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Production of light (anti)nuclei in pp collisions at $$\sqrt{s} = 5.02$$ TeV

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The study of the production of nuclei and antinuclei in pp collisions has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. In this paper, the production of protons, deuterons and $$^{3}\mathrm {He}$$ 3 He and their charge conjugates at midrapidity is studied as a function of the charged-particle multiplicity in inelastic pp collisions at $$\sqrt{s}=5.02$$ s = 5.02 TeV using the ALICE detector. Within the uncertainties, the yields of nuclei in pp collisions at $$\sqrt{s}=5.02$$ s = 5.02 TeV are compatible with those in pp collisions at different energies and to those in p–Pb collisions when compared at similar multiplicities. The measurements are compared with the expectations of coalescence and Statistical Hadronisation Models. The results suggest a common formation mechanism behind the production of light nuclei in hadronic interactions and confirm that they do not depend on the collision energy but on the number of produced particles.
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Eur. Phys. J. C (2022) 82:289
https://doi.org/10.1140/epjc/s10052-022-10241-z
Regular Article - Experimental Physics
Production of light (anti)nuclei in pp collisions at s=5.02 TeV
ALICE Collaboration
CERN, 1211 Geneva 23, Switzerland
Received: 15 December 2021 / Accepted: 21 March 2022 / Published online: 4 April 2022
© CERN for the beneﬁt of the ALICE collaboration 2022
Abstract The study of the production of nuclei and antin-
uclei in pp collisions has proven to be a powerful tool to
investigate the formation mechanism of loosely bound states
in high-energy hadronic collisions. In this paper, the produc-
tion of protons, deuterons and 3He and their charge conju-
gates at midrapidity is studied as a function of the charged-
particle multiplicity in inelastic pp collisions at s=5.02
TeV using the ALICE detector. Within the uncertainties, the
yields of nuclei in pp collisions at s=5.02 TeV are com-
patible with those in pp collisions at different energies and to
those in p–Pb collisions when compared at similar multiplic-
ities. The measurements are compared with the expectations
of coalescence and Statistical Hadronisation Models. The
results suggest a common formation mechanism behind the
production of light nuclei in hadronic interactions and con-
ﬁrm that they do not depend on the collision energy but on
the number of produced particles.
1 Introduction
Light (anti)nuclei are abundantly produced in ultrarelativis-
tic heavy-ion collisions [13] at the Large Hadron Collider
(LHC), but their measurement in pp collisions is challeng-
ing due to their lower production yields. As a consequence,
until few years ago there were only few measurements of the
production rates of (anti)nuclei in small collision systems
[1,46]. This has recently changed thanks to the large pp
data samples collected by ALICE at the LHC, which allow
us to perform more precise and differential measurements of
the production of light (anti)nuclei. In this paper, we present
the detailed study of the multiplicity and transverse momen-
tum dependence of (anti)proton, (anti)deuteron and (anti)3He
production in pp collisions at s=5.02 TeV. The results
shown in the following are the most accurate obtained so far
in small systems and represent the full compilation of data
available for pp collisions at different energies at the end of
theLHCRun2.
e-mail: alice-publications@cern.ch
The production mechanism of light (anti)nuclei in high-
energy hadronic collisions is not fully understood. The
classes of models used for comparison with the experimental
results are the Statistical Hadronisation Models (SHM) and
the coalescence models. SHMs assume that particles origi-
nated from an excited region evenly occupy all the available
states in phase space [7]. Pb–Pb collisions, characterised by
a large extension of the particle-emitting source and hence
considered as large systems, are described according to a
grand canonical ensemble [8]. On the contrary, pp and p–Pb
collisions, which are characterised by a small size and are
considered as small systems, must be described based on a
canonical ensemble, requiring the local conservation of the
appropriate quantum numbers [9]. The expression Canonical
Statistical Model (CSM) is used to underline the canonical
description.
An important observable that provides information on the
production mechanism is the ratio between the pT-integrated
yields of nuclei and protons. The measured d/p and 3He/p
ratios show a rather constant behaviour as a function of cen-
trality in Pb–Pb collisions. In contrast to that, they increase
in pp and p–Pb collisions with increasing multiplicity, ﬁnally
reaching the values measured in Pb–Pb collisions [1,10,11].
The constant nuclei-to-proton ratios in large collision sys-
tems is predicted by the SHMs [12], while the experimen-
tally determined difference between small and large systems
can be qualitatively explained as an effect of the canonical
suppression of the nuclei yields for small system sizes. The
prediction of the CSM saturates towards the grand canonical
value at larger system size [13].
