2024 193 12 July

Non-prompt charm-hadron production in p–Pb collisions

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

The production cross sections of $\mathrm{D^{0}}$, $\mathrm{D^{+}}$, and
$\mathrm{\Lambda_{c}^{+}}$ hadrons originating from beauty-hadron decays (i.e.
non-prompt) were measured for the first time at midrapidity in proton–lead
(p–Pb) collisions at the center-of-mass energy per nucleon pair of
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. Nuclear modification factors
($R_{\mathrm{pPb}}$) of non-prompt $\mathrm{D^{0}}$, $\mathrm{D^{+}}$, and
$\mathrm{\Lambda_{c}^{+}}$ are calculated as a function of the transverse
momentum ($p_{\mathrm{T}}$) to investigate the modification of the momentum
spectra measured in p–Pb collisions with respect to those measured in
proton–proton (pp) collisions at the same energy. The $R_{\mathrm{pPb}}$
measurements are compatible with unity and with the measurements in the prompt
charm sector, and do not show a significant $p_{\mathrm{T}}$ dependence. The
$p_{\mathrm{T}}$-integrated cross sections and $p_{\mathrm{T}}$-integrated
$R_{\mathrm{pPb}}$ of non-prompt $\mathrm{D^{0}}$ and $\mathrm{D^{+}}$ mesons
are also computed by extrapolating the visible cross sections down to
$p_{\mathrm{T}}$ = 0. The non-prompt D-meson $R_{\mathrm{pPb}}$ integrated
over $p_{\mathrm{T}}$ is compatible with unity and with model calculations
implementing modification of the parton distribution functions of nucleons
bound in nuclei with respect to free nucleons. The non-prompt
$\mathrm{\Lambda_{c}^{+}/D^{0}}$ and $\mathrm{D^{+}/D^{0}}$ production ratios
are computed to investigate hadronisation mechanisms of beauty quarks into
mesons and baryons. The measured ratios as a function of $p_{\mathrm{T}}$
display a similar trend to that measured for charm hadrons in the same
collision system.

##  1 Introduction

Measurements of heavy-flavour hadron production in hadronic collisions provide
crucial tests for calculations based on quantum chromodynamics (QCD). Due to
their large masses with respect to the QCD energy scale, heavy quarks (i.e.
charm and beauty) are primarily produced at the early stages of the collision
via hard-scattering processes with large momentum transfer, legitimising the
calculations of inclusive production cross sections via perturbative QCD
(pQCD). These calculations rely on a factorisation scheme where the $p_{\rm
T}$-differential production cross sections of charm or beauty hadrons are
calculated as a convolution of three terms: (i) the parton distribution
functions (PDFs) of the incoming nucleons, which describe the Bjorken-$x$
distributions of quarks and gluons within the incoming hadrons, (ii) the
partonic scattering cross section, calculated as a perturbative series in
powers of the strong coupling constant $\alpha_{\mathrm{S}}$, and (iii) the
fragmentation function parametrising the non-perturbative evolution of a heavy
quark into a given heavy-flavour hadron species. The fragmentation functions
are determined from measurements in $\rm e^{+}e^{-}$ collisions [1] and used
to compute the production cross section in hadronic collisions, under the
assumption that the relevant hadronisation processes are “universal”, i.e.
independent of the collision energy and system.

To isolate the effects of hadronisation, heavy-flavour hadron-to-hadron
production yield ratios are especially effective, since the PDFs and the
partonic interaction cross sections are common to all charm or beauty hadron
species and their effects cancel out in the yield ratios when using the
factorisation approach. Measurements of non-strange charm and beauty-meson
production cross sections in pp and p–Pb collisions at the LHC [2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12] show that the meson-to-meson ratios are described by the
pQCD calculations at next-to-leading order accuracy with all-order resummation
of next-to-leading logarithms, such as FONLL [13, 14] and GM-VFNS [15, 16, 17,
18], and by PYTHIA 8 event generator using the Monash tune [19, 20], which is
tuned on $\rm e^{+}e^{-}$ collisions. However, all these calculations largely
underpredict the production of charm and beauty baryons [21, 22, 23, 24]. In
addition, charm and beauty baryon-to-meson yield ratios, measured at mid- and
forward rapidity at the LHC, show significant deviations from the values
measured in $\rm e^{+}e^{-}$ collisions [25, 26, 27, 28, 29, 22, 30, 31, 21,
32, 33, 34, 24, 35, 36], indicating that the assumption of universality of the
hadronisation process across collision systems might no longer be valid at the
LHC [6, 37, 14]. The reconstruction of prompt charm hadrons, which are
produced from the decay of excited charm states or from charm-quark
hadronisation, and of non-prompt charm hadrons, which stem from the decay of
beauty hadrons, provides a good approach for probing the distinct sectors of
charm and beauty. The prompt charm baryon-to-meson production ratios were
measured in p–Pb collisions by the LHCb Collaboration at both forward
($1.5<y_{\rm lab}<4.0$ in the laboratory-frame) and backward ($-5.0<y_{\rm
lab}<-2.5$) rapidity regions [32, 38]. Comparatively, these findings indicate
an augmented baryon-to-meson yield ratios measured at forward/backward
rapidity with respect to the corresponding measurements in $\rm e^{+}e^{-}$
and ep collisions, although this is smaller compared to the enhancement
observed when considering midrapidity measurements [26, 29, 22]. In the beauty
sector, the ALICE Collaboration measured production cross sections of non-
prompt $\mathrm{D^{0}}$ and $\mathrm{\Lambda_{c}^{+}}$ hadrons at midrapidity
($|y|<$ 0.5) in pp collisions at $\sqrt{s}$ = 13 TeV [36]. The measured
baryon-to-meson production ratio shows an enhancement similar to that observed
in the charm sector, and the enhancement at midrapidity is similar to the one
observed at forward rapidity by the LHCb Collaboration measuring the
$\rm{\Lambda_{b}^{0}}$-baryon production relative to that of B mesons in pp
and p–Pb collisions [33, 34, 24, 35]. Modification of charm and beauty baryon-
to-meson ratios from $\rm e^{+}e^{-}$ to pp and p–Pb collisions suggests the
influence of the hadronic or partonic environment on the hadronisation process
[39]. Further hadronisation effects, apart from pure in-vacuum fragmentation,
like recombination (or coalescence) of charm quarks with quarks or di-quarks
from a thermal medium [40, 41, 42, 43], statistical hadronisation including
contributions from undiscovered higher-mass resonant states [44, 45, 46], and
string formation beyond the leading-colour approximation [47, 48], serve as
examples of implementations considered by theorists to refine the modelling of
hadronisation to baryons.

Measurements of heavy-flavour hadron production in proton–nucleus collisions
also allow to study various effects related to the presence of nuclei in the
colliding system, denoted as cold-nuclear-matter (CNM) effects. In the initial
state of the collisions, the PDFs of inbound nucleons are modified by the
nuclear environment as compared to free nucleons, depending on the parton
momentum fraction $x$, the squared momentum transfer $Q^{2}$ in the hard
scattering processes, and the nucleus mass number $A$ [49, 50]. At LHC
energies and midrapidity ($|y_{\rm lab}|<0.5$), the most relevant effect on
the PDF is called shadowing. It corresponds to a reduction of the parton
densities at $x$ lower than $10^{-2}$, which becomes stronger when $Q^{2}$
decreases and the nucleus mass number $A$ increases. This effect, induced by
the high phase-space density of small-$x$ partons [51, 52, 53, 54], can be
described within the factorisation scheme by means of phenomenological
parametrisations, denoted as nuclear PDFs (nPDFs). The modification of the
small-$x$ parton dynamics can significantly reduce the charm and beauty hadron
yield with respect to pp collisions at low $p_{\rm T}$. Furthermore, multiple
scattering of partons in the nucleus can modify the kinematic distribution of
the produced hadrons. Partons can lose energy in the initial stages of the
collision via initial-state radiation [55] or experience transverse momentum
broadening due to multiple soft collisions before the heavy-quark pair is
produced [56, 57]. These initial-state effects are expected to have an
influence on charm-hadron production at low and intermediate $p_{\rm T}$
($p_{\rm T}<4$ GeV/$c$). For this reason, measurements of the charm- and
beauty-hadron production cross section and its nuclear modification factor
$R_{\rm pPb}$, which is defined as the ratio of the production cross section
in p–Pb to that in pp collisions scaled by the mass number of the Pb nucleus
($A_{\mathrm{Pb}}$), down to low $p_{\rm T}$ could provide important
information, helping to significantly reduce the uncertainties on the gluon
nPDFs at small $x$ [58, 59].

In addition to the aforementioned initial-state effects, final-state effects
may also be responsible for modifications of heavy-flavour hadron yields and
momentum distributions. Measurements in the light- and heavy-flavour sectors
in high-multiplicity pp and p–Pb collisions at different collision energies
showed significant flow-like effects [60, 61, 21]. These effects resemble
those observed in high-energy nucleus–nucleus collisions and are ascribed to
quark–gluon plasma formation. In this picture, particles of larger mass are
boosted to higher transverse momenta due to a common velocity field [62].
However, baryon production at intermediate $p_{\rm T}$ may also be enhanced as
a result of hadronisation via quark recombination [63].

The ALICE and CMS Collaborations measured the $R_{\rm pPb}$ of D and B meson
in p–Pb collisions, finding values close to unity within the rapidity ranges
$|y_{\rm lab}|<$ 0.5 [64] and $|y_{\rm lab}|<$ 2.4 [65], respectively. In
contrast, the LHCb Collaboration measurements at forward (2.5 $<y_{\rm lab}<$
3.5) and backward rapidity (-3.5 $<y_{\rm lab}<$ -2.5) [35], evidence a
suppression of up to 20% for beauty mesons in the forward rapidity interval
and no significant suppression suppression in the backward rapidity interval.
Model calculations based on nPDFs describe well these observations.

In the baryon sector, the ALICE Collaboration found that the
$\mathrm{\Lambda_{c}^{+}}$ $R_{\rm pPb}$ depends on $p_{\rm T}$, being below
unity at low $p_{\rm T}$ and above unity at high $p_{\rm T}$ [26]. Simulations
based on POWHEG+PYTHIA 6 [66, 67], combined with EPPS16 nPDF [54], reproduce
the results at low $p_{\rm T}$ but do not describe the measured trend at
intermediate $p_{\rm T}$. The $\rm{\Lambda_{b}^{0}}$ measurements in p–Pb
collisions at large rapidities by the LHCb Collaboration are consistent with
the corresponding measurements in pp collisions within uncertainties [35].

In this article, possible effects related to the modification of hadronisation
mechanisms, and initial and final-state effects at midrapidity ($|y_{\rm
lab}|<0.5$) in p–Pb collisions in the beauty sector are investigated. The
$p_{\rm T}$-differential production cross sections and nuclear modification
factors of non-prompt $\mathrm{D^{0}}$, $\rm D^{+}$, and
$\mathrm{\Lambda_{c}^{+}}$ hadrons in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV are reported. The $\mathrm{D^{0}}$ meson is
reconstructed in the interval 1 $<p_{\rm T}<$ 24 GeV/$c$, while the $\rm
D^{+}$ and $\mathrm{\Lambda_{c}^{+}}$ hadrons are reconstructed in the
interval 2 $<p_{\rm T}<$ 24 GeV/$c$. By integrating the $p_{\rm
T}$-differential results and extrapolating to $p_{\rm T}$ = 0 using pQCD
calculations, the $p_{\rm T}$-integrated non-prompt $\mathrm{D^{0}}$ and $\rm
D^{+}$ production cross sections are computed. The paper is organised as
follows. Section 2 describes the ALICE apparatus and the analysed data
samples. Section 3 details the analysis methods used and outlines the
corrections applied to calculate the $p_{\rm T}$-differential production cross
sections. Section 4 describes the sources of systematic uncertainty. The
results are presented in Section 5. Finally, a summary is given in Section 6.

