[table]capposition=top

2019 024 15 February

Multiplicity dependence of (anti-)deuteron in pp collisions

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

In this letter, the production of deuterons and anti-deuterons in pp
collisions at $\sqrt{s}=7$ TeV is studied as a function of the charged-
particle multiplicity density at mid-rapidity with the ALICE detector at the
LHC. Production yields are measured at mid-rapidity in five multiplicity
classes and as a function of the deuteron transverse momentum
($p_{\mathrm{T}}$). The measurements are discussed in the context of
hadron–coalescence models. The coalescence parameter $B_{2}$, extracted from
the measured spectra of (anti-)deuterons and primary (anti-)protons, exhibits
no significant $p_{\mathrm{T}}$-dependence for $p_{\mathrm{T}}<3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, in agreement with the
expectations of a simple coalescence picture. At fixed transverse momentum per
nucleon, the $B_{2}$ parameter is found to decrease smoothly from low
multiplicity $\mathrm{p\kern-0.50003ptp}$ to Pb–Pb collisions, in qualitative
agreement with more elaborate coalescence models. The measured mean transverse
momentum of (anti-)deuterons in pp is not reproduced by the Blast-Wave model
calculations that simultaneously describe pion, kaon and proton spectra, in
contrast to central Pb–Pb collisions. The ratio between the
$p_{\mathrm{T}}$-integrated yield of deuterons to protons, d/p, is found to
increase with the charged-particle multiplicity, as observed in inelastic pp
collisions at different centre-of-mass energies. The d/p ratios are reported
in a wide range, from the lowest to the highest multiplicity values measured
in pp collisions at the LHC.

##  1 Introduction

The production of light nuclei and anti-nuclei in elementary collisions has
been described by phenomenological models in which nucleons coalesce into
nuclei [1, 2, 3, 4]. According to these models, a pair of independent final-
state nucleons that are nearby in space and have similar velocities can
transfer energy to the rest of the system to form a deuteron or an anti-
deuteron. The production rate of the (anti-)deuteron obtained by coalescence
is thus related to those of its constituent protons and neutrons. In order to
provide a quantitative description of this process the coalescence parameter
$B_{2}$, which relates the deuteron production to the square product of
nucleon yields, is extracted. These models have successfully been tested with
deuteron and anti-deuteron production measured in pp collisions at the CERN
ISR [5, 6] and Tevatron [7], photo-production and deep inelastic scattering of
electrons at HERA [8, 9], electron-positron collisions at ARGUS [Argus], BaBar
[Babar], CLEO [10] and at LEP [11]. Results on the production of light
(anti-)nuclei in inelastic pp collisions at
$\sqrt{s}~{}=0.9,2.76~{}$and$~{}7\,\mathrm{~{}TeV}$ have been reported by the
ALICE Collaboration in [12, 13] and the validity of coalescence models [1, 2,
3, 4] at the Large Hadron Collider (LHC) has also been discussed. Light nuclei
and their anti-matter counterparts are rarely produced in elementary
reactions. In pp collisions at LHC energies, the cost to add one constituent
nucleon to a nucleus amounts to a reduction factor of the yield (also called
“penalty factor”) of about 1000 [13]. Heavy-ion collisions, on the other hand,
constitute a more abundant source of light (anti-)nuclei, as reported by ALICE
[12, 14, 15]. A penalty factor of about 300 has been extracted in central
Pb–Pb collisions at the LHC [15].

In Pb–Pb collisions, the yields of light (anti-)nuclei up to the mass number
$A$ = 4 have been successfully described together with other light-flavour
hadrons in the thermal-statistical approach with one common chemical freeze-
out temperature [16, 17, 15]. Compared to hydrodynamic-inspired models (e.g.
Blast-Wave model [18]), the measured deuteron $p_{\mathrm{T}}$ spectra and
elliptic-flow coefficient ($v_{2}$) suggest common kinetic freeze-out
conditions for deuterons and primary pions, kaons and protons [12, 14].
Furthermore, the relative deuteron-to-proton yields (d$/$p) increase by about
a factor two from inelastic pp to central Pb–Pb collisions, where the values
[12] are in agreement with the statistical-thermal model [17]. A coalescence
approach that neglects the size of the particle emitting source (hereafter
denoted as “simple coalescence”) fails in reproducing the deuteron $B_{2}$ and
$v_{2}$ measured in Pb–Pb collisions [12, 14]. A formulation of the
coalescence model that takes into account the size of the particle-emitting
source has been proposed to describe the behaviour in large systems [4]. In
smaller systems one has to consider that the size of the deuteron may be as
large as or even larger than the size of the emitting source.

The abundances of nuclei are very sensitive to the freeze-out conditions, to
the dynamics, and the size of the emitting source. For these reasons, a
systematic comparison of the production of light nuclei across different
collision systems and, in particular, in events with similar final-state
multiplicity but very different initial conditions and collision geometry can
shed light on the production mechanisms. Thanks to the high statistics data
sample collected by ALICE, the deuteron and anti-deuteron production in pp
collisions can be studied differentially as a function of the charged-particle
multiplicity and the transverse momentum ($p_{\mathrm{T}}$), complementing the
previous measurements in pp and Pb–Pb collisions.

This letter is organised as follows: in Sec. 2 the experimental apparatus, the
analysis technique and the estimation of the systematic uncertainties are
described. The results on multiplicity dependent $p_{\mathrm{T}}$-differential
and $p_{\mathrm{T}}$-integrated yields and the anti-deuteron over deuteron
ratio are reported in Sec. 3, which also contains a detailed discussion of the
results. Conclusions follow in Sec. 4.

##  2 Experimental details

###  2.1 The ALICE detector

A comprehensive description of the ALICE apparatus and its performance can be
found in [19, 20]. In this section, the detectors used for the analysis
discussed in this paper are described. Deuteron spectra are measured at mid-
rapidity ($|y|<0.5$) relying on the tracking and particle identification (PID)
capabilities of the central-barrel detectors, which are located in a solenoid
magnet providing a $B$ = 0.5 T field, parallel to the beam direction ($z$-axis
in the ALICE reference frame).

