[table]capposition=top

2019 248 28 October

$\mathrm{K}^{*}(\mathrm{892})^{0}$ and $\mathrm{\phi(1020)}$ production at
midrapidity in pp collisions at $\sqrt{s}$ = 8 TeV

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

The production of $\mathrm{K}^{*}(\mathrm{892})^{0}$ and $\mathrm{\phi(1020)}$
in pp collisions at $\sqrt{s}$ = 8 TeV was measured using Run 1 data collected
by the ALICE collaboration at the LHC. The $p_{\mathrm{T}}$-differential
yields d${}^{\mathrm{2}}N$/d$y$d$p_{\mathrm{T}}$ in the range 0 $<$
$p_{\mathrm{T}}$ $<$ 20 GeV/$c$ for $\mathrm{K}^{*0}$ and 0.4 $<$
$p_{\mathrm{T}}$ $<$ 16 GeV/$c$ for $\phi$ have been measured at midrapidity,
$\left|y\right|~{}$$<$ 0.5. Moreover, improved measurements of the
$\mathrm{K}^{*0}(892)$ and $\phi(1020)$ at $\sqrt{s}$ = 7 TeV are presented.
The collision energy dependence of $p_{\mathrm{T}}$ distributions,
$p_{\mathrm{T}}$-integrated yields and particle ratios in inelastic pp
collisions are examined. The results are also compared with different
collision systems. The values of the particle ratios are found to be similar
to those measured at other LHC energies. In pp collisions a hardening of the
particle spectra is observed with increasing energy, but at the same time it
is also observed that the relative particle abundances are independent of the
collision energy. The $p_{\mathrm{T}}$-differential yields of
$\mathrm{K}^{*0}$ and $\phi$ in pp collisions at $\sqrt{s}$ = 8 TeV are
compared with the expectations of different Monte Carlo event generators.

##  1 Introduction

The study of resonances plays an important role in understanding particle
production mechanisms. Particle production at LHC energies has both soft and
hard-scattering origins. The hard scatterings are perturbative processes and
are responsible for production of high-$p_{\mathrm{T}}$ particles, whereas the
bulk of the particles are produced due to soft interactions, which are non-
perturbative in nature. High-$p_{\mathrm{T}}$ particles originate from
fragmentation of jets and their yield can be calculated by folding the
perturbative Quantum Chromodynamics (pQCD) calculations for elementary parton-
parton scatterings with universal fragmentation functions determined from
experimental data [1, 2, 3]. The production yield of low-$p_{\mathrm{T}}$
particles can not be estimated from the first principles of QCD, hence
predictions require phenomenological models in the non-perturbative regime. In
this paper, we discuss $\mathrm{K}^{*0}(892)$ and $\phi(1020)$ production in
pp collisions at $\sqrt{s}$ = 8 TeV. The $\phi(1020)$ meson is a vector meson
consisting of strange quarks ($\mathrm{s\overline{s}}$). The production of
$\mathrm{s\overline{s}}$ pairs was found to be significantly suppressed,
compared to $\mathrm{u\overline{u}}$ and $\mathrm{d\overline{d}}$ pairs in pp
collisions due to the larger mass of the strange quark [4, 5]. The
$\mathrm{K}^{*0}(892)$ is a vector meson with a similar mass to the
$\phi(1020)$, but differs in strangeness content by one unit, which may help
in understanding the strangeness production dynamics. Measurements of particle
production in inelastic pp collisions provide input to tune the QCD inspired
Monte Carlo (MC) event generators such as EPOS [6], PYTHIA [7] and PHOJET [8,
9]. Furthermore, the measurements in inelastic pp collisions at $\sqrt{s}$ = 8
TeV reported in this paper serve as reference data to study nuclear effects in
proton$-$lead (p–Pb) and lead$-$lead (Pb–Pb) collisions.

In this article, the $p_{\mathrm{T}}$-differential and
$p_{\mathrm{T}}$-integrated yields and the mean transverse momenta of
$\mathrm{K}^{*0}(892)$ and $\phi(1020)$ at midrapidity in pp collisions at
$\sqrt{s}$ = 8 TeV are presented. The energy dependence of the
$p_{\mathrm{T}}$ distributions and particle ratios to the yields of charged
pions and kaons in pp collisions is examined and discussed. The yields of
pions and kaons measured previously by ALICE [10, 11, 12] at $\sqrt{s}$ = 0.9,
2.76 and 7 $\rm{TeV}$ are used to obtain the yields in pp collisions at
$\sqrt{s}$ = 8 TeV. Moreover, updated measurements of the
$\mathrm{K}^{*0}(892)$ and $\phi(1020)$ at $\sqrt{s}$ = 7 TeV are presented;
our first measurements for that collision system were published in Ref. [13].
These results include an extension of the $\mathrm{K}^{*0}(892)$ measurement
to high $p_{\mathrm{T}}$ and an improved re-analysis of the $\phi(1020)$. This
measurement has updated track-selection cuts, which are identical to those
described for the measurements at $\sqrt{s}$ = 8 TeV, has an improved estimate
of the systematic uncertainties, and extends to greater values of
$p_{\mathrm{T}}$. Throughout this paper, the results for K${}^{*}(892)^{0}$
and $\mathrm{\overline{K}}^{*}(892)^{0}$ are averaged and denoted by the
symbol $\mathrm{K}^{*0}$, while $\phi(1020)$ is denoted by $\phi$ unless
specified otherwise.

This article is organized as follows. The experimental setup is briefly
explained in Sec. 2 and the analysis procedure is given in Sec. 3. The results
and discussions are presented in Sec. 4 followed by the conclusions in Sec. 5.

##  2 Experimental setup

The ALICE detector can be used to reconstruct and identify particles over a
wide momentum range, thanks to the low material budget, the moderate magnetic
field (0.5 T) and the presence of detectors with excellent particle
identification (PID) techniques. A comprehensive description of the detector
and its performance during Run 1 of the LHC is reported in Refs. [14, 15].