##  2 Experimental setup and data sample

The ALICE apparatus [68] consists of a set of detectors for particle
reconstruction and identification at midrapidity ($|\eta|<0.9$) embedded in a
solenoidal magnet, a forward ($-4<\eta<-2.5$) muon spectrometer, and a set of
forward and backward detectors for triggering and event characterisation.
Typical detector performance in pp, p–Pb, and Pb–Pb collisions is presented in
[69]. The reconstruction of heavy-flavour hadrons from their hadronic decay
products at midrapidity primarily relies on the Inner Tracking System (ITS)
[70], the Time Projection Chamber (TPC) [71], and the Time-Of-Flight detector
(TOF) [72] for tracking, primary and decay vertex reconstruction, and charged-
particle identification (PID). The V0 detector arrays [73] are used for
triggering and event selection.

The data sample used in this analysis are from proton–lead collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV collected in 2016. The events were recorded
with a minimum-bias (MB) interaction trigger that required coincident signals
in both scintillator arrays of the V0 detector, which covers the full azimuth
in the pseudorapidity intervals $-3.7<\eta<-1.7$ and $2.8<\eta<5.1$. The V0
timing information was used together with that from the Zero-Degree
Calorimeter (ZDC) [69] for offline rejection of beam-beam or beam-gas
interactions occurring outside the nominal colliding bunches.

To ensure uniform acceptance in pseudorapidity, events were required to have a
reconstructed collision vertex located within $\pm 10$ cm from the nominal
collision point along the beam-line direction. Events composed of several
interactions per bunch crossing, whose probability was below 0.5%, were
rejected using an algorithm based on track segments, defined within the two
innermost ITS layers, to detect multiple interaction vertices [69]. The
influence of potentially remaining pile-up events is on the percent level and
does not have an impact on the final results of the presented analysis. After
these selections, the data sample consisted of about 600 million events,
corresponding to an integrated luminosity $\mathcal{L}_{\mathrm{int}}=292\pm
11~{}\upmu\text{b}^{-1}$ [74]. During the p–Pb data taking period, the beam
energies were $4$ TeV for protons and $1.58$ TeV per nucleon for lead nuclei.
With this beam configuration, the nucleon–nucleon center-of-mass system moves
in rapidity by $\Delta y_{\rm cms}=0.465$ in the direction of the proton beam.
The charm-hadron analyses were performed in the laboratory-frame interval
$|y_{\rm lab}|<0.5$, leading to a shifted center-of-mass rapidity coverage of
$-0.96<y_{\rm cms}<0.04$.

##  3 Analysis technique

###  3.1 Non-prompt $\mathrm{D^{0}}$, $\rm D^{+}$, and
$\mathrm{\Lambda_{c}^{+}}$ raw yields

The $\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ charm
hadrons, along with their charge conjugates, were reconstructed via the
following hadronic decay channels: $\mathrm{D^{0}}\to\rm{K}^{-}\pi^{+}$ with
branching ratio BR $=(3.95\pm 0.03)\%$, $\rm D^{+}\to\pi^{+}\rm{K}^{-}\pi^{+}$
with BR $=(9.38\pm 0.16)\%$,
$\mathrm{\Lambda_{c}^{+}}\to\mbox{$\mathrm{p}$}\rm{K}^{-}\pi^{+}$ with BR
$=(6.28\pm 0.32)\%$, and $\mathrm{\Lambda_{c}^{+}}\to\mbox{$\mathrm{p}$}{\rm
K^{0}_{S}}$ with ${\text{BR}=(1.59\pm 0.08)\%}$, followed by
$\mathrm{K^{0}_{S}}\to\pi^{+}\pi^{-}$ with BR $=(69.20\pm 0.05)\%$) [75]. The
$\mathrm{D^{0}}$-, $\rm D^{+}$-, and $\mathrm{\Lambda_{c}^{+}}$-hadron
candidates were defined by combining pairs or triplets of tracks reconstructed
with the proper charge sign. While for the
$\mathrm{\Lambda_{c}^{+}}\to\mathrm{pK_{s}^{0}}$ candidates, the V-shaped
decay of the $\mathrm{K_{\rm s}^{0}}$ meson into two pion-track candidates was
combined with a proton-track candidate using a Kalman-Filter vertexing
algorithm [76], as described in [21]. All daughter tracks were required to be
reconstructed within $|\eta|<0.8$, with at least 70 associated space points in
the TPC, $\chi^{2}/\rm{ndf}<2$ of the fit quality of the TPC tracks (where ndf
is the number of degrees of freedom involved in the track fit procedure), and
a minimum of 2 (out of 6) reconstructed clusters in the ITS, with at least one
in either of the two innermost layers. These track-selection criteria reduce
the D-meson and $\mathrm{\Lambda_{c}^{+}}$-baryon acceptance in rapidity,
which drops steeply to zero for $|y_{\text{lab}}|>0.5$ at low $p_{\rm T}$ and
for $|y_{\text{lab}}|>0.8$ at high $p_{\rm T}$. Therefore, a $p_{\rm
T}$-dependent fiducial acceptance region
$|y_{\text{lab}}|<y_{\text{fid}}(p_{\rm T})$ was applied to grant a uniform
acceptance in the considered rapidity range. The $y_{\text{fid}}(p_{\rm T})$
was defined as a second-order polynomial function, increasing from $0.5$ to
$0.8$ in the transverse momentum range $0<p_{\rm T}<5$ GeV/$c$, and as a
constant term, $y_{\text{fid}}=0.8$, for $p_{\rm T}>5$ GeV/$c$.

The $\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ decay weakly
with a mean proper decay length ($c\tau$) of about $123$, $312$, and $60$
$\upmu$m, respectively [75]. Charm hadrons coming from beauty-hadron decays
are even more displaced from the primary vertex since their estimated $c\tau$
is about $500$ $\upmu$m, as for beauty hadrons. Therefore, these analyses were
based on the reconstruction of decay-vertex topologies displaced from the
primary vertex and, according to the selection applied, it is possible not
only to separate candidates from the combinatorial background, but also the
contributions of prompt and non-prompt charm hadrons.

To reduce the large combinatorial background and to separate the contributions
of prompt and non-prompt charm hadrons, a machine-learning approach with
multi-class classification, based on Boosted Decision Trees (BDT), implemented
in the XGBoost library [77, 78], was adopted. For the BDT training, signal
samples of prompt and non-prompt charm hadrons were obtained from simulations
using the PYTHIA 8 event generator [19] (Monash-13 tune [20]), embedded in an
underlying p–Pb collision generated with HIJING 1.36 [79], to describe better
the charged-particle multiplicity and detector occupancy observed in the data.
Background samples were extracted from candidate invariant-mass distributions
within the range of $5\sigma<|\Delta M|<9\sigma$ in the data, where $\Delta M$
represents the difference between the candidate invariant mass and the nominal
mass of the hadron candidate, and $\sigma$ represents the invariant-mass
resolution.

Before the training, loose selections were applied based on the decay
kinematics and topologies along with the PID information of the decay-product
tracks. The PID selections were based on the difference between the measured
and expected detector signals for a given particle species hypothesis, in
units of the detector resolution ($n^{\mathrm{det}}_{\sigma}$). Protons,
pions, and kaons were selected by requiring compatibility with the respective
hypothesis within three standard deviations ($3\sigma$) for both the TPC
specific energy loss and the TOF time-of-flight. For tracks without a measured
signal in the TOF, the PID selections relied only on information from the TPC.

Independent BDT models were trained for each $p_{\rm T}$ interval of the
analysis of each D-meson species and the two $\mathrm{\Lambda_{c}^{+}}$ decay
channels using different variables related to the displaced decay-vertex
topology and the PID information of the decay tracks. The main variables used
were (i) the distance of closest approach between the reconstructed tracks and
the primary vertex, (ii) the distance between the charm-hadron decay vertex
and the primary vertex, (iii) the charm-hadron impact parameter, (iv) the
cosine of the pointing angle between the charm-hadron candidate line-of-flight
and its reconstructed momentum. In the case of the
$\mathrm{\Lambda_{c}^{+}}\to\mbox{$\mathrm{p}$}{\rm K^{0}_{S}}$ decay,
additional training variables related to the decay topology of the $\rm
K^{0}_{S}$ and $\mathrm{\Lambda_{c}^{+}}$ were used as in [21]. The three BDT
output scores are related to the candidate probability of being a prompt charm
hadron, a non-prompt charm hadron, or combinatorial background. Selections on
the non-prompt and combinatorial background BDT scores, corresponding to a
requirement of a low probability for a candidate to be combinatorial
background and a high probability to be non-prompt, were optimised to obtain a
high non-prompt charm-hadron fraction in the inclusive signals while
maintaining a reliable signal extraction, meaning a statistical significance
larger than 3, as done in [2, 80].

The raw yields of $\mathrm{D^{0}}$, $\rm D^{+}$, and
$\mathrm{\Lambda_{c}^{+}}$ hadrons, including particles and antiparticles,
were extracted via binned maximum-likelihood fits to the invariant-mass ($M$)
distributions of the selected charm-hadron candidates. The raw yields were
extracted in transverse-momentum intervals in the range $1<p_{\rm T}<24$
GeV/$c$ for $\mathrm{D^{0}}$ mesons, and $2<p_{\rm T}<24$ GeV/$c$ for $\rm
D^{+}$ mesons and $\mathrm{\Lambda_{c}^{+}}$ baryons. The fitting function was
composed of an exponential or polynomial term for describing the background
and a Gaussian term for the signal. To improve the stability of the fits, the
widths of the charm-hadron signal peaks were fixed to the values extracted
from data samples enhanced with prompt candidates, given the naturally larger
abundance of prompt compared to non-prompt charm hadrons. As part of the
systematic uncertainty analysis, the width parameter was varied to determine
its impact on the systematic uncertainty associated with the raw-yield
extraction. For the $\mathrm{D^{0}}$ mesons, the contribution of signal
candidates to the invariant-mass distribution with the wrong mass assigned to
the $\mathrm{D^{0}}$-decay tracks, referred to as reflections, was included in
the fit, and estimated as explained in [80]. The contribution of reflections
to the raw yield is about 1–2%, depending on $p_{\rm T}$. Examples of
invariant-mass distributions together with the result of the fits and the
estimated non-prompt fractions ($f_{\text{non-prompt}}^{\mathrm{raw}}$) are
reported in Fig. 1, for the $3<p_{\rm T}<4$ GeV/$c$, $5<p_{\rm T}<6$ GeV/$c$,
and $4<p_{\rm T}<8$ GeV/$c$ intervals of the $\mathrm{D^{0}}$, $\rm D^{+}$,
and $\mathrm{\Lambda_{c}^{+}}$ hadrons, respectively.

Figure 1: Invariant-mass distributions of $\mathrm{D^{0}}$-, $\rm D^{+}$-, and
$\mathrm{\Lambda_{c}^{+}}$-hadron candidates, and their charge conjugates in
selected $p_{\rm T}$ intervals. The blue solid lines show the total fit
functions as described in the text and the red dashed lines show the fit
function describing the combinatorial background. For $\mathrm{D^{0}}$-meson
candidates, the solid green line represents the contribution of the
reflections. The mean ($\mu$) and fixed standard deviation ($\sigma$) of the
signal fit function, along with the raw-yield ($S$) values, are reported
together with their statistical uncertainties resulting from the fit. The
fraction of non-prompt candidates in the measured raw yield ($f_{\text{non-
prompt}}^{\mathrm{raw}}$) is reported with its statistical and systematic
uncertainties.