In coalescence models, (anti)nuclei are formed by nucle-
ons close in phase space [14]. In this approach, the coales-
cence parameter BArelates the production of (anti)protons
to the one of (anti)nuclei. BAis deﬁned as
BApp
T=1
2πpA
T
d2NA
dydpA
T1
2πpp
T
d2Np
dydpp
TA
,(1)
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289 Page 2 of 16 Eur. Phys. J. C (2022) 82 :289
where pTis the transverse momentum, ythe rapidity and N
the number of particles. The labels p and Aare used to denote
properties related to protons and nuclei with mass number A,
respectively. The production spectra of the (anti)protons are
evaluated at the transverse momentum of the nucleus divided
by the mass number, so that pp
T=pA
T/A. Neutron spectra
are assumed to be equal to proton spectra, due to the isospin
symmetry restoration in hadron collisions at the LHC. Since
the coalescence process is expected to occur at the late stages
of the collision, the BAparameter is related to the emission
volume. In a simple coalescence approach, which describes
the uncorrelated particle emission from a point-like source,
BAis expected to be independent of pTand multiplicity. In
this context, the measurements of the nuclei-to-proton ratios
and of the BAparameters in pp collisions at s=5.02 TeV
reported in this paper are important to complete the present
picture of the production of light nuclei in small systems.
In addition, the increased statistics exploited in the present
analysis will allow us to better constrain the models, thus to
provide important inputs to both the theoretical and experi-
mental communities.
2 The ALICE apparatus
A detailed description of the ALICE detectors can be found in
mation is given on the sub-detectors used to perform the
analysis presented in this work, namely the V0, the Inner
Tracking System (ITS), the Time Projection Chamber (TPC)
and the Time-of-Flight (TOF). All of them are located inside
a solenoidal magnet creating a magnetic ﬁeld parallel to the
beam line, with an intensity of 0.5 T for the data sample here
considered.
The V0 detector [17] is formed by two arrays of scintilla-
tion counters placed around the beam pipe on either side of
the interaction point. They cover the pseudorapidity ranges
2.8η5.1 (V0A) and 3.7η≤−1.7(V0C).The
collision multiplicity is estimated using the signal amplitude
in the V0 detector, which is also used as a trigger detector.
More details will be given in Sect. 3.
The ITS [18] provides high resolution track points in the
proximity of the interaction region and consists of three sub-
systems. Going from the innermost to the outermost subsys-
tem, we ﬁnd: two layers of Silicon Pixel Detectors (SPD),
two layers of Silicon Drift Detectors (SDD) and two layers
equipped with double-sided Silicon Strip Detectors (SSD).
The ITS extends radially from 3.9 to 43 cm, it is hermetic in
azimuth and it covers the pseudorapidity range |η|<0.9.
The same pseudorapidity range is covered by the TPC
[19], which is the main tracking detector, consisting of a hol-
low cylinder whose axis coincides with the nominal beam
axis. The active volume, ﬁlled with a Ne/CO2/N2gas mix-
85 cm and an outer radius of about 250 cm. The trajectory
of a charged particle is estimated using up to 159 combined
measurements (clusters) of drift times and radial positions
of the ionisation electrons. The charged-particle tracks are
then reconstructed by combining the hits in the ITS and the
measured clusters in the TPC. The TPC is also used for par-
ticle identiﬁcation (PID) by measuring the speciﬁc energy
loss (dE/dx) in the TPC gas. In pp collisions, the dE/dxin
the TPC is measured with a resolution of 5.2% [15].
The TOF [20] covers the full azimuth for the pseudorapid-
ity interval |η|<0.9. The detector is based on the Multigap
Resistive Plate Chambers (MRPC) technology and is located,
with a cylindrical symmetry, at an average distance of 380
cm from the beam axis. The particle identiﬁcation is based
on the difference between the measured time of ﬂight and
its expected value, computed for each mass hypothesis from
track momentum and length. A precise starting signal for the
measurement of the time of ﬂight by the TOF is provided by
the T0 detector, consisting of two arrays of Cherenkov coun-
ters, T0A and T0C, which cover the pseudorapidity regions
4.61 η4.92 and 3.28 η2.97, respectively [21].
The overall resolution on the particles time of ﬂight, includ-
ing the start time, is 80 ps.
3 Data sample
This analysis is based on approximately 900 million pp colli-
sions (events) at s=5.02 TeV collected in 2017 by ALICE
at the LHC. Events are selected by a minimum-bias (MB)
trigger, requiring at least one hit in each of the two V0 detec-
tors. An additional ofﬂine rejection is performed to remove
events with more than one reconstructed primary vertex (pile-
up events) and events triggered by interactions of the beam
with the residual gas in the LHC beam pipe [17]. In total,
1.8% of the collected events are rejected due to these selec-
tions.
