frac{\left.\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}\right|_{-0.3<y<0}}{\left.\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}\right|_{0<y<0.3}}$
(1)

where
$\rm{d}^{2}\it{N}/\rm{d}\it{p}_{\rm{T}}\rm{d}\it{y}|_{-\mathrm{0.3}<y<\mathrm{0}}$
is the particle yield in the rapidity ($y$) interval –0.3 $<y<$ 0, considered
as the Pb-going direction, and
$\rm{d}^{2}\it{N}/\rm{d}\it{p}_{\rm{T}}\rm{d}\it{y}|_{\mathrm{0}<y<\mathrm{0.3}}$
is the particle yield in the rapidity interval 0 $<y<$ 0.3, corresponding to
the p-going direction. From the experimental point of view, the
$Y_{\mathrm{asym}}$ is a powerful observable because systematic uncertainties
cancel out in the ratio and hence it can better discriminate rapidity-
dependent effects among models [18, 17, 16]. Gluon saturation effects at low
Bjorken $x$ values [7, 18] may affect the transverse momentum distribution of
hadron production at large rapidities in the p-going direction in p–Pb
collisions at LHC energies. The gluon saturation effects depend on the
colliding nuclei and rapidity as A${}^{1/3}e^{\lambda y}$, where $A$
represents the mass number [18], and $\lambda$ is a parameter whose value lies
between 0.2 and 0.3, and is obtained from fits to the HERA measurements [8].
The effect of rapidity dependence on particle production is tested by
measuring the ratios of integrated yield (d$N/$d$y$) and mean transverse
momentum $\left(\langle p_{\rm T}\rangle\right)$ at given $y$ to the values at
$y=0$, i.e. denoted as (d$N/$d$y$)/(d$N/$d$y)_{y=0}$ and $\langle p_{\rm
T}\rangle$/$\langle p_{\rm T}\rangle_{y=0}$. It is also important to study the
variation with rapidity of the nuclear modification factor between central and
non-central collisions. This factor
$\left(Q_{\mathrm{CP}}(p_{\mathrm{T}})\right)$ is defined as

$\it{Q}_{\mathrm{CP}}(p_{\mathrm{T}})=\left.\frac{\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}}{\langle
N_{\mathrm{coll}}\rangle}\right|_{\textrm{HM}}\Bigg{/}\left.\frac{\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}}{\langle
N_{\mathrm{coll}}\rangle}\right|_{\textrm{LM}},$ (2)

where $\langle N_{\mathrm{coll}}\rangle$ is the average number of
nucleon–nucleon collisions in low-multiplicity (LM) and high-multiplicity (HM)
events, respectively. The multiplicity dependence of $\rm{K}^{\rm{*0}}$ and
$\phi$ meson production at midrapidity was studied in pp, p–Pb, and Pb–Pb
collisions at LHC energies and reported in Refs. [26, 34, 27, 14]. The
lifetime of the $\rm{K}^{\rm{*0}}$ meson is about 4 fm/$c$, which is
comparable to the lifetime of the hadronic phase. In contrast, the lifetime of
the $\phi$ meson is 10 times higher. The $\rm{K}^{\rm{*0}}$ and $\phi$ mesons
are thus useful probes of the late-stage evolution of high-energy hadronic
collisions. As they have similar mass but differ in their strangeness content
by one unit, they are suitable candidates to understand the modification of
particle production due to rescattering effects and the role of the
strangeness content, as discussed in Refs. [29, 26, 34, 28].

This article reports the first measurements of the rapidity dependence of
K${}^{*}(892)^{0}~{}$and $\mathrm{\phi(1020)}~{}$mesons production in p–Pb
collisions at center-of-mass energy per nucleon–nucleon collisions at
$\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV by the ALICE experiment at the LHC. The
large size of the data sample and the excellent particle identification (PID)
provide opportunities to extend these measurements in a wider rapidity
interval and multiplicity classes compared to earlier measurements [23, 24,
26, 27, 28, 29]. This enables the investigation of the nuclear effects on the
particle production in p–Pb collisions. The $p_{\rm T}$ spectra,
$Y_{\mathrm{asym}}(p_{\mathrm{T}})$ and $\it{Q}_{\mathrm{CP}}(p_{\mathrm{T}})$
are studied in the rapidity range -1.2 $<y<$ 0.3 and three multiplicity
classes along with a measurement on the multiplicity-integrated sample.
Similar measurements for charged particles and strange hadrons at RHIC and the
LHC energies were reported in Refs. [7, 18, 16].

The measurements presented here are compared with various model predictions
such as EPOS-LHC [35], EPOS3 with and without UrQMD [36, 37, 38, 39], DPMJET
[40], HIJING [41] and PYTHIA8/Angantyr [42]. EPOS-LHC is an event generator
for minimum-bias hadronic interactions that incorporates a parameterization of
flow based on LHC data [35]. It is an event generator based on multiple
partonic scatterings described using Gribov’s Reggeon field theory formalism,
supplemented with collective hadronization and the core-corona mechanism from
pp to A–A collisions [35]. EPOS3 is an event generator based on 3$+$1D viscous
hydrodynamical evolution in the Gribov-Regge multiple scattering framework,
which is used to understand hadronic resonances and their interactions in the
partonic and hadronic medium. The UrQMD model introduces the description of
rescattering and regeneration effects in the hadronic phase [36, 38, 39].
DPMJET is a QCD-inspired dual parton model based on the formalism of the
Gribov-Glauber approach that treats the soft- and hard- scattering
interactions differently [40]. HIJING is used to study jet and the associated
particle production in high energy collisions and is based on QCD-inspired
models, including multiple minijet production, soft excitation, nuclear
shadowing of parton distribution functions, and jet interaction in dense
matter. Due to nuclear shadowing, the parton distribution functions of quarks
and gluons are expected to differ from the simple superposition of their
distribution in a nucleon. The initial nuclear shadowing effect on particle
production is tested using two shadowing depth constant values 0.1 and 0 that
represent the HIJING model predictions with and without shadowing [41].
PYTHIA8/Angantyr is an event generator based on the Fritiof model [43], which
includes the features of multi-parton interactions and diffractive excitation
in each nucleon–nucleon (NN) sub-collision. It acts as a baseline for
understanding the non-collective background in the observables sensitive to
collective behavior, as PYTHIA8 does not include a collective expansion stage
in its description of pp collisions [42]. The comparison of data with the
results from these phenomenological models helps to understand the relative
contribution of the nuclear effects on the particle production in p–Pb
collisions.

For the results presented here, K${}^{*}(892)^{0}$ and
$\mathrm{\overline{K}}^{*}(892)^{0}$ are averaged and denoted by the symbol
$\rm{K}^{\rm{*0}}$, while $\mathrm{\phi(1020)}~{}$is denoted by $\phi$. The
article is organized as follows. In Section 2, the data sample, event and
track selection criteria, the analysis techniques, the procedure of extraction
of the yields, and the study of the systematic uncertainties are discussed. In
Section 3, the results on the $p_{\rm T}$ spectra, the d$N$/d$y$, the $\langle
p_{\rm{T}}\rangle$, the $Y_{\mathrm{asym}}$ and the ${Q}_{\mathrm{CP}}$ in
p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV are presented.
Finally, the results are summarized in Section 4.

##  2 Data analysis

Measurements of $\rm{K}^{\rm{*0}}$ and $\phi$ meson production are carried out
on the data sample collected in 2016 during the second LHC run with p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV. The resonances are
reconstructed from their decay products by using the invariant-mass method.
The considered decay channels are $\rm{K}^{\rm{*0}}$
$\rightarrow\rm{K}^{+}\pi^{-}$ and its charge conjugate, and $\phi$
$\rightarrow\rm{K}^{+}\rm{K}^{-}$ with respective branching ratios (BR) of
66.6 $\%$ and 49.2 $\%$ [26, 27]. In the p–Pb configuration, the 208Pb beam
with energy of 1.58 TeV per nucleon collides with a proton beam with an energy
of 4 TeV resulting in collisions at a nucleon–nucleon center-of-mass energy
$\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV [26]. It leads to the rapidity in the
center-of-mass frame being shifted by $\Delta y=-0.465$ in the direction of
the proton beam with respect to the laboratory frame. The measurements are
performed in the rapidity range -1.2 $<y<$ 0.3 for five rapidity intervals
with width of 0.3 units and three multiplicity classes along with a
multiplicity-integrated class. The details of the ALICE detector setup and its
performance can be found in Refs. [44, 45]. The measurements are carried out
with the ALICE central barrel detectors, which are utilized for tracking, PID,
and primary vertex reconstruction and are housed inside a solenoidal magnet
with a magnetic field of 0.5 T. The main detectors that are used for the
analyses presented here are the Inner Tracking System (ITS) [46], the Time
Projection Chamber (TPC) [47], and the TOF (Time-Of-Flight) [48] detectors.
These detectors have full azimuthal coverage and have a common pseudorapidity
coverage of $|\eta|<$ 0.9.