###  3.2 Yield corrections and non-prompt fraction estimations

The $p_{\rm T}$-differential production cross sections of non-prompt
$\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ hadrons at
midrapidity were computed as:

$\left.\cfrac{\mathrm{d}^{2}\sigma^{\mathrm{H}_{\mathrm{c}}}}{\mathrm{d}p_{\rm
T}\mathrm{d}y}\right|_{|y_{\rm
lab}|<0.5}=\cfrac{1}{2}\times\cfrac{f_{\text{non-prompt}}^{\text{raw}}(p_{\rm
T})\times\left.N^{\mathrm{H}_{\mathrm{c}}+\overline{\mathrm{H}}_{\mathrm{c}},\mathrm{raw}}(p_{\rm
T})\right|_{|y_{\mathrm{lab}}|<y_{\text{fid}}(p_{\rm T})}}{\Delta p_{\rm
T}\times c_{\Delta y}(p_{\rm
T})\times(\mathrm{Acc}\times\varepsilon)^{\text{non-prompt}}(p_{\rm
T})}\cfrac{1}{\mathrm{BR}\times\mathcal{L}_{\mathrm{int}}}~{},$ (1)

where
$N^{\mathrm{H}_{\mathrm{c}}+\overline{\mathrm{H}}_{\mathrm{c}},\mathrm{raw}}$
(sum of particles and antiparticles) represents the raw yields extracted in
each $p_{\rm T}$ interval, and the factor 1/2 is included to account that the
raw yields contain both particles and antiparticles, while the production
cross sections are given as an average of particles and antiparticles. The
$f_{\text{non-prompt}}^{\text{raw}}$ factor represents the raw non-prompt
fraction needed to account for the residual contribution of prompt charm
hadrons in the extracted non-prompt raw yields. In addition, the yields were
further divided by the width of the $p_{\rm T}$ interval ($\Delta p_{\rm T}$),
the correction factor for the rapidity coverage $c_{\Delta y}$, computed as
the ratio between the generated hadron yield in $\Delta y=2y_{\rm fid}$ and
that in $|y_{\rm lab}|<0.5$, as explained in [64], as well as the acceptance
times efficiency of non-prompt charm hadrons
$(\mathrm{Acc}\times\varepsilon)^{\text{non-prompt}}$, the BR of the decay
channel, and the integrated luminosity $\mathcal{L}_{\mathrm{int}}$.

Figure 2: Acceptance-times-efficiency factors for $\mathrm{D^{0}}$, $\rm
D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ hadrons as a function of $p_{\rm T}$.

Possible differences in the $p_{\rm T}$ shape of prompt and non-prompt charm
hadrons between data and Monte Carlo (MC) simulations were corrected by
weighting the simulated $p_{\rm T}$ distribution of prompt charm hadrons and
of the beauty-hadron parent, respectively. For D mesons, the weights were
computed by dividing the $p_{\rm T}$ spectrum predicted by FONLL calculations
and the one obtained from PYTHIA 8 simulations. The FONLL $p_{\rm T}$ spectra
of prompt and non-prompt D mesons in p–Pb collisions were computed using the
predictions in pp collisions at $\sqrt{s}=5.02$ TeV [13, 81], assuming that
the $R_{\rm pPb}$ of D and B mesons are compatible with unity, in the rapidity
range of this study. This assumption is based on the D-meson $R_{\rm pPb}$
measurements at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV at midrapidity by the
ALICE Collaboration [64] and B-meson $R_{\rm pPb}$ measurements at
$\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV at forward/backward rapidity by the LHCb
Collaboration [35], that are in agreement with models that predict B-meson
$R_{\rm pPb}$ values compatible with unity at midrapidity, within the
theoretical uncertainties. The energy dependence of the $R_{\rm pPb}$
measurement is neglected. The procedure to compute the $p_{\rm T}$ spectrum
based on FONLL calculations for the prompt $\mathrm{\Lambda_{c}^{+}}$
($\rm{\Lambda_{b}^{0}}$) hadrons takes into account three essential
components: the FONLL predicted $p_{\rm T}$ distribution for prompt
$\mathrm{D^{0}}$ (B) mesons in pp collisions at $\sqrt{s}=5.02$ TeV, the
prompt $\mathrm{\Lambda_{c}^{+}}$/$\mathrm{D^{0}}$
($\rm{\Lambda_{b}^{0}}/\mathrm{B}^{0}$) ratio [21, 33] in the same collision
system and energy, and the prompt $\mathrm{\Lambda_{c}^{+}}$ $R_{\rm pPb}$ at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV measured by the ALICE Collaboration [21].
The weights on prompt $\mathrm{\Lambda_{c}^{+}}$ ($\rm{\Lambda_{b}^{0}}$)
$p_{\rm T}$ shape were derived as the product of these three components
divided by the prompt $\mathrm{\Lambda_{c}^{+}}$ ($\rm{\Lambda_{b}^{0}}$) MC
$p_{\rm T}$ distribution from PYTHIA 8\. In addition, the weights on non-
prompt $\mathrm{\Lambda_{c}^{+}}$ were derived from $\rm{\Lambda_{b}^{0}}$
based on the $p_{\rm T}$ correlation between $\rm{\Lambda_{b}^{0}}$ and non-
prompt $\mathrm{\Lambda_{c}^{+}}$ from $\rm{\Lambda_{b}^{0}}$ decays simulated
by PYTHIA 8.

The $(\mathrm{Acc}\times\varepsilon)$ correction was obtained from
simulations, as described in Section 3.1, using samples not employed for the
BDT training. The $(\mathrm{Acc}\times\varepsilon)$ factors, computed for non-
prompt $\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ hadrons
as a function of $p_{\rm T}$, after applying all the selections, are shown in
Fig. 2. The selection applied to obtain the non-prompt enhanced samples
strongly suppresses the prompt charm-hadron efficiency. The prompt charm-
hadron acceptance-times-efficiency $(\mathrm{Acc}\times\varepsilon)$ is
smaller than the non-prompt one by factors varying from 20 to 60 for D mesons
and 5 to 13 for $\mathrm{\Lambda_{c}^{+}}$ baryons, depending on the $p_{\rm
T}$ interval.

A data-driven procedure, based on the construction of data samples with
different abundances of prompt and non-prompt candidates, was used to estimate
the fraction $f_{\text{non-prompt}}^{\mathrm{raw}}$ of non-prompt
$\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ hadrons in the
extracted yields. Let $i\in\\{1;n\\}$ designate a set among $n\in\mathbb{N}$
selection sets. Each set of BDT selection $i$ is associated with an extracted
raw-yields value ($Y_{i}$), which relates to the corrected yield of prompt
($N_{\mathrm{prompt}}$) and non-prompt ($N_{\mathrm{non-prompt}}$) charm
hadrons via the corresponding prompt
$(\mathrm{Acc}\times\varepsilon)_{i}^{\mathrm{prompt}}$ and non-prompt
$(\mathrm{Acc}\times\varepsilon)_{i}^{\mathrm{non-prompt}}$ efficiency as
follows:

$(\mathrm{Acc}\times\varepsilon)^{\rm prompt}_{i}\times N_{\rm
prompt}+(\mathrm{Acc}\times\varepsilon)^{\text{non-prompt}}_{i}\times
N_{\text{non-prompt}}-Y_{i}=\delta_{i}~{},$ (2)

where $\delta_{i}$ represents a residual that accounts for the equation not
holding precisely due to the uncertainties of $Y_{i}$,
$(\mathrm{Acc}\times\varepsilon)^{\text{non-prompt}}_{i}$, and
$(\mathrm{Acc}\times\varepsilon)^{\rm prompt}_{i}$. In the case of
$n\geqslant$ 2 sets, a $\chi^{2}$ function can be defined based on Eq. 2,
which can be minimised to obtain $N_{\rm prompt}$ and $N_{\text{non-prompt}}$
as explained in [36, 2].

Figure 3 shows an example of the raw-yield distribution as a function of the
BDT-based selection employed in the minimisation procedure for
$\mathrm{D^{0}}$ mesons in $3<p_{\rm T}<4$ GeV/$c$ (left panel). The leftmost
data point of the distribution is the raw yield corresponding to the looser
selections on the BDT outputs related to the candidate probability of being a
non-prompt charm hadron. In contrast, the rightmost one corresponds to the
tightest selections. The right panel shows the $p_{\rm T}$ distributions of
the raw non-prompt fraction $f_{\text{non-prompt}}^{\mathrm{raw}}$ obtained
for the set of selection criteria adopted in the analysis for non-prompt
$\mathrm{D^{0}}$, $\rm D^{+}$,
$\mathrm{\Lambda_{c}^{+}}\to\mathrm{pK^{-}\pi^{+}}$, and
$\mathrm{\Lambda_{c}^{+}}\to\mathrm{pK^{0}_{S}}$. The fraction $f_{\text{non-
prompt}}^{\mathrm{raw}}$ of $\mathrm{D^{0}}$, $\rm D^{+}$, and
$\mathrm{\Lambda_{c}^{+}}$ hadrons ranges from 42 to 90% depending on the
decay channel and the $p_{\rm T}$ interval.

Figure 3: Left panel: example of raw-yield distribution as a function of the
BDT-based selection employed in the data-driven procedure adopted to determine
$f_{\text{non-prompt}}^{\mathrm{raw}}$ of $\mathrm{D^{0}}$ mesons. Right
panel: $f_{\text{non-prompt}}^{\mathrm{raw}}$ fractions as a function of
$p_{\rm T}$ obtained for the set of selection criteria adopted in the analysis
for non-prompt $\mathrm{D^{0}}$, $\rm D^{+}$,
$\mathrm{\Lambda_{c}^{+}}\to\mathrm{pK^{-}\pi^{+}}$, and
$\mathrm{\Lambda_{c}^{+}}\to\mathrm{pK^{0}_{S}}$. The vertical bars and empty
boxes represent the statistical and systematic uncertainties, respectively.

##  4 Systematic uncertainties

The measurement of the $p_{\rm T}$-differential production cross section of
non-prompt charm hadrons was affected by the following sources of systematic
uncertainties: (i) extraction of the raw yield from the invariant-mass
distribution, (ii) non-prompt fraction estimation, (iii) corrections to the
generated $p_{\rm T}$ shape in simulations, (iv) charm-hadron selection
efficiency, and (v) track-reconstruction efficiency. The systematic
uncertainties of the PID selection efficiency were found to be negligible, as
observed in prompt charm hadron measurements [64, 21]. In addition, the
$p_{\rm T}$-differential production cross section was affected by the
uncertainties on the branching ratios of the considered charm-hadron decays
[75] and a systematic uncertainty on the overall normalisation induced by the
uncertainties on the integrated luminosity of $3.7\%$ [74]. The values of the
systematic uncertainties for some representative $p_{\rm T}$ intervals were
summarised in Table 1. The contributions of the different sources were
considered to be uncorrelated and were summed in quadrature to obtain the
total systematic uncertainty.

Table 1: Summary of the relative systematic uncertainties on the measurement of non-prompt $\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ production cross sections in different $p_{\rm T}$ intervals. Hadron | $\mathrm{D^{0}}\left(\to\rm{K}^{-}\pi^{+}\right)$ | $\rm D^{+}\left(\to\pi^{+}\rm{K}^{-}\pi^{+}\right)$ | $\mathrm{\Lambda_{c}^{+}}\left(\to\mbox{$\mathrm{p}$}\rm{K}^{-}\pi^{+}\right)$ | $\mathrm{\Lambda_{c}^{+}}\left(\to\mbox{$\mathrm{p}$}\mathrm{K^{0}_{S}}\right)$
---|---|---|---|---
$p_{\rm T}$ (GeV/$c$) | 1–2 | 10–12 | 2–3 | 10–12 | 2–4 | 12–24 | 2–4 | 8–12
Signal yield | 3% | 2% | 6% | 5% | 7% | 15% | 10% | 9%
Fraction estimation | 3% | 1% | 2% | 3% | 10% | 15% | 10% | 10%
$p_{\rm T}$ shape in MC | 7% | 0% | 1% | 0% | 5% | 0% | 5% | 0%
Selection efficiency | 5% | 4% | 6% | 3% | 8% | 8% | 7% | 7%
Tracking efficiency | 2.0% | 2.5% | 3.7% | 4.0% | 6.0% | 6.0% | 5.0% | 5.0%
Branching ratio [75] | 0.8% | 1.7% | 5.1% | 5.0%
Luminosity [74] | 3.7%

The systematic uncertainty on the raw yield extraction was evaluated for each
charm-hadron species by repeating the fits to the invariant-mass distribution
for each $p_{\rm T}$ interval of the analyses, varying the fit range, the
functional form of the background fit function, the bin size of the invariant
mass spectrum, and the width of the Gaussian function used to model the signal
peaks. The latter was varied within the uncertainty of the value obtained from
the fits to the prompt candidate enhanced data sample. The systematic
uncertainty was defined as the root mean square of the distribution of the
signal yields obtained from the described variations and ranged from 2 to
$15\%$ depending on the hadron species and the $p_{\rm T}$ interval.