The production of (anti)nuclei is measured around midra-
pidity, within a rapidity range of |y|<0.5, and within the
pseudorapidity interval |η|<0.8 to maximise the detector
performance. The selected tracks are required to have at least
70 reconstructed points in the TPC and two points in the ITS
in order to guarantee good track momentum and dE/dxres-
olution in the relevant pTranges. In addition, at least one hit
in the SPD is required to ensure a resolution of the distance
of closest approach to the primary vertex better than 300 µm,
both along the beam axis (DCAz) and in the transverse plane
(DCAxy)[15]. The quality of the accepted tracks is checked
by requiring the χ2per TPC reconstructed point and per ITS
reconstructed point to be less than 4 and 36, respectively.
Finally, tracks originating from kink topologies of kaon and
pion decays are rejected.
123
Eur. Phys. J. C (2022) 82 :289 Page 3 of 16 289
Data are divided into multiplicity intervals classiﬁed by
a roman numeral from I to X, going from the highest to
the lowest multiplicity [10]. In order to achieve a higher
statistical precision, classes are merged into nine classes
for (anti)protons and (anti)deuterons and into two classes
for (anti)helion. The multiplicity classes are deﬁned from
the mean of the V0 signal amplitudes as percentiles of the
INEL >0 pp cross section, where INEL >0 events are
deﬁned as collisions with at least one charged particle in
the pseudorapidity region |η|<1[22]. The mean charged-
particle multiplicities for each class, dNch/dη, are listed in
Table 1.
4 Data analysis
4.1 Raw yield extraction
The ﬁrst important step in the analysis is the particle identiﬁ-
cation. As already shown in previous works [1,6,10,23,24],
the identiﬁcation of (anti)nuclei is performed with two dif-
ferent methods, depending on the particle species and on the
transverse momentum. For (anti)protons and (anti)deuterons
with pT<1GeV/c, the identiﬁcation relies on the mea-
surement of the dE/dxusing the TPC. The number of signal
candidates is extracted through a ﬁt with a Gaussian with two
exponential tails to the nσTPC distribution for each pTinterval.
The nσTPC is deﬁned as the difference between the measured
and the expected dE/dxfor each particle species, divided
by dE/dxresolution of the TPC. For pT1GeV/c,itis
more difﬁcult to separate (anti)protons and (anti)deuterons
from other charged particles of |Z|=1. Therefore, PID
is performed using the TOF detector information in addi-
tion. The squared mass of the particle is evaluated as m2=
p2t2
TOF/L21/c2, where tTOF is the measured time of
ﬂight, Lis the length of the track and pis the momentum of
the particle. In order to reduce the background, the tracks are
in addition required to have |nσTPC|<3. The squared mass
distributions of the signal are ﬁtted with a Gaussian func-
tion with an exponential tail. Background originating from
other particle species or from the random match of a TOF
hit with another track signiﬁcantly increases with pTand is
modelled with the sum of Gaussian and exponential func-
tions. For (anti)helion, only the TPC dE/dxmeasurement is
used, because their signal in the TPC can be easily separated
from the one of other particle species, due to the electric
charge (Z =2). The raw yield of (anti)helion is obtained
through a ﬁt of the nσTPC with a Gaussian function for the
signal and a Gaussian function for the contamination com-
ing from (anti)triton, where present. When the background
is negligible, the raw yield is extracted by directly count-
ing the (anti)nuclei candidates. Otherwise, the TPC dE/dx
and TOF squared mass distributions are ﬁtted with the afore-
mentioned models, using an extended-maximum-likelihood
approach and the yield is obtained as a ﬁt parameter. In the
signal extraction, the ﬁt quality is monitored and a successful
Pearson test is required with the probability to reject a true
hypothesis of 5%.
4.2 Efﬁciency and acceptance correction
The raw yield must be corrected to take into account the
tracking efﬁciency and the detector acceptance. This correc-
tion is evaluated from Monte Carlo (MC) simulated events,
which are generated using the event generator PYTHIA8.21
(Monash2013 tune) [25]. However, since PYTHIA8 does not
handle the production of nuclei properly, it is necessary to
inject (anti)nuclei on top of each generated event. In each pp
collision, one deuteron, one antideuteron, one helion or one
antihelion are injected, randomly chosen from a ﬂat rapidity
distribution in the range |y|<1 and a ﬂat pTdistribution
in the range pT∈[0,10]GeV/c. The GEANT4 [26] trans-
port code is exploited to describe the hadronic interaction
of the particles propagating through the detector material.
