2021 184 10 September

D meson-charged particle azimuthal correlations at 13 TeV

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

Angular correlations of heavy-flavour and charged particles in high-energy
proton–proton collisions are sensitive to the production mechanisms of heavy
quarks and to their fragmentation as well as hadronisation processes. The
measurement of the azimuthal-correlation function of prompt D mesons with
charged particles in proton–proton collisions at a centre-of-mass energy of
$\sqrt{s}=13$ TeV with the ALICE detector is reported, considering $\rm
D^{0}$, $\rm D^{+}$, and $\rm D^{*+}$ mesons in the transverse-momentum
interval $3<p_{\rm T}<36$ GeV/$c$ at midrapidity ($|y|<0.5$), and charged
particles with $p_{\rm T}>0.3$ GeV/$c$ and pseudorapidity $|\eta|<0.8$. This
measurement has an improved precision and provides an extended transverse-
momentum coverage compared to previous ALICE measurements at lower energies.
The study is also performed as a function of the charged-particle
multiplicity, showing no modifications of the correlation function with
multiplicity within uncertainties. The properties and the transverse-momentum
evolution of the near- and away-side correlation peaks are studied and
compared with predictions from various Monte Carlo event generators. Among
those considered, PYTHIA8 and POWHEG+PYTHIA8 provide the best description of
the measured observables. The obtained results can provide guidance on tuning
the generators.

##  1 Introduction

The study of angular correlations of heavy-flavour (charm and beauty)
particles in ultra-relativistic hadronic collisions allows the investigation
of fundamental properties of quantum chromodynamics (QCD) in the heavy-flavour
domain [1, 2]. In particular, the angular-correlation function between prompt
D mesons and charged particles in proton–proton (pp) collisions is sensitive
to the mechanisms of charm-quark production, fragmentation, and hadronisation
into charm hadrons. The term “prompt” refers to D mesons originating both from
direct charm-quark fragmentation and from the strong decay of excited charm
resonances, and excludes D mesons produced from beauty-hadron weak decays. The
typical structure of the two-dimensional correlation function between
“trigger” D mesons and “associated” charged particles, expressed in terms of
the pseudorapidity difference ($\Delta\eta=\eta_{\rm ch}-\eta_{\rm D}$) and
azimuthal angle difference ($\Delta\varphi=\varphi_{\rm ch}-\varphi_{\rm D}$),
features a near-side (NS) peak, centred at ($\Delta\varphi,\Delta\eta)=(0,0)$,
and an away-side (AS) peak at $\Delta\varphi=\pi$ that is elongated along
$\Delta\eta$ [3]. Both peaks sit on top of an approximately flat continuum
extending over the full ($\Delta\varphi,\Delta\eta$) range. The height and
width of the two correlation peaks are sensitive to the charm-quark production
mechanisms.

Due to their large mass, the production of charm-quark pairs occurs through
hard parton–parton scattering processes with large momentum transfers, and can
be described by perturbative QCD (pQCD) calculations. While in leading-order
(LO) processes the two quarks are produced back-to-back in azimuth, the next-
to-leading-order (NLO) production mechanisms, such as flavour excitation and
gluon splitting, can break this topology and alter the shape of the two
correlation peaks [4]. Recent studies at the LHC suggest a relevant
contribution from gluon splitting to heavy-quark production, possibly
underestimated by Monte Carlo (MC) event generators with LO or NLO accuracy
[5, 6]. The analysis of the properties of the near-side peak also allows for
detailing the fragmentation and hadronisation processes which, starting from a
coloured charm quark, lead to the formation of a D meson surrounded by a spray
of colourless particles, experimentally identifiable as a charm jet. The
production cross section of jets containing D mesons, as well as the jet
momentum fraction carried by the D meson along the jet-axis direction, were
recently measured by the ALICE and ATLAS Collaborations [7, 8]. In this
regard, a systematic and differential analysis of the near-side correlation
peak in terms of transverse momenta of trigger D meson ($p_{\rm T}^{\rm D}$)
and other associated fragmenting particles ($p_{\rm T}^{\rm assoc}$), and of
the angular distance of associated particles from the D mesons, can provide
additional information with respect to measurements that treat charm jets as a
whole entity.

In recent years, the study of high-multiplicity pp collisions has become of
particular interest. The ALICE Collaboration has measured a faster-than-linear
increase of prompt D-meson self-normalised yields for increasing relative
event multiplicity in pp collisions at a centre-of-mass energy of $\sqrt{s}=7$
TeV, employing both central- and forward-rapidity multiplicity estimators [9].
A similar behaviour was also seen for open-beauty and hidden-charm hadrons,
pointing towards sensitivity of heavy-quark production processes to event
multiplicity. Complementary information on a possible dependence of charm-
quark fragmentation and hadronisation on event multiplicity can be provided by
the study of D-meson and charged-particle azimuthal correlations as a function
of the event multiplicity, searching in particular for modifications of the
near-side peak structure. This measurement is also crucial to validate the
assumptions adopted to measure the elliptic-flow coefficient of D mesons and
heavy-flavour decay muons in high-multiplicity pp collisions at $\sqrt{s}=13$
TeV by CMS [10] and ATLAS [11], respectively. In these measurements, the
elliptic-flow coefficient is extracted from two-particle correlation function
of such heavy-flavour particles with charged particles, and the short-range
correlation peaks related to heavy-quark fragmentation are removed from the
correlation function exploiting low-multiplicity events, assuming independence
of the correlation peaks from the event multiplicity.

MC event generators, like PYTHIA [12, 13], EPOS [14, 15], or HERWIG [16, 17,
18], or pQCD calculations coupled to parton-shower software, such as POWHEG
[19, 20], are widely used to reproduce ultra-relativistic hadronic collisions
and provide predictions for a wide variety of physics observables. As
discussed in Ref. [21], depending on the treatment of the various collision
stages and implementation of specific features in each generator, such as hard
parton–parton scattering matrix elements, parton-showering model,
hadronisation algorithm, and underlying event generation, different
predictions for D-meson and charged-particle correlation function will be
obtained. A comparison of the predicted features of the correlation
observables, in particular the peak yields and widths, with data measurements,
can allow for validating and setting constraints to the MC generators [22].

A proper understanding of heavy-flavour correlations in pp collisions is also
crucial in view of future studies in ultra-relativistic heavy-ion collisions.
In the first stages of such collisions a deconfined state of strongly-coupled
matter, the quark–gluon plasma (QGP), is created. While traversing the medium,
heavy quarks interact with the QGP constituents through radiative and
collisional processes [23, 24], losing energy and having their original
directions modified. This is expected to lead to a modification of the
angular-correlation function between final-state heavy-flavour hadrons and
associated charged particles, with respect to that observed in pp collisions.
Quantifying such modifications allows for investigation of specific properties
of the QGP and its dynamics [2]. In particular, the angular-correlation
function is sensitive to the relative contributions of the two energy-loss
processes, and can shed light on the path-length dependence of energy loss
[25, 26, 27, 28]. Some first indications in this direction were provided by a
recent measurement of $\rm D^{0}$-meson and charged-hadron angular
correlations in gold–gold collisions at a centre-of-mass energy per nucleon
pair of $\sqrt{s_{\mathrm{NN}}}=200$ GeV performed by the STAR Collaboration
at RHIC [29]. Validating MC event generators against the correlation function
of heavy-flavour particles measured in pp collisions is thus fundamental for a
correct understanding of the same observables that will be measured in the
future in lead–lead (Pb–Pb) collisions at the LHC.

In this article, ALICE measurements of azimuthal correlations of prompt $\rm
D^{0}$, $\rm D^{+}$, and $\rm D^{*+}$ mesons, together with their charge
conjugates, with associated charged particles in pp collisions at
$\sqrt{s}=13$ TeV at midrapidity are reported. For prompt $\rm D^{0}$-meson
triggers the results of the correlation analysis are also reported as a
function of the charged-particle event multiplicity, measured at forward and
backward rapidity. With respect to previous ALICE publications in pp
collisions [3, 21], the new measurements extend the $p_{\rm T}$ range of D
mesons up to 36 GeV/$c$, and significantly improve the precision of the
measured observables in the common $p_{\rm T}$ range. Additionally, the
measurements presented here, along with previous ALICE results at
$\sqrt{s}=5.02$ and 7 TeV, enable the study of the possible evolution of the
correlation distributions and of the peak features as a function of the
collision centre-of-mass energy.

The article is organised based on the following structure. Section 2 describes
the ALICE apparatus, as well as the data and MC samples used for this study.
Section 3 highlights the procedure followed to obtain the azimuthal
correlation function and to extract physical observables from it. In Section
4, the sources of systematic uncertainties affecting the results are detailed.
In Section 5, the analysis results are presented and discussed, and a
comparison with various model predictions is shown. Further model studies
highlighting the specific contributions to the correlation function from
initial- and final-state radiation and multi-parton interactions are reported
in Section 6. A summary of the paper and its physics message is outlined in
Section 7.