The systematic uncertainty on the value of $f_{\text{non-
prompt}}^{\text{raw}}$ obtained with the data-driven approach was estimated by
varying the number of BDT selections employed in the data-driven method as
described in Section 3.2. A systematic uncertainty ranging from 1 to 15% was
assigned.

The systematic effect due to the dependence of the efficiencies on the
generated $p_{\rm T}$ distribution of heavy-flavour hadrons was estimated by
evaluating the production cross section after weighting the $p_{\rm T}$ shape
of the PYTHIA 8 generator to match the central one predicted by FONLL
calculations, as well as the upper- and lower-edge of the predictions which
account for the uncertainties due to the choice of the heavy-quark masses,
factorisation and renormalisation scales, and the uncertainties on the CTEQ6.6
PDFs [82]. The weights were applied to the $p_{\rm T}$ distributions of prompt
charm hadrons and of the beauty hadron parent in the case of non-prompt charm
hadrons. The assigned systematic uncertainty, considering the root mean square
of the production cross section distributions obtained for minimal and maximal
FONLL predictions with respect to the central (default) ones, reached up to
$7\%$.

The systematic uncertainty on the selection efficiency originates from
imperfections in the description of the kinematic and topological variables of
the candidates and of the detector resolutions and alignments in the
simulation. It was estimated by comparing the production cross sections
obtained by repeating the analysis with different selections on the BDT
outputs, resulting in a significant modification of the efficiency values. The
assigned systematic uncertainty ranged from 3 to 8%.

The systematic uncertainties on the track reconstruction efficiency were
estimated by considering the uncertainty due to track quality selections and
the uncertainty due to the TPC–ITS track matching efficiency as discussed in
[64, 21]. It ranged from 2 to 6%, depending on the candidate species and
$p_{\rm T}$ interval.

##  5 Results

###  5.1 Production cross sections

The $p_{\rm T}$-differential production cross sections of non-prompt
$\mathrm{D^{0}}$ mesons, $\rm D^{+}$ mesons, and $\mathrm{\Lambda_{c}^{+}}$
baryons in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, measured in
the rapidity interval $-0.96<y_{\rm cms}<0.04$, are shown in Fig. 4 in
comparison to those measured for prompt hadrons at the same center-of-mass
energy [64, 21]. The measurement of prompt $\rm D^{+}$ is the one reported in
[64], scaled for the BR $=(8.98\pm 0.28)\%$ of the $\rm
D^{+}\to\pi^{+}\rm{K}^{-}\pi^{+}$ decay reported in [83]. The non-prompt
$\mathrm{\Lambda_{c}^{+}}$-baryon production cross section was obtained by
computing a weighted average of the production cross sections measured for the
two decay channels,
$\mathrm{\Lambda_{c}^{+}}\to\mbox{$\mathrm{p}$}\rm{K}^{-}\pi^{+}$ and
$\mathrm{\Lambda_{c}^{+}}\to\mbox{$\mathrm{p}$}{\rm K^{0}_{S}}$, using the
inverse of the quadratic sum of the relative statistical and uncorrelated
systematic uncertainties as weights. The systematic uncertainties related to
the tracking, luminosity, and generated $p_{\rm T}$ spectrum in the MC
simulations are treated as correlated between the two decay channels; the
uncertainty of the branching ratios is partially correlated as described in
[75], while all the other sources of systematic uncertainties are considered
fully uncorrelated.

Figure 4: $p_{\rm T}$-differential production cross sections of non-prompt
$\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, in comparison with the
corresponding production cross section of prompt hadrons from [64, 21]. The
measurement of prompt $\rm D^{+}$ mesons is the one reported in [64], with
decay BR discussed in the text. The vertical bars and empty boxes represent
the statistical and systematic uncertainties (without branching ratio and
luminosity contributions), respectively.

The production cross section integrated in $p_{\rm T}$ in the visible $p_{\rm
T}$ interval of the analyses and for the results extrapolated down to $p_{\rm
T}=0$ are reported in Tables 2 and 3, respectively. All the systematic
uncertainties were propagated as fully correlated among the measured $p_{\rm
T}$ intervals, except for the one associated with the raw-yield extraction.
The visible production cross sections were extrapolated down to $p_{\rm T}=0$
for non-prompt $\mathrm{D^{0}}$ and $\rm D^{+}$ mesons using FONLL predictions
for beauty-hadron production in pp collisions and the PYTHIA 8 generator,
employed to describe the decay kinematics of beauty hadrons
($\mathrm{h}_{\mathrm{b}}$) into charm mesons. These predictions were found to
be compatible with the measurements performed in pp collisions, as shown in
[36]. In order to take into account the different system sizes with respect to
pp collisions, the predictions were scaled by $A_{\mathrm{Pb}}$, assuming a
flat B-meson $R_{\rm pPb}$ at unity over the whole $p_{\rm T}$ range at
midrapidity, according to LHCb data [35]. The systematic uncertainties on the
extrapolation factor were estimated by considering: (i) the FONLL
uncertainties, (ii) the beauty fragmentation fractions $f(\mathrm{b\to
h_{b}})$, (iii) the branching ratios of the $\mathrm{h_{b}\to D+X}$ decays,
and (iv) the variation of the $p_{\rm T}$ spectrum shape using EvtGen package
for the description of the beauty-hadron decays [84]. Contribution (ii) was
estimated by considering an alternative set of beauty fragmentation fractions
measured in $\mathrm{p\bar{p}}$ collisions [1] while the default one is from
$\mathrm{e^{+}e^{-}}$ collisions. For (iii), the branching ratios implemented
in PYTHIA 8 were reweighted to reproduce the measured values reported in [75].
It is not possible to extrapolate the non-prompt $\mathrm{\Lambda_{c}^{+}}$
production cross section down to $p_{\rm T}$ = 0 given the absence of model
calculations in p–Pb collisions for beauty baryons.

Table 2: Production cross sections in the measured $p_{\rm T}$ range for non-prompt charm hadrons in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. Hadron | Kinematic range (GeV/$c$) |  $\mathrm{d}\mathit{\sigma}_{\mathrm{pPb}}^{\mathrm{visible}}/\mathrm{d}\mathit{y}|_{|y_{\rm lab}|<0.5}$ ($\upmu$b)
---|---|---
$\mathrm{D^{0}}$ | $1<p_{\rm T}<24$ | $3128\pm 183\text{ (stat.) }\pm 187\text{ (syst.) }\pm 116\text{ (lumi.) }\pm 24\text{ (BR) }$
$\rm D^{+}$ | $2<p_{\rm T}<24$ | $726\pm 101\text{ (stat.) }\pm 42\text{ (syst.) }\pm 27\text{ (lumi.) }\pm 12\text{ (BR) }$
$\mathrm{\Lambda_{c}^{+}}$ | $2<p_{\rm T}<24$ | $1404\pm 364\text{ (stat.) }\pm 171\text{ (syst.) }\pm 52\text{ (lumi.) }\pm 70\text{ (BR) }$
Table 3: Production cross sections in the range $p_{\rm T}>0$ for non-prompt charm hadrons in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. Hadron | Extr. factor to |  $\mathrm{d}\sigma_{\mathrm{pPb}}/\mathrm{d}y|_{|y_{\rm lab}|<0.5}$ ($\upmu$b)
---|---|---
| $p_{\rm T}>0$ |
$\mathrm{D^{0}}$ | $1.275^{+0.014}_{-0.048}$ | $3989\pm 234\text{ (stat.) }\pm 282\text{ (syst.) }\pm 148\text{ (lumi.) }\pm 30\text{ (BR) }^{+200}_{-307}(\rm{extr.})$
$\rm D^{+}$ | $2.21^{+0.05}_{-0.19}$ | $1604\pm 222\text{ (stat.) }\pm 111\text{ (syst.) }\pm 59\text{ (lumi.) }\pm 27\text{ (BR) }^{+36}_{-140}(\rm{extr.})$

###  5.2 Nuclear modification factors

The nuclear modification factor $R_{\mathrm{pPb}}$ is computed as

$R_{\rm
pPb}=\cfrac{1}{A_{\mathrm{Pb}}}\cfrac{\mathrm{d}^{2}\sigma_{\mathrm{pPb}}/\mathrm{d}p_{\rm
T}\mathrm{d}y}{\mathrm{d}^{2}\sigma_{\mathrm{pp}}/\mathrm{d}p_{\rm
T}\mathrm{d}y}~{},$ (3)

where $\mathrm{d}^{2}\sigma_{\mathrm{pPb}}/\mathrm{d}p_{\rm T}\mathrm{d}y$
represents the $p_{\rm T}$-differential production cross section within
$-0.96<y_{\rm cms}<0.04$ in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$
TeV. In the analysis of the non-prompt D mesons,
$\mathrm{d}^{2}\sigma_{\mathrm{pp}}/\mathrm{d}p_{\rm T}\mathrm{d}y$
corresponds to the production cross section in pp collisions at the same
center-of-mass energy at midrapidity ($|y_{\rm lab}|<0.5$), taken from [2]. In
the case of the non-prompt $\mathrm{\Lambda_{c}^{+}}$ analysis, the pp
reference was computed adopting the non-prompt $\mathrm{\Lambda_{c}^{+}}$
$\mathrm{d}^{2}\sigma_{\mathrm{pp}}/\mathrm{d}p_{\rm T}\mathrm{d}y$ measured
in pp collisions at $\sqrt{s}=13$ TeV at midrapidity ($|y|<0.5$) [36], scaled
to account for the different collision energy. The scaling factor was computed
as the ratio of the B production cross section from FONLL at $\sqrt{s}=13$ and
$5.02$ TeV. This is justified given: (i) the compatible $p_{\rm T}$-dependence
of the 13-to-5.02 TeV ratio of mesons and baryons in the charm sector at
midrapidity [6], (ii) the agreement with the FONLL calculations of charm
mesons at midrapidity and beauty meson at forward rapidity [85, 86], and (iii)
the assumption that the beauty baryons have a similar scaling as the beauty
mesons, as observed in the charm sector [36]. A similar behavior is found in
the beauty sector [87], though with much larger uncertainties. The shift in
rapidity between pp and p–Pb collisions was corrected by using FONLL
predictions for the B meson production cross sections in the two rapidity
intervals, and applying the estimated correction to the non-prompt
$\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{\Lambda_{c}^{+}}$ measurements.
The corresponding correction ranges from 0.9 to 2.3%, increasing at higher
$p_{\rm T}$ [64]. The systematic uncertainties of the p–Pb and pp measurements
were treated as uncorrelated within the same $p_{\rm T}$ interval and were
propagated quadratically, with the exception of the BR which cancels out in
the ratio.

The non-prompt $\mathrm{D^{0}}$ and $\rm D^{+}$ $R_{\rm pPb}$ are compatible
over the full $p_{\rm T}$ range within the current uncertainties. In order to
have a more precise measurement, the average of their $R_{\rm pPb}$ was
computed, using the inverse of the quadratic sum of the statistical and
uncorrelated systematic uncertainties as weights. The systematic uncertainty
of the average was computed by propagating the uncertainties through the
weighted average while assuming the contributions from tracking efficiency and
normalisation to be fully correlated.

The left panel of Fig. 5 shows the average $R_{\rm pPb}$ of non-prompt
$\mathrm{D^{0}}$ and $\rm D^{+}$ mesons, and the average $R_{\rm pPb}$ of
prompt $\mathrm{D^{0}}$, $\rm D^{+}$, and $\rm D^{*+}$ mesons [64]. The
$R_{\rm pPb}$ of prompt and non-prompt charm mesons are compatible with each
other and with unity over the entire $p_{\rm T}$ interval of the measurements
within the statistical and systematic uncertainties. The comparison between
the $R_{\rm pPb}$ of prompt [21] and non-prompt $\mathrm{\Lambda_{c}^{+}}$
baryons is shown in the right panel of Fig. 5. The prompt
$\mathrm{\Lambda_{c}^{+}}$-baryon $R_{\rm pPb}$ shows deviation from unity,
highlighting modifications of the $p_{\rm T}$ spectrum in p–Pb collisions with
respect to pp collisions, due to effects beyond nPDFs that may relate to the
hadronisation process or to the presence of an expanding medium [26]. The non-
prompt $\mathrm{\Lambda_{c}^{+}}$-baryon $R_{\rm pPb}$ is compatible both with
unity and with the prompt $\mathrm{\Lambda_{c}^{+}}$-baryon measurements.
Given its large uncertainties, it is not possible to conclude about a possible
trend versus $p_{\rm T}$.