The correction is deﬁned as the ratio between the number
of reconstructed (anti)nuclei in the rapidity range |y|<0.5
and in the pseudorapidity interval |η|<0.8 and the num-
ber of generated ones in |y|<0.5. The correction is com-
puted separately for each (anti)nucleus and for the TPC and
TOF analyses. Moreover, the raw signal needs to be corrected
for trigger inefﬁciencies. The selected events are requested
to have at least one charged-particle in the pseudorapidity
region |η|<1 (INEL >0) [22]. Some INEL >0 events can
be lost due to the ﬁnite trigger efﬁciency (event loss) and all
the particles produced in those events are lost as well (signal
loss). Hence, it is necessary to correct the spectra for the event
and the signal losses. The correction must be evaluated from
MC simulations because the number of rejected events and
lost particles is only known there. For (anti)protons, this cor-
rection is directly computed from the MC simulation because
their production is handled by the event generator. On the
contrary, (anti)nuclei are injected on top of a pp collision and
a direct estimation from the MC is not possible, because there
would be a bias in the number of lost (anti)nuclei. For this
reason, the correction for pions, kaons and protons is evalu-
ated in this case in a different MC data set with no injected
nuclei and the average value is used for (anti)deuterons and
(anti)helions. Further details on this method can be found
in [10,23]. This correction is negligible at high multiplicity
(<1‰) and becomes relevant at low multiplicity (up to 14%
for (anti)protons and (anti)deuterons, 2% for (anti)helions,
in the low pTregion pT<1GeV/c).
4.3 Secondary (anti)nuclei contamination
The contribution of secondary (anti)nuclei, i.e. (anti)nuclei
that are not produced directly in the collision, must be sub-
tracted from the total measured yields. Secondary nuclei
are mostly produced in the interaction of particles with the
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289 Page 4 of 16 Eur. Phys. J. C (2022) 82 :289
Tabl e 1 Multiplicity classes for the different measurements, with
the corresponding charged-particle multiplicity density at midrapidity
dNch/dηand percentiles of the INEL >0 pp cross section, and pT-
integrated yields dN/dyfor the different species. For protons, statistical
uncertainties are negligible with respect to systematic uncertainties
Class V0 percentile dNch/dη|ηlab |<0.5dN/dy
p(×101)d(×104)3He (×107)
I 0–1% 18.5±0.25.0±0.0±0.310.7±0.2±0.7
II 1–5% 14.5±0.24.0±0.0±0.28.10 ±0.07 ±0.39
III 5–10% 11.9±0.23.4±0.0±0.26.36 ±0.05 ±0.32
IV–V 10–20% 9.7±0.12.8±0.0±0.24.92 ±0.03 ±0.24
VI 20–30% 7.8±0.12.2±0.0±0.13.60 ±0.03 ±0.18
VII 30–40% 6.3±0.11.8±0.0±0.12.65 ±0.03 ±0.14
VIII 40–50% 5.2±0.11.5±0.0±0.11.98 ±0.02 ±0.09
IX 50–70% 3.9±0.11.1±0.0±0.11.28 ±0.01 ±0.06
X 70–100% 2.4±0.10.6±0.0±0.10.48 ±0.01 ±0.06
I–III 0–10% 13.6±0.25.4±0.3±0.7
IV–X 10–100% 4.9±0.11.5±0.1±0.4
INEL >0 0–100% 5.5±0.11.5±0.0±0.12.29 ±0.01 ±0.12 1.7±0.1±0.4
vacuum beam pipe and the detector material. Moreover, an
important contribution to secondary (anti)protons is also
given by the weak decay of heavier particles. All particles
coming from strong and electromagnetic decays are consid-
ered as primary. (Anti)deuterons and (anti)helions receive a
negligible background contribution from weak decays, since
the only known contribution comes from the decays of hyper-
triton (3
Hd+p+πand 3
H3He + π) and their antimat-
ter counterparts, whose production is known to be suppressed
in pp collisions [6]. Finally, the production of secondary
antideuterons and antihelions from material is extremely rare
due to baryon number conservation. The fraction of primary
(anti)nuclei is evaluated through a template ﬁt to the DCAxy
distribution of the data, as described in [1]. The templates
for primary and secondary (anti)protons and deuterons are
obtained from MC simulations. For (anti)protons, two tem-
plates are used to describe both (anti)protons from weak
decays and from material. While the template for primary
(anti)helions is extracted from the MC as well, this is not
possible for the template for secondaries, due to the very rare
production of antihelion. For this reason, the (anti)proton
template at half the (anti)helion pTis used as a proxy for the
(anti)helion one. This procedure is based on the assumption
that the DCAxy distributions of secondary (anti)helions can
be represented by the DCAxy distributions of (anti)protons
at a transverse momentum which is scaled with the rigidity
p/zof (anti)helion, where zis the (anti)helion electric charge.