###  2.1 Event and track selection and particle identification

The trigger and event selection criteria are the same as those discussed in
previous publications [26, 27]. The events are selected with a minimum-bias
trigger based on the coincidence of signals in two arrays of 32 scintillator
detectors covering full azimuth and the pseudorapidity regions 2.8 $<$ $\eta$
$<$ 5.1 (V0A) and –3.7 $<$ $\eta$ $<$ –1.7 (V0C) [49]. The primary vertex of
the collision is determined using the charged tracks reconstructed in the ITS
and the TPC. Events are selected whose reconstructed primary vertex position
lies within $\pm$10 cm from the center of the detector along the beam
direction. The Silicon Pixel Detector (SPD) which is the innermost detector of
the ITS, is used to reject events in which multiple collision vertices are
found (pile-up) [46]. In this work, approximately 540 million events are
selected with the criteria described above. The minimum-bias events are
further divided into three multiplicity classes, which are expressed in
percentiles according to the total charge deposited in the V0A detector [49].
The yield of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons is measured in five rapidity
regions -1.2 $<y<$ -0.9, -0.9 $<y<$ -0.6, -0.6 $<y<$ -0.3, -0.3 $<y<$ 0 and 0
$<y<$ 0.3 for the multiplicity classes 0–10$\%$, 10–40$\%$, 40–100$\%$ in
addition to the multiplicity-integrated (0–100$\%$) measurement, corresponding
to all minimum-bias events. The 10$\%$ of the events with the highest
multiplicity of charged particles correspond to the 0–10$\%$ class and
similarly, the 40–100$\%$ class corresponds to the lowest multiplicity. The
$\langle N_{\mathrm{coll}}\rangle$ values are estimated from a Glauber model
analysis [50] of the charged particle multiplicity distribution in the V0A
detector, and they are 13.8 $\pm$ 3.8, 10.5 $\pm$ 3.9 and 4.0 $\pm$ 2.6,
respectively for 0–10$\%$, 10–40$\%$, and 40–100$\%$ multiplicity classes
taken from Ref. [51]. Charged-particle tracks reconstructed in the TPC with
$p_{\rm T}>$ 0.15 GeV/$c$ and pseudorapidity $|\eta|<$ 0.8 are selected for
the analysis. The selected charged tracks should have crossed at least 70 out
of 159 readout-pad rows of the TPC. The distance of closest approach of the
track to the primary vertex in the longitudinal direction (DCAz) is required
to be less than 2 cm. In the transverse plane (xy) a $p_{\rm T}$-dependent
selection of DCA${}_{xy}(p_{\rm T})<$ 0.0105 + 0.035 $p_{\rm T}^{-1.1}$ cm is
applied. The $\rm{K}^{\rm{*0}}$ and $\phi$ mesons are reconstructed from their
decay daughters (pions and kaons), which are identified by measuring the
specific ionization energy loss (d$E$/d$x$) in the TPC [47] and their time-of-
flight information using the TOF [48]. For the selection of pions and kaons,
the measured $\langle\textrm{d}E/\textrm{d}x\rangle$ is required to be within
$n\sigma_{\mathrm{TPC}}$ from the expected
$\langle\textrm{d}E/\textrm{d}x\rangle$ values for a given mass hypothesis,
where $\sigma_{\mathrm{TPC}}$ is the TPC
$\langle\textrm{d}E/\textrm{d}x\rangle$ resolution. The values of $n$ are
momentum-dependent ($p$) and are set to 6$\sigma_{\mathrm{TPC}}$,
3$\sigma_{\mathrm{TPC}}$, and 2$\sigma_{\mathrm{TPC}}$ in the momentum
intervals $p$ $<$ 0.3 GeV/$c$, 0.3 $<$ $p$ $<$ 0.5 GeV/$c$ and $p$ $>$ 0.5
GeV/$c$, respectively. If the TOF information is available for the considered
tracks, it is used for pion and kaon identification in addition to the TPC one
by requiring the time-of-flight of the particle to be within
3$\sigma_{\mathrm{TOF}}$ from the expected value for the considered mass
hypothesis, where $\sigma_{\mathrm{TOF}}$ is the time-of-flight resolution of
the TOF.

###  2.2 Yield extraction

The $\rm{K}^{\rm{*0}}$ and $\phi$ resonances are reconstructed from their
decay products using the invariant-mass reconstruction technique described in
Refs. [26, 27]. The invariant-mass distributions of K${}^{\pm}\pi^{\mp}$ and
K+K- pairs in the same event are reconstructed. The shape of uncorrelated
background is estimated using two techniques, namely mixed-event and like-sign
methods. In the mixed-event method, the shape of the uncorrelated-background
distribution for $\rm{K}^{\rm{*0}}$ ($\phi$) is obtained by combining pions
(kaons) from a given event with opposite-sign kaons from other events. Each
event is mixed with five different events to reduce the statistical
uncertainties of the estimated uncorrelated-background distribution. The
events which are mixed are required to have similar characteristics, i.e. the
longitudinal position of the primary vertices should differ by less than 1 cm,
and the multiplicity percentiles, computed from the V0A amplitude, should
differ by less than 5$\%$. The mixed-event distributions for
$\rm{K}^{\rm{*0}}$ ($\phi$) candidates are normalized in the invariant mass
interval 1.1 $<M_{\mathrm{K\pi}}<$ 1.15 GeV/$c^{2}$ (1.06 $<M_{\mathrm{KK}}<$
1.09 GeV/$c^{2}$), which is well separated from signal peak.

Figure 1: Invariant-mass distributions after combinatorial background
subtraction for $\rm{K}^{\rm{*0}}$ and $\phi$ candidates in the multiplicity
class 0–10$\%$ and transverse momentum range 2.2 $\leq$ $p_{\mathrm{T}}$ $<$
3.0 GeV/$c$ in the rapidity interval -0.3 $<y<$ 0 (panels (a) and (b)) and 0
$<y<$ 0.3 (panels (c) and (d)). The $\rm{K}^{\rm{*0}}$ peak is described by a
Breit-Wigner function whereas the $\phi$ peak is fitted with a Voigtian
function. The residual background is described by a polynomial function of
order 2.

In the like-sign method, tracks with the same charge from the same event are
paired to estimate the uncorrelated background contribution. The invariant-
mass distribution for the uncorrelated background is obtained as the geometric
mean 2$\sqrt{n^{++}\times n^{--}}$, where $n^{++}$ and $n^{--}$ are the number
of positive-positive and negative-negative pairs in each invariant-mass
interval, respectively. The mixed-event technique is used as the default
method to extract the yields for both $\rm{K}^{\rm{*0}}$ and $\phi$ mesons,
while the difference with respect to the yield obtained using the
combinatorial background from the like-sign method is included in the
estimation of the systematic uncertainty. After the subtraction of the
combinatorial background, the invariant-mass distribution consists of a
resonance peak sitting on the top of a residual background of correlated
pairs. The residual background originates from correlated pairs from jets,
misidentification of pions and kaons from $\rm{K}^{\rm{*0}}$ and $\phi$ meson
decays, and partially reconstructed decays of higher-mass particles [26].
Figure 1 shows the ${K^{\pm}\rm{\pi^{\mp}}}$ and ${\rm{K^{+}K^{-}}}$
invariant-mass distributions after subtraction of mixed-event background in
the transverse momentum interval 2.2 $\leq$ $p_{\mathrm{T}}$ $<$ 3.0 GeV/$c$
for the rapidity intervals -0.3 $<y<$ 0 (panels (a) and (b)) and 0 $<y<$ 0.3
(panels (c) and (d)) in the 0–10$\%$ multiplicity class.