##  2 ALICE detector, data, and MC samples

A complete description of the ALICE detector and its performance can be found
in Refs. [30, 31]. The reconstruction of D mesons and charged particles was
performed using detectors installed in the central barrel, with a
pseudorapidity coverage of $|\eta|<0.9$ and a magnetic field of $B=0.5$ T
parallel to the beam axis. In particular, the Inner Tracking System (ITS) [32]
and the Time Projection Chamber (TPC) [33] were employed for the
reconstruction of charged tracks and of primary and secondary vertices. The
TPC, together with the Time-of-Flight (TOF) detector [34], also provided
charged-particle identification (PID) information. The analysis also relied on
detectors located along the beam line, at forward and backward rapidity. The
V0 detector [35] is a set of scintillators covering the pseudorapidity ranges
$2.8<\eta<5.1$ (V0A) and $-3.7<\eta<-1.7$ (V0C), used for triggering,
background-event rejection, and event-multiplicity estimation. The T0 detector
is an array of Cherenkov counters, located along the beam line, at a distance
of $+370$ cm (T0A) and $-70$ cm (T0C) from the nominal interaction point, and
provides the collision starting time needed by the TOF [36].

The data sample used for the analysis consisted of pp collisions at
$\sqrt{s}=13$ TeV collected during the 2016, 2017, and 2018 data taking
periods, with a total integrated luminosity of about 29 nb-1, based on the
visible cross section measured with the V0 detector [37]. The collisions were
recorded if they satisfied a minimum-bias trigger, requiring the presence of
signals in both V0 detectors in coincidence with a bunch crossing in the ALICE
interaction region. This trigger was fully efficient for selecting events
containing D mesons with $p_{\rm T}>1$ GeV/$c$. Contamination of tracks from
pile-up events (multiple collisions occurring in the same bunch crossing) was
suppressed by discarding events where multiple primary vertices were
reconstructed with the Silicon Pixel Detector (SPD), which constitutes the
first two layers of the ITS. Timing information provided by the V0, as well as
the correlation between the number of hits and the number of track segments in
the SPD, were employed to reject beam–gas interactions. Only events with a
reconstructed primary vertex within $\pm 10$ cm from the nominal centre of the
ALICE detector along the beam direction were considered to grant a uniform
acceptance for the central-barrel detectors.

The multiplicity-differential analysis was performed in four independent
multiplicity classes, defined in terms of the total energy deposit in the V0
detectors by charged particles passing through them (V0M amplitude). The
rapidity gap between the V0 detectors and the central barrel in which the D
mesons and charged particles were reconstructed assured the absence of
significant auto-correlations between the correlation peaks and the
multiplicity estimate. The V0M amplitudes were converted to percentiles of the
inelastic collisions with at least one charged particle produced in $|\eta|<1$
(INEL$>$0), corresponding to about 75% of the total inelastic cross section,
as described in Ref. [38].

The corresponding INEL$>$0 percentiles ($\sigma$/$\sigma_{\rm INEL>0}$) of the
four V0M multiplicity classes are reported in Table 1, together with the
related average number of charged particles, $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ in $|\eta|<0.5$. A specific high-multiplicity trigger (V0HM)
was used for the V0M multiplicity class I, to enhance the statistical
precision of this particular class. The V0HM trigger recorded only events with
a multiplicity large enough to pass a threshold of V0M amplitude. This trigger
covered the whole span of V0M multiplicity class I. Only the data periods
granting a uniform efficiency of the V0HM trigger inside the range covered by
V0M multiplicity class I were considered for the multiplicity-differential
analysis, resulting in an integrated luminosity specific to the V0HM trigger
of about 7.7 pb-1.

Table 1: The percentiles of the INEL$>$0 cross section of the four V0M-based event-multiplicity classes and the corresponding midrapidity charged-particle multiplicities. Systematic uncertainties on the charged-particle multiplicity values, derived from [38], are also reported. V0M multiplicity class | I | II | III | IV
---|---|---|---|---
$\sigma$/$\sigma_{\rm INEL>0}$ (%) | 0–0.0915 | 0.0915–9.149 | 9.149–27.50 | 27.50–100
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ | 31.15 $\pm$ 0.40 | 18.39 $\pm$ 0.23 | 11.46 $\pm$ 0.15 | 4.41 $\pm$ 0.06

To evaluate the corrections to the azimuthal-correlation measurements, several
MC simulations of pp collisions at $\sqrt{s}=13$ TeV were used, produced with
the PYTHIA 6.4.25 event generator [12] with the Perugia-2011 tune [39]. For
the corrections specific to D mesons, a sample of pp collisions was produced
with the same generator, with each event containing either a ${\rm
c}\overline{\rm c}$ or a ${\rm b}\overline{\rm b}$ pair in the rapidity range
$[-1.5,1.5]$. In addition, simulated events satisfying a minimum threshold of
midrapidity charged-particle multiplicity were employed, as they provided
sufficient statistical precision to evaluate the corrections for the V0M
multiplicity class I. The simulations included the full description of the
detector geometry, response, and conditions during the data taking via the
GEANT3 package [40].

##  3 Analysis overview

The procedure for the evaluation of the D-meson (intending, in the context of
this study, $\rm D^{0}$, $\rm D^{*}(2010)^{+}$, and $\rm D^{+}$ mesons) and
charged-particle azimuthal correlation function and the related corrections is
described in Section 3.1 for the multiplicity-integrated analysis. The
multiplicity-differential analysis largely followed the same approach,
although some of the quantities and the corrections were evaluated
independently in each V0M multiplicity class, or with a slightly modified
procedure. Such differences are highlighted in Section 3.2. The extraction of
physical observables from the fully-corrected correlation function, in common
between the two studies, is discussed in Section 3.3.

###  3.1 Evaluation and correction of the azimuthal correlation function for
the multiplicity-integrated analysis

All stages of the analysis were mostly unaltered with respect to those
performed for the same study in pp collisions at $\sqrt{s}=5.02$ TeV, and are
comprehensively described in Ref. [21]. Thus, they will be only briefly
summarised in the following.

$\rm D^{0}$-, $\rm D^{*}(2010)^{+}$-, and $\rm D^{+}$-meson candidates and
their charge conjugates, used as trigger particles in the analysis, were
reconstructed from their hadronic decay channels ${\rm D^{0}\to{\rm
K}^{-}\pi^{+}}$, with branching ratio BR = (3.95 $\pm$ 0.03)%, ${\rm
D^{+}\to{\rm K}^{-}\pi^{+}\pi^{+}}$ with BR = (9.38 $\pm$ 0.16)%, and ${\rm
D^{*+}\to\rm D^{0}\pi^{+}}\to{\rm K}^{-}\pi^{+}\pi^{+}$ with BR = (2.67 $\pm$
0.03)% [41]. A topological selection, exploiting the characteristic
displacement of the D-meson decay vertices with respect to the primary vertex,
and particle-identification information on the D-meson decay products were
employed to suppress the combinatorial background. Further details on the
selection are provided in Ref. [42]. The same criteria were followed in this
analysis, apart from an optimisation of the selection values performed on the
specific samples used to further increase the signal-to-background ratio of
D-meson candidates. A fit to the invariant-mass distribution of selected
D-meson candidates was performed as described in Ref. [42], in order to
extract the D-meson yield, $S_{\mathrm{peak\ region}}$, in a $\pm 2\sigma$
region from the centre of the invariant-mass signal peak, where $\sigma$ is
the width of the Gaussian component of the fit function describing the signal
peak. The associated particles included charged primary [43] pions, kaons,
protons, electrons, and muons with $p_{\rm T}^{\rm assoc}>0.3$ GeV/$c$ and
$|\eta|<0.8$. The decay products of the trigger D meson were excluded from the
associated-particle sample. The tracks reconstructed in the ALICE central
barrel were accepted as associated particles if they satisfied selection
criteria based on the quality of their reconstruction in the ITS and TPC
detectors, as detailed in Ref. [3]. Additionally, a maximum distance of
closest approach (DCA) of the track to the primary vertex of 1 cm in the
transverse ($xy$) plane and along the beam line ($z$-direction) was required.
This selection suppressed the contamination of non-primary particles to about
5% for $0.3<p_{\rm T}^{\rm assoc}<1$ GeV/$c$, falling to below 1% for $p_{\rm
T}^{\rm assoc}>2$ GeV/$c$. As a result of the applied selection criteria, the
associated-track reconstruction and selection efficiency ranged from about
$80\%$ for $p_{\rm T}^{\rm assoc}=0.3$ GeV/$c$ up to about $90\%$, increasing
with $p_{\rm T}^{\rm assoc}$.