The detectors used for this analysis are described in the following. The V0
detectors are two plastic scintillator arrays used for triggering and event
characterization. They are placed along the beam direction at $3.3$ m (V0A)
and $-0.9$ m (V0C) on either side of the interaction point with a
pseudorapidity coverage of $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively.
The Inner Tracking System (ITS), which is located between 3.9 cm and 43 cm
radial distance from the beam axis, is made up of six layers of cylindrical
silicon detectors (2 layers of silicon pixels, 2 layers of silicon drift and 2
layers of double-side silicon strips). As it provides high-resolution space
points close to the interaction point, the momentum and angular resolution of
the tracks reconstructed in the Time Projection Chamber (TPC) is improved. The
TPC is the main tracking device covering full azimuthal acceptance and the
pseudorapidity range $-0.9<\eta<0.9$. It is a 92 $\mathrm{m}^{3}$ cylindrical
drift chamber filled with an active gas. It is divided into two parts by a
central cathode and the end plates consist of multi-wire proportional
chambers. The TPC is also used for particle identification via the measurement
of the specific ionization energy loss ($\mathrm{d}E/\mathrm{d}x$) in the gas.
The Time of Flight (TOF) detector surrounds the TPC and consists of large
multigap resistive plate chambers. It has pseudorapidity coverage
$-0.9<\eta<0.9$, full azimuthal acceptance and an intrinsic time resolution of
$<$ 50 ps. The TOF is used for particle identification at intermediate
momenta. The particle identification techniques based on the TPC and TOF
signals are presented in detail in the next section.

##  3 Data analysis

The measurements of $\mathrm{K}^{*0}$ and $\phi$ meson production in pp
collisions at $\sqrt{s}$ = 8 TeV (7 TeV) were performed during Run 1 data
taking with the ALICE detector in 2012 (2010) using a minimum bias trigger as
discussed in Sec. 3.1. A total of around 45M events were analysed for both
$\sqrt{s}$ = 7 and 8 TeV and the corresponding integrated luminosities are
0.72 $\rm{nb^{-1}}$ and 0.81 $\rm{nb^{-1}}$, respectively. The
$\mathrm{K}^{*0}$ and $\phi$ resonances are reconstructed via their hadronic
decay channels with large branching ratios (BR): $\mathrm{K}^{*0}$
$\rightarrow$ $\pi^{\pm}$$\mathrm{K}^{\mp}$ with BR = 66.6$\%$ and $\phi$
$\rightarrow$ $\mathrm{K}^{+}\mathrm{K}^{-}$ with BR = 49.2$\%$ [16]. Some
older measurements of $\phi$ used a value of 48.9% for the $\phi$
$\rightarrow$ $\mathrm{K}^{+}\mathrm{K}^{-}$ branching ratio [17]; when
comparing different $\phi$ measurements, the older results are scaled to
account for the new branching ratio.

###  3.1 Event and track selection

For pp collisions at $\sqrt{s}$ = 8 TeV, the events were selected with a
minimum bias trigger based on a coincidence signal in V0A and V0C. For pp
collisions at $\sqrt{s}$ = 7 TeV, the trigger condition is same as in [13].
The ITS and TPC are used for tracking and reconstruction of charged particles
and of the primary vertex. Events having the primary vertex coordinate along
the beam axis within 10 cm from the nominal interaction point are selected.
Pile-up events are rejected if more than one vertex is found with the Silicon
Pixel Detector (SPD). A primary track traversing the TPC induces signals on a
maximum of 159 tangential pad-rows, each corresponding to one cluster used in
track reconstruction. For this analysis high quality charged tracks are used
to select pion and kaon candidates coming from the decays of $\mathrm{K}^{*0}$
and $\phi$. Tracks are required to have at least 70 TPC clusters and a
$\chi^{2}$ per track point ($\chi^{2}/N_{\mathrm{clusters}}$) of the track fit
in the TPC less than 4. Moreover, tracks must be associated with at least one
cluster in the SPD. To ensure a uniform acceptance by avoiding the edges of
the TPC, tracks are selected within $|\eta|$ $\textless$ 0.8. In order to
reduce contamination from secondary particles coming from weak decays, cuts on
the distance of closest approach to the primary vertex in the transverse plane
(DCAxy) and longitudinal direction (DCAz) are applied. The value of DCAxy is
required to be less than 7 times its resolution:
DCA${}_{xy}(p_{\mathrm{T}})~{}\textless~{}(0.0105+0.035p_{\mathrm{T}}^{-1.1}$)
cm ($p_{\mathrm{T}}$ in GeV/$c$) and DCAz is required to be less than 2 cm. To
improve the global resolution, the $p_{\mathrm{T}}$ of each track is choosen
to be greater than 0.15 GeV/$c$.

In the TPC, particles are identified by measuring the d$E$/d$x$ in the TPC
gas, whereas in the TOF it is done by measuring the time of flight. The
particles in the TPC are selected using a cut on the difference of the mean
value of the d$E$/d$x$ to the expected d$E$/d$x$ value for a given species
divided by the resolution $\sigma_{\rm{TPC}}$. This cut is expressed in units
of the estimated $\sigma_{\rm{TPC}}$. As described below, this is optimized
for each analysis and depends on the signal-to-background ratio and on the
transverse momentum. Particles are identified in the TOF by comparing the
measured time of flight to the expected one for a given particle species. The
cut is expressed in units of the estimated resolution $\sigma_{\rm{TOF}}$. The
TOF allows pions and kaons to be unambiguously identified up to momentum
$p\approx 1.5~{}\mathrm{GeV}/c$ and also removes contamination from electrons.
The two mesons can be distinguished from (anti)protons up to $p$ $\approx$ 2.5
GeV/$c$.

For $\mathrm{K}^{*0}$ and $\phi$ reconstruction three TPC PID selection
criteria are used, depending on the momentum of the daughter particle. For pp
collisions at $\sqrt{s}$ = 8 TeV, both pions and kaons are selected using a
cut of $\mid\rm{N}\sigma_{\mathrm{TPC}}\mid<2.0$ for
$p(K^{\pm},\pi^{\pm})~{}>~{}0.4~{}\mathrm{GeV}/c$. Here,
$p(K^{\pm},\pi^{\pm})$ denotes the momenta of pions and kaons. Similarly, for
$p(K^{\pm},\pi^{\pm})~{}<~{}0.3$ GeV/$c$, a cut of
$|\rm{N}\sigma_{\mathrm{TPC}}|~{}<~{}6.0$ is applied, while a cut of
$|\rm{N}\sigma_{\mathrm{TPC}}|~{}<4.0$ for
$0.3~{}<p(K^{\pm},\pi^{\pm})~{}<~{}0.4~{}\mathrm{GeV}/c~{}$ is applied. For
the new analysis of the $\mathrm{K}^{*0}$ ($\phi$) at $\sqrt{s}$ = 7 TeV, the
specific energy loss for pion and kaon candidates is required to be within 2
(3) $\sigma_{\rm{TPC}}$ of the expected mean, irrespective of the momentum.
Also, a TOF 3$\sigma_{\rm{TOF}}$ veto cut is applied for $\mathrm{K}^{*0}$ for
both $\sqrt{s}$ = 7 and 8 TeV. “TOF veto” means that the TOF 3$\sigma$ cut is
applied only for cases where the track matches a hit in the TOF.