The signal peak is fitted with a Breit-Wigner and a Voigtian function
(convolution of Breit-Wigner and Gaussian functions) for $\rm{K}^{\rm{*0}}$
and $\phi$ resonances, respectively. For the $\rm{K}^{\rm{*0}}$, a pure Breit-
Wigner is used because the invariant mass resolution is negligible with
respect to the natural width of the resonance peak. A second-order polynomial
function is used to describe the shape of the residual background for both
resonances. The fit to the invariant-mass distribution is performed in the
interval 0.75 $<M_{\rm{K}\pi}<$ 1.15 GeV/$c^{2}$ (0.99 $<M_{\mathrm{KK}}<$
1.07 GeV/$c^{2}$) for $\rm{K}^{\rm{*0}}$($\phi$). The widths of
$\rm{K}^{\rm{*0}}$ and $\phi$ peaks are fixed to their known widths
$\Gamma$(K*0) $=$ 47.4 $\pm$ 0.6 MeV/$c^{2}$, $\Gamma$($\phi$) $=$ 4.26 $\pm$
0.04 MeV/$c^{2}$ [52], whereas the resolution parameter of the Voigtian
function for $\phi$ is kept as a free parameter. In the estimation of the
systematic uncertainties, the width of the Breit-Wigner is taken as a free
parameter. The mass and width values extracted from the fit have similar
magnitude and trend with $p_{\rm T}$ as reported in previous publications [26,
27, 53, 34]. In the present study, it is found that the mass and width
obtained from the fit are independent of rapidity and multiplicity for both
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons. The sensitivity of the systematic
uncertainty to the choice of the fitting range, normalization interval of the
mixed-event background, shape of the residual background function, width, and
resolution parameters have been studied by varying the fit configuration, as
described in Section 2.3. The raw yields of $\rm{K}^{\rm{*0}}$ and $\phi$
mesons are extracted in the transverse momentum range from 0.8 to 16 GeV/$c$
for various rapidity intervals and multiplicity classes.
To obtain the transverse momentum spectra, the raw yields are normalized by
the number of accepted non-single-diffractive (NSD) events and corrected for
the branching ratio and the detector acceptance ($A$) times the reconstruction
efficiency ($\epsilon_{\rm rec}$). The $A\times\epsilon_{\rm rec}$ is obtained
from a Monte Carlo (MC) simulation based on the DPMJET [40] event generator
and the GEANT3 package to model the transport of the generated particles
through the ALICE detector [54]. The $A\times\epsilon_{\rm rec}$ is defined as
the ratio of the reconstructed $p_{\rm T}$ spectra of $\rm{K}^{\rm{*0}}$
($\phi$) mesons in a given rapidity interval to the generated ones in the same
rapidity interval. The track and PID selection criteria applied to the decay
products of resonances in the MC are identical to those used in the data.
Since the efficiency depends on $p_{\rm T}$ and the $p_{\rm T}$ distributions
of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons from DPMJET are different from the
real data, a re-weighting procedure is applied to match the generated $p_{\rm
T}$ shapes to the measured ones.

The effect of the re-weighting on $A\times\epsilon_{\mathrm{rec}}$ depends on
$p_{\rm T}$ and amounts to $\sim$5–17$\%$ at $p_{\rm T}$ $<1.5$ GeV/$c$. At
higher $p_{\rm T}$, the effect is negligible. The effect of re-weighting also
depends on rapidity at low $p_{\rm T}$. The re-weighted
$A\times\epsilon_{\mathrm{rec}}$ is used to correct the raw $p_{\rm T}$
distribution. The $A\times\epsilon_{\mathrm{rec}}$ is calculated for each
rapidity interval and multiplicity class considered in the analysis. The
$A\times\epsilon_{\mathrm{rec}}$ as a function of $p_{\rm T}$ shows a rapidity
dependence for a given multiplicity class, however, no significant
multiplicity dependence of $A\times\epsilon_{\mathrm{rec}}$ is observed for a
given rapidity interval.

###  2.3 Systematic uncertainties

The procedure to estimate the systematic uncertainties is similar to the one
adopted in previous analyses [26, 27]. The sources of systematic uncertainties
on the measured yield of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons are signal
extraction, track selection criteria, PID, global tracking efficiency,
uncertainty on the material budget of the ALICE detector, and the hadronic
interaction cross section in the detector material. A summary of the
systematic uncertainties on the $p_{\rm T}$ spectra is given in Table 1. The
uncertainty due to signal extraction is estimated from the variation of the
yields when varying the invariant mass fit range, the treatment of the Breit-
Wigner width in the fits, the mixed-event background normalization interval,
the choice of residual background function, and the method to determine the
combinatorial background. The fitting range is varied by 50 MeV$/c^{2}$ for
$\rm{K}^{\rm{*0}}$ and 10 MeV$/c^{2}$ for $\phi$. The normalization interval
of the mixed-event background is varied by 150 (50) MeV$/c^{2}$ with respect
to the default value for $\rm{K}^{\rm{*0}}$ ($\phi$). The width of
$\rm{K}^{\rm{*0}}$ and $\phi$ resonances is left as a free parameter in the
fit, instead of fixing it to the world-average value. For $\phi$ resonances,
the effect on the yield due to the variation of resolution parameter ($\sigma$
of the Gaussian function in the Voigtian distribution) is also considered. The
residual background is parameterized using first-order and third-order
polynomial functions for estimating its contributions to the systematic
uncertainties. The combinatorial background from the like-sign method is used
instead of the one from event mixing. The estimated systematic uncertainties
due to the yield extraction is 5.2$\%$ for $\rm{K}^{\rm{*0}}$ and 3.3$\%$ for
$\phi$. The systematic effects due to charged track selection have been
studied by varying the selection criteria on the number of crossed rows in the
TPC, the ratio of the numbers of TPC crossed rows to findable clusters, and
the DCA to the primary vertex of the collisions. The estimated uncertainties
due to the track selection is 2.5$\%$ for $\rm{K}^{\rm{*0}}$ and about 5$\%$
for the $\phi$ mesons. To estimate the systematic uncertainty due to the PID,
the selections on the d$E/$d$x$ and time-of-flight of the pions and kaons are
varied. Two momentum-independent selections: 2$\sigma_{\rm{TPC}}$ with
3$\sigma_{\rm{TOF}}$ and 2$\sigma_{\rm{TPC}}$ only, are used for both
$\rm{K}^{\rm{*0}}$ and $\phi$. The estimated systematic uncertainties are
3$\%$ for $\rm{K}^{\rm{*0}}$ and 1.7$\%$ for $\phi$. The uncertainty due to
the global tracking efficiency, description of the detector material budget in
the simulation, and the cross sections for hadronic interactions in the
material are taken from Ref. [26]. The total systematic uncertainty is taken
as the quadratic sum of all contributions leading to 7.5$\%$ for
$\rm{K}^{\rm{*0}}$ and 7.3$\%$ for $\phi$ mesons. No multiplicity and rapidity
dependence of the systematic uncertainties is observed. Therefore, the
systematic uncertainties on the $p_{\rm T}$ spectra determined for minimum-
bias events in the rapidity interval 0 $<y<$ 0.3 are assigned in all rapidity
intervals and multiplicity classes.

Table 1: Relative systematic uncertainties for $\rm{K}^{\rm{*0}}$ and $\phi$
yields in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV. The quoted
relative uncertainties are averaged over $p_{\rm T}$ in the range 0.8–16
GeV/$c$. The total systematic uncertainty is the sum in quadrature of the
uncertainties due to each source.

Systematic uncertainty |  $\rm{K}^{\rm{*0}}$ |  $\phi$
---|---|---
Yield extraction ($\%$) | 5.2 | 3.3
Track selection ($\%$) | 2.5 | 5.0
Particle identification ($\%$) | 3.0 | 1.7
Global tracking efficiency ($\%$) | 3.0 | 2.1
Material budget ($\%$) | 1.2 | 2.2
Hadronic Interaction ($\%$) | 1.9 | 2.4
Total ($\%$) | 7.5 | 7.3

The systematic uncertainties on $Y_{\rm{asym}}$ are estimated by considering
the same approaches and variations as for the corrected yields. The systematic
uncertainties due to signal extraction and PID are uncorrelated among
different rapidity intervals whereas the other sources of systematic
uncertainties such as track selections, global tracking uncertainties,
material budget and hadronic interactions are correlated and cancel out in the
$Y_{\rm{asym}}$ ratio. For the uncorrelated sources of uncertainty, the same
variations considered for the yields were studied by estimating their effects
on the $Y_{\rm{asym}}$ ratio. The resulting uncertainty was estimated to be
about 2.5$\%$ (2$\%$) for $\rm{K}^{\rm{*0}}$ ($\phi)$ mesons. No multiplicity
and rapidity dependence of the uncertainties is observed for $Y_{\rm{asym}}$.
Therefore, the systematic uncertainties determined for minimum-bias events are
assigned to the ratios in the different rapidity intervals and multiplicity
classes. The systematic uncertainties on the ratios
(d$N/$d$y$)/(d$N/$d$y)_{y=0}$ and $\langle p_{\rm T}\rangle$/$\langle p_{\rm
T}\rangle_{y=0}$ as a function of rapidity are calculated in a similar way as
for $Y_{\rm{asym}}$. The systematic uncertainties on (
d$N/$d$y$)/(d$N/$d$y)_{y=0}$ and $\langle p_{\rm T}\rangle$/$\langle p_{\rm
T}\rangle_{y=0}$ are 2.2$\%$ (2$\%$) and 1.2$\%$ (1$\%$) for
$\rm{K}^{\rm{*0}}$ ($\phi)$, respectively.

##  3 Results and discussion

The rapidity and multiplicity dependence results on the $p_{\rm T}$ spectra,
the d$N$/d$y$, the $\langle p_{\rm T}\rangle$, the $Y_{\mathrm{asym}}$, and
the ${Q}_{\mathrm{CP}}$ in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$
5.02 TeV are discussed. The measurements are also compared with various model
predictions.