Selected D-meson candidates within $\pm 2\sigma$ from the centre of the
invariant-mass signal peak (“peak region”) were correlated with associated
particles reconstructed and selected in the same event. A two-dimensional
angular-correlation function, $C(\Delta\varphi,\Delta\eta)_{\mathrm{peak\
region}}$, was built for each of the five D-meson $p_{\rm T}$ intervals,
ranging from 3 to 36 GeV/$c$, and for the associated track $p_{\rm T}$
interval $p_{\rm T}^{\rm assoc}>0.3$ GeV/$c$ and its sub-ranges: $0.3<p_{\rm
T}^{\rm assoc}<1$ GeV/$c$, $1<p_{\rm T}^{\rm assoc}<2$ GeV/$c$, and $2<p_{\rm
T}^{\rm assoc}<3$ GeV/$c$. The limited detector acceptance and efficiency for
the reconstruction and selection of D-meson candidates and associated
particles were accounted for by weighting each correlation pair by
1/$(A\times\epsilon)^{\rm assoc}\times 1$/($A\times\epsilon)^{\rm trig}$,
where $A$ and $\epsilon$ represent the acceptance and efficiency factors,
respectively, evaluated using MC simulations. The $(A\times\epsilon)^{\rm
trig}$ values were dependent on the event multiplicity. In particular, the
D-meson selection efficiency decreased for low-multiplicity events, due to the
degraded resolution on the primary-vertex position, which enters into several
topological selection criteria. To account for this dependency, the
$(A\times\epsilon)^{\rm trig}$ weights were evaluated and applied in narrow
intervals of SPD tracklet multiplicity. The entries of the invariant-mass
distributions of D-meson candidates were also scaled by
1/($A\times\epsilon)^{\rm trig}$ to allow a correct per-trigger normalisation
of the correlation function, as detailed later. Additional losses due to pair
acceptance effects were taken into account by applying a mixed-event
correction. Specifically, D-meson candidate triggers were correlated with
associated charged particles from other events with similar midrapidity event
multiplicity and primary vertex location along the beam axis. Track segments
reconstructed by associating hits in the two SPD layers and pointing to the
reconstructed primary vertex (SPD tracklets) were used as the midrapidity
multiplicity estimator for the event classification. In this way, a mixed-
event correlation function,
$\mathrm{ME}(\Delta\varphi,\Delta\eta)_{\mathrm{peak\ region}}$, was built and
used to weight the same-event correlation function
$C(\Delta\varphi,\Delta\eta)_{\mathrm{peak\ region}}$.

The correlation function $C(\Delta\varphi,\Delta\eta)_{\mathrm{peak\ region}}$
also included a contribution from background D-meson candidates. This
contribution was statistically removed by employing a sideband-subtraction
technique. A sideband-region correlation distribution,
$C(\Delta\varphi,\Delta\eta)_{\rm{sidebands}}$, was built by considering as
trigger particles $\rm D^{0}$\- and $\rm D^{+}$-meson candidates 4–8$\sigma$
from the centre of the invariant-mass signal peak, in both directions, and
$\rm D^{*+}$-meson candidates 5–10$\sigma$ to the right of the invariant-mass
signal peak centre. A mixed-event correction was applied to the sideband-
region correlation function, following the same procedure described above for
$C(\Delta\varphi,\Delta\eta)_{\mathrm{peak\ region}}$. Subsequently, the
sideband-region correlation function was subtracted from that of the peak
region to obtain the signal correlation function,
$C(\Delta\varphi,\Delta\eta)_{\mathrm{signal}}$. The above procedure is
described in Eq. 1

$\centering\tilde{C}_{\rm{signal}}(\Delta\varphi,\Delta\eta)=\frac{1}{S_{\mathrm{peak\
region}}}\left(\frac{C(\Delta\varphi,\Delta\eta)}{\mathrm{ME}(\Delta\varphi,\Delta\eta)}\bigg{|}_{\mathrm{peak\
region}}-\frac{B_{\mathrm{peak\
region}}}{B_{\mathrm{sidebands}}}\frac{C(\Delta\varphi,\Delta\eta)}{\mathrm{ME}(\Delta\varphi,\Delta\eta)}\bigg{|}_{\mathrm{sidebands}}\right),\@add@centering$
(1)

where the factor $1/S_{\mathrm{peak\ region}}$ provides a per-trigger
normalisation to the signal correlation function, as denoted by a $\tilde{C}$
symbol. The terms $B_{\mathrm{peak\ region}}$ and $B_{\rm sidebands}$ quantify
the number of background D-meson candidate triggers in the invariant-mass peak
region and sidebands, respectively.

The two-dimensional correlation function
$\tilde{C}_{\rm{signal}}(\Delta\varphi,\Delta\eta)$ was integrated in the
range $|\Delta\eta|<1$, obtaining the per-trigger azimuthal correlation
function $\tilde{C}_{\rm{signal}}(\Delta\varphi)$, in order to grant
sufficient statistical precision. For the same reason, due to its symmetry
around $\Delta\varphi=0$ and $\Delta\varphi=\pi$, the correlation function was
restricted to the $0\leq\Delta\varphi\leq\pi$ interval, averaging the
symmetric points in the ranges [0, $\pi$] and [$-\pi$, 0].

The residual contamination of non-primary associated tracks satisfying the DCA
selection criteria was removed by multiplying
$\tilde{C}_{\rm{signal}}(\Delta\varphi)$ by a $\Delta\varphi$-differential
purity correction factor $p_{\rm prim}(\Delta\varphi)$, evaluated from MC
simulations. A slight increase with $p_{\rm T}^{\rm assoc}$ was observed for
the $\Delta\varphi$-averaged value of this factor, which ranged between 0.94
and 0.99. Modulations as a function of $\Delta\varphi$ up to 2% were obtained.
The fraction of prompt D mesons ($f_{\rm prompt}$) accounted for approximately
$90\%$ of D mesons accepted by the topological and PID selection, with a
slight increase for increasing $p_{\rm T}$. The remaining contribution was
composed of D mesons produced by beauty-hadron decays (feed-down D mesons).
Thus, the azimuthal correlation function
$\tilde{C}_{\rm{signal}}(\Delta\varphi)$ included a contribution from feed-
down D-meson candidate triggers. For small $\Delta\varphi$ values, the shape
of this contribution was distorted by the topological selection applied to the
D-meson candidates, which was more efficient in selecting beauty-hadron decays
featuring a small opening angle between the D-meson candidate trigger and the
other decay particles. The natural shape of the feed-down contribution to the
azimuthal correlation function was recovered by evaluating the amount of the
distortion via MC studies, and applying a correction factor $b_{\rm B\mathchar
45\relax bias}(\Delta\varphi)$ to the data correlation function, as explained
in detail in Ref. [21]. The correction amounted to a maximum of 4.5% for
$\Delta\varphi=0$ and was substantially smaller for larger $\Delta\varphi$
values. After applying this correction, the feed-down contribution to the
measured correlation function was removed as follows. A template of the per-
trigger azimuthal correlation function from feed-down D-meson triggers,
$\tilde{C}^{\rm MC\ templ}_{\rm{feed\mathchar 45\relax down}}(\Delta\varphi)$,
was evaluated for each $p_{\rm T}$ range with the PYTHIA6 event generator with
Perugia-2011 tune at generator level (i.e. without detector effects and
selection criteria). After being rescaled to the expected fraction of feed-
down D-meson candidate triggers, $1-f_{\rm prompt}$, this contribution was
subtracted from the purity-corrected azimuthal-correlation function. The
fully-corrected, per-trigger azimuthal correlation function of prompt D mesons
and charged particles was obtained with this procedure, as summarised in Eq. 2

$\centering\frac{1}{N_{\rm D}}\times\frac{{\rm d}N^{\rm assoc}}{{\rm
d}\Delta\varphi}(\Delta\varphi)=\frac{1}{f_{\rm prompt}}\left[b_{\rm
B\mathchar 45\relax bias}(\Delta\varphi)\times p_{\rm
prim}(\Delta\varphi)\times\tilde{C}_{\rm{signal}}(\Delta\varphi,\Delta\eta)-\left(1-f_{\rm
prompt}\right)\tilde{C}^{\rm MC\ templ}_{\rm{feed\mathchar 45\relax
down}}(\Delta\varphi)\right].\@add@centering$ (2)

###  3.2 Details specific to the multiplicity-differential analysis

For the multiplicity-differential analysis, only $\rm D^{0}$ mesons and their
charge conjugates were used as trigger particles. The same selection criteria
chosen for the multiplicity-integrated case were used for the $\rm
D^{0}$-meson candidate triggers and the associated charged particles. The
evaluation of the two-dimensional correlation function for the peak region and
the sidebands of the $\rm D^{0}$-meson invariant-mass distributions was
performed independently in each of the four V0M multiplicity classes,
considering the same $p_{\rm T}$ ranges of the multiplicity-integrated
analysis, with the exception of $24<p_{\rm T}^{\rm D}<36$ GeV/$c$, where the
amount of collected data was not sufficient for performing the study. The
invariant-mass distributions of the V0M multiplicity class I were
characterised by a larger data sample and a larger statistical significance of
the $\rm D^{0}$ mass peak, profiting from the usage of the V0HM trigger,
although they also showed a lower signal-to-background ratio due to the
enhanced underlying-event activity.

For each V0M multiplicity class, the per-trigger azimuthal correlation
function was obtained following Eq. 1 and Eq. 2, but some of the quantities
entering these equations were evaluated with a modified procedure. For the
mixed-event correction, a different classification of the events in terms of
SPD tracklet multiplicity needed to correlate $\rm D^{0}$ mesons and charged
particles from events with similar features was considered for each V0M
multiplicity class, since the SPD tracklet multiplicity distributions obtained
for each V0M multiplicity class were significantly different. The MC events
used to evaluate the values of 1/($A\times\epsilon)^{\rm trig}$, for each V0M
multiplicity class, were reweighted in order to reproduce the corresponding
SPD tracklet multiplicity measured in data. The same values of charged-
particle reconstruction and selection efficiency were instead used for the
four V0M multiplicity classes since a negligible dependence of the efficiency
on the event multiplicity was found in previous ALICE studies in the same
collision system [44].