From the innermost radius of 3.9 cm (distance from the centre of the beam
vacuum pipe) to the outermost radius of 43 cm, the Inner Tracking System (ITS)
includes two layers of Silicon Pixel Detector (SPD), two Silicon Drift
Detector (SDD) layers, and two Silicon Strip Detector (SSD) layers. The
different ITS sub-systems have full azimuth and a common pseudorapidity
coverage of $|\eta|<0.9$ in the acceptance. The spatial precision of the ITS,
its proximity to the beam pipe, and its very low material budget [21] enable a
precise determination of the primary vertex and of the track impact parameter
(i.e. the distance of closest approach of the track to the primary vertex) in
the transverse plane, for which a resolution better than 75 $\mu$m is achieved
for tracks with $p_{\mathrm{T}}$ > 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ [21].

The Time Projection Chamber (TPC) is the main tracking device of the
experiment and surrounds the ITS with an active volume ranging from 85 cm to
247 cm in radius with full azimuthal coverage in the pseudorapidity interval
$|\eta|<0.9$. It provides up to 159 space points to determine the particle
trajectory and measure its momentum. Moreover, the specific ionisation energy-
loss of particles inside the TPC volume is measured with a resolution of 5$\%$
in pp collisions, exploited here for PID.

The Time-Of-Flight (TOF) system [22], an array of 1593 Multi-gap Resistive
Plate Chambers, completes the set of detectors used for PID in the analysis
presented in this letter. It is located at a radial distance of about 3.8 m,
covering full azimuth in the pseudorapidity interval $|\eta|<0.9$. The event
time of the collision is obtained on an event-by-event basis either using the
TOF detector, or the T0 detector, or a combination of the two [23]. The T0
detector consists of two arrays of Cherenkov counters, located on both sides
of the interaction point at $z=350$ cm and $z=-70$ cm from the nominal vertex
position. The time-of-flight of the particles is determined with a resolution
of about 120 ps in pp collisions.

Between the TOF and the TPC, the Transition Radiation Detector (TRD) is
positioned at a radial distance between 2.9 and 3.7 m from the beam axis, with
pseudorapidity coverage of $|\eta|<0.8$. Since 2014, all eighteen TRD
supermodules are installed, covering full azimuth. In 2010, when the data used
for the analysis presented here were collected, only seven sectors were
present. Although the TRD is not used in this analysis, its detector material
plays a role in the efficiency corrections, described in Sec. 2.5.

The V0 detector consists of two scintillator arrays built around the beam pipe
on either side of the interaction point at $z=329$ cm and $z=-88$ cm, and
covering the pseudorapidity ranges $2.8\leq\eta\leq 5.1$ (V0-A) and -3.7
$\leq\eta\leq$ -1.7 (V0-C). This detector is used for triggering and
background suppression. It is also employed for classifying events according
to multiplicity, as further detailed in the next section.

###  2.2 Event selection and multiplicity classes

The analysis is based on a data sample of 237 million minimum-bias triggered
pp collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$. The minimum-bias trigger
requires a hit in either the V0 or the SPD, in coincidence with the crossing
of proton bunches from the two beams. The timing information provided by the
V0 detector as well as the correlation between the SPD hit multiplicity and
the number of SPD track segments pointing to the primary vertex are used
offline to reject the contamination from beam-gas events, achieving a purity
of the minimum-bias event sample of 99.7$\%$ as estimated in [20]. The pileup
rejection is performed by rejecting offline the events with more than one
reconstructed vertex in the SPD. The residual fraction of events with pileup
ranges from about $10^{-4}$ to $10^{-2}$ for the lowest and highest
multiplicity classes, respectively. Events are also required to have a primary
vertex reconstructed by the SPD within $\pm$ 10 cm from the nominal
interaction point along the beam direction. The sample selected with the above
criteria contains 172 million events.

The results are reported for an event class (INEL>0) characterised by at least
one charged particle being produced in the pseudorapidity interval $|\eta|$ <
1, corresponding to about 75$\%$ of the total inelastic cross-section. INEL>0
events are selected experimentally by requiring that at least one track
segment (tracklet) is reconstructed in the SPD. This selection can be affected
by inefficiencies associated with the tracklet reconstruction. Thus the
selected number of events used for the normalisation of the yields is
corrected for the 8.5$\%$ loss due to inefficiency in the lowest multiplicity
class and for less than 1.2$\%$ loss for all other classes, as estimated in
[24].

In order to study deuteron production as a function of multiplicity, the
selected events are classified using the “V0M” forward multiplicity estimator,
based on the total energy deposited in both the V0 scintillator arrays (V0-A
and V0-C). The V0M amplitude is linearly proportional to the total number of
charged particles produced in the V0 detectors acceptance. Since deuteron
production is measured at mid-rapidity, an independent estimator is preferred
as an event classifier to avoid auto-correlation biases. In each V0M event
class the average charged-particle multiplicity density
($\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$) is measured at mid-
rapidity and results are reported in the following as a function of
$\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$.

For the event classes relevant for this analysis, the values of
$\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$ and the fraction of the
INEL>0 cross section are reported in Tab. 1. Roman numerals are used to
indicate each of the ten event classes in which the measurement of other
light-flavour hadron yields, and protons in particular, have been performed as
reported in [24, 25]. Considering the deuteron statistics needed for the
present analysis, some of these classes have been combined as indicated in the
table.

Multiplicity Class |  $\sigma$/$\sigma_{\rm INEL>0}$ | $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$
---|---|---
I+II | 0 - 4.7 $\%$ | $17.47\pm 0.52$
III | 4.7 - 9.5 $\%$ | $13.50\pm 0.40$
IV+V | 9.5 - 19 $\%$ | $10.76\pm 0.30$
VI+VII | 19 - 38 $\%$ | $7.54\pm 0.23$
VIII+IX+X | 38 - 100 $\%$ | $3.30\pm 0.13$
I to X | 0 - 100 $\%$ | $5.96\pm 0.23$
Table 1: Charged-particle multiplicity ($\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta\rangle$) measured at mid-rapidity ($\left|\eta\right|$ <
0.5) and its corresponding fraction of the INEL>0 cross section
($\sigma$/$\sigma_{\rm INEL>0}$) for each of the multiplicity classes selected
with the V0M estimator and relevant for this analysis, indicated by roman
numerals [24]. The uncertainties are the square-root of the sum in quadrature
of statistical and systematic contributions and represent one standard
deviation.