###  3.1 Transverse momentum spectra

Figure 2 and Fig. 3 show the $p_{\rm T}$ spectra of $\rm{K}^{\rm{*0}}$ and
$\phi$ mesons in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV for
five rapidity intervals within -1.2 $<y<$ 0.3 and for two multiplicity classes
0–10$\%$ and 40–100$\%$, respectively. The ratios of the $p_{\rm T}$ spectra
in different rapidity intervals to that in the interval 0 $<y<$ 0.3 are
presented in the bottom panels of Fig. 2 and Fig. 3. The measured $p_{\rm T}$
spectra of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons in the 0–10$\%$ multiplicity
class show a rapidity dependence at low $p_{\rm T}$ ($<$ 5 GeV/$c$) indicating
that the production of these resonances is higher in the Pb-going direction
($y<$ 0) than in the p-going direction ($y>$ 0). For high $p_{\rm T}$, no
rapidity dependences are observed.

Figure 2:  Top panels: The transverse momentum spectra of $\rm{K}^{\rm{*0}}$
for five rapidity intervals within $-$1.2 $<y<$ 0.3 and for two multiplicity
classes (0–10$\%$, 40–100$\%$) in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$
= 5.02 TeV. The data for different rapidity intervals are scaled for better
visibility. Bottom panels: The ratios of the $p_{\rm T}$ spectra in various
rapidity intervals to that in the interval 0 $<y<$ 0.3 for a given
multiplicity class. The statistical and systematic uncertainties are shown as
bars and boxes around the data points, respectively. Figure 3:  Top panels:
The transverse momentum spectra of $\phi$ for five rapidity intervals within
$-$1.2 $<y<$ 0.3 and for two multiplicity classes (0–10$\%$, 40–100$\%$) in
p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The data for different
rapidity intervals are scaled for better visibility. Bottom panels: The ratios
of the $p_{\rm T}$ spectra in various rapidity intervals to that in the
interval 0 $<y<$ 0.3 for a given multiplicity class. The statistical and
systematic uncertainties are shown as bars and boxes around the data points,
respectively.

###  3.2 Integrated particle yield and mean transverse momentum

The d$N/$d$y$ and the $\langle p_{\rm T}\rangle$ are obtained from the
transverse momentum spectra in the measured $p_{\rm T}$ interval and using a
fit function to account for the contribution of $\rm{K}^{\rm{*0}}$ and $\phi$
mesons in unmeasured regions. The spectra are fitted with a Lévy-Tsallis
function [55] and the fit function is extrapolated to unmeasured regions at
low $p_{\rm T}$ ( $<$ 0.8 GeV/$c$). The integral of the fit function in the
extrapolated region accounts for 33$\%$ (39$\%$) of the total yield in the
0–10$\%$ (40–100$\%$) multiplicity class for both $\rm{K}^{\rm{*0}}$ and
$\phi$ mesons. The contribution of the extrapolated yield at low $p_{\rm T}$
is the same for all rapidity intervals. The contribution of the yield in the
unmeasured region at high $p_{\rm T}$ ( $>$ 16 GeV/$c$) is negligible for both
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons. The extrapolated yield contribution at
low $p_{\rm T}$ obtained with different fitting functions (i.e.,
$m_{\mathrm{T}}$-exponential, Bose-Einstein and Boltzmann-Gibbs Blast-Wave
function [56]) and that obtained with the default Lévy-Tsallis function is
5$\%$ (8$\%$) for the 0–10$\%$ (40–100$\%$) included as the systematic
uncertainties in the d$N/$d$y$ and it varies by 2–5 $\%$ for the $\langle
p_{\mathrm{T}}\rangle$. In Fig. 4 the d$N/$d$y$ (top panels) and $\langle
p_{\rm T}\rangle$ (bottom panels) of $\rm{K}^{\rm{*0}}$ (left) and $\phi$
(right) mesons are shown as a function of $y$ for minimum-bias p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The central values of the d$N/$d$y$ of
both $\rm{K}^{\rm{*0}}$ and $\phi$ mesons decrease slightly from the rapidity
interval $-$1.2 $<y<$ $-$0.9 to 0 $<y<$ 0.3 even though within the systematic
uncertainties all the data points are compatible among each other.
Nevertheless, considering that the systematic uncertainties are mostly
correlated among the rapidity intervals, the measured d$N/$d$y$ values suggest
a decreasing trend with increasing $y$ in the rapidity interval covered by the
measurement. The $\langle p_{\rm T}\rangle$ is constant as a function of
rapidity for both $\rm{K}^{\rm{*0}}$ and $\phi$ resonances.

Figure 4: The $p_{\rm T}$ integrated yield (d$N/\mathrm{d}y$) (top panels) and
mean transverse momentum ($\langle p_{\mathrm{T}}\rangle$) (bottom panels) for
$\rm{K}^{\rm{*0}}$ (left) and $\phi$ (right) mesons as a function of $y$
measured for the multiplicity class 0-100$\%$ in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV. The predictions from EPOS-LHC [35],
EPOS3 with and without UrQMD [38, 39], DPMJET [40], HIJING [41], and
PYTHIA8/Angantyr [42] are shown as different curves. The statistical
uncertainties are represented as bars whereas the boxes indicate total
systematic uncertainties.

The model predictions from EPOS-LHC [35], EPOS3 with and without UrQMD [38,
39], DPMJET [40], HIJING [41], and PYTHIA8/Angantyr [42] are also shown in the
Fig. 4. In general, the models show a similar trend with rapidity as the data
except EPOS3 with and without UrQMD for $\langle p_{\rm T}\rangle$, which
shows a pronounced decreasing trend with rapidity. All the model predictions
shown in Fig. 4 underestimate the $\langle p_{\rm T}\rangle$ of both meson
species. For the d$N/$d$y$, HIJING and EPOS3 with and without UrQMD
overpredict the measured values for both $\rm{K}^{\rm{*0}}$ and $\phi$, while
PYTHIA8/Angantyr overpredicts the $\rm{K}^{\rm{*0}}$ and underpredicts the
$\phi$ yield. EPOS-LHC provides the best overall description of the d$N/$d$y$
and $\langle p_{\rm T}\rangle$ measurements for $\rm{K}^{\rm{*0}}$ and $\phi$
mesons. The $\langle p_{\rm T}\rangle$ also shows a flat behavior as a
function of rapidity for all the considered multiplicity classes as it can be
seen in Fig. 10 of Appendix A.

A similar behavior in the average transverse kinetic energy as a function of
rapidity for strange hadrons was reported in Ref. [16]. The rapidity
dependence of d$N/$d$y$ and $\langle p_{\rm T}\rangle$ for $\rm{K}^{\rm{*0}}$
and $\phi$ mesons in the multiplicity class 0–100$\%$ is further studied by
dividing the d$N/$d$y$ and $\langle p_{\rm T}\rangle$ values in a given
rapidity interval by the corresponding values at $y=0$, as shown in Fig. 5.
The d$N/$d$y$ and $\langle p_{\rm T}\rangle$ value at $y=0$ is computed from
the $p_{\rm T}$ spectrum measured in the rapidity interval -0.3$<y<$0.3. The
systematic uncertainties on these ratios are estimated by studying the effects
of the variations directly on the ratios as discussed in Section 2.3. This
procedure takes into account the correlation of the systematic uncertainties
across rapidity bins: as a result, these ratios have smaller systematic
uncertainties than those on the d$N/$d$y$ and $\langle p_{\rm T}\rangle$, and
allow for a better insight into the $y$ dependence. The ratio
(d$N/$d$y$)/(d$N/$d$y)_{y=0}$ decreases with rapidity, whereas $\langle
p_{\mathrm{T}}\rangle$/$\langle p_{\mathrm{T}}\rangle_{y=0}$ shows a flat
behavior within uncertainties as a function of rapidity for $\rm{K}^{\rm{*0}}$
and $\phi$ mesons. The measurements are compared with various model
predictions. The predictions from HIJING qualitatively reproduce the trend and
are the closest to the data for both $\rm{K}^{\rm{*0}}$ and $\phi$. The
predictions from PYTHIA8/Angantyr, DPMJET, EPOS-LHC, EPOS3 with and without
UrQMD show a decreasing trend of (d$N/$d$y$)/(d$N/$d$y)_{y=0}$ with increasing
$y$, but the rapidity dependence is less pronounced than the one in data, as
it can be seen by the fact that they all tend to underestimate the measured
yield ratios in the lowest rapidity intervals, especially for
$\rm{K}^{\rm{*0}}$ meson.

For $\langle p_{\mathrm{T}}\rangle$/$\langle p_{\mathrm{T}}\rangle_{y=0}$ as a
function of $y$, also shown in Fig. 5, EPOS3 with and without UrQMD
overestimate the measurements at low $y$ and predict a marked decreasing trend
of $\langle p_{\mathrm{T}}\rangle$/$\langle p_{\mathrm{T}}\rangle_{y=0}$ with
rapidity, which is not supported by the data. From the other models, less
pronounced trends are expected, which are consistent with the data. In
particular, HIJING predicts a slightly decreasing $\langle
p_{\mathrm{T}}\rangle$/$\langle p_{\mathrm{T}}\rangle_{y=0}$ with increasing
rapidity, while PYTHIA8/Angantyr, DPMJET, and EPOS-LHC predict a slightly
increasing trend.