The purity correction, $p_{\rm prim}(\Delta\varphi)$, was evaluated
independently for each V0M multiplicity class, by applying the same MC
reweighting procedure used for the $\rm D^{0}$-meson efficiency evaluation. A
very small dependence on event multiplicity was obtained, with the overall
differences smaller than $0.5\%$ between the values obtained in the four V0M
multiplicity classes and those evaluated for the multiplicity-integrated
analysis. Similarly, the correction factor $b_{\rm B\mathchar 45\relax
bias}(\Delta\varphi)$ was estimated separately for each of the four V0M
multiplicity classes. A slight increase of the correction of about 1–2%
depending on the $p_{\rm T}$ range was obtained with decreasing event
multiplicity. The largest value of $b_{\rm B\mathchar 45\relax
bias}(\Delta\varphi)$ was about $5.5\%$ for V0M multiplicity class IV at
$\Delta\varphi=0$ for the lowest $p_{\rm T}^{\rm D}$ interval and largest
$p_{\rm T}^{\rm assoc}$ interval. The feed-down subtraction procedure was left
unaltered for the evaluation of the central values of the correlation
function, assuming no modification of the prompt $\rm D^{0}$-meson fraction
and beauty-quark fragmentation with event multiplicity. However, as described
in more detail in Section 4, an additional systematic uncertainty was
considered, accounting for a possible variation of the feed-down-to-prompt
$\rm D^{0}$-meson production ratio with event multiplicity, which would impact
the value of $f_{\rm prompt}$.

###  3.3 Quantitative evaluation of correlation peak features

Based on their consistency within uncertainties, an average of the azimuthal-
correlation functions for $\rm D^{0}$, $\rm D^{+}$, and $\rm D^{*}(2010)^{+}$
meson triggers was evaluated for the multiplicity-integrated analysis. The
average was obtained by weighting the correlation function from each species
by the inverse of the quadratic sum of its statistical and systematic
uncertainties uncorrelated among the three D-meson species. For each $p_{\rm
T}$ interval, the averaged azimuthal correlation function was fitted with the
following function

$f(\Delta\varphi)=a+\frac{Y_{\rm NS}\times\beta}{2\alpha\Gamma(1/\beta)}\times
e^{-\left(\frac{\Delta\varphi}{\alpha}\right)^{\beta}}+\frac{Y_{\rm
AS}}{\sqrt{2\pi}\sigma_{\rm AS}}\times
e^{-\frac{(\Delta\varphi-\pi)^{2}}{2\sigma^{2}_{\rm AS}}}.$ (3)

This function is composed of a generalised-Gaussian component for the
description of the near-side peak (with the mean fixed at $\Delta\varphi=0$),
a Gaussian component for the away-side peak (with the mean fixed at
$\Delta\varphi=\pi$), and a constant term (baseline) to account for the flat
contribution that lies beneath the two correlation peaks. To grant sufficient
stability to the fit, the $\beta$ parameter of the generalised Gaussian was
fixed to the value obtained for the correlation distribution predicted by
PYTHIA8 simulations at generator level. In Eq. 3, the baseline value $a$ was
fixed to the weighted average of the points in the range
$\pi/4<|\Delta\varphi|<\pi/2$ (transverse region), to reduce the fit
sensitivity to statistical fluctuations. The inverse of the squared
statistical uncertainties of the points were used as weights. The fit to the
correlation function allowed the extraction of quantitative observables that
characterise the correlation peaks. In particular, the near- and away-side
peak yields were obtained as the integral of the components describing each
correlation peak, and their widths were parameterised by the quantities
$\alpha\sqrt{\Gamma(3/\beta)/\Gamma(1/\beta)}$ (square root of the
generalised-Gaussian variance) and $\sigma_{\rm AS}$, respectively.

##  4 Systematic uncertainties

###  4.1 Systematic uncertainties for the multiplicity-integrated analysis

The azimuthal correlation function obtained from the multiplicity-integrated
analysis is affected by several systematic uncertainties due to the specific
procedure and assumptions introduced for its evaluation. In the following, the
approach used to estimate each systematic uncertainty source is briefly
described.

The evaluation of $S_{\mathrm{peak\ region}}$ and $B_{\mathrm{peak\ region}}$
from the fit to the D-meson invariant-mass distributions (as described in
Section 3.1 and Eq. 1) introduced a systematic uncertainty on the correlation
function. The uncertainty was estimated by varying the fit procedure,
specifically, by modelling the background distribution with a linear function
or a second-order polynomial function instead of an exponential function (for
$\rm D^{0}$ and $\rm D^{+}$ mesons only, where there is not a straightforward
choice for the background fit function), considering a different histogram
binning, varying the fit range, fixing the mean of the Gaussian term
describing the mass peak to the world-average D-meson mass [41], or fixing the
Gaussian width to the value obtained from MC studies. A systematic uncertainty
ranging from 0.5% to 1.5%, depending on the $p_{\rm T}^{\rm D}$ range and
similar for all D-meson species, was estimated from the corresponding
variation of the azimuthal-correlation function. No dependence on
$\Delta\varphi$ was found.

A 0.5% to 2% systematic uncertainty, depending on $p_{\rm T}^{\rm D}$ range
and D-meson species, was introduced due to the possible dependence of the
shape of the background correlation function on the invariant-mass value of
the trigger D meson. This source of uncertainty was estimated by evaluating
$\tilde{C}_{\rm{sidebands}}(\Delta\varphi,\Delta\eta)$ considering different
invariant-mass sideband ranges. For $\rm D^{0}$ and $\rm D^{+}$ mesons, for
which a sideband was defined on each side of the invariant-mass signal peak,
$\tilde{C}_{\rm{sidebands}}(\Delta\varphi,\Delta\eta)$ was also evaluated
considering only the left or the right sideband. No azimuthal dependence was
observed for this uncertainty.

The evaluation of the associated-particle reconstruction efficiency via MC
studies introduced a further systematic uncertainty, estimated by varying the
quality selection criteria applied on the reconstructed tracks, i.e. removing
or tightening the request on minimum number of ITS clusters, requiring a hit
on at least one of the two SPD layers, or varying the request on the minimum
number of space points reconstructed in the TPC. An uncertainty of 4% to 5%
was estimated, independent of the D-meson species, and no significant trend in
$\Delta\varphi$ was observed.

A systematic uncertainty affecting the D-meson reconstruction efficiency,
related to potentially different distributions of the topological variables in
MC and data, was estimated by testing a set of tighter and looser topological
selections on D-meson candidates. An uncertainty ranging from 0.5% to 2% was
assigned and the effect on the azimuthal correlation function was found to be
$\Delta\varphi$ independent.

The correlation function has an uncertainty related to the evaluation of the
residual contamination from secondary particles [43]. To determine this, the
analysis was repeated by varying the DCA selection in the $xy$ plane from 0.1
cm to 2.4 cm and re-evaluating the purity correction of primary tracks for
each variation. This resulted in a maximum, $\Delta\varphi$-independent,
systematic uncertainty of 2% on the azimuthal-correlation function.

In addition to the above contributions, which all act as a scale uncertainty,
the azimuthal correlation function is also affected by
$\Delta\varphi$-dependent systematic uncertainties. The uncertainty on the
evaluation of the beauty feed-down contribution to the azimuthal correlation
function was determined by employing alternate templates of feed-down
azimuthal-correlation functions, obtained from different event generators
(PYTHIA6 with the Perugia-2010 tune [39] and PYTHIA8 with the 4C tune [45]),
and by varying the value of $f_{\rm prompt}$ following the procedure described
in Ref. [42]. A $\Delta\varphi$-dependent uncertainty was obtained with a
maximum value of 5%. The near-side region for the feed-down D-meson component
of the correlation function was affected by a bias, favouring topologies with
a small opening angle between the D meson and the other beauty-hadron decay
products. This was corrected for as discussed in Section 3.1, and a
$\Delta\varphi$-dependent bilateral and symmetric uncertainty for a possible
over- or under-correction of this bias was evaluated as detailed in Ref. [21].
The largest value of the uncertainty was found to be 2.5% for
$\Delta\varphi\approx 0$.

The estimated systematic uncertainty values from each of the above sources
affecting the azimuthal correlation function are summarised in Table 2. The
overall systematic uncertainty in each $\Delta\varphi$ bin of the correlation
function was obtained as the sum in quadrature of the aforementioned
contributions.

The systematic uncertainties on the peak observables were evaluated by
considering several contributions: (i) the impact on the physical observables
induced by the baseline position was estimated by considering alternate
$\Delta\varphi$ ranges for determining its value and repeating the fit;
similarly, the possible bias induced by fixing the $\beta$ parameter of the
near-side to the predicted PYTHIA8 value was estimated by allowing $\beta$ to
vary within $\pm 20\%$ of that value. For each observable, the root-mean-
square of the relative variations from these alternative fits with respect to
the central value of the observable was considered; (ii) the impact of the
$\Delta\varphi$-dependent uncertainty on the correlation function was
accounted for by coherently shifting its points to the upper and lower edges
of their $\Delta\varphi$-dependent systematic uncertainty values. The fit was
repeated and the variation of each observable value with respect to the
default value was considered in each direction; (iii) the overall
$\Delta\varphi$-independent systematic uncertainty acts as a scaling factor on
the correlation function, hence it impacted the near- and away-side peak yield
values by the same relative amount. The overall systematic uncertainty on the
peak yields was therefore obtained by summing in quadrature the contributions
from (i), (ii), and (iii). For the near-side and away-side widths, which are
insensitive to scale factors, the sum in quadrature of only the contributions
from (i) and (ii) was considered.

