Measurements of heavy-flavor production as a function of multiplicity with
ALICE at the LHC

Yoshini Bailung1$\star$ on behalf of the ALICE Collaboration

1 Department of Physics, Indian Institute of Technology Indore, Madhya
Pradesh, India *<EMAIL_ADDRESS>
50th International Symposium on Multiparticle Dynamics
(ISMD2021)
12-16 July 2021 10.21468/SciPostPhysProc.?

## Abstract

In this contribution, the production of heavy-flavor hadrons as a function of
multiplicity, via the study of the $\mathbf{D}$-meson and heavy-flavor hadron
decay leptons self-normalized yields in pp collisions at the center of mass
energy $\bm{\sqrt{s}=13}$ TeV is discussed. Comparisons are made with similar
measurements of J/$\bm{\psi}$ at $\bm{\sqrt{s}=13}$ TeV and various model
calculations. The $\mathbf{\Lambda_{c}^{+}/D^{0}}$ and
$\mathbf{D^{+}_{s}/D^{0}}$ yield ratios in different multiplicity intervals in
pp collisions at $\bm{\sqrt{s}=13}$ TeV are also reported. In addition, the
ALICE measurement of $\mathbf{\Lambda_{c}^{+}}$ production in p–Pb collisions
at $\bm{\sqrt{s_{\rm{NN}}}}$ = 5.02 TeV down to transverse momentum
($\bm{p_{\rm T}}$) = 0 GeV/$\bm{c}$ is presented. Finally, the nuclear
modification factor is shown for open charm hadrons at $\bm{\sqrt{s}=5.02}$
TeV in p–Pb collisions. Finally, measurements of the elliptic flow of heavy-
flavor hadron decay leptons in p–Pb systems are presented, which hint towards
a possible collective behaviour in high multiplicity p–Pb collisions.

##  1 Introduction

###  1.1 Physics motivation

Heavy quarks (charm and beauty) are produced at the initial stages of the
relativistic hadronic collisions via hard scattering processes. The study of
heavy-flavor hadron production provides a stringent test to perturbative
quantum chromodynamics (pQCD) calculations in pp collisions and can help in
disentangling cold nuclear matter (CNM) effects in p–Pb collisions. Analysis
of charm production as a function of charged-particle multiplicity allows the
investigation of the role of multi-parton interactions (MPI), color-
reconnection (CR) mechanisms, and the interplay between the hard and soft
particle production in pp and p–Pb collisions. Heavy-flavor hadron production
measurements in high multiplicity pp and p–Pb collisions indicate possible
modification of the particle spectra compared to minimum bias measurements.
These results raise questions about the collective nature of the QCD matter
produced in small systems.

###  1.2 Analysis Strategy

Several detectors in ALICE [1] are used to reconstruct charm hadrons in
various rapidities ($y$) from their:

  1. 1.

hadronic decay channels, $\rm{D^{0}\rightarrow K^{-}\pi^{+}}$;
$\rm{D^{+}\rightarrow K^{-}\pi^{+}\pi^{+}}$; $\rm{D^{*+}\rightarrow
D^{0}\pi^{+}}$; $\rm{D_{s}^{+}\rightarrow K^{-}K^{+}\pi^{+}}$;
$\rm{\Lambda_{c}^{+}\rightarrow pK^{-}\pi^{+}}$;
$\rm{\Lambda_{c}^{+}\rightarrow pK^{0}_{s}}$;
$\rm{\Sigma_{c}^{0}\rightarrow\Lambda^{+}_{c}\pi^{-}}$;
$\rm{\Sigma_{c}^{++}\rightarrow\Lambda^{+}_{c}\pi^{+}}$;
$\rm{\Xi_{c}^{0}\rightarrow\Xi^{-}_{c}\pi^{+}}$;
$\rm{\Xi_{c}^{+}\rightarrow\Xi^{-}\pi^{-}\pi^{+}}$;
$\rm{\Omega_{c}^{0}\rightarrow\Omega^{-}\pi^{+}}$

  2. 2.