Similar studies of the ratio $\langle p_{\mathrm{T}}\rangle$/$\langle
p_{\mathrm{T}}\rangle_{y=0}$ of charged hadrons in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV compared with the predictions of
hydrodynamics and color-glass condensate (CGC) model were reported in [33].
Predictions from hydrodynamic calculations show a decrease in $\langle p_{\rm
T}\rangle$ with rapidity, whereas CGC predicts an increase in $\langle p_{\rm
T}\rangle$ with rapidity [33], while the data are flat within uncertainties.
The d$N/$d$y$ and $\langle p_{\rm T}\rangle$ increase with multiplicity at
midrapidity as observed for light-flavor hadrons and resonances in pp and p–Pb
collisions[56, 26, 27]. A similar behavior is observed in this article for
$\rm{K}^{\rm{*0}}$ and $\phi$ in all the different rapidity intervals shown in
Fig.10 in Appendix A.

Figure 5: The $p_{\rm T}$ integrated yield (d$N/\mathrm{d}y$) (upper panels)
and mean transverse momentum $\left(\langle p_{\rm T}\rangle\right)$ (bottom
panels) for $\rm{K}^{\rm{*0}}$ (left) and $\phi$ (right) mesons as a function
of $y$, divided by the d$N/\mathrm{d}y$ and $\langle p_{\mathrm{T}}\rangle$ at
$y=0$ for the multiplicity class 0–100$\%$ in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV. The predictions from EPOS-LHC [35],
EPOS3 with and without UrQMD [38, 39], DPMJET [40], HIJING [41], and
PYTHIA8/Angantyr [42] are shown as different curves. The statistical
uncertainties are represented as bars whereas the boxes indicate total
systematic uncertainties.

###  3.3 Rapidity asymmetry

The rapidity asymmetry ($Y_{\mathrm{asym}}$) is calculated from
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons yields in -0.3$<y<$0 and 0$<y<$0.3, as
defined by Equation 1. Figure 6 shows the $Y_{\mathrm{asym}}$ of
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons in the measured $p_{\rm T}$ intervals for
various multiplicity classes in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ =
5.02 TeV.

Figure 6: Rapidity asymmetry ($Y_{\mathrm{asym}}$) of K∗0 (red circles) and
$\phi$ (blue squares) meson production as a function of $p_{\mathrm{T}}$ in
the rapidity range 0 $<$ $|y|$ $<$ 0.3 for various multiplicity classes in
p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The statistical
uncertainties are shown as bars whereas the boxes represent the systematic
uncertainties on the measurements.

The $Y_{\mathrm{asym}}$ values for $\rm{K}^{\rm{*0}}$ and $\phi$ as a function
of $p_{\rm T}$ are consistent within uncertainties for all multiplicity
classes. The $Y_{\mathrm{asym}}$ values deviate from unity at low $p_{\rm T}$
( $<$ 5 GeV/$c$), suggesting the presence of a rapidity dependence in the
nuclear effects. The deviations are more significant for events with high
multiplicity. The $Y_{\mathrm{asym}}$ values are consistent with unity at high
$p_{\rm T}$ ( $>$ 5 GeV/$c$) for all multiplicity classes, suggesting the
absence of nuclear effects at high $p_{\rm T}$ for the production of
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons in p–Pb collisions. Similar results have
been reported for charged hadrons, pions, protons in d–Au collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV by the STAR Collaboration [18] and for
charged hadrons and multi-strange hadrons in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV by the CMS Collaboration as discussed in
Refs. [16, 17]. Figure 7 shows the comparison of the measured
$Y_{\mathrm{asym}}$ for $\rm{K}^{\rm{*0}}$ and $\phi$ mesons as a function of
$p_{\rm T}$ in minimum-bias events (0-100$\%$) with the model predictions from
EPOS-LHC, HIJING with and without shadowing, DPMJET, PYTHIA8/Angantyr, and
EPOS3 with and without UrQMD.

Figure 7: The comparison of experimental results of $Y_{\mathrm{asym}}$ for
$\rm{K}^{\rm{*0}}$ and $\phi$ meson production as a function of
$p_{\mathrm{T}}$ in the rapidity range 0 $<|y|<$ 0.3 with the model
predictions from EPOS-LHC [35], EPOS3 with and without UrQMD [38, 39], DPMJET
[40], HIJING [41], and PYTHIA8/Angantyr [42]. Data points are shown with blue
markers, and model predictions are shown by different color bands, where bands
represent the statistical uncertainity of the model. The statistical
uncertainties on the data points are represented as bars whereas the boxes
indicate total systematic uncertainties.

HIJING with and without shadowing, and EPOS3 with and without UrQMD describe
the measured $Y_{\mathrm{asym}}$ at low $p_{\rm T}$ within uncertainties, but
they significantly overestimate the data at high $p_{\rm T}$, predicting an
increasing trend with $p_{\rm T}$ (more pronounced for $\rm{K}^{\rm{*0}}$ than
for $\phi$) that is not supported by the measurements, which are consistent
with a flat or decreasing trend for both meson species. Model predictions from
EPOS-LHC, PYTHIA8/Angantyr, and DPMJET for $\rm{K}^{\rm{*0}}$ and DPMJET for
$\phi$ at high $p_{\rm T}$ are in agreement with the data within
uncertainties.

###  3.4 Nuclear modification factor

The nuclear modification factor ${Q}_{\mathrm{CP}}$ is calculated from the
$\rm{K}^{\rm{*0}}$ and $\phi$ yields normalized to $\langle
N_{\mathrm{coll}}\rangle$ in high multiplicity (central) and low multiplicity
(peripheral) collisions, as defined by Equation 2. Figure 8 shows the
${Q}_{\mathrm{CP}}$ of $\rm{K}^{\rm{*0}}$ (red circles) and $\phi$ (blue
squares) mesons as a function of $p_{\rm T}$ for 0–10$\%$ / 40–100$\%$ (top
panels) and 10–40$\%$ / 40–100$\%$ (bottom panels) in various rapidity
intervals within the range $-$1.2 $<$ $y$ $<$ 0.3 for p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The ${Q}_{\mathrm{CP}}$ of $\phi$ mesons
seems to be slightly higher than the $\rm{K}^{\rm{*0}}$ one for the ratio of
0–10$\%$ / 40–100$\%$, however, the results for the two meson species are
consistent within uncertainties for the ratio 10–40$\%$ / 40–100$\%$ for all
measured rapidity intervals. An enhancement at intermediate $p_{\rm T}$ (2.2
$<p_{\rm T}<$ 5.0 GeV/$c$), reminiscent of the Cronin effect, is seen for
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons in the ${Q}_{\mathrm{CP}}$. This
enhancement is more pronounced at high negative rapidity, i.e., in the Pb-
going direction, and for high multiplicity events. The more pronounced Cronin-
like enhancement for the 0-10$\%$ multiplicity class suggests that multiple
scattering effects are more relevant for high multiplicity (central)
collisions. At high $p_{\rm T}$ ($>$ 5 GeV/$c$), the $Q_{\mathrm{CP}}$ values
are greater than unity, which is a known feature of $Q_{\mathrm{pPb}}$ 111It
is defined as the ratio of the yield per equivalent number of nucleon–nucleon
collisions at a given centrality or multiplicity class in p–Pb collisions to
the yield in minimum-bias pp collisions at the same center-of-mass energy. and
$Q_{\mathrm{CP}}$ when the centrality or multiplicity classes are defined with
the V0 detector, and it is interpreted as a selection bias due to the
multiplicity estimator [51]. The results for $\rm{K}^{\rm{*0}}$ and $\phi$
mesons are consistent between each other within uncertainties.

Figure 8: The ${Q}_{\mathrm{CP}}$ of $\rm{K}^{\rm{*0}}$ (red circles) and
$\phi$ (blue squares) mesons as a function of $p_{\rm T}$ for 0–10$\%$ /
40–100$\%$ (top panels) and 10–40$\%$ / 40–100$\%$ (bottom panels) in various
rapidity intervals within the range $-$1.2 $<$ $y$ $<$ 0.3 in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The statistical and systematic
uncertainties are represented by vertical bars and boxes, respectively.

To quantify the rapidity dependence of the nuclear modification factor, the
${Q}_{\mathrm{CP}}$ values of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons for
intermediate $p_{\rm T}$ (2.2 $<p_{\rm T}<$ 5.0 GeV/$c$) are shown as a
function of rapidity in Fig. 9. The values of ${Q}_{\mathrm{CP}}$ at
intermediate $p_{\rm T}$ show a faster decrease from the rapidity interval
$-$1.2 $<y<$ $-$ 0.9 to 0 $<y<$ 0.3 for 0–10$\%$ / 40–100$\%$ than for
10–40$\%$ / 40–100$\%$, indicating a stronger rapidity dependence of the
Cronin-like enhancement in events with high multiplicity. The stronger
rapidity dependence for 0–10$\%$ / 40–100$\%$ can be inferred from the slope
parameter ($\alpha$) of the linear function fit to the ${Q}_{\mathrm{CP}}$ of
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons reported in Fig. 9. The slope of the
$\phi$ meson ${Q}_{\mathrm{CP}}$ is slightly larger than the
$\rm{K}^{\rm{*0}}$ one. A similar conclusion on the $\eta$ dependence of
nuclear modification factors of charged hadrons was reported by the BRAHMS
Collaboration [7].