###  2.3 Track selection and particle identification

In order to ensure good quality, tracks are selected according to the
following criteria. For each track, at least two reconstructed points are
required in the ITS (including at least one in the SPD) and 70 out of a
maximum of 159 in the TPC. The track-fit quality is assured by requiring the
$\chi^{2}$ per space point in the TPC to be less than 4. Daughter tracks from
reconstructed kinks in the TPC volume are rejected in order to keep only
tracks pointing to the primary vertex. To limit the contamination from
secondary particles from material (see Sec. 2.4), requirements are imposed on
the Distance of Closest Approach of each track to the primary vertex along the
beam direction (DCAz) and in the transverse plane (DCAxy) to be less than 1 cm
and 0.1 cm, respectively. The fiducial pseudo-rapidity region is defined as
$|\eta|<0.8$, which ensures a uniform acceptance in the detectors involved.

The identification of (anti-)deuterons is achieved by exploiting the
measurement of their specific ionisation energy-loss, provided by the TPC, and
via the measurement of the time-of-flight of the particles, performed with the
TOF. Due to the different acceptance of the two detectors, the TPC is used
without the TOF for $p_{\mathrm{T}}$ < 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, where the separation of
deuterons from light hadrons is very effective. Deuterons and anti-deuterons
are selected by requiring an energy loss compatible, within $\pm 3\sigma$,
with the value expected for particles having the mass and charge of the
deuteron, where $\sigma$ is the resolution of the particle energy loss in the
TPC. For $p_{\mathrm{T}}>1$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
TOF information is required together with that from the TPC. The squared mass
of the particles, $m_{\rm TOF}^{2}=p^{2}\,(t_{\rm TOF}^{2}/L^{2}-1/c^{2})$, is
then determined from the measured time-of-flight ($t_{\rm TOF}$), the momentum
($p$) and the track length ($L$), after the $3\sigma$ selection on the
particle energy-loss in the TPC. Figure 1 shows an example of the obtained
$m_{\rm TOF}^{2}$ distribution around the anti-deuteron peak for a selected
$p_{\mathrm{T}}$ interval and in the highest multiplicity class (I+II). The
$m_{\rm TOF}^{2}$ distribution is fitted using a Gaussian function with an
exponential tail towards higher masses for the signal that reflects the TOF
detector time response [22]. To describe the background the sum of two
exponential functions is used. They account for those tracks erroneously
associated to a TOF hit and for the tail of the (anti-)proton signal. For both
the TPC-only and TOF-TPC analyses the yields of deuterons and anti-deuterons
are separately extracted in each $p_{\mathrm{T}}$ interval and for each
multiplicity class.

Figure 1: TOF squared-mass distribution ($m_{\rm TOF}^{2}$) around the anti-
deuteron peak for a selected $p_{\mathrm{T}}$ interval and in the highest
multiplicity class. The solid red line represents a fit of a Gaussian function
plus an exponential right tail to the anti-deuteron signal, the grey dashed
line the fit of the background performed using the sum of two exponential
functions, and the solid blue line is the sum of the signal and background
components.

###  2.4 Rejection of secondary deuterons

The sample of identified deuterons is contaminated by those that originate
from interactions of primary particles with the detector material, e.g. knock-
out or pick-up, which are highly suppressed for anti-deuterons. The
corresponding correction, only for matter, is estimated as in [13] and is
based on a fit to the distribution of the DCAxy. The latter is determined as
the sum of two contributions: the signal of primary deuterons appears as a
Gaussian-like peak centred around zero whereas secondary nuclei contribute to
the flat underlying background. The fraction of secondary deuterons is about
40$\%$ at $p_{\mathrm{T}}$ $\simeq$ 0.6
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and decreases exponentially as
the transverse momentum increases until it becomes smaller than 5$\%$ above
1.4 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. It is observed that this
does not depend on multiplicity and therefore a correction based on the
multiplicity-integrated data sample is used to minimise the statistical
uncertainties.

###  2.5 Acceptance and efficiency

After subtracting the contamination from secondary particles, raw yields are
corrected for acceptance and tracking efficiency
($\mathrm{Acc}\times\epsilon$). This correction allows one to account for the
limited acceptance of the detectors, the particle absorption in the detector
material – mainly due to energy loss and multiple-scattering processes – and
the partial inefficiencies due to detector dead zones and inactive readout
channels. The $\mathrm{Acc}\times\epsilon$ is computed by using Monte Carlo
(MC) generated events. Standard event generators for pp collisions, e.g.
PHOJET [26] or PYTHIA [27] do not consider the production of nuclei. To
include light (anti-)nuclei, these are injected into underlying PHOJET events
with flat momentum and rapidity distributions. The ALICE detector description
is based on the GEANT3 particle transport code [28]. As discussed in [12],
GEANT3 includes only an approximate description of the interactions of light
nuclei with the detector material. The $\mathrm{Acc}\times\epsilon$ is reduced
by 6$\%$ when TOF PID is used, due to the extra (anti-)deuterons lost because
of hadronic interactions that GEANT3 does not account for. This correction is
based on the fraction of (anti-)deuterons absorbed in the TRD modules
installed between TPC and TOF, studied in data and MC simulations. More
details can be found in [13].

As already mentioned in Sec. 2.2, the $p_{\mathrm{T}}$-differential yields are
normalised to INEL>0 events. Raw yields need to be further corrected for the
amount of (anti-)deuteron signals lost because of the event selection. This
correction is expected to be dependent on multiplicity. Simulations enriched
with nuclei, such as those used to determine $\mathrm{Acc}\times\epsilon$, are
not appropriate for its estimation, because the mean number of charged
particles per event is not well described. In this respect, a MC simulation
(based on PYTHIA as event generator) that reproduces the charged-particle
multiplicity measured in the data can be safely used. Since such simulations
do not contain nuclei, the fraction of signal lost in the event selection is
estimated for (anti-)deuterons by extrapolating the ones determined for pions,
kaons and protons. This has been done by exploiting the linear dependence of
the lost signal as a function of the mass of the particles, which was observed
in simulations. For the lowest multiplicity class, the resulting fraction of
deuteron loss is about 4$\%$ at $p_{\mathrm{T}}$ $\simeq$ 0.6
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and rapidly decreases as the
transverse momentum increases until it becomes smaller than 1$\%$ above 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. For higher multiplicities, the
correction is negligible.