###  3.2 Raw yield extraction

The $\mathrm{K}^{*0}$ ($\phi$) meson is reconstructed through its dominant
hadronic decay channel
$\mathrm{K}^{*0}\rightarrow\pi^{\pm}\mathrm{K}^{\mp}~{}\mathrm{~{}}(\phi\rightarrow~{}\mathrm{K}^{+}\mathrm{K}^{-}$)
by calculating the invariant mass of its daughters at the primary vertex. The
invariant mass distribution of the decay daughter pairs is constructed by
taking unlike-sign pairs of K and $\pi$ (K) candidates for $\mathrm{K}^{*0}$
($\phi$) in the same event. The rapidity of the $\pi$K (KK) pairs is required
to lie within the range $|y_{\mathrm{pair}}|$ $\textless$ 0.5. As an example,
the $\pi$K (KK) invariant mass distribution for $\sqrt{s}$ = 8 TeV is shown in
Fig. 1 for $0<p_{\mathrm{T}}<0.2$ GeV/$c$
($0.6~{}<~{}p_{\mathrm{T}}~{}<~{}0.7$ GeV/$c$).

Figure 1: (Color online) (Upper panels) Invariant mass distributions (closed
black point) for the $\mathrm{K}^{*0}$ (left) and $\phi$ (right) in pp
collisions at 8 TeV in the $p_{\mathrm{T}}$ range 0 $<$ $p_{\mathrm{T}}$ $<$
0.2 GeV/$c$ and 0.6 $<$ $p_{\mathrm{T}}$ $<$ 0.7 GeV/$c$, respectively. The
combinatorial background (open red circles) is estimated using unlike-sign
pairs from different events (mixed event). The statistical uncertainties are
shown as bars. (Lower panels) $\mathrm{K}\pi~{}$(left) and KK (right)
invariant mass distributions in the same $p_{\mathrm{T}}$ ranges after
combinatorial background subtraction together with the fits to the signal and
background contribution.

The shape of the uncorrelated background is obtained via the event mixing
technique, calculating the invariant mass distribution of unlike-sign
$\pi^{\pm}$$\mathrm{K}^{\mp}$ ($\mathrm{K}^{*0}$) or
$\mathrm{K}^{+}\mathrm{K}^{-}$ ($\phi$) combinations from different events, as
shown in the upper panel of Fig. 1. To reduce statistical uncertainties each
event was mixed with 5 other similar events. For $\sqrt{s}$ = 8 TeV, the mixed
event background is normalized in the mass range $1.1<$ $M_{\rm{K}\pi}$
$<1.5~{}\mathrm{GeV}/c^{2}$ ($1.04<$ $M_{\rm{KK}}$
$<1.06~{}\mathrm{GeV}/c^{2}$) for $\mathrm{K}^{*0}$($\phi$) so that it has the
same integral as the unlike-charge distribution in that normalization region.
For $\sqrt{s}$ = 7 TeV, the mixed event background is normalized in the mass
range $1.1<$ $M_{\rm{K}\pi}$ $<1.15~{}\mathrm{GeV}/c^{2}$ and $1.048<$
$M_{\rm{KK}}$ $<1.052~{}\mathrm{GeV}/c^{2}$ for $\mathrm{K}^{*0}$ and $\phi$,
respectively. To avoid mismatches due to different acceptances and to assure a
similar event structure, only tracks from events with similar vertex positions
($\Delta z$ $<$ 1 cm) and track multiplicities ($\Delta n$ $<$ 5) are mixed.
For the $\phi$ meson in pp collisions at $\sqrt{s}$ = 7 TeV, the multiplicity
difference for event mixing is restricted to $\Delta n$ $\leq$ 10\. This
combinatorial background is subtracted from the unlike-charge mass
distribution in each $p_{\mathrm{T}}$ bin. Due to an imperfect description of
the combinatorial background, as well to the presence of a correlated
background, a residual background still remains. The correlated background can
arise from correlated $\mathrm{K}\pi~{}$(KK) pairs for
$\mathrm{K}^{*0}$($\phi$), misidentified particle decays, or jets.

The $\mathrm{K}^{*0}$ raw yield is extracted from the
$\mathrm{K}\pi~{}$invariant mass distribution in different $p_{\mathrm{T}}$
bins between 0 and 20 GeV/$c$. After the combinatorial background subtraction
the invariant mass distribution is fitted with the combination of a Breit-
Wigner function for the signal peak and a second-order polynomial for the
residual background. The fit function for $\mathrm{K}^{*0}$ is given by

$\frac{\mathrm{d}N}{\mathrm{d}M_{\mathrm{\mathrm{K}^{\pm}\mathrm{\pi}^{\mp}}}}=\frac{A}{2\pi}\times\frac{\Gamma_{0}}{(M_{\mathrm{K}^{\pm}\mathrm{\pi}^{\mp}}-m_{0})^{2}+\frac{\Gamma_{0}^{2}}{4}}+(BM_{\mathrm{\mathrm{K}^{\pm}\mathrm{\pi}^{\mp}}}^{2}+CM_{\mathrm{\mathrm{K}^{\pm}\mathrm{\pi}^{\mp}}}+D).$
(1)

Here $m_{\mathrm{0}}$ is the fitted mass pole of the $\mathrm{K}^{*0}$,
$\Gamma_{\mathrm{0}}$ is the resonance width and $A$ is the yield of the
$\mathrm{K}^{*0}$ meson. $B$, $C$ and $D$ are the fit parameters in the
second-order polynomial.

The $\phi$ raw yield is extracted from the KK invariant mass distribution in
different $p_{\mathrm{T}}$ bins between 0.4 and 16 GeV/$c$ after the
combinatorial background subtraction. For the $\phi$ fit function, the
detector mass resolution is taken into account due to the smaller width of the
$\phi$ meson. This is achieved by using a Breit-Wigner function convoluted
with a Gaussian function, which is known as Voigtian function. The KK
invariant mass distribution is fitted with the combination of a Voigtian
function for the signal peak and a second-order polynomial for the residual
background. The fit function for $\phi$ is given by

$\frac{\mathrm{d}N}{\mathrm{d}M_{\mathrm{KK}}}=\frac{A\Gamma_{0}}{(2\pi^{3/2})\sigma}\times\int\limits_{-\infty}^{+\infty}\mathrm{exp}\Bigg{(}\frac{(M_{\mathrm{KK}}-m^{\prime})^{2}}{2\sigma^{2}}\Bigg{)}\frac{1}{(m^{\prime}-m_{0})^{2}+\frac{\Gamma_{0}^{2}}{4}}\mathrm{d}m^{\prime}+(BM_{\mathrm{KK}}^{2}+CM_{\mathrm{KK}}+D).$
(2)

Here $m_{\mathrm{0}}$ is the fitted mass pole of the $\phi$,
$\Gamma_{\mathrm{0}}$ is the resonance width fixed to the value in vacuum and
$\sigma$ is the $p_{\mathrm{T}}$-dependent mass resolution, which ranges from
1 to 3 MeV/$\it{c^{2}}$.