Figure 9: The $Q_{\mathrm{CP}}$ of $\rm{K}^{\rm{*0}}$ (red circles) and $\phi$
(blue squares) mesons as a function of rapidity for 0–10$\%$ / 40–100$\%$
(solid markers) and 10–40$\%$ / 40–100$\%$ (open markers) in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV. The solid and doted lines represents
the linear fit to data. The statistical and systematic uncertainties are
represented by vertical bars and boxes on the measurements, respectively.

##  4 Summary

The transverse momentum differential yields of $\rm{K}^{\rm{*0}}$ and $\phi$
mesons have been measured in the rapidity interval $-$1.2 $<y<$ 0.3 for
various multiplicity classes over the transverse momentum range 0.8 $<p_{\rm
T}<$16 GeV/$c$ in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV
with the ALICE detector. The $p_{\rm T}$ spectra of $\rm{K}^{\rm{*0}}$ and
$\phi$ mesons show a multiplicity and rapidity dependence at low $p_{\rm T}$,
whereas the spectral shapes are similar for all multiplicity classes and
rapidity intervals at high $p_{\rm T}$ ($>$ 5 GeV/${c}$). This suggests that
nuclear effects influence $\rm{K}^{\rm{*0}}$ and $\phi$ meson production at
low $p_{\rm T}$. The (d$N/$d$y$)/(d$N/$d$y)_{y=0}$ ratios decreases with
increasing rapidity in the measured interval -1.2 $<y<$0.3, whereas the
average transverse momentum $\left(\langle p_{\rm T}\rangle\right)$ and the
$\langle p_{\rm T}\rangle$/$\langle p_{\rm T}\rangle_{y=0}$ ratios show a flat
behavior for both $\rm{K}^{\rm{*0}}$ and $\phi$ mesons. The rapidity
dependence of $\mathrm{d}N/\mathrm{d}y$, $\langle p_{\rm T}\rangle$ and their
ratios with respect to the corresponding values at $y$ $\mathrm{=0}$ are
compared with model predictions for minimum-bias events. The EPOS-LHC model,
which includes parameterized flow, provides the best description for the
magnitudes of $\rm{K}^{\rm{*0}}$ and $\phi$ $\mathrm{d}N/\mathrm{d}y$ and
$\langle p_{\rm T}\rangle$, whereas HIJING predictions are in closest
agreement with the measured rapidity dependence, which is studied via the
ratios (d$N/$d$y$)/(d$N/$d$y)_{y=0}$ and $\langle p_{\rm T}\rangle$/$\langle
p_{\rm T}\rangle_{y=0}$. The $Y_{\mathrm{asym}}$ ratios for $\rm{K}^{\rm{*0}}$
and $\phi$ mesons as a function of $p_{\rm T}$ show deviations from unity at
low $p_{\rm T}$ for high multiplicity events, while, their values are
consistent with unity within uncertainties at high $p_{\rm T}$ in the measured
multiplicity and rapidity intervals. The $Y_{\mathrm{asym}}$ ratios of
$\rm{K}^{\rm{*0}}$ and $\phi$ mesons are found to be consistent between each
other within uncertainties in the measured kinematic region. The measured
deviations of $Y_{\mathrm{asym}}$ from unity at low $p_{\rm T}$ suggest the
presence of rapidity dependent nuclear effects such as multiple scattering,
nuclear shadowing, parton saturation, and energy loss in cold nuclear matter.
None of the models presented here is able to describe the $Y_{\mathrm{asym}}$
of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons at low $p_{\rm T}$. The nuclear
modification factors between the central and peripheral collisions
${Q}_{\mathrm{CP}}$ for $\rm{K}^{\rm{*0}}$ and $\phi$ mesons as a function of
$p_{\rm T}$ show a bump, with a maximum around $p_{\rm T}$ =3 GeV/$c$,
suggestive of the Cronin effect. This Cronin-like enhancement is more
pronounced for large negative rapidities (in the Pb-going direction) and for
more central (higher multiplicity) collisions. The measurements reported in
this paper confirm that nuclear effects play an important role in particle
production in p–Pb collisions at the LHC energies. They will contribute, along
with previous and upcoming measurements of other hadron species, to constrain
models and event generators.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: Marie Skłodowska Curie, Strong 2020 - Horizon 2020, European Research Council (grant nos. 824093, 896850, 950692), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland; Programa de Apoyos para la Superación del Personal Académico, UNAM, Mexico.

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##  Appendix A Multiplicity and rapidity dependence of d$N/\mathrm{d}y$ and
$\langle{p}_{\mathrm{T}}\rangle$

Figure 10 shows the multiplicity dependence of the d$N/\mathrm{d}y$ and
$\langle{p}_{\mathrm{T}}\rangle$ of $\rm{K}^{\rm{*0}}$ and $\phi$ mesons as a
function of $y$ in p–Pb collisions at $\sqrt{{s}_{\mathrm{NN}}}$ = 5.02 TeV.
The d$N/\mathrm{d}y$ and the $\langle p_{\rm T}\rangle$ increase with
multiplicity for a given rapidity interval. The d$N/\mathrm{d}y$ shows a weak
rapidity dependence with large uncertainties, and suggesting a more pronounced
dependence for events in the highest multiplicity class (0–10$\%$). The
$\langle p_{\rm T}\rangle$ shows a flat behavior as a function of rapidity for
all multiplicity classes in the measured rapidity interval. Similar behavior
in the average transverse kinetic energy as a function of rapidity for strange
hadrons was reported in Ref. [16].

Figure 10: The $p_{\rm T}$ integrated yield (d$N/\mathrm{d}y$) (top panels)
and mean transverse momentum $\left(\langle p_{\rm T}\rangle\right)$ (bottom
panels) for $\rm{K}^{\rm{*0}}$ (left panels) and $\phi$ (right panels) mesons
as a function of $y$ measured for the multiplicity classes 0–10$\%$, 10–40$\%$
and 40–100$\%$ in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 TeV.
The statistical uncertainties are represented as bars whereas boxes indicate
the total systematic uncertainties on the measurements.