###  4.2 Systematic uncertainties for the multiplicity-differential analysis

Some of the systematic uncertainties affecting the correlation function were
estimated separately in each of the V0M multiplicity class, following the same
prescriptions described in Section 4.1. In particular, this was done for the
uncertainties on the yield extraction and background correlation shape since
they are related to the features of the invariant-mass distributions, which
show a significant multiplicity evolution. The uncertainty related to the bias
affecting the topological selection of feed-down $\rm D^{0}$ mesons was also
re-evaluated, since a slight multiplicity dependence of the related correction
was found. Similar values of the uncertainty were obtained compared to the
multiplicity-integrated case. For the subtraction of the beauty feed-down
contribution, an additional systematic uncertainty was considered, related to
a possible multiplicity dependence of the relative fraction of feed-down $\rm
D^{0}$ mesons in the $\rm D^{0}$-meson raw yields that determines the amount
of the feed-down contribution. The evaluation of this uncertainty followed a
similar procedure as the one described in Ref. [9], and led to an asymmetry of
the feed-down systematic uncertainty, which increased up to ${}^{+5\%}_{-9\%}$
for the V0M multiplicity class I. For the other systematic uncertainty sources
affecting the azimuthal-correlation function, the same values estimated for
the multiplicity-integrated analysis were adopted. The uncertainty values for
the multiplicity-differential analysis are reported in Table 2.

Table 2: The list of the systematic uncertainty contributions affecting the azimuthal correlation function and their typical values. If not specified, the uncertainties do not depend on $\Delta\varphi$. Analysis | Multiplicity-integrated | Multiplicity-differential
---|---|---
Yield extraction | 0.5–1.5% | 1–2%
Background $\Delta\varphi$ function | 0.5–2% | 1–3%
Associated-track reconstruction efficiency | 4–5% | 4–5%
D-meson efficiency | 0.5–2% | 0.5–2%
Primary-particle purity | 1–2% | 1–2%
Feed-down subtraction |  $\leq$5%, $\Delta\varphi$-dependent |  $\leq^{+5\%}_{-9\%}$, $\Delta\varphi$-dependent
Selection bias to feed-down contribution |  $\leq$2.5%, $\Delta\varphi$-dependent |  $\leq$3%, $\Delta\varphi$-dependent

The evaluation of the systematic uncertainties on the near- and away-side peak
observables was unmodified with respect to the procedure described in Section
4.1 for the multiplicity-integrated analysis. In addition, the impact on the
peak observables related to the possible presence of long-range azimuthal
correlations between $\rm D^{0}$ mesons and charged particles in high-
multiplicity collisions was studied by replacing in Eq. 3 the constant term
with a $v_{2\Delta}$-like modulation. The elliptic-flow coefficient values of
$\rm D^{0}$ mesons and charged particles adopted to evaluate the modulation
were defined based on the measurements in Ref. [10] and Ref. [46],
respectively. For the V0M multiplicity class I, variations within 2% were
found for all observables and $p_{\rm T}$ ranges except for the range 3
$<p_{\rm T}^{\rm D}<$ 5 GeV/$c$, where a reduction of the near- and away-side
peak yields as large as 8% was observed. These differences were assigned as a
systematic uncertainty.

##  5 Results

###  5.1 Multiplicity-integrated results in pp collisions at $\sqrt{s}=13$ TeV

For the multiplicity-integrated analysis, the azimuthal correlation function
of D mesons with charged particles was computed for the five D-meson $p_{\rm
T}$ intervals $3<p_{\rm T}^{\rm D}<5$ GeV/$c$, $5<p_{\rm T}^{\rm D}<8$
GeV/$c$, $8<p_{\rm T}^{\rm D}<16$ GeV/$c$, $16<p_{\rm T}^{\rm D}<24$ GeV/$c$,
and $24<p_{\rm T}^{\rm D}<36$ GeV/$c$, and for associated particle $p_{\rm T}$
range $p_{\rm T}^{\rm assoc}>0.3$ GeV/$c$ and the sub-intervals $0.3<p_{\rm
T}^{\rm assoc}<1$ GeV/$c$, $1<p_{\rm T}^{\rm assoc}<2$ GeV/$c$, and $2<p_{\rm
T}^{\rm assoc}<3$ GeV/$c$.

Figure 1: Average of the azimuthal-correlation functions of $\rm D^{0}$, $\rm
D^{+}$, and $\rm D^{*+}$ mesons with associated particles, after the baseline
subtraction, in pp collisions at $\sqrt{s}$ = 5.02 [21], 7 [3], and 13 TeV,
for 3 $<p_{\rm T}^{\rm D}<$ 5 GeV/$c$, 8 $<p_{\rm T}^{\rm D}<$ 16 GeV/$c$, and
16 $<p_{\rm T}^{\rm D}<$ 24 GeV/$c$ (from left to right) and 0.3 $<p_{\rm
T}^{\rm assoc}<$ 1 GeV/$c$, 1 $<p_{\rm T}^{\rm assoc}<$ 2 GeV/$c$ (top and
bottom panels, respectively). Data at $\sqrt{s}$ = 7 TeV are not available for
all the $p_{\mathrm{T}}$ regions. Statistical and $\Delta\varphi$-dependent
systematic uncertainties are shown as vertical error bars and boxes,
respectively, and $\Delta\varphi$-independent uncertainties are written as
text. The uncertainties from the subtraction of the baseline are displayed as
boxes at $\Delta\varphi>\pi$.

Figure 2: Near-side (left panel) and away-side (right panel) peak yields
(first row) and widths (third row) obtained from a fit to the azimuthal
correlation function after the baseline subtraction. The measurements are
compared with ALICE results obtained in pp collisions at $\sqrt{s}$ = 5.02 TeV
[21] and 7 TeV [3], for 0.3 $<p_{\rm T}^{\rm assoc}<$ 1 GeV/$c$, 1 $<p_{\rm
T}^{\rm assoc}<$ 2 GeV/$c$. Only near-side observables were computed in the
$\sqrt{s}$ = 7 TeV analysis. The ratios to the $\sqrt{s}=5.02$ TeV results are
shown in the second and fourth rows for yields and widths, respectively.

Figure 1 shows examples of correlation functions obtained from the analysis in
pp collisions at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV, compared with
results previously reported by ALICE in pp collisions at $\sqrt{s}$ = 5.02 TeV
[21] and $\sqrt{s}$ = 7 TeV [3] (the latter is available only for two
kinematic ranges). The baseline value is closely related to the number of
charged particles produced at midrapidity, and therefore has a strong
dependence on $\sqrt{s}$, due to the increase of charged-particle production
with increasing centre-of-mass energy [47]. It was subtracted from the
correlation functions in order to focus the comparison on the peak features.
The shape of the distribution after the baseline subtraction and the
properties of the correlation peaks at the three centre-of-mass energies agree
within uncertainties. The analysis at $\sqrt{s}=13$ TeV profits from a larger
data sample, resulting in substantially smaller point-by-point statistical
fluctuations (up to 50% with respect to $\sqrt{s}=5.02$ TeV results in the
range $16<p_{\rm T}^{\rm D}<24$ GeV/$c$), and leading to smaller uncertainties
from the subtraction of the baseline.

More quantitative results are provided by the comparison of the near- and
away-side peak yields and widths in pp collisions at different centre-of-mass
energies, presented in Fig. 2. The results for pp collisions at $\sqrt{s}=7$
TeV were obtained after refitting the correlation functions measured in Ref.
[3] with the improved function described in Eq. 3, and evaluating the
systematic uncertainties accordingly. The near-side peak yield values obtained
from the $\sqrt{s}=13$ TeV data are compatible within the uncertainties with
those at lower energies, exhibiting the same increasing trend of the yields
with $p_{\rm T}^{\rm D}$ in both the $p_{\rm T}^{\rm assoc}$ intervals shown.
An overall agreement is also observed between the $\sqrt{s}=5.02$, 7, and 13
TeV results for the near-side widths. From the $\sqrt{s}=13$ TeV results, an
indication of a near-side peak narrowing for increasing $p_{\rm T}^{\rm D}$
emerges, in particular for the $1<p_{\rm T}^{\rm assoc}<2$ GeV/$c$ range, that
was not observed at lower energies because of the lower precision. This peak
narrowing could be originated by two simultaneous effects: (i) a more
collimated angular pattern of the partons fragmented from charm quarks; (ii)
an increased collinearity of charm and anti-charm quarks produced from gluon-
splitting mechanism. Both effects are related to the increased boost, on
average, of the fragmenting (splitting) parton when considering D-meson
triggers with larger $p_{\rm T}$. An agreement within the uncertainties is
also observed for the away-side peak results, and similar conclusions as those
expressed for the near-side peak can be drawn. For the away-side observables
only results at $\sqrt{s}=5.02$ TeV are available for the comparison (and only
for a restricted set of kinematic ranges), since the azimuthal-correlation
functions for pp collisions at $\sqrt{s}=7$ TeV were not precise enough to
allow the characterisation of the away-side region, as discussed in Ref. [3].