semi-leptonic decay channels, B, D-meson $\rightarrow\rm{e}+X$; B, D-meson
$\rightarrow\mu+X$; $\rm{\Xi_{c}^{0}\rightarrow\Xi^{-}e^{+}\nu_{e}}$;
$\rm{\Lambda_{c}^{+}\rightarrow\Lambda e^{+}\nu_{e}}$

The Silicon-Pixel Detector (SPD), which constitutes the two innermost layers
of the Inner Tracking System (ITS), is used as a multiplicity estimator via
the number of track segments reconstructed from two hits in the two layers of
the SPD, pointing to the primary vertex. In addition, multiplicity is
estimated based on the percentile distribution of the V0 amplitude in the V0
detector. The multiplicity intervals are converted to charged-particle
multiplicity density ($\rm{d}\it{N}_{\rm ch}/\rm{d}\eta$) intervals within
pseudorapidity $|\eta|<1$. The ITS is also used for secondary-vertex
reconstruction and tracking. The particle identification is carried out by the
Time Projection Chamber (TPC), the Time Of Flight (TOF) detector, and the
Electromagnetic Calorimeter (EMCal) for high $p_{\rm T}$ electrons. The muons
are reconstructed at forward rapidity (2.5 <$y$< 4) using the muon
spectrometer.

##  2 Results

###  2.1 Heavy-flavor hadron production in pp collisions

Heavy-flavor hadron production measurements as a function of multiplicity are
expressed in the form of self-normalized yields, where the yields in the
corresponding multiplicity interval ($\rm{Y^{mult}}$) are presented relative
to those in the integrated multiplicity sample ($\rm{Y^{mult\ int}}$).

$\rm{Y_{corr}^{mult}}=\left(\frac{Y^{mult}}{((Acc\times\epsilon_{prompt}^{mult})\times\it{N}\rm_{event}^{mult})/\epsilon^{trg}_{mult}}\right)\Biggm{/}\left(\frac{Y^{mult\
int}}{((Acc\times\epsilon_{prompt}^{mult\ int})\times\it{N}\rm_{event}^{mult\
int})/\epsilon^{trg}_{mult\ int}}\right)$ (1)

Here, $\rm{Y^{mult}}$ is the raw yield,
$\rm{Acc\times\epsilon_{prompt}^{mult}}$ is the acceptance$\times$efficiency
factor, $\rm{\it{N}\rm^{mult}_{event}}$ is the number of events, and
$\rm{\epsilon^{trg}_{mult}}$ is the trigger efficiency for a particular
multiplicity interval. In Fig. 1, the average D-meson self-normalized yields
at midrapidity ($|y|<0.5$) as a function of charged-particle multiplicity in
pp collisions at $\sqrt{s}$= 13 TeV are presented for different $p_{\rm T}$
intervals. The multiplicity dependence of D-meson yields shows a faster than
linear increase. They are compared to model predictions from EPOS3 [2] and the
3-pomeron Color Glass Condensate model (CGC) [3]. EPOS3 with a hydrodynamic
evolution shows good agreement with a faster than linear increase of D-meson
yields at low and intermediate $p_{\rm T}$. EPOS3 without hydrodynamics
predicts a small increase, leading to underestimation of the results. The
3-pomeron CGC largely overestimates the self-normalized yields of D-mesons.

Figure 1: Average $\rm{D^{0}}$, $\rm{D^{+}}$, $\rm{D^{*+}}$ meson self-
normalized yields in various $p_{\rm T}$ intervals as a function of charged-
particle multiplicity in pp collisions at $\sqrt{s}$= 13 TeV compared to
different model predictions[2, 3]. The systematic uncertainties on D-meson
yield as well as on $\rm{d}\it{N}_{\rm
ch}/\rm{d}\eta$/$\langle$$\rm{d}\it{N}_{\rm ch}/\rm{d}\eta$ $\rangle$ is
depicted as boxes.