The contribution of secondary nuclei is observed to be more
relevant at low pT(20% for protons, 40% for deuterons and
90% for helions) and to decrease exponentially with increas-
ing transverse momentum.
4.4 Systematic uncertainties
One contribution of the systematic uncertainties comes from
the adopted track selection criteria. This uncertainty is eval-
uated by varying the selections, as done in [10]. The effect of
the subtraction of secondary (anti)nuclei is studied with the
variation of the DCAzand DCAxy selections as well. This
is the most relevant contribution for (anti)helion at low pT,
decreasing with pT. The estimation of the systematic uncer-
tainty related to the raw signal extraction depends on the
considered species. For (anti)protons, the difference between
the signal extracted by direct count and the one extracted
from the ﬁt is taken into account. For (anti)deuterons, this is
obtained by varying the interval in which the direct counting
of (anti)deuterons is performed. Finally, for (anti)helion a
toy MC has been developed in order to generate 10000 TPC
dE/dxsamples that are compatible with the default one. A
possible bias in the signal extraction process is investigated
by reﬁtting each distribution and looking into the variation
of the extracted yields. Another source of systematic uncer-
tainty is given by the incomplete knowledge of the material
budget of the detector in the MC simulations. This is eval-
uated by comparing different MC simulations in which the
material budget of the ALICE detector was varied by ±4.5%
[15] after conversions. This value corresponds to the uncer-
tainty on the determination of the material budget obtained
by measuring photon conversions. The imperfect knowledge
of the hadronic interaction cross section of (anti)nuclei in
the material contributes to the systematic uncertainty as well
and depends on the particle species. Similarly, an uncertainty
related to the ITS-TPC matching is considered and eval-
uated from the difference between the ITS-TPC matching
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Eur. Phys. J. C (2022) 82 :289 Page 5 of 16 289
Tabl e 2 Summary of the contributions to the systematic uncertainties
of the yield for the INEL >0 event class for the different species
pT(GeV/c) p (%) d (%) 3He (%)
0.3 3.5 0.7 3.4 0.9 4.2
Track selection <19.5 <12 <14
Secondary particles 3.5 5 1 <116 2.5
Signal extraction 1 1.5 <17.5 <14
Material budget 2 <1<1<14.5 <1
Hadronic interaction <1<11.5 2 1 <1
ITS-TPC matching 1 2.5 1 2.5 2 2.5
Trigger inefﬁciency 2 <1<1<1<1<1
Total 4.5 11 3 9 17 7
efﬁciencies in data and MC. Finally, the trigger inefﬁciency
is also a source of systematic uncertainties. The uncertainty
is assumed to be half of the difference between the signal
loss correction (described in Sect. 4.2) and unity. It strongly
depends on the event multiplicity: it is negligible at high
multiplicity and contributes up to 7% in the lowest event
class for (anti)deuterons and (anti)helions. Where present, it
decreases with increasing pT. The list of all the sources of
systematic uncertainty for the INEL >0 multiplicity class
is reported in Table 2. The average values between matter
and antimatter are reported for (anti)protons, (anti)deuterons
and (anti)helions, for the lowest and highest pTvalues of the
measured spectra.