A similar comparison was performed using simulated pp collisions obtained with
PYTHIA6 (with Perugia-2011 tune) and POWHEG+PYTHIA6 [48, 19, 20] event
generators. A slight increase of the near-side yield values (5–10% depending
on the $p_{\rm T}$ range) and a mild decrease of the away-side yield values
(10–15%) was observed when increasing the centre-of-mass energy from
$\sqrt{s}=5.02$ to 13 TeV, with small differences between the two generators.
This could be ascribed to an increased contribution of NLO production
processes (already included in the hard scattering in POWHEG+PYTHIA6, and
accounted for during the parton-shower development in PYTHIA6), as well as to
a harder charm-quark $p_{\rm T}$ spectrum at larger centre-of-mass energies.
These differences are within the overall precision of the data measurements.
No visible energy dependence for both near- and away-side peak widths was
found, for both generators, as observed in data.

###  5.2 Results for different V0M multiplicity classes

The azimuthal-correlation functions evaluated in the four classes of V0M
multiplicity are compared in Fig. 3, for the four available $\rm D^{0}$-meson
$p_{\rm T}$ ranges (one per column) and the four different $p_{\rm T}^{\rm
assoc}$ intervals (one per row). The baseline value largely increased from V0M
multiplicity class IV towards V0M multiplicity class I, as expected due to the
very different underlying-event activity, and it was subtracted from the
correlation functions. This comparison suggests a similar shape and $p_{\rm
T}$ evolution of the azimuthal-correlation function, as well as consistent
near- and away-side features for the four V0M multiplicity classes.

Figure 3: Azimuthal-correlation functions of $\rm D^{0}$ mesons with
associated particles, after the subtraction of the baseline, in pp collisions
at $\sqrt{s}$ = 13 TeV, for 3 $<p_{\rm T}^{\rm D}<$ 5 GeV/$c$, 5 $<p_{\rm
T}^{\rm D}<$ 8 GeV/$c$, 8 $<p_{\rm T}^{\rm D}<$ 16 GeV/$c$, and 16 $<p_{\rm
T}^{\rm D}<$ 24 GeV/$c$ (from left to right) and $p_{\rm T}^{\rm assoc}>$ 0.3
GeV/$c$, 0.3 $<p_{\rm T}^{\rm assoc}<$ 1 GeV/$c$, 1 $<p_{\rm T}^{\rm assoc}<$
2 GeV/$c$, 2 $<p_{\rm T}^{\rm assoc}<$ 3 GeV/$c$ (from top to bottom) for
different multiplicity classes estimated with V0M. The four multiplicity
classes are shown with different marker styles. Statistical and
$\Delta\varphi$-dependent systematic uncertainties are shown as vertical error
bars and boxes, respectively, and $\Delta\varphi$-independent uncertainties
are written as text. The uncertainties from the subtraction of the baseline
are displayed as boxes at $\Delta\varphi>\pi$.

The near-side peak yield and width values obtained from the fit to the
azimuthal correlation function in the four V0M multiplicity classes, for the
same kinematic ranges, are shown in Fig. 4 (first and third rows,
respectively). Apart from a tension for low $p_{\rm T}^{\rm D}$, 2 $<p_{\rm
T}^{\rm assoc}<$ 3 GeV/$c$, the yield measurements follow a similar increasing
trend with $p_{\rm T}^{\rm D}$. Similar values are observed from the near-side
peak widths. These results indicate no significant modification of the charm
fragmentation and hadronisation in collisions of varying charged-particle
multiplicities. The ratios of the yield and width results in V0M classes II,
III, and IV over those in V0M class I, shown in the second and fourth rows of
Fig. 4, respectively, also confirm this conclusion.

The evaluation of away-side peak yields and widths as a function of the event
multiplicity were performed only in the integrated associated particle
interval $p_{\rm T}^{\rm assoc}>0.3$ GeV/$c$, due to their large sensitivity
to point-by-point statistical fluctuations. The away-side peak observable
values for each of the four V0M multiplicity classes are shown in Fig. 5,
together with the ratios of the values in the V0M classes II, III and IV over
the values in the V0M class I. As observed for the near-side, the same
increasing trend with $\rm D^{0}$ $p_{\rm T}$ is present for the yields, among
the four V0M multiplicity classes. A hint of narrowing of the away-side peak,
visible in the multiplicity-integrated results at $\sqrt{s}=13$ TeV, can also
be seen in the multiplicity-dependent results. The away-side yield and width
values are fully consistent within the uncertainties among all four V0M
classes.

Though with sizeable uncertainties, these measurements point towards
consistency of the jet-induced correlation peak structure and shape in high-
and low-multiplicity events, and thus contribute to confirm the assumptions
done in the measurements of the elliptic-flow coefficient of charm particles
in high-multiplicity pp collisions [10, 11].

Figure 4: Near-side associated peak yields (top row) and widths (third row)
measured in pp collisions at $\sqrt{s}$ = 13 TeV, for the four V0M
multiplicity classes, shown with different marker styles. The ratios of yield
(width) values in each V0M class with respect to those in the V0M class I are
shown in the second (fourth) row. Results are presented as a function of the
$\rm D^{0}$-meson $p_{\rm T}$, for $p_{\rm T}^{\rm assoc}>$ 0.3 GeV/$c$ and
the sub-ranges 0.3 $<p_{\rm T}^{\rm assoc}<$ 1 GeV/$c$, 1 $<p_{\rm T}^{\rm
assoc}<$ 2 GeV/$c$, and 2 $<p_{\rm T}^{\rm assoc}<$ 3 GeV/$c$ (from left to
right). Statistical and systematic uncertainties are shown as vertical error
bars and boxes, respectively.

Figure 5: Away-side associated peak yields (left) and widths (right) measured
in pp collisions at $\sqrt{s}$ = 13 TeV, for the four V0M multiplicity
classes, shown with different marker styles. The ratios of the observable
values in each V0M class with respect to those in V0M class I are represented
in the bottom insets. Results are presented as a function of the $\rm
D^{0}$-meson $p_{\rm T}$, for $p_{\rm T}^{\rm assoc}>$ 0.3 GeV/$c$.
Statistical and systematic uncertainties are shown as vertical error bars and
boxes, respectively.

###  5.3 Comparison of the ALICE results with model predictions

The near- and away-side peak yields measured in pp collisions at $\sqrt{s}=13$
TeV and reported in Section 5.1 were compared to predictions from several
event generators. This allowed for verifying, for each model, whether its
specific implementation of the processes leading from charm-quark production
to final-state particles was adequate for describing the measured observables.
A detailed description of the models used for the comparison is provided in
Ref. [21]. These models include PYTHIA8 [13] with 4C [45] tune, PYTHIA6 [12]
with Perugia-2011 tune [39], POWHEG+PYTHIA8 [48, 19, 20] with hard-scattering
matrix elements evaluated at NLO or at LO accuracy, HERWIG 7 [16, 17], and
EPOS 3.117 [14, 15].

For each model, the average of the $\rm D^{0}$, $\rm D^{+}$, and $\rm D^{*+}$
azimuthal-correlation functions with charged particles was evaluated, using
the same prescriptions applied for data analysis in terms of kinematic and
particle-species selections. The evaluation of the peak observables from the
fit to the correlation distribution followed the same approach employed on
data, except for the estimation of the baseline. Since the statistical
fluctuations in the transverse region are negligible for the models, the
minimum of the azimuthal correlation function was directly considered as the
baseline value. A systematic uncertainty on the peak observables was then
assigned by performing an alternate fit, fixing the baseline as the weighted
average of the two lowest points of the azimuthal-correlation function.

The near-side peak observable trends for both models and data are illustrated
in Fig. 6 as a function of the trigger D-meson $p_{\rm T}$, in the $p_{\rm
T}^{\rm assoc}>0.3$ GeV/$c$ interval and in the other three kinematic sub-
ranges. The first and third rows show the yield and the width values, while
the second and the fourth show the ratios of model predictions with respect to
data. In these ratio panels, model statistical and systematic uncertainties
are shown as error bars and boxes, respectively, while data statistical and
systematic uncertainties are summed in quadrature, and the resulting
uncertainty is represented as a solid grey band. The increasing trend of the
near-side yield with the trigger particle $p_{\rm T}$ seen in data is obtained
by all the MC predictions, but with different strengths. A hierarchy can be
observed for the yield values, with EPOS systematically providing the largest
yields, followed by POWHEG+PYTHIA8 NLO, POWHEG+PYTHIA8 LO, and then by PYTHIA6
and PYTHIA8. HERWIG predicts the lowest yields for $p_{\rm T}^{\rm D}<8$
GeV/$c$ and $p_{\rm T}^{\rm assoc}>1$ GeV/$c$. Its predicted yield values for
the other kinematic ranges, instead, are generally in between PYTHIA and
POWHEG+PYTHIA8. The best description of the measurements is provided by the
POWHEG+PYTHIA8 and by PYTHIA generators, with POWHEG+PYTHIA8 (both NLO and LO)
generally performing better at lower $p_{\rm T}^{\rm D}$ and PYTHIA (both
versions) at higher $p_{\rm T}^{\rm D}$. A slight difference is observed
between the NLO and LO implementations of POWHEG+PYTHIA8, with the former
providing larger yields (by 5 to 15%, increasing with the D-meson $p_{\rm
T})$, and overall providing a better description of the data in the lower
$p_{\rm T}^{\rm D}$ region, while the latter has a better agreement with data
above 8 GeV/$c$. These differences can be understood in terms of the different
relative contribution of the NLO production mechanisms, as already discussed
in Ref. [21]. HERWIG predictions tend to underestimate the value of the near-
side yield in the kinematic region $p_{\rm T}^{\rm D}<8$ GeV/$c$ and $p_{\rm
T}^{\rm assoc}>1$ GeV/$c$, while for the other kinematic regions the
predictions are compatible with the data. EPOS predictions (not available for
the range $24<p_{\rm T}<36$ GeV/$c$) overestimate the near-side yield
measurements by a factor of about 2 through all the studied kinematic ranges.
Generally, smaller differences are obtained for the widths of the various
models with respect to those observed for the yields. POWHEG+PYTHIA8 NLO
predicts the broadest near-side peaks. The near-side width data measurements
hint towards a slight sharpening of the near-side peak width with increasing
$p_{\rm T}^{\rm D}$, while most of the models describe the width as nearly
flat. However, all models are able to reproduce the measured width within the
uncertainties.