Figure 5: Left panel: average $p_{\rm T}$-differential $R_{\rm pPb}$ of prompt
$\mathrm{D^{0}}$, $\rm D^{+}$, and $\mathrm{D}^{*}$ [64], and non-prompt
$\mathrm{D^{0}}$ and $\rm D^{+}$ mesons. Right panel: $p_{\rm T}$-differential
$R_{\rm pPb}$ of prompt [21] and non-prompt $\mathrm{\Lambda_{c}^{+}}$
baryons. The vertical bars and empty boxes represent the statistical and
systematic uncertainties, respectively. The black-filled box at $R_{\rm
pPb}=1$ represents the normalisation systematic uncertainty.

The $p_{\rm T}$-integrated $R_{\rm pPb}$ values for non-prompt
$\mathrm{D^{0}}$ and $\rm D^{+}$ mesons in $-0.96<y_{\rm cms}<0.04$ were
calculated from the extrapolated $p_{\rm T}$-integrated production cross
sections reported above and the non-prompt $\mathrm{D^{0}}$\- and $\rm
D^{+}$-meson production cross sections measured in pp collisions at
$\sqrt{s}=5.02$ TeV [2]. The resulting $R_{\rm pPb}$ values of non-prompt
$\mathrm{D^{0}}$ and $\rm D^{+}$ mesons in p–Pb collisions are:

$\displaystyle R_{\rm pPb}^{\mathrm{non\text{-}prompt}\ \mathrm{D^{0}}}(p_{\rm
T}>0,-0.96<y_{\rm cms}<0.04)$ $\displaystyle=1.04\pm 0.11(\mathrm{stat.})\pm
0.12(\mathrm{syst.})^{+0.06}_{-0.11}(\rm{extr.})~{},$ $\displaystyle R_{\rm
pPb}^{\mathrm{non\text{-}prompt}\ \rm D^{+}}(p_{\rm T}>0,-0.96<y_{\rm
cms}<0.04)$ $\displaystyle=0.86\pm 0.19(\mathrm{stat.})\pm
0.11(\mathrm{syst.})^{+0.03}_{-0.11}(\rm{extr.})~{}.$

The $p_{\rm T}$-integrated $R_{\rm pPb}$ values of non-prompt D mesons are
compatible with unity within uncertainties, which is consistent with a not
significant modification of production cross section in p–Pb collisions
compared to pp collisions, as observed in the charm sector [36].

The left panel of Fig. 6 shows the $p_{\rm T}$-integrated $R_{\rm pPb}$
measured at midrapidity for non-prompt $\mathrm{D^{0}}$, $\rm D^{+}$, and
J/$\psi$ mesons by the ALICE Collaboration [88] compared to the ones of non-
prompt J/$\psi$ and $\rm B^{+}$ mesons measured at forward ($1.5<y_{\rm
cms}<4.0$, $2.5<y_{\rm cms}<3.5$) and backward ($-5.0<y_{\rm cms}<-2.5$,
$-3.5<y_{\rm cms}<-2.5$) rapidity by the LHCb Collaboration [35, 89]. The
measurements of non-prompt D, J$/\psi$, and B mesons in p–Pb collisions at
forward, backward, and midrapidity exploring different Bjorken-$x$ regions,
are sensitive to different levels of shadowing and saturation regimes. The
experimental results of $p_{\rm T}$-integrated $R_{\rm pPb}$ are compared with
model calculations of the $\mathrm{B^{+}}$ meson in p–Pb/Pb–p collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV using the HELAC-onia generator [90, 91,
92] with three different sets of nPDFs, i.e. EPPS16 [54], nCTEQ15 [93], and
EPPS16* [58]. In the calculations with EPPS16 and nCTEQ15, the model
parameters are tuned to reproduce J/$\psi$ and $\psi(\text{2S})$ cross section
measurements in pp collisions at the LHC [94, 95]. A weighting based on
several heavy-flavour measurements was applied on the nPDF set EPPS16 [54], to
obtain the nPDF set EPPS16*, as explained in [58]. The uncertainties in the
theoretical predictions arise from those of the corresponding nPDF
parameterisations. The measurements agree with the model calculations within
the uncertainties.

Figure 6: Left panel: Nuclear modification factors of non-prompt
$\mathrm{D^{0}}$ and $\rm D^{+}$ mesons measured in p–Pb collisions at
$\sqrt{s_{\rm NN}}$ = 5.02 TeV compared with the measurement of non-prompt
J/$\psi$ at midrapidity [88], and the measurements of non-prompt J/$\psi$ and
$\rm B^{+}$ mesons at forward and backward rapidity [35, 89]. The results are
also compared with B-meson $R_{\rm pPb}$ calculations using different nPDF
sets [93, 54, 58]. Right panel: $p_{\rm T}$-integrated nuclear modification
factor of prompt and non-prompt $\mathrm{D^{0}}$ mesons measured in p–Pb and
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [64, 96, 97].
Statistical (bars) and systematic (boxes) uncertainties are shown.
Extrapolation uncertainties of non-prompt $\mathrm{D^{0}}$ mesons in p–Pb and
Pb–Pb collisions are shown separately as shaded bands.

The right panel of Fig. 6 shows the $p_{\rm T}$-integrated nuclear
modification factors of prompt [64] and non-prompt $\mathrm{D^{0}}$ mesons
measured in p–Pb collisions compared with those measured in central (0-10%)
[96] and semicentral (30-50%) [97] Pb–Pb collisions. These measurements
provide an additional tool to investigate the modification of heavy-flavour
production from pp to p–Pb and Pb–Pb collisions in the beauty sector. A
$p_{\rm T}$-integrated $R_{\rm pPb}$ compatible with unity is measured for
both prompt and non-prompt charm mesons, suggesting the overall CNM effects in
the charm and beauty sector are similar in p–Pb collisions. In Pb–Pb
collisions, a hint of a different behaviour between charm and beauty is
suggested, possibly due to a higher sensitivity of charm quarks to the nPDF
modification (shadowing). Extending the measurement of beauty hadron
production down to $p_{\rm T}$ = 0, both in p–Pb and Pb–Pb collisions, will be
crucial to finally achieve a complete understanding of possible modification
of the heavy-flavour production due to CNM effects and possible different
hadronisation mechanisms across collision systems.

###  5.3 Production cross section ratios

To probe hadronisation in p–Pb collisions and its possible modification with
respect to smaller collision systems, ratios of non-prompt $\rm D^{+}$ over
non-prompt $\mathrm{D^{0}}$, and non-prompt $\mathrm{\Lambda_{c}^{+}}$ over
non-prompt $\mathrm{D^{0}}$ $p_{\rm T}$-integrated production cross sections
were computed. The systematic uncertainties were propagated to the ratios as
uncorrelated except for the ones related to tracking efficiency and
normalisation, which were treated as fully correlated. The ratios are reported
in Tables 4 and 5, respectively.

The non-prompt $\rm D^{+}/\mathrm{D^{0}}$ $p_{\rm T}$-integrated yield ratios
are reported in Table 4, together with the values measured in pp collisions
[2] at $\sqrt{s}$ = 5.02 TeV and with the one measured in $\rm e^{+}e^{-}$
collisions at LEP [1], where the error includes the statistical uncertainties,
systematic uncertainties and the uncertainties from the relevant branching
fractions. The results are compatible within experimental uncertainties, and
no dependence on the collision system or energy is observed.

Table 4: Production cross section ratios of non-prompt $\rm D^{+}$ over $\mathrm{D^{0}}$ for the measured $p_{\rm T}$ ranges at midrapidty ($|y_{\rm lab}|<0.5$) in pp collisions at $\sqrt{s}$ = 5.02 TeV [2], p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, and in $\mathrm{e^{+}e^{-}}$ collisions at $\sqrt{s}$ = 209 GeV at LEP [1]. System | Kinematic range (GeV/$c$) | Non-prompt $\rm D^{+}/\mathrm{D^{0}}$
---|---|---
pp at $\sqrt{s}$ = 5.02 TeV [2] | $2<p_{\rm T}<24$ | $0.487\pm 0.090\text{ (stat.)}$
$\pm\,0.055\text{ (syst.)}\pm 0.009\text{ (BR)}$
p–Pb at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV | $2<p_{\rm T}<24$ | $0.402\pm 0.060\text{ (stat.)}$
$\pm\,0.034\text{ (syst.)}\pm 0.011\text{ (BR)}$
$\mathrm{e^{+}e^{-}}$ at $\sqrt{s}$ = 209 GeV | – | $0.380\pm 0.025$
LEP average [1]

A possible $p_{\rm T}$ dependence was investigated by computing the $p_{\rm
T}$-differential ratios. The ratios of the $p_{\rm T}$-differential production
cross sections for prompt and non-prompt $\rm D^{+}/\mathrm{D^{0}}$ are shown
in the left panel of Fig. 7. The non-prompt $\rm D^{+}/\mathrm{D^{0}}$ ratio
is independent of $p_{\rm T}$ in the measured $p_{\rm T}$ range within the
current experimental precision and is compatible with the prompt $\rm
D^{+}/\mathrm{D^{0}}$ ratio pointing to a similar hadronisation of charm and
beauty quarks to open heavy-flavour mesons at midrapidity. This result is in
line with what was observed in the same rapidity interval in pp and Pb–Pb
collisions at different collision energies [2, 96]. In the right panel of Fig.
7, the non-prompt $\rm D^{+}/\mathrm{D^{0}}$ ratio measured in p–Pb collisions
is compared with the non-prompt $\rm D^{+}/\mathrm{D^{0}}$ ratio measured in
pp collisions at the same collision energy. The two measurements are
compatible over the full $p_{\rm T}$ range of the measurements within the
uncertainties, pointing to no significant modification of beauty quarks to
mesons within uncertainties.

Figure 7: Left panel: prompt (red) [64] and non-prompt (blue) $\rm
D^{+}/\mathrm{D^{0}}$ yield ratio as a function of $p_{\rm T}$. Right panel:
non-prompt $\rm D^{+}/\mathrm{D^{0}}$ yield ratios as a function of $p_{\rm
T}$ measured by ALICE Collaboration in pp (red) [2] and p–Pb (blue) collisions
at the same collision energy. The vertical bars and empty boxes represent the
statistical and systematic uncertainties (without the branching ratio
contribution), respectively.

The ratio between the $p_{\rm T}$-integrated production cross sections of non-
prompt $\mathrm{\Lambda_{c}^{+}}$ and $\mathrm{D^{0}}$ hadrons is reported in
Table 5, together with the one measured in pp collisions at $\sqrt{s}$ = 13
TeV ($|y|<$ 0.5) [36] and the one measured at LEP [1]. Despite the different
collision energies, an agreement within the experimental uncertainties is
observed between the measurements performed in pp and p–Pb collisions. On the
other hand, a significant difference is observed when comparing them with the
$\rm e^{+}e^{-}$ measurement obtained at LEP exhibiting a significant
enhancement in the measured $p_{\rm T}$ range, with respect to the meson
production at midrapidity in the beauty sector, as observed in the charm
sector [36].

Table 5: Cross sections ratios of non-prompt $\mathrm{\Lambda_{c}^{+}}$ and
$\mathrm{D^{0}}$ for the measured $p_{\rm T}$ ranges at midrapidity ($|y_{\rm
lab}|<0.5$) in pp collisions at $\sqrt{s}$ = 13 TeV [36], p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, and in $\mathrm{e^{+}e^{-}}$ collisions
at $\sqrt{s}$ = 209 GeV at LEP [1].