5 Results and discussion
The transverse-momentum spectra for (anti)protons,
(anti)deuterons and (anti)helions are shown in Fig. 1. In each
pTinterval, the reported yield is the average between mat-
ter and antimatter. Both of them are compatible, as already
observed in previous measurements carried out by ALICE
[1,10,11,23]. The measured spectra are ﬁtted in order to
extrapolate the yields in the unmeasured pT-region. For
(anti)protons and (anti)deuterons, data are ﬁtted with a Lévy–
Tsallis function [27], while for (anti)helion a simple expo-
nential depending on mTis used because it provides a better
description of the data. The fraction of the yield obtained
from the extrapolation depends on the considered particle
species and on the multiplicity class, since the pT-coverage is
generally different, being maximum (minimum) at high (low)
multiplicity. For (anti)protons, the extrapolation contributes
with a fraction of 10% (20%) of the total yield for the high-
est (lowest) multiplicity class, while for (anti)deuterons and
(anti)helions it contributes with a fraction of 25% (55%) and
35% (40%) of the total yield, respectively. The pT-spectra
are also ﬁtted with a Boltzmann function and a simple expo-
nential depending on pT, in order to quantify the effect of
the chosen function on the pT-integrated yield. The differ-
ence between the yields obtained with the reference and the
alternative functions is taken as systematic uncertainty. This
accounts for 2% for (anti)protons and (anti)deuterons,
depending on the transverse-momentum coverage of the
Fig. 1 Transverse-momentum spectra of (anti)protons (left),
(anti)deuterons (center) and (anti)helions (right) in the different mul-
tiplicity classes, reported in Table 1. (Anti)deuteron and (anti)proton
spectra are ﬁtted with a Lévy–Tsallis function [27], while (anti)helion
spectra are ﬁtted with an exponential function with respect to the
transverse mass mT
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289 Page 6 of 16 Eur. Phys. J. C (2022) 82 :289
Fig. 2 Mean transverse momentum of (anti)protons (left),
(anti)deuterons (centre) and (anti)helions (right) in pp collisions
at s=5.02 TeV, in high-multiplicity pp collisions at s=13 TeV
[24], in INEL >0 pp collisions at s=13 TeV [23,24,28]andat
s=7TeV[6,10,29], and in p–Pb collisions at sNN =5.02 TeV
[11,30,31]. The statistical uncertainties are represented by vertical bars
while the systematic uncertainties are represented by boxes
spectra, whereas for (anti)helions this accounts for 12% in
the highest multiplicity class and 19% in the lowest mul-
tiplicity class. The pT-integrated yields d N/dyare reported
in Table 1. For (anti)protons, the statistical uncertainties on
the yields are negligible, being 1% of the systematic uncer-
tainty. Figure 2shows the mean transverse momentum pT
as a function of charged-particle multiplicity. The results are
compared with those obtained in previous measurements and
they conﬁrm the increasing trend with multiplicity. More-
over, a clear mass ordering is present, as already observed
for other light-ﬂavoured particle species and for different
collision systems and energies [30,32].
Combining the information from the production spectra
of protons and nuclei, the coalescence parameter can be
evaluated according to Eq. (1). Figure 3shows the coales-
cence parameter as a function of transverse momentum for
(anti)deuterons (B2) and (anti)helions (B3). The B2and B3
values in the ﬁne multiplicity classes are consistent with a ﬂat
trend, while for the multiplicity-integrated sample the coa-
lescence parameter increases with pT. This behaviour was
already observed in other measurements by ALICE in pp col-
lisions [10,23] at different energies. In particular, it is now
understood that the increase with transverse momentum of
the coalescence parameter in INEL >0 collisions is, in large
part, due to the change in shape of the transverse momentum
spectra of protons in different multiplicity intervals [10]. It
is also worth mentioning that in pp collisions at high multi-
plicity (HM) [24], where the system size is larger than the
one resulting from INEL > 0 collisions, the raise with pT
cannot be neglected even in ﬁne multiplicity classes. In [24],
it was shown that the BAas a function of transverse momen-
tum can be described by coalescence predictions, assuming
a Gaussian wave function for the nuclei.
Insights into the dependence of the production mecha-
nisms on the system size can also be obtained by study-
ing the evolution of BAwith charged-particle multiplicity.
Indeed, as shown in [33], the charged-particle multiplicity
dNch/dηcan be considered as a proxy of the system size.
Figure 4shows B2and B3as a function of charged-particle
multiplicity for different collision systems and energies. The
presented measurements are obtained in transverse momen-
tum ranges with central values of pT/A=0.75 GeV/cfor
B2and pT/A=0.78 GeV/cfor B3, but the trend is alike
for other values.