Figure 6: Near-side associated peak yields (top row) and widths (third row
down) in pp collisions at $\sqrt{s}$ = 13 TeV, compared with predictions by
PYTHIA, POWHEG+PYTHIA8, HERWIG, and EPOS 3 event generators with various
configurations. Results are presented as a function of the D-meson $p_{\rm
T}$, for $p_{\rm T}^{\rm assoc}>$ 0.3 GeV/$c$, $0.3<p_{\rm T}^{\rm assoc}<1$
GeV/$c$, $1<p_{\rm T}^{\rm assoc}<2$ GeV/$c$, and $2<p_{\rm T}^{\rm assoc}<3$
GeV/$c$ (from left to right). The ratios of model predictions to data
measurements for yield (width) values are shown in the second (fourth) row
down. In these rows, model statistical and systematic uncertainties are shown
as vertical error bars and boxes, respectively, while data total uncertainties
are displayed as a solid band. Figure 7: Away-side associated peak yields (top
row) and widths (third row down) in pp collisions at $\sqrt{s}$ = 13 TeV,
compared with predictions by PYTHIA, POWHEG+PYTHIA8, HERWIG, and EPOS 3 event
generators with various configurations. Results are presented as a function of
the D-meson $p_{\rm T}$, for $p_{\rm T}^{\rm assoc}>$ 0.3 GeV/$c$, $0.3<p_{\rm
T}^{\rm assoc}<1$ GeV/$c$, $1<p_{\rm T}^{\rm assoc}<2$ GeV/$c$, and $2<p_{\rm
T}^{\rm assoc}<3$ GeV/$c$ (from left to right). The ratios of model
predictions to data measurements for yield (width) values are shown in the
second (fourth) row down. In these rows, model statistical and systematic
uncertainties are shown as vertical error bars and boxes, respectively, while
data total uncertainties are displayed as a solid band.

A similar comparison for the away-side peak is shown in Fig. 7. POWHEG+PYTHIA8
NLO and LO implementations provide the highest away-side yields, with the LO
implementation generally 5% above the NLO one, possibly due to an increased
amount of back-to-back production processes. PYTHIA6 and PYTHIA8 generally
provide slightly lower away-side yield values than POWHEG+PYTHIA8 NLO and LO
expectations, with PYTHIA8 tending to be on the lower side compared to
PYTHIA6. HERWIG predicts values lower than all the other models (about 20%
lower than POWHEG+PYTHIA8 NLO yields). EPOS predicts a stronger increasing
trend of the away-side yields with $p_{\rm T}^{\rm D}$ than the other
generators. For this observable, data uncertainties are not small enough to be
sensitive to all the differences highlighted above. The best agreement with
data is provided by PYTHIA6, PYTHIA8, and HERWIG. The POWHEG+PYTHIA8 predicted
yields, for both implementations, are on the higher side compared to data, in
particular for lower associated-particle $p_{\rm T}$. EPOS predictions tend to
underestimate the yield for $p_{\rm T}^{\rm D}<5$ GeV/$c$, while for
$16<p_{\rm T}^{\rm D}<24$ GeV/$c$ its away-side yield predictions are higher
than the measured values. The narrowing of the away-side peak with increasing
$p_{\rm T}^{\rm D}$ is clearly evident in the third row of Fig. 7, both for
model predictions and data, except for $0.3<p_{\rm T}^{\rm assoc}<1$ GeV/$c$,
where all models predict a rather flat trend. Only EPOS has a slightly
different behaviour compared to the other models, showing an approximately
flat $p_{\rm T}^{\rm D}$ trend of the away-side width over the full $p_{\rm
T}^{\rm assoc}$ range, albeit with quite large model uncertainties. In terms
of absolute values, PYTHIA6 away-side width expectations are systematically
higher than all the other models, by an overall 20$\%$, with increasing
differences for increasing $p_{\rm T}^{\rm assoc}$, and also tend to
overestimate the measured width values. All the other models predict similar
values, consistent with data except for $p_{\rm T}^{\rm D}>16$ GeV/$c$, where
they slightly overestimate the data measurements.

##  6 Parton-level studies with PYTHIA8 and POWHEG+PYTHIA8

From the comparative studies discussed in Section 5.3, PYTHIA8 and
POWHEG+PYTHIA8 provide, overall, the most accurate description of the near-
and away-side correlation peak features. A more detailed investigation was
performed using these models to expose how different stages of the event
generation that determine the formation of the final-state particles generally
influence the development of the features of the correlation peak and the
azimuthal-correlation function.

At large momentum or short distances, e.g. the hard-parton scattering leading
to heavy quark production, QCD is asymptotically free. It implies that the
coupling constant is small, so a perturbative approach can be employed. Before
hard scattering takes place, partons from the incident beam protons can
radiate gluons in the so-called initial-state radiation (ISR) process.
Similarly, outgoing partons from the hard scatterings can produce a shower of
softer particles via a final-state radiation (FSR) process. Since hadrons are
composite objects, more than one distinct hard-parton interaction can occur in
a pp collision, and proton remnants can also scatter again on each other. Such
processes are called multi-parton interactions (MPI), and are responsible for
the production of a large fraction of the particles uncorrelated with the
D-meson candidate trigger, giving a substantial contribution to the underlying
event (UE) observed in the collision final state. Additionally, as detailed in
Ref. [9], in the MPI implementation used in PYTHIA8 (which also drives the MPI
process in POWHEG+PYTHIA8 simulations) charm-quark production can occur not
only from the first (hardest) hard scattering, but also from hard processes in
the various MPI occurring in the collisions, ordered with decreasing hardness.
There is also some correlation between FSR+ISR and MPI processes, since
initial- and final-state radiations are generated from all the parton
interactions occurring in the collision, and are thus enhanced in presence of
MPI, further increasing the collision multiplicity.

In the following, PYTHIA8 and POWHEG+PYTHIA8 predictions, for standard
simulations and for events generated after deactivating the previously
mentioned parton-level contributions (FSR+ISR, and FSR+ISR+MPI), are compared.
The latter case, in particular, provides a detailed view of the correlation
function from the hard-scattering outgoing partons, though hadronisation and
decays are still present and partially modify the original, parton-level,
correlation shape. The same procedure was performed for the predictions of
near- and away-side peak yields, widths, and baseline value, which are then
compared with the data, and of the $\beta$ parameter of the near-side peak.

Figure 8 shows the observables extracted from the fit to the azimuthal
correlation function for different parton-level contributions from PYTHIA8
event generator, compared with the data, for $p_{\rm T}^{\rm assoc}>0.3$
GeV/$c$ and as a function of $p_{\rm T}^{\rm D}$. In the first column, at high
$p_{\rm T}^{\rm D}$ the near-side and away-side yields show no relevant
contribution of MPI, while FSR and ISR processes contribute to an increase of
both peak yields, as expected, since for high-momentum partons they lead to
additional production of collinear particles. Even at high $p_{\rm T}^{\rm
D}$, with all three processes switched off, PYTHIA8 predicts peak yields
amounting to roughly half of the measured yields. In the lowest $p_{\rm
T}^{\rm D}$ interval, instead, FSR, ISR, and MPI lead to a decrease of the
peak yields. In the second column, the near-side width shows no significant
modification for the various configurations, apart from a slight increase of
the width observed when switching off MPI. These insights point towards a
relevant role of hadronisation, which remains in place also in the absence of
FSR, ISR, and MPI processes, in shaping the near-side correlation peak. As
expected, the away-side peak is wider than the near-side peak because of a
combined contribution of parton-level effects. When FSR and ISR are turned
off, the peak width is substantially decreased. This could be explained by the
lack of radiation (in particular hard gluon emissions) decreasing the
deflection angle of the recoil jet. In the third column, a mild dependence is
observed for the near-side $\beta$ parameter. In the simulations, the
available sample is much larger than in data, so the $\beta$ parameter could
be left free in the fit function, and its value is compared among the
different model configurations. A very small contribution of parton-level
processes to the baseline comes directly from the hard scattering (and
subsequent hadronisation and decays), as expected since PYTHIA8 is a LO
generator. All the other processes (ISR, FSR, and MPI) contribute to the
baseline, with the MPI roughly equivalent to the sum of ISR and FSR. This is
expected since MPI mostly affect the underlying event, whose particles point
to directions largely unrelated to the trigger D-meson one. The further
increase of the baseline when activating ISR and FSR processes is due to the
fact that, as mentioned above, they act on all parton scatterings, including
those occurring in MPI.