###  2.6 Systematic uncertainties

There are several contributions to the total systematic uncertainty. Two
contributions arise from the particular set of selections applied to the
sample of tracks for the analysis and from the particle identification
procedure. The rejection of secondary deuterons also introduces an
uncertainty. Other significant uncertainties originate from the limited
knowledge of the absorption of light (anti-)nuclei in the detector material
and of the amount of material itself. The ITS-TPC track matching efficiency is
also known with finite precision. The normalisation of the
$p_{\mathrm{T}}$-differential yields to INEL>0 events is an additional source
of uncertainty. All contributions to the total systematic uncertainty are
summarised in Tab. 2 for the highest multiplicity class (I+II). More details
are presented in the following.

The systematic uncertainty related to PID is smaller at low transverse
momenta, down to $3\%$ at 0.6 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
because of a clear separation of the deuteron and anti-deuteron signals in the
TPC. At higher $p_{\mathrm{T}}$, the presence of the background, which
contaminates the signal in the TOF significantly, introduces an additional
uncertainty. The latter increases gradually from about 3$\%$ at 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ to about 22–$23\%$ for
$p_{\mathrm{T}}\approx 3$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The
uncertainty at high transverse momentum, at $p_{\mathrm{T}}\approx 3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, originates mainly from the
right tail of the proton squared-mass distribution, which strongly
contaminates the (anti-)deuteron signal in the TOF.

In the case of the TPC PID, the systematic uncertainty estimate is based on a
variation of the maximum accepted difference between the measured and expected
energy-loss value for the (anti-)deuteron-mass hypothesis. In the case of TOF
PID, the bin width of the squared-mass distribution and the range of the fit
have been varied. At intermediate transverse momenta ($1<p_{\rm T}<1.6~{}{\rm
GeV}/c$), where the background under the (anti-)deuteron signal peak in the
$m_{\rm TOF}^{2}$ distribution is almost negligible, the yield is extracted by
bin counting. This result is compared to the one obtained with the fit
procedure described in Sec. 2.3 in order to estimate the systematic
uncertainty. The uncertainty resulting from the track selection has been
estimated through variations of the specific requirements used in the
analysis. The rejection of secondary deuterons is also a source of uncertainty
at low $p_{\mathrm{T}}$ while it is negligible for anti-deuterons. The
uncertainty is estimated by varying the maximum $|$DCA${}_{z}|$ of the
accepted tracks, which has a significant impact on the estimated fraction of
primary particles. A $p_{\mathrm{T}}$-independent uncertainty of 3$\%$ is
associated with the difference between the ITS-TPC track matching efficiency
in data and MC simulations [29, 25]. The systematic uncertainty related to the
normalisation of the spectra to the INEL>0 event class is found to be not
larger than $1\%$ for all multiplicities and transverse momenta. This
uncertainty is estimated as the difference between the corresponding proton
and deuteron corrections (see Sec. 2.5).

The limited knowledge of the hadronic interaction cross section of the primary
particles in the detector material leads to a systematic uncertainty of 6$\%$
uniform in $p_{\mathrm{T}}$, as estimated in [13]. Moreover, the uncertainty
of the material budget contributes with an additional $3\%$ to the total
uncertainty. For its evaluation, the effect of varying the relative amount of
material by $\pm 10\%$ has been studied through simulations. All the mentioned
contributions have been summed in quadrature. The total systematic uncertainty
depends moderately on multiplicity: the relative difference between different
multiplicity classes is 20–30$\%$ at most.

Source | d ($\rm\overline{d}$)
---|---
$p_{\mathrm{T}}$ | 0.6 GeV/${\it c}$ | 3 GeV/${\it c}$
Particle identification | 3$\%$ | 24$\%$ (26$\%$)
Track selection | 1$\%$ | 5$\%$
Secondary nuclei | 7$\%$ (negl.) | negl.
ITS-TPC matching | 3$\%$ | 3$\%$
Norm. to INEL > 0 events | 1$\%$ | negl.
Hadronic interactions | 6$\%$ | 6$\%$
Material budget | 3$\%$ | 3$\%$
Total | 11$\%$ (8$\%$) | 26$\%$ (27$\%$)
Table 2: Systematic uncertainties on deuteron and anti-deuteron transverse-
momentum spectra at low and high $p_{\mathrm{T}}$ for the highest multiplicity
class (I+II). The values in parentheses apply to anti-deuterons and are only
given where they differ from those related to deuterons. Otherwise, where it
is not explicitly specified, the values are common to particles and anti-
particles.

##  3 Results and discussion

Figure 2: Transverse-momentum spectra of deuterons (left) and anti-deuterons (right) measured at mid-rapidity in pp collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ in the considered multiplicity classes. The vertical bars are the statistical uncertainties, the open boxes represent the systematic ones. The dashed lines correspond to individual fits to the data performed with the Lévy-Tsallis function (see Eq. 1). The spectra have been scaled with the indicated factors for better visibility. | Multiplicity Class | ${\rm d}N/{\rm d}y\,(\times 10^{-4})$ |  $\mathcal{h}p_{\rm T}\mathcal{i}$ ($\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | Extr. ($\%$)
---|---|---|---|---
| I+II | $10.14\pm 0.15\pm 1.17$ | $1.28\pm 0.01\pm 0.06$ | 23
| III | $7.01\pm 0.13\pm 0.81$ | $1.19\pm 0.02\pm 0.07$ | 27
d | IV+V | $5.76\pm 0.08\pm 0.64$ | $1.11\pm 0.01\pm 0.05$ | 29
| VI+VII | $3.55\pm 0.04\pm 0.39$ | $1.05\pm 0.01\pm 0.05$ | 30
| VIII+IX+X | $1.15\pm 0.01\pm 0.17$ | $0.82\pm 0.01\pm 0.05$ | 39
| I+II | $10.87\pm 0.18\pm 1.47$ | $1.47\pm 0.02\pm 0.16$ | 31
| III | $7.44\pm 0.15\pm 0.82$ | $1.16\pm 0.02\pm 0.06$ | 29
${\rm\overline{d}}$ | IV+V | $5.68\pm 0.13\pm 0.68$ | $1.17\pm 0.02\pm 0.10$ | 31
| VI+VII | $3.88\pm 0.06\pm 0.44$ | $1.05\pm 0.01\pm 0.07$ | 35
| VIII+IX+X | $1.07\pm 0.02\pm 0.15$ | $0.85\pm 0.01\pm 0.05$ | 39
Table 3: $p_{\mathrm{T}}$-integrated yield, $\mathrm{d}N/\mathrm{d}y$, and
mean transverse momentum, $\langle p_{\mathrm{T}}\rangle$, along with the
extrapolated fraction (Extr.) of deuterons (top) and anti-deuterons (bottom)
in pp collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ in different multiplicity
classes. The first uncertainty is statistical, the second one is the sum in
quadrature of the systematic error and the uncertainty due to the spectrum
extrapolation, as described in the text.