The measurements are compared with the theoretical pre-
dictions from [33], where two different parameterisations of
the source radius as a function of multiplicity are used (see
[33] for details). It is evident that there is no single parameter-
isation of the system size that is able to ﬁt both the measured
B2and B3. However, as stated also in [24], charged-particle
multiplicity is not a perfect proxy for the system size, because
for each multiplicity the source radius depends also on the
transverse-momentum of the particle of interest. Anyhow,
the data corresponding to the different collision systems and
energies conﬁrm a trend with multiplicity, which can be inter-
preted as an effect of the interplay between the size of the sys-
tem and that of the nucleus. Indeed, at low charged-particle
multiplicity, the system size is comparable with the size of
the nucleus (about 2 fm, depending on the nuclear species
and on the parameterisation of the model), determining the
123
Eur. Phys. J. C (2022) 82 :289 Page 7 of 16 289
Fig. 3 Coalescence parameters B2for (anti)deuterons (left) and B3for
(anti)helions (right) for different multiplicity classes. The multiplicity
decreases moving from the bottom up. The statistical uncertainties are
represented by vertical bars while the systematic uncertainties are rep-
resented by boxes. BAis shown as a function of pT/A,beingA=2
the mass number of deuteron and A=3 the mass number of helion
Fig. 4 Left: B2as a function of multiplicity in INEL >0 pp collisions
at s=5.02 TeV, in high-multiplicity pp collisions at s=13 TeV
[24], in INEL >0 pp collisions at s=13 TeV [23]andats=7TeV
[10], and in p–Pb collisions at sNN =5.02 TeV [11]. Right: B3as a
function of multiplicity in INEL >0 pp collisions at s=5.02 TeV,
in high-multiplicity pp collisions at s=13 TeV [24], in INEL >0
pp collisions at s=13 TeV [24]andats=7TeV[6], and in
p–Pb collisions at sNN =5.02 TeV [31]. The statistical uncertain-
ties are represented by vertical bars while the systematic uncertainties
are represented by boxes. The two lines are theoretical predictions of
the coalescence model based on two different parameterisations of the
system radius as a function of multiplicity
Fig. 5 Ratio between the pT-integrated yields of nuclei and protons as
a function of multiplicity for (anti)deuterons (left) and (anti)helions
(right). Measurements are performed in INEL >0 pp collisions at
s=5.02 TeV, in high-multiplicity pp collisions at s=13 TeV [24],
in INEL >0 pp collisions at s=13 TeV [23,24]andats=7TeV
[6], and in p–Pb collisions at sNN =5.02 TeV [11,31]. The statistical
uncertainties are represented by vertical bars while the systematic uncer-
tainties are represented by boxes. The two black lines are the theoretical
predictions of the Thermal-FIST statistical model [13] for two sizes of
the correlation volume VC. For (anti)deuterons, the green band repre-
sents the expectation from a coalescence model [34]. For (anti)helion,
the green and blue lines represent the expectations from a two-body and
three-body coalescence models [34]
123
289 Page 8 of 16 Eur. Phys. J. C (2022) 82 :289
slow decrease with multiplicity. On the contrary, increasing
the multiplicity the system size becomes larger and larger
than the nucleus size, making the coalescence process less
and less probable [1,33].
Figure 5shows the ratios between the pT-integrated yields
of nuclei and protons as a function of charged-particle multi-
plicity. A common trend as a function of the charged-particle
multiplicity is seen, monotonically increasing for pp and
p–Pb collisions and eventually saturating for Pb–Pb colli-
sions [24]. This is the effect of the interplay between the
different evolution with the charged-particle multiplicity of
the source size and of the particle yields [24]. The system-
atic uncertainties in this analysis are reduced with respect
to the previous ALICE measurements thanks to the recent
studies on the interaction cross section of antideuteron with
the material [35]. The experimental data are compared with
the predictions of both Thermal-FIST [13] CSM and coales-
cence model [34]. The CSM prediction is provided for dif-
ferent correlation volumes VC, from 1 to 3 times the volume
dV/dy. For both (anti)deuterons and (anti)helions, the CSM
and the coalescence model can qualitatively describe the
observed trend. A detailed study of the VCvalue is required
to determine if the CSM is able to describe simultaneously
the deuteron and helion measurement here reported. The coa-
lescence model seems to describe better the data points, and
better for (anti)deuterons than for (anti)helions, where some
tension at intermediate multiplicity is visible.
6 Conclusions
The LHC demonstrated to be an unprecedented antimatter
factory. The production of nuclei and antinuclei has been
explored at all energies delivered by the LHC during its Run
2[6,10,11,23,24,31] and a clear pattern emerged: the pro-
duction of nuclei is tightly driven by the underlying event
multiplicity. Other variables, like the collision energy or even
the colliding system (pp or p–Pb), are essentially irrelevant in
the description of the nucleosynthesis processes in hadronic
collision.