Figure 8: Near- and away-side peak yields (first column), widths (second
column), near-side peak $\beta$ parameter and baseline (third column) from
fits to the D-meson and charged particle azimuthal-correlation function, from
PYTHIA8 simulations obtained with different parton-level contributions. The
predictions are obtained for multiplicity-integrated pp collisions at
$\sqrt{s}=13$ TeV, as a function of the D-meson $p_{\rm T}$, for $p_{\rm
T}^{\rm assoc}>0.3$ GeV/$c$, and compared with ALICE data. Figure 9: Near- and
away-side peak yields (first column), widths (second column), near-side peak
$\beta$ parameter and baseline (third column) from fits to the D-meson and
charged particle azimuthal-correlation function, from POWHEG+PYTHIA8
simulations obtained with different parton-level contributions. The
predictions are obtained for multiplicity-integrated in pp collisions at
$\sqrt{s}=13$ TeV, as a function of the D-meson $p_{\rm T}$, for $p_{\rm
T}^{\rm assoc}>0.3$ GeV/$c$, and compared with ALICE data.

Figure 9 shows the same set of observables as shown in Fig. 8 and provides the
same comparison to data, but with predictions obtained from POWHEG+PYTHIA8.
Compared to Fig. 8, a larger near-side peak yield is already obtained when
ISR, FSR, and MPI processes are switched off. This can be explained with the
inclusion of NLO processes directly in the hard scattering in POWHEG, rather
than reproducing their effect in the parton shower as in PYTHIA8. Also in this
case, MPI does not contribute to the peak yield. A similar behaviour as that
of Fig. 8 is observed for the near-side peak width. The near-side peak $\beta$
parameter value shows a decreasing influence of ISR, FSR, and MPI processes
for increasing $p_{\rm T}^{\rm D}$. For the away-side peak, no major
differences with respect to PYTHIA8 are found for the yield contributions,
while a slightly lower influence of ISR and FSR is obtained for the widths,
which can also be understood with the above consideration. For the baseline, a
higher value with respect to PYTHIA8 is obtained when switching off all the
parton-level processes, consistent with the non back-to-back topology of NLO
processes (in particular, flavour excitation with a nearly flat contribution
in $\Delta\varphi$ [1]). The FSR and ISR contributions to the baseline
increase with $p_{\rm T}^{\rm D}$, in contrast to PYTHIA8, and partially drive
the rising $p_{\rm T}^{\rm D}$ trend of the baseline observed for the full
simulation.

The comparison of the contributions of the various processes to the
correlation function helps in understanding better the source of the
difference between PYTHIA8 and POWHEG+PYTHIA8 simulations observed in Section
5.3. Figure 10 displays the azimuthal correlation function of D mesons with
charged particles obtained from PYTHIA8 and POWHEG+PYTHIA8 simulations
sequentially deactivating the different parton-level contributions in pp
collisions at $\sqrt{s}=13$ TeV for $0.3<p_{\rm T}^{\rm assoc}<1$ GeV/$c$ and
$3<p_{\rm T}^{\rm D}<5$ GeV/$c$. Figure 11 shows the same quantities for a
higher momentum range, i.e. $2<p_{\rm T}^{\rm assoc}<3$ GeV/$c$ and $24<p_{\rm
T}^{\rm D}<36$ GeV/$c$.

Figure 10: Azimuthal correlation function of D mesons with charged particles
with different parton-level contributions from PYTHIA8 (left panel) and
POWHEG+PYTHIA8 simulations (right panel) in pp collisions at $\sqrt{s}=13$
TeV, for $0.3<p_{\rm T}^{\rm assoc}<1$ GeV/$c$ and $3<p_{\rm T}^{\rm D}<5$
GeV/$c$.

Figure 11: Azimuthal correlation function of D mesons with charged particles
with different parton-level contributions from PYTHIA8 (left panel) and
POWHEG+PYTHIA8 simulations (right panel) in pp collisions at $\sqrt{s}=13$
TeV, for $2<p_{\rm T}^{\rm assoc}<3$ GeV/$c$ and $24<p_{\rm T}^{\rm D}<36$
GeV/$c$.

Most of the features expressed above are seen in a more qualitative but
clearer way in these figures. In particular, the larger baseline in the case
without FSR, ISR, and MPI for POWHEG+PYTHIA8 is clearly visible for the
low-$p_{\rm T}$ range. In general, for both simulations the relevant ISR, FSR,
and MPI contributions to the baseline are obtained over the whole
$\Delta\varphi$ range when focusing in the low-momentum region, while most of
the off-peak contribution disappears when considering higher-$p_{\rm T}$
trigger and associated particles. In the high-$p_{\rm T}$ region, the
difference in the contributions to the peaks between the generators is
evident: in particular, for POWHEG+PYTHIA8 the near-side peak yield is already
larger for the case without ISR, FSR, and MPI processes. Also, at high $p_{\rm
T}$ two sharp peaks appear for PYTHIA8, when parton showering and MPI effects
are turned off, while for POWHEG+PYTHIA8 wider peaks emerge already from the
hard-scattering, due to higher-order charm-production processes. The addition
of the parton showering processes in PYTHIA8 allows to reconcile most of the
differences in the correlation peak shape, in particular for the widths, while
some residual differences remain present for the yields for the full
simulation, as discussed in Section 5.3.

##  7 Summary

A study of the azimuthal correlation function of D mesons with charged
particles, measured in pp collisions at $\sqrt{s}=13$ TeV with the ALICE
detector, was presented. The pattern of the correlation function and the
features of near- and away-side correlation peaks, extracted via a fit to the
correlation function, were characterised in five D-meson momentum ranges, from
3 to 36 GeV/$c$, and for the associated-particle range $p_{\rm T}^{\rm
assoc}>0.3$ GeV/$c$ and the three sub-ranges $0.3<p_{\rm T}^{\rm assoc}<1$
GeV/$c$, $1<p_{\rm T}^{\rm assoc}<2$ GeV/$c$, and $2<p_{\rm T}^{\rm assoc}<3$
GeV/$c$.

The measurement precision is significantly improved compared to previous ALICE
results in pp collisions at $\sqrt{s}=7$ TeV [3] and $\sqrt{s}=5.02$ TeV [21].
The correlation function shape, as well as the peak yields and widths, are
compatible within uncertainties with those lower-energy measurements,
confirming the expectation from PYTHIA8 and POWHEG+PYTHIA8 generators of
little dependence on the collision energies.

The possible evolution of the correlation function with the event multiplicity
was probed by performing the analysis in four multiplicity ranges, measured
with the V0M estimator, profiting from a dedicated high-multiplicity trigger
provided by the V0 detector. Though the uncertainties do not allow for firm
conclusions, a strong variation of the correlation function with multiplicity
is excluded, suggesting that when the charm quarks hadronise into $\rm D^{0}$
mesons, the charm-quark fragmentation and hadronisation processes are not
particularly sensitive to the event multiplicity. The overall compatibility of
the correlation-peak features for different event multiplicities tends to
support the scenario that, independently of the number of charm quarks
produced in the collision, they undergo similar fragmentation and
hadronisation into $\rm D^{0}$ mesons. Such a scenario indicates an increased,
but independent, charm production from MPI in high-multiplicity pp collisions,
and is one of the mechanisms proposed to explain the observed trend of D-meson
self-normalised yields at different relative multiplicities [9].

The measured near- and away-side peak yields and widths were compared, in the
accessible kinematic ranges, with expectations from state-of-the-art models
capable of producing peak observables, such as PYTHIA, POWHEG+PYTHIA, HERWIG,
and EPOS. Among these models, PYTHIA8 and POWHEG+PYTHIA8 provide the best
overall description of the data, HERWIG underestimates the near-side yields at
low $p_{\rm T}^{\rm D}$ and at high $p_{\rm T}^{\rm assoc}$, while EPOS
overestimates the near-side yields over the whole kinematic range, predicting
also a steeper $p_{\rm T}^{\rm D}$ dependence of the away-side yields. A study
of the influence of parton-level processes, as ISR, FSR, and MPI, on the shape
of the final-state correlation distribution and on its peak properties was
also performed with PYTHIA8 and POWHEG+PYTHIA8. These studies are important
not only for a better understanding of the underlying physics in pp
collisions, but also for interpreting possible modifications of the
correlation peaks in Pb–Pb collisions due to interactions of the heavy quarks
in the quark–gluon plasma. This measurement is expected to become accessible
during the LHC Run 3, with the upgraded ALICE detector [49, 50].

## 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; 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; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT)of Applied Science (IIST), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, 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.

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##  Appendix A The ALICE Collaboration

S. Acharya143, D. Adamová98, A. Adler76, J. Adolfsson83, G. Aglieri Rinella35,
M. Agnello31, N. Agrawal55, Z. Ahammed143, S. Ahmad16, S.U. Ahn78, I. Ahuja39,
Z. Akbar52, A. Akindinov95, M. Al-Turany110, S.N. Alam16,41, D. Aleksandrov91,
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##  Affiliation notes

I Deceased
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia
V Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VII Also at: University of Kansas, Lawrence, Kansas, United States

## Collaboration Institutes

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