To extract the raw yields of $\mathrm{K}^{*0}$ ($\phi$), for each
$p_{\mathrm{T}}$ bin the invariant mass histogram is integrated over the
region $0.801<m_{\mathrm{K}^{*0}}<0.990~{}(1.01<m_{\phi}<1.03$), i.e. a range
of 2-3 times the nominal width around the nominal mass. The integral of the
residual background function in the same range is then subtracted. The
resonance yields beyond the histogram integration regions are found by
integrating the tails of the signal fit function; these yields are then added
to the peak yield computed by integrating the histogram.

###  3.3 Normalization and correction

The $\mathrm{K}^{*0}$ and $\phi$ raw yields ($N_{\mathrm{raw}}$) are
normalized to the number of inelastic pp collisions and corrected for the
branching ratio (BR), vertex selection, detector geometric acceptance (A) and
efficiency ($\varepsilon$) and signal loss. The $\mathrm{K}^{*0}$ and $\phi$
corrected yields are obtained by

$\dfrac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=\dfrac{N_{\mathrm{raw}}\times\epsilon_{\mathrm{SL}}}{N_{\mathrm{evt}}\times\mathrm{BR}\times\mathrm{d}p_{\mathrm{T}}\times\mathrm{d}y\times\varepsilon_{\mathrm{rec}}}\times
f_{\mathrm{norm}}\times f_{\mathrm{vtx}}.$ (3)

Here $\varepsilon_{\mathrm{rec}}$ = $A\times\varepsilon$ is the correction
that accounts for the detector acceptance and efficiency. The
$\epsilon_{\mathrm{SL}}$ is the signal loss correction factor and accounts for
the loss of $\mathrm{K}^{*0}(\phi)$ mesons incurred by selecting events that
satisfy only the ALICE minimum bias trigger, rather than all inelastic events.
This is a particle species and $p_{\mathrm{T}}$-dependent correction factor
which is peaked at low $p_{\mathrm{T}}$, indicating that events that fail the
trigger selection have softer $p_{\mathrm{T}}$ spectra than the average
inelastic event. The signal loss correction factor is about 1% at
low-$p_{\mathrm{T}}$ and negligible for $p_{\mathrm{T}}>$ 1 GeV/$c$. This
correction is the ratio of the $p_{\mathrm{T}}$ spectrum from inelastic events
to the $p_{\mathrm{T}}$ spectrum from triggered events and it is evaluated
using Monte Carlo simulations.

$N_{\mathrm{evt}}$ is the number of triggered events and a trigger efficiency
(${\it f_{\mathrm{norm}}}$) is used to normalize the yield to the number of
inelastic pp collisions. The value of the inelastic normalization factor for
pp collisions at $\sqrt{s}$ = 8 TeV is 0.77 $\pm$ 0.02, which is the ratio
between the V0 visible cross section [18] and the inelastic cross section
[19]. Similarly, we correct the yield with $f_{\mathrm{vtx}}$, which is the
ratio of the number of events for which a good vertex was found to the total
number of triggered events. This is estimated to be 0.972. The new results at
7 TeV are normalized as in [13].

The $\varepsilon_{\mathrm{rec}}$ correction factor is determined with a Monte
Carlo simulation using PYTHIA8 as the event generator and GEANT3 [20] as the
transport code for the simulation of the detector response. The
$\varepsilon_{\mathrm{rec}}$ is obtained as the fraction of $\mathrm{K}^{*0}$
and $\phi$ reconstructed after passing the same event selection and track
quality cuts as used for the real events to the total number of generated
resonances. This $\varepsilon_{\mathrm{rec}}$ value is small at low
$p_{\mathrm{T}}$ and increases with increasing $p_{\mathrm{T}}$. This value is
independent of $p_{\mathrm{T}}$ above 5-6 GeV/$c$ [13].

###  3.4 Systematic uncertainties

The systematic uncertainties on the $p_{\mathrm{T}}$-differential yield,
summarised in Table 1, are due to different sources such as signal extraction,
background subtraction, track selection, global tracking uncertainty,
knowledge of the material budget and the hadronic interaction cross section.

| pp, $\sqrt{s}=8$ TeV | pp, $\sqrt{s}=7$ TeV
---|---|---
Source |  $\mathrm{K}^{*0}$ ($\%$) |  $\phi$ ($\%$ ) |  $\mathrm{K}^{*0}$ ($\%$) |  $\phi$ ($\%$ )
Signal extraction | 8.7 | 1.9 | 8.5 | 4.0
Track selection | 4.0 | 2.0 | 5.8 | 3.2
Material budget | 0 – 3.4 | 0 – 5.4 | 0 – 3.4 | 0 – 5.4
Hadronic Interaction | 0 – 2.8 | 0 – 3.1 | 0 – 2.8 | 0 – 3.1
Global tracking efficiency | 6.0 | 6.0 | 8.0 | 8.0
Branching ratio | neg. | 1.0 | neg. | 1.0
Total | 11.3 – 12.1 | 6.7 – 9.1 | 9.2 – 18.3 | 9.1 – 15.4
Table 1: Systematic uncertainties in the measurement of $\mathrm{K}^{*0}$ and
$\phi$ yields in pp collisions at $\sqrt{s}$ = 7 and 8 TeV. The global
tracking uncertainty is $p_{\mathrm{T}}$-independent, while the other single-
valued systematic uncertainties are averaged over $p_{\mathrm{T}}$. The values
given in ranges are minimum and maximum uncertainties depending on
$p_{\mathrm{T}}$.

The systematic uncertainties associated to the signal extraction are estimated
by varying the fitting ranges, the order of residual backgrounds (from 1st
order to 3rd order), the width parameter and the mixed event background
normalization range. The signal extraction systematic uncertainties also
include the background subtraction systematic uncertainties, which are
estimated by changing the methods used to estimate the combinatorial
background (like-sign and event-mixing). The PID cuts and the track quality
selection criteria are varied to obtain the systematic uncertainties due to
the track selection. The relative uncertainties due to signal extraction and
track selection for $\mathrm{K}^{*0}$ ($\phi$) are 8.7% (1.9%) and 4% (2%),
respectively at $\sqrt{s}$ = 8 TeV.