###  3.1 Transverse momentum spectra

The transverse momentum spectra of deuterons and anti-deuterons in the
considered multiplicity classes are shown in Fig. 2, in the left and right
panels, respectively. In order to extrapolate the spectra to low and high
$p_{\mathrm{T}}$, the distributions are individually fitted with the Lévy-
Tsallis function [30, 29],

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

where $m_{\rm T}=\sqrt{p_{\rm T}^{2}+m_{0}^{2}}$ is the transverse mass,
$m_{0}$ is the rest mass of the particle (deuteron for the present analysis)
and $n$, $C$ and $\mathrm{d}N/\mathrm{d}y$ are the free fit parameters. As
observed already in [12] for inelastic collisions and in [25] for light
hadrons, the Lévy-Tsallis function describes the spectra in all multiplicity
classes rather well. The $p_{\mathrm{T}}$-integrated yield per unit of
rapidity ($\mathrm{d}N/\mathrm{d}y$) at mid-rapidity and the mean transverse
momentum $\langle p_{\mathrm{T}}\rangle$ are reported in Tab. 3. These are
obtained by integrating the $p_{\mathrm{T}}$-differential yields in the
measured $p_{\mathrm{T}}$ region and the fitted Lévy-Tsallis function in the
extrapolated regions at low and high $p_{\mathrm{T}}$. The fraction of yield
contained in these two regions is also reported in the table. The first
uncertainty of $\mathrm{d}N/\mathrm{d}y$ and $\langle p_{\mathrm{T}}\rangle$
reported in Tab. 3 represents the statistical uncertainty, whereas the second
is the systematic uncertainty. The latter includes the uncertainty due to the
extrapolation of the spectra, which amounts to about 4 to $9\%$ (from high to
low multiplicity) of the integrated yield and to about 1 to $5\%$ of the mean
$p_{\mathrm{T}}$. Both these estimates are derived by fitting the spectra with
other functional forms, which describe the low and the high $p_{\mathrm{T}}$
regions of the spectra in a different way. These include Boltzmann, Fermi-
Dirac, Bose-Einstein, $m_{\rm T}$-exponential and $p_{\mathrm{T}}$-exponential
distributions [31].

Table 3 shows that the yield of deuterons and anti-deuterons increases with
multiplicity, mirroring the fact that the number of constituent nucleons per
event is also rising [25]. The multiplicity dependence of the $\langle
p_{\mathrm{T}}\rangle$ reflects the observed hardening of the deuteron and
anti-deuteron spectra from low to high multiplicity.

The anti-deuteron to deuteron ratio is shown in Fig. 3 for the considered
multiplicity classes. These ratios are compatible with unity within $2\sigma$
(where $\sigma$ is the uncertainty in each $p_{\mathrm{T}}$ bin) in the
measured $p_{\mathrm{T}}$ range and for all multiplicity classes, and are in
agreement with results for protons [25]. According to coalescence models,
${\rm\overline{d}}/{\rm d}$ is equal to $({\rm\overline{p}}/{\rm p})^{2}$ and
the anti-proton to proton ratio is indeed compatible with unity [25],
independent of $p_{\mathrm{T}}$ and of charged-particle multiplicity. For each
multiplicity class, the average of the anti-deuteron to deuteron ratio over
all $p_{\mathrm{T}}$ bins in Fig. 3 is reported in Tab. 4.

Figure 3: Anti-deuteron to deuteron ratio as a function of $p_{\mathrm{T}}$ in the considered multiplicity classes in pp collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$. The vertical bars represent the statistical uncertainty and the open boxes the systematic ones. Multiplicity Class | ${\rm\overline{d}}/{\rm d}$
---|---
I+II | $0.93\pm 0.03\pm 0.13$
III | $1.01\pm 0.04\pm 0.15$
IV+V | $0.92\pm 0.03\pm 0.13$
VI+VII | $0.96\pm 0.03\pm 0.13$
VIII+IX+X | $0.93\pm 0.03\pm 0.14$
Table 4: Anti-deuteron to deuteron ratio averaged over all measured
$p_{\mathrm{T}}$ bins in each multiplicity class in pp collisions at
$\sqrt{s}~{}=7\,\mathrm{~{}TeV}$. The first uncertainty is statistical and the
second is the systematic contribution.

###  3.2 Coalescence parameter $B_{2}$

The production of light nuclei and anti-nuclei in pp collisions is expected to
be the result of the coalescence of protons and neutrons that are nearby in
space and have similar velocities at the last stage of the collision. This
process is described by models with the parameter $B_{A}$, where $A$ is the
mass number of the nucleus under study. Here, it corresponds to $B_{2}$, which
relates the invariant differential yield of deuterons to the one of protons
via the following equation [1, 4]

$\frac{1}{2\pi p_{\rm T}^{\rm d}}\frac{{\rm d}^{2}N^{\rm d}}{{\rm d}p_{\rm
T}^{\rm d}{\rm d}y}=B_{2}\;\left(\frac{1}{2\pi p_{\rm T}^{\rm p}}\frac{{\rm
d}^{2}N^{\rm p}}{{\rm d}p_{\rm T}^{\rm p}{\rm d}y}\right)^{2}\,.$ (2)

In Eq. 2 the proton yield is measured at a value of half of the deuteron
transverse momentum i.e. $p_{\rm T}^{\rm p}=p_{\rm T}^{\rm d}/2$ and neutrons
are assumed to have the same invariant differential yield as protons. Figure 4
shows the $B_{2}$ parameter computed according to Eq. 2 as a function of the
transverse momentum per nucleon ($p_{\rm T}/A$) for the different multiplicity
classes, scaled by constant factors. The differential yields for deuterons and
anti-deuterons shown in Fig. 2 are used. The $p_{\mathrm{T}}$ spectra of
(anti-)protons are those published in [25]. The statistical uncertainties in
Fig. 4 are dominated by those of (anti-)deuterons, while the systematic
uncertainties by those of (anti-)protons, because the proton term enters to
the square power in Eq. 2. In any of the considered multiplicity classes,
within the experimental precision $B_{2}$ does not show a significant
$p_{\mathrm{T}}$ dependence as expected in a simple coalescence model [1],
where a point-like source is assumed that emits nucleons without any
correlation between proton and neutron momenta.