System | Kinematic range (GeV/$c$) | Non-prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$
---|---|---
pp at $\sqrt{s}$ = 13 TeV [36] | $2<p_{\rm T}<24$ | $0.55\pm 0.07\text{ (stat.)}\pm 0.06\text{ (syst.)}$
p–Pb at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV | $2<p_{\rm T}<24$ | $0.78\pm 0.21\text{ (stat.)}\pm 0.22\text{ (syst.)}$
$\mathrm{e^{+}e^{-}}$ at $\sqrt{s}$ = 209 GeV, LEP average [1] | – | $0.124\pm 0.016$

Figure 8: Top-left panel: non-prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$
yield ratios as a function of $p_{\rm T}$ measured by ALICE in pp (red) [36]
and p–Pb (blue) collisions compared with the $\rm{\Lambda_{b}^{0}}$
$/\mathrm{B}^{0}$ ratio (green) [24] measured by the LHCb Collaboration at
forward rapidity (2 $<y_{\rm lab}<$ 4.5) in pp collisions. Top-right panel:
prompt (red) [21] and non-prompt (blue)
$\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$ yield ratios as a function of
$p_{\rm T}$ measured by ALICE in $-0.96<y_{\rm cms}<0.04$ together with the
$\Lambda_{\mathrm{b}}^{0}/\mathrm{B}^{0}$ yield ratio (green) [35] measured by
LHCb in $2.5<y_{\rm cms}<3.5$. Bottom panel: ratios of the nuclear
modification factor of non-prompt $\mathrm{\Lambda_{c}^{+}}$ and non-prompt
$\mathrm{D^{0}}$ at midrapidity (blue), and the $\rm{\Lambda_{b}^{0}}$ and
$\mathrm{B}^{0}$ at forward and backward rapidity measured by LHCb (red) [35].

In order to gain further information about modification of hadronisation
mechanisms in the beauty sector, the ratio of the $p_{\rm T}$-differential
production cross sections of non-prompt $\mathrm{\Lambda_{c}^{+}}$ and
$\mathrm{D^{0}}$ hadrons measured in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV is computed and shown in the top-left
panel of Fig. 8. It is compared to the analogous ratio measured in pp
collisions at $\sqrt{s}$ = 13 TeV [36] and with the
$\rm{\Lambda_{b}^{0}}/\mathrm{B}^{0}$ ratio measured by the LHCb Collaboration
at forward rapidity (2 $<y_{\rm lab}<$ 4.5) in pp collisions at $\sqrt{s}$ =
13 TeV [24]. The baryon-to-meson ratio shows a decreasing trend with
increasing $p_{\rm T}$ in both pp and p–Pb collisions. The baryon enhancement
suggested at low $p_{\rm T}$ is qualitatively similar to what was measured in
pp collisions, where it was explained by different modelling of hadronisation
mechanisms beyond pure in-vacuum fragmentation. Notable among these are the
coalescence or recombination of charm quarks with quarks from a thermal medium
[40, 42, 43], the statistical hadronisation that takes into account
undiscovered higher charm resonant states [45, 46], and the string formation
beyond the leading colour approximation [47, 48]. The lack of similar models
for the beauty hadrons in p–Pb collisions, that could also account for the
presence of the Pb nucleons in the collisions, prevents any conclusion about
the origin of this modification in p–Pb collisions. Neglecting a possible
dependence on the collision energy, which is not observed in the charm sector
[6], the measurement in p–Pb collisions hints at a higher non-prompt
$\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$ yield ratio in 2 $<p_{\rm T}<$ 12
GeV$/c$ with respect to the pp one, similarly to what is more precisely
measured for the prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$ [21] and
$\mathrm{\Xi_{c}^{0}}/\mathrm{D^{0}}$ ratios [98] and for the
$\rm{\Lambda_{b}^{0}}/\mathrm{B}^{0}$ ratio ($-3.5<y_{\rm lab}<-2.5$ and 2.5
$<y_{\rm lab}<$ 3.5) [35]. This difference suggests a possible hardening of
the beauty baryon $p_{\rm T}$ spectra, consistent with a radial flow scenario,
where the shift to higher $p_{\rm T}$ depends on the particle mass. Similar
spectrum modifications in p–Pb collisions were also observed in the
strangeness sector by the ALICE and CMS Collaborations [60, 99], and were
found to be in line with the effect of radial flow predicted by hydrodynamic
models such as EPOS LHC [100]. Future precise measurements down to $p_{\rm T}$
= 0 will be crucial to assess potential differences on the beauty baryon
yields and collective motion in pp and p–Pb collisions.

As shown in the top-right panel of Fig. 8, the non-prompt baryon-to-meson
ratio is compatible with the prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$
[21] within the uncertainties in the measured $p_{\rm T}$ range in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The results are also
compared with the $\mathrm{\Lambda^{0}_{b}/B^{0}}$ yield ratio measured by the
LHCb Collaboration at $2.5<y_{\rm cms}<3.5$ [35] in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV. The LHCb measurement is compatible with
both the prompt and non-prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$
ratios, despite the difference in energy, rapidity, and the slight difference
in $p_{\rm T}$ coverage between the ALICE and LHCb measurements. This suggests
that the hadronisation modifications for beauty quarks may mirror those for
charm quarks [37]. The $\rm{\Lambda_{b}^{0}}/\mathrm{B}^{0}$ ratio from the
LHCb Collaboration is lower than the non-prompt
$\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$ ratio in the low-$p_{\rm T}$
interval when compared to both collision systems. However, the large
experimental uncertainties over the full $p_{\rm T}$ ranges prevent from
drawing strong conclusions.

Assuming that the modifications of hadronisation mechanisms of heavy quarks
are similar in pp and p–Pb collisions, one would expect the double ratio of
non-prompt $\mathrm{\Lambda_{c}^{+}}$ ($\rm{\Lambda_{b}^{0}}$) over
$\mathrm{D^{0}}$ ($\mathrm{B}^{0}$) production in p–Pb to pp collisions (non-
prompt $R_{\rm pPb}^{\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}}$ or $R_{\rm
pPb}^{\rm{\Lambda_{b}^{0}}/\text{B}^{0}}$) to be consistent with unity. This
quantity corresponds to the ratio of nuclear modification factors of baryons
over mesons. The bottom panel of Fig. 8 shows the $p_{\rm T}$-integrated
($p_{\rm T}$ $>2~{}\text{GeV/}c$) $R_{\rm pPb}$ of non-prompt
$\mathrm{\Lambda_{c}^{+}}$ baryons divided by that of non-prompt
$\mathrm{D^{0}}$ mesons, compared with the same ratio for
$\rm{\Lambda_{b}^{0}}$ baryons and $\mathrm{B}^{0}$ mesons measured by the
LHCb Collaboration [35] as a function of $y_{\rm cms}$. The result in
$-0.96<y_{\rm cms}<0.04$ is consistent with unity within the uncertainties.
However, more precise measurements exploiting larger collected data samples,
are required to conclude on a possible rapidity dependence of beauty-baryon
hadronisation.

##  6 Summary

The first measurements of non-prompt $\mathrm{D^{0}}$-, $\rm D^{+}$-, and
$\mathrm{\Lambda_{c}^{+}}$-hadron production at midrapidity in p–Pb collisions
are reported. Extrapolating the visible non-prompt D meson production cross
sections down to $p_{\rm T}=0$, the $p_{\rm T}$-integrated $R_{\rm pPb}$ of D
mesons is computed. Within the uncertainties, the $p_{\rm T}$-integrated
$R_{\rm pPb}$ of non-prompt D mesons is consistent with unity. Similarly, the
$p_{\rm T}$-integrated $R_{\rm pPb}$ of non-prompt $\mathrm{D^{0}}$ is
compatible with prompt $\mathrm{D^{0}}$. The $p_{\rm T}$-differential $R_{\rm
pPb}$ of non-prompt D mesons and $\mathrm{\Lambda_{c}^{+}}$ is compatible with
unity and the measurements in the charm sector, in the measured $p_{\rm T}$
range, within uncertainties. However, due to the current experimental
uncertainties, it remains challenging to clearly differentiate between a flat
trend compatible with unity, and the trend observed for prompt
$\mathrm{\Lambda_{c}^{+}}$ in p–Pb collisions as a function of $p_{\rm T}$.
The prompt and non-prompt yield ratios are compatible within current
experimental uncertainties for both $\rm D^{+}$/$\mathrm{D^{0}}$ and
$\mathrm{\Lambda_{c}^{+}}$/$\mathrm{D^{0}}$. The $p_{\rm T}$-differential non-
prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$ in p–Pb collisions is
compatible with the non-prompt $\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}$ ratio
and $\rm{\Lambda_{b}^{0}}$/$\text{B}^{0}$ ratio measured in pp collisions. The
$p_{\rm T}$-integrated non-prompt $R_{\rm
pPb}^{\mathrm{\Lambda_{c}^{+}}/\mathrm{D^{0}}}$ was measured at midrapidity
and is compatible with the $p_{\rm T}$-integrated $R_{\rm
pPb}^{\rm{\Lambda_{b}^{0}}/\text{B}^{0}}$ measured by the LHCb Collaboration.
The results indicate no significant CNM effects in the beauty sector within
uncertainties. These novel measurements in p–Pb collisions provide important
insights, enriching the understanding of nPDF models and the modification of
beauty quark hadronisation mechanisms. In addition, these measurements
represent an important input for constraining theoretical models for heavy-
flavour hadron production in p–Pb collisions, which are still lacking at the
moment. With the major upgrade of the ALICE detector for Run 3, larger data
samples, and foreseen upgrades for Run 4, ALICE will significantly advance
this field in the near future.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: Czech Science Foundation (grant no. 23-07499S), Czech Republic; European Research Council (grant no. 950692), European Union; ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, European Union - NextGenerationEU; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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##  Appendix A The ALICE Collaboration