##  Appendix B The ALICE Collaboration

S. Acharya 124,131, D. Adamová 86, A. Adler69, G. Aglieri Rinella 32, M.
Agnello 29, N. Agrawal 50, Z. Ahammed 131, S. Ahmad 15, S.U. Ahn 70, I. Ahuja
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136, A. Augustinus 32, R. Averbeck 98, S. Aziz 72, M.D. Azmi 15, A. Badalà 52,
Y.W. Baek 40, X. Bai 98, R. Bailhache 63, Y. Bailung 47, R. Bala 91, A.
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Bhat91, M.A. Bhat 4, B. Bhattacharjee 41, L. Bianchi 24, N. Bianchi 48, J.
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63, G. Boca 21,54, F. Bock 87, T. Bodova 20, A. Bogdanov139, S. Boi 22, J. Bok
57, L. Boldizsár 135, A. Bolozdynya139, M. Bombara 37, P.M. Bond 32, G. Bonomi
130,54, H. Borel 127, A. Borissov 139, H. Bossi 136, E. Botta 24, L. Bratrud
63, P. Braun-Munzinger 98, M. Bregant 109, M. Broz 35, G.E. Bruno 97,31, M.D.
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32, S. Costanza 21,54, J. Crkovská 95, P. Crochet 124, R. Cruz-Torres 74, E.
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Y. Ding 125,6, R. Divià 32, D.U. Dixit 18, Ø. Djuvsland20, U. Dmitrieva 139,
A. Dobrin 62, B. Dönigus 63, A.K. Dubey 131, J.M. Dubinski132, A. Dubla 98, S.
Dudi 90, P. Dupieux 124, M. Durkac105, N. Dzalaiova12, T.M. Eder 134, R.J.
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I. Fokin 95, S. Fokin 139, E. Fragiacomo 56, E. Frajna 135, U. Fuchs 32, N.
Funicello 28, C. Furget 73, A. Furs 139, J.J. Gaardhøje 83, M. Gagliardi 24,
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79, A. Kurepin 139, A.B. Kurepin 139, S. Kushpil 86, J. Kvapil 100, M.J. Kweon
57, J.Y. Kwon 57, Y. Kwon 137, S.L. La Pointe 38, P. La Rocca 26, Y.S. Lai74,
A. Lakrathok104, M. Lamanna 32, R. Langoy 118, P. Larionov 48, E. Laudi 32, L.
Lautner 32,96, R. Lavicka 102, T. Lazareva139, R. Lea 130,54, J. Lehrbach 38,
R.C. Lemmon 85, I. León Monzón 108, M.M. Lesch 96, E.D. Lesser 18, M.
Lettrich96, P. Lévai 135, X. Li10, X.L. Li6, J. Lien 118, R. Lietava 100, B.
Lim 16, S.H. Lim 16, V. Lindenstruth 38, A. Lindner45, C. Lippmann 98, A. Liu
18, D.H. Liu 6, J. Liu 116, I.M. Lofnes 20, V. Loginov139, C. Loizides 87, P.
Loncar 33, J.A. Lopez 95, X. Lopez 124, E. López Torres 7, P. Lu 98,117, J.R.
Luhder 134, M. Lunardon 27, G. Luparello 56, Y.G. Ma 39, A. Maevskaya139, M.
Mager 32, T. Mahmoud42, A. Maire 126, M. Malaev 139, N.M. Malik 91, Q.W.
Malik19, S.K. Malik 91, L. Malinina VII,140, D. Mal’Kevich139, D. Mallick 80,
N. Mallick 47, G. Mandaglio 30,52, V. Manko 139, F. Manso 124, V. Manzari 49,
Y. Mao 6, G.V. Margagliotti 23, A. Margotti 50, A. Marín 98, C. Markert 107,
M. Marquard63, N.A. Martin95, P. Martinengo 32, J.L. Martinez113, M.I.
Martínez 44, G. Martínez García 103, S. Masciocchi 98, M. Masera 24, A. Masoni
51, L. Massacrier 72, A. Mastroserio 128,49, A.M. Mathis 96, O. Matonoha 75,
P.F.T. Matuoka109, A. Matyja 106, C. Mayer 106, A.L. Mazuecos 32, F. Mazzaschi
24, M. Mazzilli 32, J.E. Mdhluli 120, A.F. Mechler63, Y. Melikyan 139, A.
Menchaca-Rocha 66, E. Meninno 102,28, A.S. Menon 113, M. Meres 12, S.
Mhlanga112,67, Y. Miake122, L. Micheletti 55, L.C. Migliorin125, D.L. Mihaylov
96, K. Mikhaylov 140,139, A.N. Mishra 135, D. Miśkowiec 98, A. Modak 4, A.P.
Mohanty 58, B. Mohanty 80, M. Mohisin Khan IV,15, M.A. Molander 43, Z.
Moravcova 83, C. Mordasini 96, D.A. Moreira De Godoy 134, I. Morozov 139, A.
Morsch 32, T. Mrnjavac 32, V. Muccifora 48, E. Mudnic33, S. Muhuri 131, J.D.
Mulligan 74, A. Mulliri22, M.G. Munhoz 109, R.H. Munzer 63, H. Murakami 121,
S. Murray 112, L. Musa 32, J. Musinsky 59, J.W. Myrcha132, B. Naik 120, R.
Nair 79, B.K. Nandi46, R. Nania 50, E. Nappi 49, A.F. Nassirpour 75, A. Nath
95, C. Nattrass 119, A. Neagu19, A. Negru123, L. Nellen 64, S.V. Nesbo34, G.
Neskovic 38, D. Nesterov139, B.S. Nielsen 83, E.G. Nielsen 83, S. Nikolaev
139, S. Nikulin 139, V. Nikulin 139, F. Noferini 50, S. Noh 11, P. Nomokonov
140, J. Norman 116, N. Novitzky 122, P. Nowakowski 132, A. Nyanin 139, J.
Nystrand 20, M. Ogino 76, A. Ohlson 75, V.A. Okorokov 139, J. Oleniacz 132,
A.C. Oliveira Da Silva 119, M.H. Oliver 136, A. Onnerstad 114, C. Oppedisano
55, A. Ortiz Velasquez 64, A. Oskarsson75, J. Otwinowski 106, M. Oya93, K.
Oyama 76, Y. Pachmayer 95, S. Padhan46, D. Pagano 130,54, G. Paić 64, A.
Palasciano 49, S. Panebianco 127, J. Park 57, J.E. Parkkila 32,114, S.P.
Pathak113, R.N. Patra91, B. Paul 22, H. Pei 6, T. Peitzmann 58, X. Peng 6,
L.G. Pereira 65, H. Pereira Da Costa 127, D. Peresunko 139, G.M. Perez 7, S.
Perrin 127, Y. Pestov139, V. Petráček 35, V. Petrov 139, M. Petrovici 45, R.P.
Pezzi 103,65, S. Piano 56, M. Pikna 12, P. Pillot 103, O. Pinazza 50,32, L.
Pinsky113, C. Pinto 96,26, S. Pisano 48, M. Płoskoń 74, M. Planinic89, F.
Pliquett63, M.G. Poghosyan 87, S. Politano 29, N. Poljak 89, A. Pop 45, S.
Porteboeuf-Houssais 124, J. Porter 74, V. Pozdniakov 140, S.K. Prasad 4, S.
Prasad 47, R. Preghenella 50, F. Prino 55, C.A. Pruneau 133, I. Pshenichnov
139, M. Puccio 32, S. Qiu 84, L. Quaglia 24, R.E. Quishpe113, S. Ragoni 100,
A. Rakotozafindrabe 127, L. Ramello 129,55, F. Rami 126, S.A.R. Ramirez 44,
T.A. Rancien73, R. Raniwala 92, S. Raniwala92, S.S. Räsänen 43, R. Rath 47, I.
Ravasenga 84, K.F. Read 87,119, A.R. Redelbach 38, K. Redlich V,79, A.
Rehman20, P. Reichelt63, F. Reidt 32, H.A. Reme-Ness 34, Z. Rescakova37, K.
Reygers 95, A. Riabov 139, V. Riabov 139, R. Ricci 28, T. Richert75, M.
Richter19, W. Riegler 32, F. Riggi 26, C. Ristea 62, M. Rodríguez Cahuantzi
44, K. Røed 19, R. Rogalev 139, E. Rogochaya 140, T.S. Rogoschinski 63, D.
Rohr 32, D. Röhrich 20, P.F. Rojas44, S. Rojas Torres 35, P.S. Rokita 132, F.
Ronchetti 48, A. Rosano 30,52, E.D. Rosas64, A. Rossi 53, A. Roy 47, P. Roy99,
S. Roy46, N. Rubini 25, O.V. Rueda 75, D. Ruggiano 132, R. Rui 23, B.
Rumyantsev140, P.G. Russek 2, R. Russo 84, A. Rustamov 81, E. Ryabinkin 139,
Y. Ryabov 139, A. Rybicki 106, H. Rytkonen 114, W. Rzesa 132, O.A.M. Saarimaki
43, R. Sadek 103, S. Sadovsky 139, J. Saetre 20, K. Šafařík 35, S.K. Saha 131,
S. Saha 80, B. Sahoo 46, P. Sahoo46, R. Sahoo 47, S. Sahoo60, D. Sahu 47, P.K.
Sahu 60, J. Saini 131, K. Sajdakova37, S. Sakai 122, M.P. Salvan 98, S.
Sambyal 91, T.B. Saramela109, D. Sarkar 133, N. Sarkar131, P. Sarma41, V.
Sarritzu 22, V.M. Sarti 96, M.H.P. Sas 136, J. Schambach 87, H.S. Scheid 63,
C. Schiaua 45, R. Schicker 95, A. Schmah95, C. Schmidt 98, H.R. Schmidt94,
M.O. Schmidt 32, M. Schmidt94, N.V. Schmidt 87,63, A.R. Schmier 119, R.
Schotter 126, J. Schukraft 32, K. Schwarz98, K. Schweda 98, G. Scioli 25, E.
Scomparin 55, J.E. Seger 14, Y. Sekiguchi121, D. Sekihata 121, I. Selyuzhenkov
98,139, S. Senyukov 126, J.J. Seo 57, D. Serebryakov 139, L. Šerkšnytė 96, A.
Sevcenco 62, T.J. Shaba 67, A. Shabanov139, A. Shabetai 103, R. Shahoyan32, W.
Shaikh99, A. Shangaraev 139, A. Sharma90, D. Sharma46, H. Sharma106, M. Sharma
91, N. Sharma90, S. Sharma 91, U. Sharma 91, A. Shatat 72, O. Sheibani113, K.
Shigaki 93, M. Shimomura77, S. Shirinkin 139, Q. Shou 39, Y. Sibiriak 139, S.
Siddhanta 51, T. Siemiarczuk 79, T.F. Silva 109, D. Silvermyr 75, T.
Simantathammakul104, R. Simeonov 36, G. Simonetti32, B. Singh91, B. Singh 96,
R. Singh 80, R. Singh 91, R. Singh 47, V.K. Singh 131, V. Singhal 131, T.
Sinha 99, B. Sitar 12, M. Sitta 129,55, T.B. Skaali19, G. Skorodumovs 95, M.
Slupecki 43, N. Smirnov 136, R.J.M. Snellings 58, E.H. Solheim 19, C.
Soncco101, J. Song 113, A. Songmoolnak104, F. Soramel 27, S. Sorensen 119, R.
Spijkers 84, I. Sputowska 106, J. Staa 75, J. Stachel 95, I. Stan 62, P.J.
Steffanic 119, S.F. Stiefelmaier 95, D. Stocco 103, I. Storehaug 19, M.M.
Storetvedt 34, P. Stratmann 134, S. Strazzi 25, C.P. Stylianidis84, A.A.P.
Suaide 109, C. Suire 72, M. Sukhanov 139, M. Suljic 32, V. Sumberia 91, S.
Sumowidagdo 82, S. Swain60, A. Szabo12, I. Szarka 12, U. Tabassam13, S.F.
Taghavi 96, G. Taillepied 98,124, J. Takahashi 110, G.J. Tambave 20, S. Tang
124,6, Z. Tang 117, J.D. Tapia Takaki VI,115, N. Tapus123, M.G. Tarzila45, A.
Tauro 32, A. Telesca 32, L. Terlizzi 24, C. Terrevoli 113, G. Tersimonov3, S.
Thakur 131, D. Thomas 107, R. Tieulent 125, A. Tikhonov 139, A.R. Timmins 113,
M. Tkacik105, T. Tkacik 105, A. Toia 63, N. Topilskaya 139, M. Toppi 48, F.
Torales-Acosta18, T. Tork 72, A.G. Torres Ramos 31, A. Trifiró 30,52, A.S.
Triolo 30,52, S. Tripathy 50, T. Tripathy 46, S. Trogolo 32, V. Trubnikov 3,
W.H. Trzaska 114, T.P. Trzcinski 132, R. Turrisi 53, T.S. Tveter 19, K.
Ullaland 20, B. Ulukutlu 96, A. Uras 125, M. Urioni 54,130, G.L. Usai 22, M.
Vala37, N. Valle 21, S. Vallero 55, L.V.R. van Doremalen58, M. van Leeuwen 84,
C.A. van Veen 95, R.J.G. van Weelden 84, P. Vande Vyvre 32, D. Varga 135, Z.
Varga 135, M. Varga-Kofarago 135, M. Vasileiou 78, A. Vasiliev 139, O. Vázquez
Doce 96, V. Vechernin 139, E. Vercellin 24, S. Vergara Limón44, L. Vermunt 58,
R. Vértesi 135, M. Verweij 58, L. Vickovic33, Z. Vilakazi120, O. Villalobos
Baillie 100, G. Vino 49, A. Vinogradov 139, T. Virgili 28, V. Vislavicius83,
A. Vodopyanov 140, B. Volkel 32, M.A. Völkl 95, K. Voloshin139, S.A. Voloshin
133, G. Volpe 31, B. von Haller 32, I. Vorobyev 96, N. Vozniuk 139, J.
Vrláková 37, B. Wagner20, C. Wang 39, D. Wang39, M. Weber 102, A. Wegrzynek
32, F.T. Weiglhofer38, S.C. Wenzel 32, J.P. Wessels 134, S.L. Weyhmiller 136,
J. Wiechula 63, J. Wikne 19, G. Wilk 79, J. Wilkinson 98, G.A. Willems 134, B.
Windelband95, M. Winn 127, J.R. Wright 107, W. Wu39, Y. Wu 117, R. Xu 6, A.K.
Yadav 131, S. Yalcin71, Y. Yamaguchi93, K. Yamakawa93, S. Yang20, S. Yano93,
Z. Yin 6, I.-K. Yoo 16, J.H. Yoon 57, S. Yuan20, A. Yuncu 95, V. Zaccolo 23,
C. Zampolli 32, H.J.C. Zanoli58, F. Zanone 95, N. Zardoshti 32,100, A.
Zarochentsev 139, P. Závada 61, N. Zaviyalov139, M. Zhalov 139, B. Zhang 6, S.
Zhang 39, X. Zhang 6, Y. Zhang117, M. Zhao 10, V. Zherebchevskii 139, Y.
Zhi10, N. Zhigareva139, D. Zhou 6, Y. Zhou 83, J. Zhu 98,6, Y. Zhu6, G.
ZinovjevI,3, N. Zurlo 130,54