Figure 4: Coalescence parameter $B_{2}$ of (anti-)deuterons as a function of
the transverse momentum per nucleon, $p_{\rm T}/A$, in the considered
multiplicity classes in pp collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$. The
vertical bars represent the statistical uncertainties, the open boxes the
systematic ones. The distributions in each class are scaled by constant
factors to improve visibility. Figure 5: Coalescence parameter
$B_{2}^{\prime}$ of anti-deuterons as a function of the transverse momentum
per nucleon $p_{\rm T}/A$ (red shaded band, see text for details). The result
is compared with the experimental data for $B_{2}$ measured in inelastic pp
collisions at $\sqrt{s}~{}=7\,\mathrm{~{}TeV}$ [13].

In [13], where the results have been reported for inelastic pp collisions
without any selection on the event multiplicity, the $B_{2}$ parameter (red
circles in Fig. 5) was found to increase with the transverse momentum. This
trend was reproduced by an afterburner model [32], which looks for
correlations between nucleons produced by QCD-inspired event generators, and
explained as a hard scattering effect [13]. In this work the coalescence
parameter is re-evaluated for the multiplicity-integrated sample, indicated
hereafter as $B_{2}^{\prime}$, by means of the following equation

$B_{2}^{\prime}=\frac{\sum\limits_{i={\rm I+II}}^{\rm
VIII\;to\;X}\;\;(N_{i}/N)\;B_{2}^{i}\;(S_{{\rm
p}}^{i})^{2}}{\left(\;\sum\limits_{i={\rm I+II}}^{\rm
VIII\;to\;X}\;\;(N_{i}/N)\;S_{{\rm p}}^{i}\right)^{2}}\,,$ (3)

where $S_{\rm p}^{i}=1/(2\pi p_{\rm T}){\rm d}^{2}N_{\rm p}^{i}/({\rm d}p_{\rm
T}{\rm d}y)$ is the invariant differential yield of protons or anti-protons
[25], and $N_{i}/N$ the fraction of events in the $i$-th multiplicity class.
The set of the $p_{\mathrm{T}}$-independent $B_{2}^{i}$ measured in this work
are also used as inputs of Eq. 3. The result for $\rm\overline{d}$ is shown in
Fig. 5 as a red shaded band, after being normalised to inelastic collisions
via the scaling factor 0.852 [33]. The width of the band represents an
uncertainty of about 4$\%$. This uncertainty includes a 2-3$\%$ contribution
obtained by considering finer multiplicity classes than those used in the
anti-deuteron analysis (anti-proton spectra are measured in [25], $B_{2}$ has
been interpolated), summed in quadrature to a 3$\%$ difference between
deuteron and anti-deuteron results. The level of agreement with the
experimental points from [13] indicates that part of the rise of $B_{2}$, in
the measured $p_{\rm T}/A$ range, can be explained within a simple coalescence
picture as a consequence of the hardening of the proton spectra with
increasing multiplicity. The hint for deviation at high $p_{\mathrm{T}}$
leaves room for additional hard scattering effects, as the one invoked in [13,
32].

It is worth noting that once the $B_{2}$ parameter is measured directly from
the multiplicity-integrated sample and normalised to inelastic collisions, the
result obtained here is in agreement with the one published in [13]. In
central Pb–Pb collisions the coalescence parameter exhibits an increasing
trend with the transverse momentum [12] that might be attributed to the
presence of collective flow [34].

Figure 6: Coalescence parameter $B_{2}$ of (anti-)deuterons as a function of
charged-particle multiplicity at mid-rapidity in pp and Pb–Pb collisions [12]
at the LHC at the transverse momentum per nucleon of 0.7 < $p_{\rm T}/A$ < 0.8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The open boxes represent the
systematic uncertainties.

The $B_{2}$ parameter for one selected interval of transverse momentum per
nucleon (0.7 < $p_{\rm T}/A$ < 0.8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) is shown in Fig. 6 as a
function of charged-particle multiplicity density at mid-rapidity and compared
to the measurements in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=2.76\,\mathrm{~{}TeV}$ [12]. In a simple
coalescence model [1, 3], the $B_{2}$ parameter is expected to be dependent
only on the maximum relative momentum of the constituent nucleons coalescing
in the bound state and therefore no multiplicity dependence is predicted. In
pp collisions (dark green circles in Fig. 6), the extracted $B_{2}$ is
observed to vary by about 25$\%$ from the lowest to the highest multiplicity
reached in the present analysis. This effect is more pronounced in Pb–Pb
collisions and suggests that the increasing volume of the particle-emitting
source – which reduces the coalescence probability – has to be taken into
account, as done in more elaborate coalescence models [4].

Figure 7: Mean transverse momentum $\langle p_{\mathrm{T}}\rangle$ of
deuterons and protons as a function of charged-particle multiplicity at mid-
rapidity in pp collisions at the LHC. The open boxes represent the total
systematic uncertainty while the contribution that is uncorrelated across
multiplicity (where estimated) is shown with the shaded boxes. The full shaded
area corresponds to the expected mean $p_{\mathrm{T}}$ of deuterons from a
simple coalescence model assuming a $p_{\mathrm{T}}$-independent $B_{2}$
value. The hollow and dashed areas correspond to the mean $p_{\mathrm{T}}$ of
protons and deuterons calculated by using the Blast-Wave parameters that
simultaneously fit to the pion, kaon and proton spectra.