The self-normalized yields of electrons from heavy-flavor hadron decays in pp
collisions at midrapidity at $\sqrt{s}$= 13 TeV for $p_{\rm T}$ < 4.5 GeV/$c$
are shown in the left panel of Fig. LABEL:fig:leptonSNY. The results are
compared to PYTHIA8 Monash tune with MPI and CR turned on[4]. Possible auto-
correlation effects that could arise from the measurement of the charged-
particle distribution in the same pseudorapidity region as the charm hadrons
could play a role, producing the faster than linear trend as a function of
charged-particle multiplicity [5]. Muon production from the decay of heavy-
flavor hadrons is measured at forward rapidity in pp collisions at $\sqrt{s}$=
8 TeV, shown on the right panel of Fig. LABEL:fig:leptonSNY. The results are
underestimated by predictions from EPOS3. In Fig. 3, the same results are put
together with self-normalized yields from J/$\psi$[6] and electrons from
heavy-flavor hadron decays as a function of charged-particle multiplicity in
pp collisions at $\sqrt{s}$= 13 TeV at compatible $p_{\rm T}$ intervals.

Figure 3: Average D-meson, J/$\psi$ [6], and heavy-flavor hadron decay
electrons self-normalized yields as a function of charged-particle
multiplicity at midrapidity in pp collisions at $\sqrt{s}$= 13 TeV at
compatible low (left) and high (right) $p_{\rm T}$ intervals. The bottom
panels show the comparison of double ratios between the species.

The $\rm{\Lambda_{c}^{+}/D^{0}}$ and $\rm{D_{s}^{+}/D^{0}}$ yield ratios in pp
collisions at $\sqrt{s}$= 13 TeV as a function of $p_{\rm T}$, in different
multiplicity intervals are presented in Fig. 4. The
$\rm{\Lambda_{c}^{+}/D^{0}}$ ratio depicts a multiplicity dependence that
hints to a modification of hadronization mechanisms with multiplicity. The
PYTHIA8 (Monash) [4] tuned to $\rm{e^{+}e^{-}}$ collisions highly
underestimates these baryon-to-meson yield ratios. The trend with multiplicity
is qualitatively described by PYTHIA8 with CR Mode 2 [7]. The
$\rm{D_{s}^{+}/D^{0}}$ ratios do not show any visible multiplicity dependence,
and the results are compatible with the $p_{\rm T}$-integrated measurements at
$\rm{e^{+}e^{-}}$ collisions [8].

Figure 4: (Left) $\rm{\Lambda_{c}^{+}/D^{0}}$ and (right)
$\rm{D_{s}^{+}/D^{0}}$ yield ratios in different multiplicity intervals versus
$p_{\rm T}$ measured in pp collisions at $\sqrt{s}$= 13 TeV. Comparisons are
shown for $\rm{\Lambda_{c}^{+}/D^{0}}$ ratios with different PYTHIA8 tunes [4,
7].

###  2.2 Heavy-flavor hadron production in p–Pb collisions

In Fig. 5, the $\rm{\Lambda_{c}^{+}/D^{0}}$ ratios measured in p–Pb collisions
at $\sqrt{s_{\rm NN}}$= 5.02 TeV is presented [9]. The most recent results
extend the measurement down to $p_{\rm T}$ = 0 GeV/$c$. At low $p_{\rm T}$,
the $\rm{\Lambda_{c}^{+}/D^{0}}$ ratios in p–Pb collisions is lower than in pp
collisions, the opposite is observed at intermediate $p_{\rm T}$. This can be
a consequence of radial flow or a modification in the hadronization mechanism
in p–Pb systems. The nuclear modification factor which is defined as:

$R_{\rm{pPb}}=\frac{\rm{d\sigma_{pPb}/d\it{p}_{\rm{T}}}}{A\cdot\rm{d\sigma_{pp}/d\it{p}_{\rm{T}}}}$
(2)

helps to quantify the CNM effects. In (2)
$\rm{d\sigma_{pp(pPb)}/d\it{p}_{\rm{T}}}$ are the $p_{\rm T}$-differential
cross sections in pp and p–Pb collisions for a corresponding center of mass
energy, and $A$ is the atomic mass number of Pb. In Fig. 5, the $R_{\rm pPb}$
results are shown for p–Pb collisions at $\sqrt{s_{\rm NN}}$= 5.02 TeV. In the
left panel, the $\rm{\Lambda_{c}^{+}}$ $R_{\rm pPb}$ is compared to D-meson
$R_{\rm pPb}$ [10], in which a clear suppression is seen at low $p_{\rm T}$
for $\rm{\Lambda_{c}^{+}}$ followed by an enhancement at intermediate $p_{\rm
T}$. In the right panel, model calculations by POWHEG + PYTHIA6 [11, 12] and
the POWLANG transport model [13] are shown. POWHEG with PYTHIA6 assumes
hadronization via fragmentation, and the model agrees with the results at low
$p_{\rm T}$, however departing at intermediate $p_{\rm T}$. The POWLANG model
assumes the formation of a hot deconfined medium, implementing hadronization
via fragmentation and quark recombination. The model predicts the suppression
for $p_{\rm T}$ < 3 GeV/$c$, as it incorporates nuclear shadowing, although it
deviates from the measurements at intermediate and high $p_{\rm T}$.

Figure 5: (Left) $\rm{\Lambda_{c}^{+}/D^{0}}$ as as function of $p_{\rm T}$
measured in p–Pb collisions at $\sqrt{s_{\rm NN}}$= 5.02 TeV [9]. (Right)
$\rm{\Lambda_{c}^{+}}$ $R_{\rm pPb}$ as a function of $p_{\rm T}$ compared to
D-meson results [10] and model predictions[11, 12, 13].

In Fig. 6, the elliptic flow ($v_{2}$) of heavy-flavor hadron decay leptons in
p–Pb collisions is displayed. In general, the $n^{th}$-order anisotropic flow
coefficients are written as $v_{n}=\langle\cos[n(\phi-\Psi_{R})]\rangle$,
where $\phi$ is the azimuthal angle of a particle and $\Psi_{R}$ is the
$n^{th}$ harmonic symmetry plane angle. $v_{2}$ is sensitive to the initial
collision geometry and has dominant contribution in non-central
collisions[14]. The measurement for inclusive muons was performed at 2.5 <$y$<
4 at $\sqrt{s_{\rm NN}}$= 8.16 TeV and for electrons at $|y|<0.8$ at
$\sqrt{s_{\rm NN}}$= 5.02 TeV [15]. The muon production is dominated by heavy-
flavor hadron decays for $p_{\rm T}$ > 2 GeV/$c$. The results show a positive
$v_{2}$ in central p–Pb events, which hints at the possibility of collective
phenomena in high-multiplicity p–Pb collisions.

Figure 6: Elliptic flow of inclusive muons as a function of $p_{\rm T}$ in
p–Pb collisions at $\sqrt{s_{\rm NN}}$= 8.16 TeV compared to the results for
heavy-flavor hadron decay electrons at $\sqrt{s_{\rm NN}}$= 5.02 TeV [15].

##  3 Conclusion

The self-normalized yield measurements of heavy-flavor hadron production as a
function of multiplicity show a stronger than linear trend. Measurements of
D-meson, J/$\psi$, and heavy-flavor decay leptons are compatible in similar
$p_{\rm T}$ intervals. These measurements are compared to different
theoretical calculations. In p–Pb collisions, measurements of
$\rm{\Lambda_{c}^{+}/\rm{D^{0}}}$ yield ratios down to $p_{\rm T}$ = 0 GeV/$c$
at $\sqrt{s_{\rm NN}}$= 5.02 TeV indicate a deviation from measurements in pp
collisions. The $\rm{\Lambda_{c}^{+}}$ $R_{\rm pPb}$ shows clear differences
at low and intermediate $p_{\rm T}$ when compared to D-meson measurements.
Finally, a positive $v_{2}$ is measured for inclusive heavy-flavor decay muons
in central p–Pb collisions at 2.5 <$y$< 4 and heavy-flavor decay electrons at
$|y|<0.8$.

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