## Affiliation Notes

I Deceased
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VI Also at: University of Kansas, Lawrence, Kansas, United States
VII Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Science and Technology, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 California Polytechnic State University, San Luis Obispo, California, United
States
6 Central China Normal University, Wuhan, China
7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
9 Chicago State University, Chicago, Illinois, United States
10 China Institute of Atomic Energy, Beijing, China
11 Chungbuk National University, Cheongju, Republic of Korea
12 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovak Republic
13 COMSATS University Islamabad, Islamabad, Pakistan
14 Creighton University, Omaha, Nebraska, United States
15 Department of Physics, Aligarh Muslim University, Aligarh, India
16 Department of Physics, Pusan National University, Pusan, Republic of Korea
17 Department of Physics, Sejong University, Seoul, Republic of Korea
18 Department of Physics, University of California, Berkeley, California,
United States
19 Department of Physics, University of Oslo, Oslo, Norway
20 Department of Physics and Technology, University of Bergen, Bergen, Norway
21 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
22 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
28 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
29 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
30 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
31 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
32 European Organization for Nuclear Research (CERN), Geneva, Switzerland
33 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
34 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
35 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
36 Faculty of Physics, Sofia University, Sofia, Bulgaria
37 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
38 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
39 Fudan University, Shanghai, China
40 Gangneung-Wonju National University, Gangneung, Republic of Korea
41 Gauhati University, Department of Physics, Guwahati, India
42 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
43 Helsinki Institute of Physics (HIP), Helsinki, Finland
44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
45 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
46 Indian Institute of Technology Bombay (IIT), Mumbai, India
47 Indian Institute of Technology Indore, Indore, India
48 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
49 INFN, Sezione di Bari, Bari, Italy
50 INFN, Sezione di Bologna, Bologna, Italy
51 INFN, Sezione di Cagliari, Cagliari, Italy
52 INFN, Sezione di Catania, Catania, Italy
53 INFN, Sezione di Padova, Padova, Italy
54 INFN, Sezione di Pavia, Pavia, Italy
55 INFN, Sezione di Torino, Turin, Italy
56 INFN, Sezione di Trieste, Trieste, Italy
57 Inha University, Incheon, Republic of Korea
58 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovak Republic
60 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
61 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
62 Institute of Space Science (ISS), Bucharest, Romania
63 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
64 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
65 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
66 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
67 iThemba LABS, National Research Foundation, Somerset West, South Africa
68 Jeonbuk National University, Jeonju, Republic of Korea
69 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
70 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
71 KTO Karatay University, Konya, Turkey
72 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France
73 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 Nara Women’s University (NWU), Nara, Japan
78 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
79 National Centre for Nuclear Research, Warsaw, Poland
80 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
81 National Nuclear Research Center, Baku, Azerbaijan
82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia
83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež,
Czech Republic
87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States
89 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
90 Physics Department, Panjab University, Chandigarh, India
91 Physics Department, University of Jammu, Jammu, India
92 Physics Department, University of Rajasthan, Jaipur, India
93 Physics Program and International Institute for Sustainability with Knotted
Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan
94 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
95 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
96 Physik Department, Technische Universität München, Munich, Germany
97 Politecnico di Bari and Sezione INFN, Bari, Italy
98 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata,
India
100 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France
104 Suranaree University of Technology, Nakhon Ratchasima, Thailand
105 Technical University of Košice, Košice, Slovak Republic
106 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
107 The University of Texas at Austin, Austin, Texas, United States
108 Universidad Autónoma de Sinaloa, Culiacán, Mexico
109 Universidade de São Paulo (USP), São Paulo, Brazil
110 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
111 Universidade Federal do ABC, Santo Andre, Brazil
112 University of Cape Town, Cape Town, South Africa
113 University of Houston, Houston, Texas, United States
114 University of Jyväskylä, Jyväskylä, Finland
115 University of Kansas, Lawrence, Kansas, United States
116 University of Liverpool, Liverpool, United Kingdom
117 University of Science and Technology of China, Hefei, China
118 University of South-Eastern Norway, Kongsberg, Norway
119 University of Tennessee, Knoxville, Tennessee, United States
120 University of the Witwatersrand, Johannesburg, South Africa
121 University of Tokyo, Tokyo, Japan
122 University of Tsukuba, Tsukuba, Japan
123 University Politehnica of Bucharest, Bucharest, Romania
124 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
125 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
126 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
127 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
128 Università degli Studi di Foggia, Foggia, Italy
129 Università del Piemonte Orientale, Vercelli, Italy
130 Università di Brescia, Brescia, Italy
131 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
132 Warsaw University of Technology, Warsaw, Poland
133 Wayne State University, Detroit, Michigan, United States
134 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
135 Wigner Research Centre for Physics, Budapest, Hungary
136 Yale University, New Haven, Connecticut, United States
137 Yonsei University, Seoul, Republic of Korea
138 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
139 Affiliated with an institute covered by a cooperation agreement with CERN
140 Affiliated with an international laboratory covered by a cooperation
agreement with CERN