###  3.3 Mean transverse momentum

The mean transverse momenta of deuterons and protons are shown as a function
of the charged-particle multiplicity in pp collisions in Fig. 7. The
difference between deuteron and proton mean momenta is significant, except at
extremely low charged-particle multiplicity. In high-multiplicity pp
collisions, the ratio between the $\langle p_{\mathrm{T}}\rangle$ of deuterons
and protons is about 1.2 and is smaller than the value (about 1.6) measured in
central Pb–Pb collisions [12], where the established mass ordering is in
general attributed to the emission of particles from a radially expanding
source.
In pp collisions the multiplicity dependence of the deuteron mean transverse
momentum is well reproduced by computing the deuteron spectra using Eq. 2 with
the proton spectra as input and assuming, as in a simple coalescence model, a
$p_{\mathrm{T}}$-independent $B_{2}$ value. Note that in central Pb–Pb
collisions the Blast-Wave model [18] – a hydrodynamic-inspired model which
describes particle production assuming that these are emitted from an
expanding thermalised source – simultaneously fits light nuclei (deuterons and
${}^{3}{\rm He}$) together with light hadrons [12]. On the contrary, in pp
collisions, the $\langle p_{\mathrm{T}}\rangle$ of deuterons is not correctly
reproduced by using the Blast-Wave parameters that simultaneously describe
pion, kaon and proton spectra from [25], as clearly shown in Fig. 7. Since the
Blast-Wave model is able to reproduce experimental data solely in Pb–Pb
collisions, we have evidence that a full hydrodynamic approach does not
concurrently describe the production of light hadrons and nuclei in pp
collisions. The latter is consistent with a coalescence picture where the
formation of weakly bound composite particles is expected to occur only at the
last stage of the system evolution after the collision, namely after the
kinetic freeze-out.

###  3.4 Deuteron-to-proton ratio

Figure 8 shows the ratio between the $p_{\mathrm{T}}$-integrated yield of
deuterons and protons as a function of multiplicity, including all the
presently available measurements performed at the LHC. For computing the
multiplicity-dependent ratio in pp collisions at
$\sqrt{s}~{}=7\,\mathrm{~{}TeV}$, the deuteron yields reported in Tab. 3 are
used. The $\mathrm{d}N/\mathrm{d}y$ of protons are those reported in [24]. In
a naive approach, one would predict an increase of the deuteron-to-proton
ratio since the number of nucleons increases with the charged-particle
multiplicity. In pp collisions, the observed trend of the d/p ratio is in
qualitative agreement with this expectation, further supported by the fact
that the systematic uncertainties are expected to be largely correlated across
multiplicity. In more sophisticated coalescence models [4], the source volume
is also taken into account and the rise of the d/p ratio is expected to be the
result of an enhanced nucleon density, and not simply related to the nucleon
abundances. The prediction of [4] qualitatively describes the data if the rise
in the nucleon abundance dominates over the increase in the volume size in pp
collisions. No significant multiplicity dependence of the d/p ratio is
observed in Pb–Pb collisions within the achieved experimental precision [12],
in agreement with expectations from thermal-statistical models [16, 35].

Figure 8: Ratio between the $p_{\mathrm{T}}$-integrated yield of deuterons and
protons as a function of charged-particle multiplicity at mid-rapidity in pp
(this work) and Pb–Pb collisions [12] at the LHC. The deuteron-to-proton ratio
measured in inelastic pp collisions at
$\sqrt{s}~{}=0.9,2.76~{}$and$~{}7\,\mathrm{~{}TeV}$ [13] has also been
reported.

##  4 Conclusions

The transverse-momentum spectra of deuterons and anti-deuterons in pp
collisions at $\sqrt{s}$ = 7 TeV have been presented in five multiplicity
classes. They are combined with the primary proton spectra to extract the
coalescence parameter $B_{2}$. The latter exhibits an approximately constant
behaviour with the transverse momentum per nucleon in multiplicity classes in
the measured $p_{\rm T}/A$ range, in agreement with a simple coalescence
model, where uncorrelated particle emission from a point-like source is
assumed. A simple coalescence picture cannot, however, explain the
multiplicity dependence of the $B_{2}$ parameter at fixed transverse momentum
($p_{\rm T}/A$ = 0.75 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$),
observed also in Pb–Pb collisions. Instead, these observations point toward a
dependence of the coalescence process on the volume of the particle-emitting
source. In fact, the increasing volume of the particle-emitting source with
multiplicity plays an effective role in reducing the coalescence probability
as predicted by more elaborate models. These models are able to describe data
even in the smallest colliding system at the LHC, as reported in this letter,
where the spatial extension of the source is comparable to the deuteron size.
Coalescence model calculations, precisely correlating the size of the hadronic
emission region with the multiplicity, need to be performed to quantitatively
support the current interpretation of the results.

The mean transverse momentum of deuterons has been measured as a function of
the charged-particle multiplicity. In pp collisions, the hydrodynamic-inspired
Blast-Wave model, which assumes that the particles are emitted thermally from
an expanding source, does not describe the production of nuclei with identical
freeze-out conditions as lighter hadrons. While in central Pb–Pb collisions
there is evidence that nuclei and anti-nuclei participate in the expansion of
the fireball together with non-composite light hadrons, in
$\mathrm{p\kern-0.50003ptp}$ collisions such evidence is missing.

All presently available measurements of the $p_{\mathrm{T}}$-integrated d/p
ratio at the LHC have been discussed as a function of the charged-particle
multiplicity. The observed multiplicity dependence of the d$/$p ratio suggests
that the rise with multiplicity of the number of nucleons available for
coalescence is faster than the increase of the source volume in small
colliding systems at the LHC. The multiplicity dependence of d$/$p, as well as
that of $B_{2}$, hints at a continuous evolution of deuteron production from
low-multiplicity pp to Pb–Pb collisions. Measurements at intermediate
multiplicities, such as those reached in p–Pb collisions, are being performed
to confirm this picture.

The observed similarities between $\mathrm{p\kern-0.50003ptp}$ and heavy-ion
collisions can be traced back to common underlying production mechanisms of
light (anti-)nuclei. The differences, such as the one appearing in the mean
transverse momentum of deuterons, are extremely interesting because they can
shed light on the possibility that nuclei may emerge at different stages of
the collision depending on the initial conditions.