The global tracking uncertainty is calculated using ITS and TPC clusters for
charged decay daughters. The relative systematic uncertainty due to the global
tracking efficiency is 3$\%$ for charged particles, which results in a 6$\%$
effect for the $\pi\rm{K}$ and $\mathrm{KK}$ pairs used in the reconstruction
of the $\mathrm{K}^{*0}$ and $\phi$, respectively. The systematic uncertainty
due to the residual uncertainty in the description of the material in the
Monte Carlo simulation contributes up to 3.4$\%$ for $\mathrm{K}^{*0}$ (5.4%
for $\phi$). The systematic uncertainty due to the hadronic interaction cross
section in the detector material is estimated to be up to 2.8% for
$\mathrm{K}^{*0}$ and up to 3.1% for $\phi$. The uncertainties are accordingly
propagated to the $\mathrm{K}^{*0}$ and $\phi$ [21, 22]. The total systematic
uncertainties, which are found to be $p_{\mathrm{T}}$ dependent, range in from
11.3% to 12.1% for $\mathrm{K}^{*0}$ and from 6.7% to 9.1% for $\phi$. The
uncertainties at $\sqrt{s}$ = 7 TeV are similarly estimated, totalling to
comparable values, as seen in Table 1.

##  4 Results and discussion

###  4.1 Transverse momentum spectra and differential yield ratios

Here, we report the measurement of $\mathrm{K}^{*0}$ and $\phi$ in inelastic
pp collisions at $\sqrt{s}$ = 8 TeV in the range up to $p_{\mathrm{T}}$ $=$ 20
GeV/$c$ for $\mathrm{K}^{*0}$ and up to $p_{\mathrm{T}}$ $=$ 16 GeV/$c$ for
$\phi$. Also, we present the new measurements of $\mathrm{K}^{*0}$ and $\phi$
in inelastic pp collisions at $\sqrt{s}$ = 7 TeV in the range up to
$p_{\mathrm{T}}$ $=$ 20 GeV/$c$ for $\mathrm{K}^{*0}$ and up to
$p_{\mathrm{T}}$ $=$ 21 GeV/$c$ for $\phi$. The re-analyzed $\mathrm{K}^{*0}$
and $\phi$ spectra in pp collisions at $\sqrt{s}$ = 7 TeV agree with the
previously published values [13] within a few percent at low $p_{\mathrm{T}}$.
At higher $p_{\mathrm{T}}$ ($\gtrsim 3$ GeV/$c$ for $\mathrm{K}^{*0}$ and
$\gtrsim 2$ GeV/$c$ for $\phi$), the old and re-analyzed results can differ by
up to 20%, although their systematic uncertainties still overlap. For both
energies, the first bin of $\mathrm{K}^{*0}$ starts at $p_{\mathrm{T}}$ $=$ 0
GeV/$c$ and for $\phi$, it starts at $p_{\mathrm{T}}$ $=$ 0.4 GeV/$c$. In Fig.
2, we show the transverse momentum spectra of $\mathrm{K}^{*0}$ and $\phi$ at
midrapidity $\left|y\right|~{}$$<$ 0.5 and fitted with the Lévy-Tsallis
distribution [23, 24]. The ratio of the measured data to the Lévy-Tsallis fit
shows good agreement of data with model within systematic uncertainties. The
fit parameters are shown in Table 2.

Figure 2:  (Color online) Upper panels shows the $p_{\mathrm{T}}$ spectra of
$\mathrm{K}^{*0}$ and $\phi$ in inelastic pp collisions at 7 TeV (left) and 8
TeV (right) and fitted with the Lévy-Tsallis distribution [23, 24]. The
normalization uncertainty in the spectra is ${}^{+7.3}_{-3.5}$% for 7 TeV and
2.69% for 8 TeV. The vertical bars show statistical and the boxes show
systematic uncertainties. The lower panels show the ratio of data to the Lévy-
Tsallis fit. Here, the bars show the systematic uncertainty.

The energy evolution of the transverse momentum spectra for $\mathrm{K}^{*0}$
and $\phi$ is studied by calculating the ratio of
$p_{\mathrm{T}}$-differential yields for inelastic events at $\sqrt{s}$ = 7
and 8 TeV to those at $\sqrt{s}$ = 2.76 TeV [25]. This is shown in Fig. 3. The
differential yield ratio to 2.76 TeV is consistent for 7 and 8 TeV within
systematic uncertainties. The systematic uncertainties at both collision
energies are largely uncorrelated. Therefore, the sum of these in quadrature
is taken as systematic uncertainty on the ratios. For both $\mathrm{K}^{*0}$
and $\phi$, the differential yield ratio is independent of $p_{\mathrm{T}}$
within systematic uncertainties up to about 1 GeV/$c$ for the different
collision energies. This suggests that the particle production mechanism in
soft scattering regions is independent of collision energy over the measured
energy range. An increase in slope of the differential yield ratios is
observed for $p_{\mathrm{T}}>$ 1-2 GeV/$c$.

| pp, $\sqrt{s}=8$ TeV | pp, $\sqrt{s}=7$ TeV
---|---|---
Particles | T (MeV) | n | T (MeV) | n
$\mathrm{K}^{*0}$ | 260 $\pm$ 5 | 6.65 $\pm$ 0.03 | 261 $\pm$ 6 | 6.92 $\pm$ 0.15
$\phi$ | 306 $\pm$ 6 | 7.28 $\pm$ 0.03 | 299 $\pm$ 5 | 7.17 $\pm$ 0.04

Table 2: Parameters extracted from the Lévy-Tsallis fit to the
$\mathrm{K}^{*0}$ and $\phi$ transverse momentum spectra in inelastic pp
collisions at $\sqrt{s}$ = 7 and 8 TeV.

Figure 3: (Color online) Ratios of transverse-momentum spectra of
$\mathrm{K}^{*0}$ and $\phi$ in inelastic events at $\sqrt{s}$ = 7 and 8 TeV
to the transverse-momentum spectra in pp collisions at $\sqrt{s}$ = 2.76 TeV.
The statistical and systematic uncertainties are shown as vertical error bars
and boxes, respectively. The normalization uncertainties are indicated by
boxes around unity.