S. Acharya 127, D. Adamová 86, A. Agarwal135, G. Aglieri Rinella 32, L.
Aglietta24, M. Agnello 29, N. Agrawal 25, Z. Ahammed 135, S. Ahmad 15, S.U.
Ahn 71, I. Ahuja 37, A. Akindinov 141, V. Akishina38, M. Al-Turany 97, D.
Aleksandrov 141, B. Alessandro 56, H.M. Alfanda 6, R. Alfaro Molina 67, B. Ali
15, A. Alici 25, N. Alizadehvandchali 116, A. Alkin 104, J. Alme 20, G. Alocco
52, T. Alt 64, A.R. Altamura 50, I. Altsybeev 95, J.R. Alvarado 44, C.O.R.
Alvarez44, M.N. Anaam 6, C. Andrei 45, N. Andreou 115, A. Andronic 126, E.
Andronov 141, V. Anguelov 94, F. Antinori 54, P. Antonioli 51, N. Apadula 74,
L. Aphecetche 103, H. Appelshäuser 64, C. Arata 73, S. Arcelli 25, R. Arnaldi
56, J.G.M.C.A. Arneiro 110, I.C. Arsene 19, M. Arslandok 138, A. Augustinus
32, R. Averbeck 97, D. Averyanov 141, M.D. Azmi 15, H. Baba124, A. Badalà 53,
J. Bae 104, Y.W. Baek 40, X. Bai 120, R. Bailhache 64, Y. Bailung 48, R. Bala
91, A. Balbino 29, A. Baldisseri 130, B. Balis 2, D. Banerjee 4, Z. Banoo 91,
V. Barbasova37, F. Barile 31, L. Barioglio 56, M. Barlou78, B. Barman41, G.G.
Barnaföldi 46, L.S. Barnby 115, E. Barreau 103, V. Barret 127, L. Barreto 110,
C. Bartels 119, K. Barth 32, E. Bartsch 64, N. Bastid 127, S. Basu 75, G.
Batigne 103, D. Battistini 95, B. Batyunya 142, D. Bauri47, J.L. Bazo Alba
101, I.G. Bearden 83, C. Beattie 138, P. Becht 97, D. Behera 48, I. Belikov
129, A.D.C. Bell Hechavarria 126, F. Bellini 25, R. Bellwied 116, S.
Belokurova 141, L.G.E. Beltran 109, Y.A.V. Beltran 44, G. Bencedi 46, A.
Bensaoula116, S. Beole 24, Y. Berdnikov 141, A. Berdnikova 94, L. Bergmann 94,
M.G. Besoiu 63, L. Betev 32, P.P. Bhaduri 135, A. Bhasin 91, B. Bhattacharjee
41, L. Bianchi 24, J. Bielčík 35, J. Bielčíková 86, A.P. Bigot 129, A.
Bilandzic 95, G. Biro 46, S. Biswas 4, N. Bize 103, J.T. Blair 108, D. Blau
141, M.B. Blidaru 97, N. Bluhme38, C. Blume 64, G. Boca 21,55, F. Bock 87, T.
Bodova 20, J. Bok 16, L. Boldizsár 46, M. Bombara 37, P.M. Bond 32, G. Bonomi
134,55, H. Borel 130, A. Borissov 141, A.G. Borquez Carcamo 94, E. Botta 24,
Y.E.M. Bouziani 64, L. Bratrud 64, P. Braun-Munzinger 97, M. Bregant 110, M.
Broz 35, G.E. Bruno 96,31, V.D. Buchakchiev 36, M.D. Buckland 85, D. Budnikov
141, H. Buesching 64, S. Bufalino 29, P. Buhler 102, N. Burmasov 141, Z.
Buthelezi 68,123, A. Bylinkin 20, S.A. Bysiak107, J.C. Cabanillas Noris 109,
M.F.T. Cabrera116, M. Cai 6, H. Caines 138, A. Caliva 28, E. Calvo Villar 101,
J.M.M. Camacho 109, P. Camerini 23, F.D.M. Canedo 110, S.L. Cantway 138, M.
Carabas 113, A.A. Carballo 32, F. Carnesecchi 32, R. Caron 128, L.A.D.
Carvalho 110, J. Castillo Castellanos 130, M. Castoldi 32, F. Catalano 32, S.
Cattaruzzi 23, C. Ceballos Sanchez 142, R. Cerri24, I. Chakaberia 74, P.
Chakraborty 136, S. Chandra 135, S. Chapeland 32, M. Chartier 119, S.
Chattopadhay135, S. Chattopadhyay 135, S. Chattopadhyay 99, M. Chen39, T.
Cheng 97,6, C. Cheshkov 128, V. Chibante Barroso 32, D.D. Chinellato 111, E.S.
Chizzali II,95, J. Cho 58, S. Cho 58, P. Chochula 32, Z.A. Chochulska136, D.
Choudhury41, P. Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T.
Chujo 125, M. Ciacco 29, C. Cicalo 52, M.R. Ciupek97, G. ClaiIII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 31, M. Colocci 25, M. Concas 32, G.
Conesa Balbastre 73, Z. Conesa del Valle 131, G. Contin 23, J.G. Contreras 35,
M.L. Coquet 103, P. Cortese 133,56, M.R. Cosentino 112, F. Costa 32, S.
Costanza 21,55, C. Cot 131, P. Crochet 127, R. Cruz-Torres 74, P. Cui 6, M.M.
Czarnynoga136, A. Dainese 54, G. Dange38, M.C. Danisch 94, A. Danu 63, P. Das
80, P. Das 4, S. Das 4, A.R. Dash 126, S. Dash 47, A. De Caro 28, G. de
Cataldo 50, J. de Cuveland38, A. De Falco 22, D. De Gruttola 28, N. De Marco
56, C. De Martin 23, S. De Pasquale 28, R. Deb 134, R. Del Grande 95, L. Dello
Stritto 32, W. Deng 6, K.C. Devereaux18, P. Dhankher 18, D. Di Bari 31, A. Di
Mauro 32, B. Diab 130, R.A. Diaz 142,7, T. Dietel 114, Y. Ding 6, J. Ditzel
64, R. Divià 32, Ø. Djuvsland20, U. Dmitrieva 141, A. Dobrin 63, B. Dönigus
64, J.M. Dubinski 136, A. Dubla 97, P. Dupieux 127, N. Dzalaiova13, T.M. Eder
126, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D. Elia 50, B. Erazmus 103,
F. Ercolessi 25, B. Espagnon 131, G. Eulisse 32, D. Evans 100, S. Evdokimov
141, L. Fabbietti 95, M. Faggin 23, J. Faivre 73, F. Fan 6, W. Fan 74, A.
Fantoni 49, M. Fasel 87, A. Feliciello 56, G. Feofilov 141, A. Fernández
Téllez 44, L. Ferrandi 110, M.B. Ferrer 32, A. Ferrero 130, C. Ferrero IV,56,
A. Ferretti 24, V.J.G. Feuillard 94, V. Filova 35, D. Finogeev 141, F.M.
Fionda 52, E. Flatland32, F. Flor 138,116, A.N. Flores 108, S. Foertsch 68, I.
Fokin 94, S. Fokin 141, U. FolloIV,56, E. Fragiacomo 57, E. Frajna 46, U.
Fuchs 32, N. Funicello 28, C. Furget 73, A. Furs 141, T. Fusayasu 98, J.J.
Gaardhøje 83, M. Gagliardi 24, A.M. Gago 101, T. Gahlaut47, C.D. Galvan 109,
D.R. Gangadharan 116, P. Ganoti 78, C. Garabatos 97, J.M. Garcia44, T. García
Chávez 44, E. Garcia-Solis 9, C. Gargiulo 32, P. Gasik 97, H.M. Gaur38, A.
Gautam 118, M.B. Gay Ducati 66, M. Germain 103, R.A. Gernhaeuser95, C.
Ghosh135, M. Giacalone 51, G. Gioachin 29, S.K. Giri135, P. Giubellino 97,56,
P. Giubilato 27, A.M.C. Glaenzer 130, P. Glässel 94, E. Glimos 122, D.J.Q.
Goh76, V. Gonzalez 137, P. Gordeev 141, M. Gorgon 2, K. Goswami 48, S.
Gotovac33, V. Grabski 67, L.K. Graczykowski 136, E. Grecka 86, A. Grelli 59,
C. Grigoras 32, V. Grigoriev 141, S. Grigoryan 142,1, F. Grosa 32, J.F.
Grosse-Oetringhaus 32, R. Grosso 97, D. Grund 35, N.A. Grunwald94, G.G.
Guardiano 111, R. Guernane 73, M. Guilbaud 103, K. Gulbrandsen 83, J.J.W.K.
Gumprecht102, T. Gündem 64, T. Gunji 124, W. Guo 6, A. Gupta 91, R. Gupta 91,
R. Gupta 48, K. Gwizdziel 136, L. Gyulai 46, C. Hadjidakis 131, F.U. Haider
91, S. Haidlova 35, M. Haldar4, H. Hamagaki 76, Y. Han 139, B.G. Hanley 137,
R. Hannigan 108, J. Hansen 75, M.R. Haque 97, J.W. Harris 138, A. Harton 9,
M.V. Hartung 64, H. Hassan 117, D. Hatzifotiadou 51, P. Hauer 42, L.B. Havener
138, E. Hellbär 97, H. Helstrup 34, M. Hemmer 64, T. Herman 35, S.G.
Hernandez116, G. Herrera Corral 8, S. Herrmann 128, K.F. Hetland 34, B.
Heybeck 64, H. Hillemanns 32, B. Hippolyte 129, I.P.M. Hobus84, F.W. Hoffmann
70, B. Hofman 59, G.H. Hong 139, M. Horst 95, A. Horzyk 2, Y. Hou 6, P.
Hristov 32, P. Huhn64, L.M. Huhta 117, T.J. Humanic 88, A. Hutson 116, D.
Hutter 38, M.C. Hwang 18, R. Ilkaev141, M. Inaba 125, G.M. Innocenti 32, M.
Ippolitov 141, A. Isakov 84, T. Isidori 118, M.S. Islam 99, S. Iurchenko141,
M. Ivanov 97, M. Ivanov13, V. Ivanov 141, K.E. Iversen 75, M. Jablonski 2, B.
Jacak 18,74, N. Jacazio 25, P.M. Jacobs 74, S. Jadlovska106, J. Jadlovsky106,
S. Jaelani 82, C. Jahnke 110, M.J. Jakubowska 136, M.A. Janik 136, T.
Janson70, S. Ji 16, S. Jia 10, T. Jiang 10, A.A.P. Jimenez 65, F. Jonas 74,
D.M. Jones 119, J.M. Jowett 32,97, J. Jung 64, M. Jung 64, A. Junique 32, A.
Jusko 100, J. Kaewjai105, P. Kalinak 60, A. Kalweit 32, A. Karasu Uysal V,72,
D. Karatovic 89, N. Karatzenis100, O. Karavichev 141, T. Karavicheva 141, E.
Karpechev 141, M.J. Karwowska 32,136, U. Kebschull 70, R. Keidel 140, M. Keil
32, B. Ketzer 42, S.S. Khade 48, A.M. Khan 120, S. Khan 15, A. Khanzadeev 141,
Y. Kharlov 141, A. Khatun 118, A. Khuntia 35, Z. Khuranova 64, B. Kileng 34,
B. Kim 104, C. Kim 16, D.J. Kim 117, E.J. Kim 69, J. Kim 139, J. Kim 58, J.
Kim 32,69, M. Kim 18, S. Kim 17, T. Kim 139, K. Kimura 92, A. Kirkova36, S.
Kirsch 64, I. Kisel 38, S. Kiselev 141, A. Kisiel 136, J.P. Kitowski 2, J.L.
Klay 5, J. Klein 32, S. Klein 74, C. Klein-Bösing 126, M. Kleiner 64, T.
Klemenz 95, A. Kluge 32, C. Kobdaj 105, R. Kohara124, T. Kollegger97, A.
Kondratyev 142, N. Kondratyeva 141, J. Konig 64, S.A. Konigstorfer 95, P.J.
Konopka 32, G. Kornakov 136, M. Korwieser 95, S.D. Koryciak 2, C. Koster84, A.
Kotliarov 86, N. Kovacic89, V. Kovalenko 141, M. Kowalski 107, V. Kozhuharov
36, G. Kozlov38, I. Králik 60, A. Kravčáková 37, L. Krcal 32,38, M. Krivda
100,60, F. Krizek 86, K. Krizkova Gajdosova 32, C. Krug 66, M. Krüger 64, D.M.
Krupova 35, E. Kryshen 141, V. Kučera 58, C. Kuhn 129, P.G. Kuijer 84, T.
Kumaoka125, D. Kumar135, L. Kumar 90, N. Kumar90, S. Kumar 50, S. Kundu 32, P.
Kurashvili 79, A. Kurepin 141, A.B. Kurepin 141, A. Kuryakin 141, S. Kushpil
86, V. Kuskov 141, M. Kutyla136, A. Kuznetsov142, M.J. Kweon 58, Y. Kwon 139,
S.L. La Pointe 38, P. La Rocca 26, A. Lakrathok105, M. Lamanna 32, A.R. Landou
73, R. Langoy 121, P. Larionov 32, E. Laudi 32, L. Lautner 32,95, R.A.N.
Laveaga109, R. Lavicka 102, R. Lea 134,55, H. Lee 104, I. Legrand 45, G.
Legras 126, J. Lehrbach 38, A.M. Lejeune35, T.M. Lelek2, R.C. Lemmon I,85, I.
León Monzón 109, M.M. Lesch 95, E.D. Lesser 18, P. Lévai 46, M. Li6, X. Li10,
B.E. Liang-gilman 18, J. Lien 121, R. Lietava 100, I. Likmeta 116, B. Lim 24,