The CSM can explain qualitatively the observed trend in
the nucleus-to-proton ratios as a function of multiplicity. On
the other hand, coalescence connects the hadron-emitting
source size with the observed production of nuclei. The size
of the hadron-emitting source increases with multiplicity and
decreases with momentum as demonstrated by recent par-
ticle correlation measurements [36]. Through this observa-
tion, coalescence can predict the yield of nuclei as a function
of both multiplicity and momentum starting from the mea-
sured proton spectrum. In this paper, it is shown that the coa-
lescence prediction agrees quantitatively with the measured
deuteron-to-proton ratio, while the helion-to-proton ratio in
pp collisions at 5.02 TeV conﬁrms the trend of the previ-
ous measurements deviating from the coalescence predic-
tion at intermediate multiplicities. However, the comparison
between the coalescence parameters with coalescence pre-
dictions show great sensitivity to different source size param-
eterisations, suggesting that some of the observed discrepan-
cies might be due to the source size determination. During
the LHC Run 3, the ALICE experiment targets an integrated
luminosity of 6 pb1for pp collisions at 5.02 (or 5.5) TeV
and up to 200 pb1at 13 TeV [37], which corresponds to a
sample larger by at least a factor 400 with respect to Run 2.
This sample will enable a simultaneous study of the produc-
tion of nuclei and the size of the system, similarly to what
has already been done in high-multiplicity pp collisions at
s=13 TeV [24].
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 pro-
vided 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; Aus-
trian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-
N36] and Nationalstiftung für Forschung, Technologie und Entwick-
lung, Austria; Ministry of Communications and High Technologies,
National Nuclear Research Center, Azerbaijan; Conselho Nacional de
Desenvolvimento Cientíﬁco e Tecnológico (CNPq), Financiadora de
Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado
de São Paulo (FAPESP) and Universidade Federal do Rio Grande do
Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Min-
istry of Science and Technology of China (MSTC) and National Nat-
ural Science Foundation of China (NSFC), China; Ministry of Sci-
ence and Education and Croatian Science Foundation, Croatia; Cen-
tro 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 Indepen-
dent Research | Natural Sciences, the VILLUM FONDEN and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of
Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and
Institut National de Physique Nucléaire et de Physique des Particules
(IN2P3) and Centre National de la Recherche Scientiﬁque (CNRS),
France; Bundesministerium für Bildung und Forschung (BMBF) and
GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany;
General Secretariat for Research and Technology, Ministry of Educa-
tion, Research and Religions, Greece; National Research, Development
and Innovation Ofﬁce, Hungary; Department of Atomic Energy Gov-
ernment of India (DAE), Department of Science and Technology, Gov-
ernment of India (DST), University Grants Commission, Governmentof
India (UGC) and Council of Scientiﬁc and Industrial Research (CSIR),
India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di
Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture,
Sports, Science and Technology (MEXT), Japan Society for the Pro-
motion of Science (JSPS) KAKENHI and Japanese Ministry of Educa-
tion, Culture, Sports, Science and Technology (MEXT)of Applied Sci-
ence (IIST), Japan; Consejo Nacional de Ciencia (CONACYT) y Tec-
nología, through Fondo de Cooperación Internacional en Ciencia y Tec-
nología (FONCICYT) and Dirección General de Asuntos del Personal
Academico (DGAPA), Mexico; Nederlandse Organisatie voor Weten-
123
Eur. Phys. J. C (2022) 82 :289 Page 9 of 16 289
schappelijk Onderzoek (NWO), Netherlands; The Research Council of
Norway, Norway; Commission on Science and Technology for Sus-
tainable Development in the South (COMSATS), Pakistan; Pontiﬁcia
Universidad Católica del Perú, Peru; Ministry of Education and Sci-
ence, National Science Centre and WUT ID-UB, Poland; Korea Insti-
tute of Science and Technology Information and National Research
Foundation of Korea (NRF), Republic of Korea; Ministry of Educa-
tion and Scientiﬁc Research, Institute of Atomic Physics, Ministry of
Research and Innovation and Institute of Atomic Physics and University
Politehnica of Bucharest, Romania; Joint Institute for Nuclear Research
(JINR), Ministry of Education and Science of the Russian Federation,
National Research Centre Kurchatov Institute, Russian Science Foun-
dation and Russian Foundation for Basic Research, Russia; Ministry of
Education, Science, Research and Sport of the Slovak Republic, Slo-
vakia; National Research Foundation of South Africa, South Africa;
Swedish Research Council (VR) and Knut and Alice Wallenberg Foun-
dation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; Suranaree University of Technology (SUT), National Sci-
ence and Technology Development Agency (NSDTA) and Ofﬁce of the
Higher Education Commission under NRU project of Thailand, Thai-
land; Turkish Energy, Nuclear and Mineral Research Agency (TEN-
MAK), 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.
Data Availability Statement This manuscript has associated data in a
data repository. [Authors’ comment: Manuscript has associated data in
a HEPData repository at https://www.hepdata.net/.]
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