###  4.2 $p_{\mathrm{T}}$-integrated yields

pp, $\sqrt{s}=8$ TeV
---
Particles | measured $p_{\mathrm{T}}$ (GeV/$c$) | d$N$/d$y$ |  $\langle p_{\mathrm{T}}\rangle$ (GeV/$c$)
$\mathrm{K}^{*0}$ | 0.0 – 20.0 | 0.101 $\pm$ 0.001 (stat.) $\pm$ 0.014 (sys.) | 1.037 $\pm$ 0.006 (stat.) $\pm$ 0.029 (sys.)
$\phi$ | 0.4 – 16.0 | 0.0335 $\pm$ 0.0003 (stat.) $\pm$ 0.0030 (sys.) | 1.146 $\pm$ 0.005 (stat.) $\pm$ 0.040 (sys.)
pp, $\sqrt{s}=7$ TeV
Particles | measured $p_{\mathrm{T}}$ (GeV/$c$) | d$N$/d$y$ |  $\langle p_{\mathrm{T}}\rangle$ (GeV/$c$)
$\mathrm{K}^{*0}$ | 0.0 – 20.0 | 0.0970 $\pm$ 0.0004 (stat.) $\pm$ 0.0103 (sys.) | 1.015 $\pm$ 0.003 (stat.) $\pm$ 0.030 (sys.)
$\phi$ | 0.4 – 21.0 | 0.0318 $\pm$ 0.0003 (stat.) $\pm$ 0.0032 (sys.) | 1.132 $\pm$ 0.005 (stat.) $\pm$ 0.023 (sys.)

Table 3: $\mathrm{K}^{*0}$ and $\phi$ integrated yields and $\langle
p_{\mathrm{T}}\rangle$ in inelastic pp collisions at $\sqrt{s}$ = 7 and 8 TeV.
The systematic uncertainties include the contributions from the uncertainties
listed in Table 1 and the choice of the spectrum fit function for
extrapolation is also included for the $\phi$. Here, “stat.” and “sys.” refer
to statistical and systematic uncertainties, respectively. In addition, the
d$N$/d$y$ has uncertainties due to normalization, which is ${}^{+7.3}_{-3.5}$%
for 7 TeV and 2.69% for 8 TeV.

Table 3 shows the $\mathrm{K}^{*0}$ and $\phi$ integrated yield (d$N$/d$y$)
and mean transverse momenta ($\langle p_{\mathrm{T}}\rangle$) in inelastic pp
collisions at $\sqrt{s}$ = 8 TeV. As the $\phi$ spectrum starts from 0.4
GeV/$c$, for the calculation of d$N$/d$y$ and $\langle p_{\mathrm{T}}\rangle$,
the spectrum is extrapolated down to $p_{\mathrm{T}}$ = 0 GeV/$c$ using a Lévy
– Tsallis fit [23, 24]. The extrapolated part amounts to about 15% of the
yield. Alternative fit functions (Boltzmann distribution, Bose-Einstein
distribution, $m_{\rm{T}}$ exponential and $p_{\mathrm{T}}$ exponential) have
been tried for the extrapolation, giving a contribution of 1.5% to the total
systematic uncertainty on d$N$/d$y$. In the case of $\mathrm{K}^{*0}$, no
extrapolation is needed as the distribution is measured for $p_{\mathrm{T}}$
$>$ 0 GeV/$c$. Table 3 also shows the d$N$/d$y$ and $\langle
p_{\mathrm{T}}\rangle$ of $\mathrm{K}^{*0}$ and $\phi$ at $\sqrt{s}$ = 7 TeV.

###  4.3 Particle ratios

For the calculation of the particle yield ratios, the values of d$N$/d$y$ for
$\pi^{+}+\pi^{-}$ and K++K- in pp collisions at $\sqrt{s}$ = 8 TeV are
estimated via extrapolation using the data points available at different LHC
collision energies [10, 11, 12] namely 0.9, 2.76 and 7 TeV. The data points
are fitted with the following polynomial function, $A(\sqrt{s})^{n}+B$. Here
$A$, $n$ and $B$ are the fit parameters. For the calculation of the
uncertainties on the extrapolated value, the central values of the data points
are shifted within their uncertainties and fitted with the same function. The
$\pi^{+}+\pi^{-}$and K++K- energy extrapolated yields in inelastic pp
collisions at $\sqrt{s}$ = 8 TeV are 4.80 $\pm$ 0.21 and 0.614 $\pm$ 0.032.
From here onwards, $\pi^{+}+\pi^{-}$ is denoted as $\pi$ and K++K- is denoted
as K.

Figure 4 shows the ratio of the d$N$/d$y$ of $\mathrm{K}^{*0}$ ($\phi$) to
that of $\pi$ in the left (right) panel, as a function of the collision
energy. $\pi$ has no strangeness content, $\mathrm{K}^{*0}$ has one unit of
strangeness, and $\phi$ is strangeness neutral but contains two strange
valence (anti)quarks. It is observed that the $\mathrm{K}^{*0}/\pi$ and
$\phi/\pi$ ratios are independent of the collision energy within systematic
uncertainties, which indicates that the chemistry of the system is independent
of the energy from the RHIC to LHC energies. This also suggests that the
strangeness production mechanisms do not depend on energy in inelastic pp
collisions at LHC energies. Figure 4 and Ref. [13] show that this flat
behaviour is observed from RHIC to LHC energies and the new result at
$\sqrt{s}$ = 8 TeV is in agreement with previous findings. It is worth
stressing that this flat behaviour is not trivial: since particle yields do in
fact increase with the collision energy, the flat ratios are indicative of the
fact that the percentage increases of d$N$/d$y$ for $\pi$, $\mathrm{K}^{*0}$
and $\phi$ as a function of the collision energy are similar from RHIC to LHC.

It is interesting to compare the particle ratios, $\mathrm{K}^{*0}/\rm{K}$ and
$\phi/\rm{K}$ measured in inelastic pp collisions with different collision
systems and collision energies in order to understand the production dynamics.
In Fig. 5 the $\mathrm{K}^{*0}/\rm{K}$ and $\phi/\rm{K}$ ratios are plotted as
a function of center-of-mass energy per nucleon pair for different collision
systems. The $\mathrm{K}^{*0}/\rm{K}$ and $\phi/\rm{K}$ ratios are independent
of the collision energy and of the colliding system. The only exception is the
$\mathrm{K}^{*0}$ in central nucleus–nucleus collisions; we attribute the
suppression of the $\mathrm{K}^{*0}/\rm{K}$ ratio to final state effects in
the late hadronic stage [26]. The behaviours of these ratios in pp collisions
agree with the predictions [27, 26] of a thermal model in the grand-canonical
limit.