S.H. Lim 16, V. Lindenstruth 38, A. Lindner45, C. Lippmann 97, D.H. Liu 6, J.
Liu 119, G.S.S. Liveraro 111, I.M. Lofnes 20, C. Loizides 87, S. Lokos 107, J.
Lömker 59, X. Lopez 127, E. López Torres 7, C. Lotteau128, P. Lu 97,120, Z. Lu
10, F.V. Lugo 67, J.R. Luhder 126, M. Lunardon 27, G. Luparello 57, Y.G. Ma
39, M. Mager 32, A. Maire 129, E.M. Majerz2, M.V. Makariev 36, M. Malaev 141,
G. Malfattore 25, N.M. Malik 91, Q.W. Malik19, S.K. Malik 91, L. Malinina
I,VIII,142, D. Mallick 131, N. Mallick 48, G. Mandaglio 30,53, S.K. Mandal 79,
A. Manea 63, V. Manko 141, F. Manso 127, V. Manzari 50, Y. Mao 6, R.W. Marcjan
2, G.V. Margagliotti 23, A. Margotti 51, A. Marín 97, C. Markert 108, P.
Martinengo 32, M.I. Martínez 44, G. Martínez García 103, M.P.P. Martins 110,
S. Masciocchi 97, M. Masera 24, A. Masoni 52, L. Massacrier 131, O. Massen 59,
A. Mastroserio 132,50, O. Matonoha 75, S. Mattiazzo 27, A. Matyja 107, A.L.
Mazuecos 32, F. Mazzaschi 32,24, M. Mazzilli 116, J.E. Mdhluli 123, Y.
Melikyan 43, M. Melo 110, A. Menchaca-Rocha 67, J.E.M. Mendez 65, E. Meninno
102, A.S. Menon 116, M.W. Menzel32,94, M. Meres 13, Y. Miake125, L. Micheletti
32, D.L. Mihaylov 95, K. Mikhaylov 142,141, N. Minafra 118, D. Miśkowiec 97,
A. Modak 134,4, B. Mohanty80, M. Mohisin Khan VI,15, M.A. Molander 43, S.
Monira 136, C. Mordasini 117, D.A. Moreira De Godoy 126, I. Morozov 141, A.
Morsch 32, T. Mrnjavac 32, V. Muccifora 49, S. Muhuri 135, J.D. Mulligan 74,
A. Mulliri 22, M.G. Munhoz 110, R.H. Munzer 64, H. Murakami 124, S. Murray
114, L. Musa 32, J. Musinsky 60, J.W. Myrcha 136, B. Naik 123, A.I. Nambrath
18, B.K. Nandi 47, R. Nania 51, E. Nappi 50, A.F. Nassirpour 17, A. Nath 94,
S. Nath135, C. Nattrass 122, M.N. Naydenov 36, A. Neagu19, A. Negru113, E.
Nekrasova141, L. Nellen 65, R. Nepeivoda 75, S. Nese 19, N. Nicassio 50, B.S.
Nielsen 83, E.G. Nielsen 83, S. Nikolaev 141, S. Nikulin 141, V. Nikulin 141,
F. Noferini 51, S. Noh 12, P. Nomokonov 142, J. Norman 119, N. Novitzky 87, P.
Nowakowski 136, A. Nyanin 141, J. Nystrand 20, S. Oh 17, A. Ohlson 75, V.A.
Okorokov 141, J. Oleniacz 136, A. Onnerstad 117, C. Oppedisano 56, A. Ortiz
Velasquez 65, J. Otwinowski 107, M. Oya92, K. Oyama 76, Y. Pachmayer 94, S.
Padhan 47, D. Pagano 134,55, G. Paić 65, S. Paisano-Guzmán 44, A. Palasciano
50, S. Panebianco 130, C. Pantouvakis27, H. Park 125, H. Park 104, J. Park
125, J.E. Parkkila 32, Y. Patley 47, R.N. Patra50, B. Paul 135, H. Pei 6, T.
Peitzmann 59, X. Peng 11, M. Pennisi 24, S. Perciballi 24, D. Peresunko 141,
G.M. Perez 7, Y. Pestov141, M.T. Petersen83, V. Petrov 141, M. Petrovici 45,
S. Piano 57, M. Pikna 13, P. Pillot 103, O. Pinazza 51,32, L. Pinsky116, C.
Pinto 95, S. Pisano 49, M. Płoskoń 74, M. Planinic89, F. Pliquett64, D.K.
Plociennik2, M.G. Poghosyan 87, B. Polichtchouk 141, S. Politano 29, N. Poljak
89, A. Pop 45, S. Porteboeuf-Houssais 127, V. Pozdniakov I,142, I.Y. Pozos 44,
K.K. Pradhan 48, S.K. Prasad 4, S. Prasad 48, R. Preghenella 51, F. Prino 56,
C.A. Pruneau 137, I. Pshenichnov 141, M. Puccio 32, S. Pucillo 24, S. Qiu 84,
L. Quaglia 24, S. Ragoni 14, A. Rai 138, A. Rakotozafindrabe 130, L. Ramello
133,56, F. Rami 129, M. Rasa 26, S.S. Räsänen 43, R. Rath 51, M.P. Rauch 20,
I. Ravasenga 32, K.F. Read 87,122, C. Reckziegel 112, A.R. Redelbach 38, K.
Redlich VII,79, C.A. Reetz 97, H.D. Regules-Medel44, A. Rehman20, F. Reidt 32,
H.A. Reme-Ness 34, Z. Rescakova37, K. Reygers 94, A. Riabov 141, V. Riabov
141, R. Ricci 28, M. Richter 20, A.A. Riedel 95, W. Riegler 32, A.G. Riffero
24, M. Rignanese27, C. Ripoli28, C. Ristea 63, M.V. Rodriguez 32, M. Rodríguez
Cahuantzi 44, S.A. Rodríguez Ramírez 44, K. Røed 19, R. Rogalev 141, E.
Rogochaya 142, T.S. Rogoschinski 64, D. Rohr 32, D. Röhrich 20, S. Rojas
Torres 35, P.S. Rokita 136, G. Romanenko 25, F. Ronchetti 49, E.D. Rosas65, K.
Roslon 136, A. Rossi 54, A. Roy 48, S. Roy 47, N. Rubini 51,25, J.A.
Rudolph84, D. Ruggiano 136, R. Rui 23, P.G. Russek 2, R. Russo 84, A. Rustamov
81, E. Ryabinkin 141, Y. Ryabov 141, A. Rybicki 107, J. Ryu 16, W. Rzesa 136,
B. Sabiu51, S. Sadovsky 141, J. Saetre 20, K. Šafařík 35, S.K. Saha 4, S. Saha
80, B. Sahoo 48, R. Sahoo 48, S. Sahoo61, D. Sahu 48, P.K. Sahu 61, J. Saini
135, K. Sajdakova37, S. Sakai 125, M.P. Salvan 97, S. Sambyal 91, D. Samitz
102, I. Sanna 32,95, T.B. Saramela110, D. Sarkar 83, P. Sarma 41, V. Sarritzu
22, V.M. Sarti 95, M.H.P. Sas 32, S. Sawan 80, E. Scapparone 51, J. Schambach
87, H.S. Scheid 64, C. Schiaua 45, R. Schicker 94, F. Schlepper 94, A.
Schmah97, C. Schmidt 97, H.R. Schmidt93, M.O. Schmidt 32, M. Schmidt93, N.V.
Schmidt 87, A.R. Schmier 122, R. Schotter 129, A. Schröter 38, J. Schukraft
32, K. Schweda 97, G. Scioli 25, E. Scomparin 56, J.E. Seger 14, Y.
Sekiguchi124, D. Sekihata 124, M. Selina 84, I. Selyuzhenkov 97, S. Senyukov
129, J.J. Seo 94, D. Serebryakov 141, L. Serkin 65, L. Šerkšnytė 95, A.
Sevcenco 63, T.J. Shaba 68, A. Shabetai 103, R. Shahoyan32, A. Shangaraev 141,
B. Sharma 91, D. Sharma 47, H. Sharma 54, M. Sharma 91, S. Sharma 76, S.
Sharma 91, U. Sharma 91, A. Shatat 131, O. Sheibani116, K. Shigaki 92, M.
Shimomura77, J. Shin12, S. Shirinkin 141, Q. Shou 39, Y. Sibiriak 141, S.
Siddhanta 52, T. Siemiarczuk 79, T.F. Silva 110, D. Silvermyr 75, T.
Simantathammakul105, R. Simeonov 36, B. Singh91, B. Singh 95, K. Singh 48, R.
Singh 80, R. Singh 91, R. Singh 97, S. Singh 15, V.K. Singh 135, V. Singhal
135, T. Sinha 99, B. Sitar 13, M. Sitta 133,56, T.B. Skaali19, G. Skorodumovs
94, N. Smirnov 138, R.J.M. Snellings 59, E.H. Solheim 19, J. Song 16, C.
Sonnabend 32,97, J.M. Sonneveld 84, F. Soramel 27, A.B. Soto-hernandez 88, R.
Spijkers 84, I. Sputowska 107, J. Staa 75, J. Stachel 94, I. Stan 63, P.J.
Steffanic 122, T. Stellhorn126, S.F. Stiefelmaier 94, D. Stocco 103, I.
Storehaug 19, N.J. Strangmann 64, P. Stratmann 126, S. Strazzi 25, A.
Sturniolo 30,53, C.P. Stylianidis84, A.A.P. Suaide 110, C. Suire 131, M.
Sukhanov 141, M. Suljic 32, R. Sultanov 141, V. Sumberia 91, S. Sumowidagdo
82, M. Szymkowski 136, S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 111,
G.J. Tambave 80, S. Tang 6, Z. Tang 120, J.D. Tapia Takaki 118, N. Tapus113,
L.A. Tarasovicova 126, M.G. Tarzila 45, G.F. Tassielli 31, A. Tauro 32, A.
Tavira García 131, G. Tejeda Muñoz 44, A. Telesca 32, L. Terlizzi 24, C.
Terrevoli 50, S. Thakur 4, D. Thomas 108, A. Tikhonov 141, N. Tiltmann 32,126,
A.R. Timmins 116, M. Tkacik106, T. Tkacik 106, A. Toia 64, R. Tokumoto92, S.
Tomassini25, K. Tomohiro92, N. Topilskaya 141, M. Toppi 49, V.V. Torres 103,
A.G. Torres Ramos 31, A. Trifiró 30,53, T. Triloki96, A.S. Triolo 32,30,53, S.
Tripathy 32, T. Tripathy 47, V. Trubnikov 3, W.H. Trzaska 117, T.P. Trzcinski
136, C. Tsolanta19, R. Tu39, A. Tumkin 141, R. Turrisi 54, T.S. Tveter 19, K.
Ullaland 20, B. Ulukutlu 95, S. Upadhyaya 107, A. Uras 128, M. Urioni 134,
G.L. Usai 22, M. Vala37, N. Valle 55, L.V.R. van Doremalen59, M. van Leeuwen
84, C.A. van Veen 94, R.J.G. van Weelden 84, P. Vande Vyvre 32, D. Varga 46,
Z. Varga 46, P. Vargas Torres65, M. Vasileiou 78, A. Vasiliev 141, O. Vázquez
Doce 49, O. Vazquez Rueda 116, V. Vechernin 141, E. Vercellin 24, S. Vergara
Limón44, R. Verma47, L. Vermunt 97, R. Vértesi 46, M. Verweij 59, L.
Vickovic33, Z. Vilakazi123, O. Villalobos Baillie 100, A. Villani 23, A.
Vinogradov 141, T. Virgili 28, M.M.O. Virta 117, A. Vodopyanov 142, B. Volkel
32, M.A. Völkl 94, S.A. Voloshin 137, G. Volpe 31, B. von Haller 32, I.
Vorobyev 32, N. Vozniuk 141, J. Vrláková 37, J. Wan39, C. Wang 39, D. Wang39,
Y. Wang 39, Y. Wang 6, A. Wegrzynek 32, F.T. Weiglhofer38, S.C. Wenzel 32,
J.P. Wessels 126, J. Wiechula 64, J. Wikne 19, G. Wilk 79, J. Wilkinson 97,
G.A. Willems 126, B. Windelband 94, M. Winn 130, J.R. Wright 108, W. Wu39, Y.
Wu 120, Z. Xiong120, R. Xu 6, A. Yadav 42, A.K. Yadav 135, Y. Yamaguchi 92, S.
Yang20, S. Yano 92, E.R. Yeats18, Z. Yin 6, I.-K. Yoo 16, J.H. Yoon 58, H.
Yu12, S. Yuan20, A. Yuncu 94, V. Zaccolo 23, C. Zampolli 32, M. Zang6, F.
Zanone 94, N. Zardoshti 32, A. Zarochentsev 141, P. Závada 62, N.
Zaviyalov141, M. Zhalov 141, B. Zhang 94,6, C. Zhang 130, L. Zhang 39, M.
Zhang127,6, S. Zhang 39, X. Zhang 6, Y. Zhang120, Z. Zhang 6, M. Zhao 10, V.
Zherebchevskii 141, Y. Zhi10, D. Zhou 6, Y. Zhou 83, J. Zhu 54,6, S. Zhu120,
Y. Zhu6, S.C. Zugravel 56, N. Zurlo 134,55

## Affiliation Notes

I Deceased
II Also at: Max-Planck-Institut fur Physik, Munich, Germany
III Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
V Also at: Yildiz Technical University, Istanbul, Türkiye
VI Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VII Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VIII Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

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