## 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 Rlégion des Pays de la Loire, France;
Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (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. Acharyaorg140&F.T.-. Acostaorg20&D. Adamováorg93&S.P. Adhyaorg140&A.
Adlerorg74&J. Adolfssonorg80&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M.
Agnelloorg31&Z. Ahammedorg140&S. Ahmadorg17&S.U. Ahnorg76&S. Aiolaorg145&A.
Akindinovorg64&M. Al-Turanyorg104&S.N. Alamorg140&D.S.D. Albuquerqueorg121&D.
Aleksandrovorg87&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg72&B.
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Keilorg34&B. Ketzerorg42&Z. Khabanovaorg89&A.M. Khanorg6&S. Khanorg17&S.A.
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Trubnikovorg2&W.H. Trzaskaorg126&T.P. Trzcinskiorg141&B.A. Trzeciakorg63&T.
Tsujiorg131&A. Tumkinorg106&R. Turrisiorg56&T.S. Tveterorg21&K.
Ullalandorg22&E.N. Umakaorg125&A. Urasorg134&G.L. Usaiorg24&A.
Utrobicicorg97&M. Valaorg38,org115&L. Valencia Palomoorg44&N. Valleorg138&N.
van der Kolkorg63&L.V.R. van Doremalenorg63&J.W. Van Hoorneorg34&M. van
Leeuwenorg63&P. Vande Vyvreorg34&D. Vargaorg144&A. Vargasorg44&M.
Vargyasorg126&R. Varmaorg48&M. Vasileiouorg83&A. Vasilievorg87&O. Vázquez
Doceorg116,org103&V. Vecherninorg111&A.M. Veenorg63&E. Vercellinorg26&S.
Vergara Limónorg44&L. Vermuntorg63&R. Vernetorg7&R. Vértesiorg144&L.
Vickovicorg35&J. Viinikainenorg126&Z. Vilakaziorg130&O. Villalobos
Baillieorg108&A. Villatoro Telloorg44&G. Vinoorg52&A. Vinogradovorg87&T.
Virgiliorg30&V. Vislaviciusorg88&A. Vodopyanovorg75&B. Volkelorg34&M.A.
Völklorg101&K. Voloshinorg64&S.A. Voloshinorg142&G. Volpeorg33&B. von
Hallerorg34&I. Vorobyevorg103,org116&D. Voscekorg115&J. Vrlákováorg38&B.
Wagnerorg22&M. Wangorg6&Y. Watanabeorg132&M. Weberorg112&S.G. Weberorg104&A.
Wegrzynekorg34&D.F. Weiserorg102&S.C. Wenzelorg34&J.P. Wesselsorg143&U.
Westerhofforg143&A.M. Whiteheadorg124&E. Widmannorg112&J. Wiechulaorg69&J.
Wikneorg21&G. Wilkorg84&J. Wilkinsonorg53&G.A. Willemsorg143,org34&E.
Willsherorg108&B. Windelbandorg102&W.E. Wittorg129&Y. Wuorg128&R. Xuorg6&S.
Yalcinorg77&K. Yamakawaorg45&S. Yanoorg136&Z. Yinorg6&H. Yokoyamaorg63&I.-K.
Yooorg18&J.H. Yoonorg60&S. Yuanorg22&V. Yurchenkoorg2&V. Zaccoloorg58,org25&A.
Zamanorg15&C. Zampolliorg34&H.J.C. Zanoliorg120&N. Zardoshtiorg34,org108&A.
Zarochentsevorg111&P. Závadaorg67&N. Zaviyalovorg106&H. Zbroszczykorg141&M.
Zhalovorg96&X. Zhangorg6&Y. Zhangorg6&Z. Zhangorg6,org133&C. Zhaoorg21&V.
Zherebchevskiiorg111&N. Zhigarevaorg64&D. Zhouorg6&Y. Zhouorg88&Z.
Zhouorg22&H. Zhuorg6&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg27,org10&M.B.
Zimmermannorg34&G. Zinovjevorg2&N. Zurloorg139&

## 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 Institute of Information Technology (CIIT), 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 for Theoretical and Experimental Physics, Moscow, Russia

org65Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org66Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org67Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org68Institute of Space Science (ISS), Bucharest, Romania

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org71Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org72Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org73iThemba LABS, National Research Foundation, Somerset West, South Africa

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org79Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org80Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org81Nagasaki Institute of Applied Science, Nagasaki, Japan

org82Nara Women’s University (NWU), Nara, Japan

org83National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org84National Centre for Nuclear Research, Warsaw, Poland

org85National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org86National Nuclear Research Center, Baku, Azerbaijan

org87National Research Centre Kurchatov Institute, Moscow, Russia

org88Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org89Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org90NRC Kurchatov Institute IHEP, Protvino, 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

org104Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org105Rudjer Bošković Institute, Zagreb, Croatia

org106Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org107Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org108School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org109Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org110Shanghai Institute of Applied Physics, Shanghai, China

org111St. Petersburg State University, St. Petersburg, Russia

org112Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org113SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org114Suranaree University of Technology, Nakhon Ratchasima, Thailand

org115Technical University of Košice, Košice, Slovakia

org116Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org117The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org118The University of Texas at Austin, Austin, Texas, United States

org119Universidad Autónoma de Sinaloa, Culiacán, Mexico

org120Universidade de São Paulo (USP), São Paulo, Brazil

org121Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org122Universidade Federal do ABC, Santo Andre, Brazil

org123University College of Southeast Norway, Tonsberg, Norway

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 Tennessee, Knoxville, Tennessee, United States

org130University of the Witwatersrand, Johannesburg, South Africa

org131University of Tokyo, Tokyo, Japan

org132University of Tsukuba, Tsukuba, Japan

org133Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org136 Université Paris-Saclay Centre d¿Études de Saclay (CEA), IRFU,
Department de Physique Nucléaire (DPhN), Saclay, France

org137Università degli Studi di Foggia, Foggia, Italy

org138Università degli Studi di Pavia, Pavia, Italy

org139Università di Brescia, Brescia, Italy

org140Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org141Warsaw University of Technology, Warsaw, Poland

org142Wayne State University, Detroit, Michigan, United States

org143Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org144Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org145Yale University, New Haven, Connecticut, United States

org146Yonsei University, Seoul, Republic of Korea