Figure 4: (Color online) Particle ratios of $\mathrm{K}^{*0}/\pi$ (left) and
$\phi/\pi$ (right) are presented for pp collisions as a function of the
collision energy. Bars (when present) represent statistical uncertainties.
Boxes represent the total systematic uncertainties or the total uncertainties
for cases when separate statistical uncertainties were not reported. [28, 29,
30, 10, 31, 26, 13, 32, 11, 12]

Figure 5: (Color online) Particle ratios of $\mathrm{K}^{*0}$/K (left) and
$\phi$/K (right) are presented for pp, high-multiplicity p–Pb, central d–Au,
and central A–A collisions [13, 12, 28, 30, 33, 34, 31, 35, 11, 36, 29, 37,
38, 39, 40, 41, 10] as a function of the collision energy. Bars (when present)
represent statistical uncertainties. Boxes represent the total systematic
uncertainties or the total uncertainties for cases when separate statistical
uncertainties were not reported. The value given by a grand-canonical thermal
model with a chemical freeze-out temperature of 156 MeV [27] is also shown.

The $\phi$/$\mathrm{K}^{*0}$ ratio as a function of center-of-mass energy is
plotted in Fig. 6. The ratio seems to be independent of collision energy and
appears to follow a behavior expected from thermal production, within
experimental uncertainties.

Figure 6: (Color online) Particle ratio $\phi$/ $\mathrm{K}^{*0}$ presented
for pp collisions [28, 29, 26, 13] as a function of the collision energy. Bars
(when present) represent statistical uncertainties. Boxes represent the total
systematic uncertainties or the total uncertainties for cases when separate
statistical uncertainties were not reported.

###  4.4 Comparison to models

QCD-inspired MC event generators like PYTHIA 8 [7], PHOJET [8, 9] and EPOS-LHC
[6] are used to study multi-particle production, which is predominantly a
soft, non-perturbative process. The measurements are compared with the MC
model predictions. PYTHIA 8 and PHOJET use the Lund string fragmentation model
[42] for the hadronisation of light and heavy quarks. We compare our data with
the Monash 2013 tune [7] for PYTHIA 8, which is an updated parameter set for
the Lund hadronisation compared to previous tunes. To describe the non-
perturbative phenomena (soft/semi-hard processes), PYTHIA 8 includes multiple
parton$-$parton interactions while PHOJET uses the Dual Parton Model [43]. For
hard scatterings, particle production in both models is based on perturbative
QCD and only considers two particle scatterings. For multiple scatterings, the
EPOS-LHC model invokes Gribov’s Reggeon Field Theory [44], which features a
collective hadronisation via the core-corona mechanism [45]. The final state
partonic system consists of longitudinal flux tubes which fragment into string
segments. The high energy density string segments form the so-called “core”
region, which evolves hydrodynamically to form the bulk part of the system in
the final state. The low-density region is known as the “corona”, which
expands and breaks via the production of quark-antiquark pairs and hadronises
using vacuum string fragmentation. Recent data from the LHC have been used
already to tune the EPOS-LHC model [6].

Figure 7 shows a comparison of the $\mathrm{K}^{*0}$ (left) and $\phi$ (right)
$p_{\mathrm{T}}$ spectra in inelastic pp collisions with PYTHIA8, PHOJET and
EPOS-LHC. The bottom panels show the ratios of the $p_{\mathrm{T}}$ spectra
from models to the $p_{\mathrm{T}}$ spectra measured by ALICE. The total
fractional uncertainties from the real data, including both statistical and
systematic uncertainties are shown as shaded boxes. PYTHIA 8 overestimates the
$p_{\mathrm{T}}$ spectrum for $\mathrm{K}^{*0}$ at very low $p_{\mathrm{T}}$
but describes it in the intermediate-$p_{\mathrm{T}}$ region and approaches
the experimental data at high $p_{\mathrm{T}}$. For the $\phi$ meson, PYTHIA 8
under predicts the yields from the experimental data by about a factor of two.
PHOJET has a softer $p_{\mathrm{T}}$ spectrum for $\mathrm{K}^{*0}$ and it
explains the data above $p_{\mathrm{T}}>$ 4 GeV/$c$. For the $\phi$ meson,
PHOJET predicts the yields similarly to PYTHIA 8 at low $p_{\mathrm{T}}$,
while it approaches the experimental data at higher $p_{\mathrm{T}}$. For the
$\mathrm{K}^{*0}$, EPOS-LHC describes the $p_{\mathrm{T}}$ spectra at low
$p_{\mathrm{T}}$ and overestimates the data above 4 GeV/$c$. For the $\phi$
meson, whereas PYTHIA and PHOJET fail to describe the
$p_{\mathrm{T}}$-spectra, the EPOS-LHC model approaches the data at low
$p_{\mathrm{T}}$ and deviates monotonically from them with increasing
$p_{\mathrm{T}}$.

Figure 7: (Color online) Comparison of the $\mathrm{K}^{*0}$ (left) and $\phi$
(right) $p_{\mathrm{T}}$ spectra measured in inelastic pp collisions with
those obtained from PYTHIA8 (Monash tune) [7], PHOJET [8, 9] and EPOS-LHC [6].
The bottom plots show the ratios of the $p_{\mathrm{T}}$ spectra from the
models to the measured $p_{\mathrm{T}}$ spectra by ALICE. The total fractional
uncertainties of the data are shown as shaded boxes.

##  5 Conclusions

Measurements of $\mathrm{K}^{*0}$ and $\phi$ production are presented at
midrapidity in inelastic pp collisions at $\sqrt{s}$ = 8 TeV in the range 0
$<$ $p_{\mathrm{T}}$ $<$ 20 GeV/$c$ for $\mathrm{K}^{*0}$ and 0.4 $<$
$p_{\mathrm{T}}$ $<$ 16 GeV/$c$ for $\phi$. Also, updated measurements at
$\sqrt{s}$ = 7 TeV are presented, which improve the results previously
published in [13]. In comparison to other LHC energies, a hardening of the
$p_{\mathrm{T}}$ spectra is observed with increasing collision energy. The
$\mathrm{K}^{*0}/\pi$ and $\phi/\pi$ ratios are independent of collision
energy within systematic uncertainties. This indicates that there is no
strangeness enhancement in inelastic pp collisions as the collision energy is
increased. Similar behavior is observed for the $\mathrm{K}^{*0}/\rm{K}$ and
$\phi/\rm{K}$ ratios as a function of collision energy. Also, no energy
dependence of the $\phi$/$\mathrm{K}^{*0}$ ratio in minimum bias pp collisions
at LHC energies is observed, which suggests there is no energy dependence of
the chemistry of the system. None of the MC models seem to explain the
$\mathrm{K}^{*0}$ spectra over the full $p_{\mathrm{T}}$ range whereas PHOJET
and PYTHIA describe the data for the intermediate and high-$p_{\mathrm{T}}$
regions. However, the MC models fail to explain the $p_{\mathrm{T}}$ spectra
of the $\phi$ meson completely. These pp results will serve as baseline for
the measurements in p–Pb and Pb–Pb collisions.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M
2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,
Austria; Ministry of Communications and High Technologies, National Nuclear
Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS),
Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa
do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of
China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry
of Education of China (MOEC) , China; Croatian Science Foundation and Ministry
of Science and Education, Croatia; Centro de Aplicaciones Tecnológicas y
Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth
and Sports of the Czech Republic, Czech Republic; The Danish Council for
Independent Research — Natural Sciences, the Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National
de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France;
Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Germany; General Secretariat for Research and
Technology, Ministry of Education, Research and Religions, Greece; National
Research, Development and Innovation Office, Hungary; Department of Atomic
Energy Government of India (DAE), Department of Science and Technology,
Government of India (DST), University Grants Commission, Government of India
(UGC) and Council of Scientific and Industrial Research (CSIR), India;
Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion
of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y
Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología
(FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA),
Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO),
Netherlands; The Research Council of Norway, Norway; Commission on Science and
Technology for Sustainable Development in the South (COMSATS), Pakistan;
Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher
Education and National Science Centre, Poland; Korea Institute of Science and
Technology Information and National Research Foundation of Korea (NRF),
Republic of Korea; Ministry of Education and Scientific Research, Institute of
Atomic Physics and Ministry of Research and Innovation and Institute of Atomic
Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of
Education and Science of the Russian Federation, National Research Centre
Kurchatov Institute, Russian Science Foundation and Russian Foundation for
Basic Research, Russia; Ministry of Education, Science, Research and Sport of
the Slovak Republic, Slovakia; National Research Foundation of South Africa,
South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg
Foundation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; National Science and Technology Development Agency (NSDTA),
Suranaree University of Technology (SUT) and Office of the Higher Education
Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy
Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine;
Science and Technology Facilities Council (STFC), United Kingdom; National
Science Foundation of the United States of America (NSF) and United States
Department of Energy, Office of Nuclear Physics (DOE NP), United States of
America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg73&J.
Adolfssonorg79&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10,org48,org53&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg75&A.
Akindinovorg90&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg86&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org27,org53&A. Alkinorg2&J. Almeorg22&T.
Altorg68&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg125&N. Apadulaorg78&L.
Aphecetcheorg114&H. Appelshäuserorg68&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg78&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
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Umakaorg125&A. Urasorg135&G.L. Usaiorg24&A. Utrobicicorg97&M.
Valaorg38,org116&N. Valleorg139&S. Valleroorg58&N. van der Kolkorg63&L.V.R.
van Doremalenorg63&M. van Leeuwenorg63&P. Vande Vyvreorg34&D. Vargaorg145&Z.
Vargaorg145&M. Varga-Kofaragoorg145&A. Vargasorg44&M. Vargyasorg126&R.
Varmaorg48&M. Vasileiouorg82&A. Vasilievorg86&O. Vázquez Doceorg103,org117&V.
Vecherninorg112&A.M. Veenorg63&E. Vercellinorg26&S. Vergara Limónorg44&L.
Vermuntorg63&R. Vernetorg7&R. Vértesiorg145&M.G.D.L.C. Vicencioorg9&L.
Vickovicorg35&J. Viinikainenorg126&Z. Vilakaziorg131&O. Villalobos
Baillieorg109&A. Villatoro Telloorg44&G. Vinoorg52&A. Vinogradovorg86&T.
Virgiliorg30&V. Vislaviciusorg87&A. Vodopyanovorg74&B. Volkelorg34&M.A.
Völklorg101&K. Voloshinorg90&S.A. Voloshinorg143&G. Volpeorg33&B. von
Hallerorg34&I. Vorobyevorg103&D. Voscekorg116&J. Vrlákováorg38&B.
Wagnerorg22&M. Weberorg113&S.G. Weberorg105,org144&A. Wegrzynekorg34&D.F.
Weiserorg102&S.C. Wenzelorg34&J.P. Wesselsorg144&E. Widmannorg113&J.
Wiechulaorg68&J. Wikneorg21&G. Wilkorg83&J. Wilkinsonorg53&G.A.
Willemsorg34&E. Willsherorg109&B. Windelbandorg102&W.E. Wittorg130&Y.
Wuorg128&R. Xuorg6&S. Yalcinorg76&K. Yamakawaorg45&S. Yangorg22&S.
Yanoorg137&Z. Yinorg6&H. Yokoyamaorg63,org133&I.-K. Yooorg18&J.H. Yoonorg60&S.
Yuanorg22&A. Yuncuorg102&V. Yurchenkoorg2&V. Zaccoloorg25,org58&A.
Zamanorg15&C. Zampolliorg34&H.J.C. Zanoliorg63,org121&N. Zardoshtiorg34&A.
Zarochentsevorg112&P. Závadaorg66&N. Zaviyalovorg107&H. Zbroszczykorg142&M.
Zhalovorg96&X. Zhangorg6&Z. Zhangorg6&C. Zhaoorg21&V. Zherebchevskiiorg112&N.
Zhigarevaorg90&D. Zhouorg6&Y. Zhouorg87&Z. Zhouorg22&J. Zhuorg6&Y. Zhuorg6&A.
Zichichiorg10,org27&M.B. Zimmermannorg34&G. Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

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

org21Department of Physics, University of Oslo, Oslo, Norway

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

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

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

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org45Hiroshima University, Hiroshima, Japan

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

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

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

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

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

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

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

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

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

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

org67Institute of Space Science (ISS), Bucharest, Romania

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

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

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

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

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

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

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

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

org76KTO Karatay University, Konya, Turkey

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

org78Lawrence Berkeley National Laboratory, Berkeley, California, United
States

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

org80Nagasaki Institute of Applied Science, Nagasaki, Japan

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

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

org83National Centre for Nuclear Research, Warsaw, Poland

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

org85National Nuclear Research Center, Baku, Azerbaijan

org86National Research Centre Kurchatov Institute, Moscow, Russia

org87Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org88Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org89NRC Kurchatov Institute IHEP, Protvino, Russia

org90NRC Kurchatov Institute - ITEP, Moscow, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

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

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

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

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

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

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

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Techonology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

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

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea