2015 091 30 March

Charm and beauty production versus charged-particle multiplicity

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

Prompt D meson and non-prompt ${\rm J}/\psi$ yields are studied as a function
of the multiplicity of charged particles produced in inelastic proton–proton
collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV. The results are
reported as a ratio between yields in a given multiplicity interval normalised
to the multiplicity-integrated ones (relative yields). They are shown as a
function of the multiplicity of charged particles normalised to the average
value for inelastic collisions (relative charged-particle multiplicity). ${\rm
D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ mesons are measured in five $p_{\rm
T}$ intervals from $1\leavevmode\nobreak\ \mathrm{GeV}/c$ to
$20\leavevmode\nobreak\ \mathrm{GeV}/c$ and for $|y|<0.5$ via their hadronic
decays. The D-meson relative yield is found to increase with increasing
charged-particle multiplicity. For events with multiplicity six times higher
than the average multiplicity of inelastic collisions, a yield enhancement of
a factor about 15 relative to the multiplicity-integrated yield in inelastic
collisions is observed. The yield enhancement is independent of transverse
momentum within the uncertainties of the measurement. The ${\rm D^{0}}$-meson
relative yield is also measured as a function of the relative multiplicity at
forward pseudo-rapidity. The non-prompt ${\rm J}/\psi$, i.e. the B hadron,
contribution to the inclusive ${\rm J}/\psi$ production is measured in the di-
electron decay channel at central rapidity. It is evaluated for $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ and $|y|<0.9$, and extrapolated to
$p_{\rm T}>0$. The fraction of non-prompt ${\rm J}/\psi$ in the inclusive
${\rm J}/\psi$ yields shows no dependence on the charged-particle multiplicity
at central rapidity. Charm and beauty hadron relative yields exhibit a similar
increase with increasing charged-particle multiplicity. The measurements are
compared to PYTHIA 8, EPOS 3 and percolation calculations.

##  1 Introduction

The study of the production of hadrons containing heavy quarks, i.e. charm and
beauty, in proton–proton (pp) collisions at the Large Hadron Collider (LHC)
provides a way to test calculations based on perturbative Quantum
Chromodynamics (pQCD) at the highest available collision energies. The
inclusive production cross sections of charm mesons measured in pp collisions
at the LHC at both central [1, 2] and forward [3] rapidity are described by
theoretical predictions based on pQCD calculations with the collinear
factorisation approach at next-to-leading order (e.g. in the general-mass
variable-flavour-number scheme, GM-VFNS [4]) or at fixed order with next-to-
leading-log resummation (FONLL [5, 6, 7, 8]) within theoretical uncertainties.
The comparisons suggest that charm production is under (over) estimated by the
central values of the FONLL (GM-VFNS) calculations. The measured D-meson
production cross sections in pp collisions at the LHC can also be described by
pQCD calculations performed in the framework of $k_{\rm T}$-factorisation in
the leading order (LO) approximation [9]. Beauty production cross section
measurements in pp collisions at $\sqrt{s}=7$ TeV [10, 11, 12, 13, 14] are
well described by implementations of FONLL and GM-VFNS [7, 15]. In the case of
B mesons, the measured cross sections are close to the central value of the
FONLL and GM-VFNS predictions. A similar situation was observed in
$\text{p}\overline{\text{p}}$ collisions at $\sqrt{s}=1.96$ TeV at the FNAL
Tevatron collider [16, 17, 18].

The measurement of heavy-flavour production in pp collisions as a function of
the charged-particle multiplicity produced in the collision could provide
insight into the processes occurring in the collision at the partonic level
and the interplay between the hard and soft mechanisms in particle production.
These aspects are expected to depend on the energy and on the impact parameter
(the distance between the colliding protons in the plane perpendicular to the
beam direction) of the pp collision [19, 20, 21]. In the impact parameter
representation of proton–proton collisions, the overlap of the nucleon wave
functions in proton–proton collisions can be described by a geometrical
picture with two separate transverse distance scales: the impact parameter of
the collision and the transverse spatial partonic distribution [22, 23, 20,
24].In particular, pp collisions with a hard parton-parton scattering are
predicted to be more central (i.e. have smaller impact parameter) than
minimum-bias events [20, 25].

The NA27 Collaboration observed in 1988 that the average charged-particle
multiplicity in events with open charm production was higher by about $20\%$
than in events without charm production [26]. A softening of the momentum
spectra of hadrons produced in association with charm was also observed. This
result was interpreted as a consequence of the more central nature of
collisions leading to charm production.

At LHC energies, two additional contributions to charm production and its
relation to multiplicity have to be considered. The first effect is the likely
larger amount of gluon radiation associated to the short distance production
processes at larger energies and particle transverse momenta. The second is
the contribution of Multiple-Parton Interactions (MPI) [27, 28, 29], i.e.
several hard partonic interactions occurring in a single pp collision. In this
context, pQCD-inspired models describe the final-state particles produced in
hadronic collisions with a two-component approach, namely an initial hard
partonic scattering process, that gives rise to collimated clusters of hadrons
(jets), and an underlying event, consisting of the final-state particles that
are not associated with the initial hard scattering. While the hard scattering
process can be computed with a pQCD approach, the description of the
underlying event, which is thought to be dominated by particles produced in
soft processes and by perturbative (mini)jets with relatively small transverse
momenta (soft MPIs), is based on a phenomenological model. In particular,
pQCD-based models of MPIs provide a consistent way to describe high
multiplicity pp collisions, and have been implemented in recent Monte Carlo
generators like PYTHIA 6 [30], PYTHIA 8 [31], and HERWIG [32]. Measurements by
the CMS Collaboration of jet and underlying event properties as a function of
multiplicity in pp collisions at $\sqrt{s}$ = 7 TeV can be better described by
event generators including MPI [33, 34]. The analysis of minijet production
performed by the ALICE Collaboration [35] indicates that high multiplicities
in pp collisions are reached through a high number of MPIs and a higher than
average number of fragments per parton. Upward fluctuations of the gluon
density in the colliding protons are also advocated to describe the results
from high multiplicity pp collisions at the LHC [21, 36, 37]. Indeed, the
transverse structure of the proton, as probed in hard partonic scattering
processes, is predicted to play a crucial role in defining the underlying
event structure and the probability of MPIs [25]. In the heavy-flavour sector,
the LHCb Collaboration reported measurements of double charm production in pp
collisions at the LHC (${\rm D^{0}}+X$, ${\rm J}/\psi+X$ and ${\rm
J}/\psi+{\rm J}/\psi$ where $X={\rm D^{0}},\,{\rm D^{+}},\,{\rm D^{+}_{\rm
s}},\,{\rm\Lambda^{+}_{\rm c}}$), which suggest that MPIs also play a role at
the hard momentum scale relevant for c$\overline{\mathrm{c}}$ production [38,
39].

The ALICE Collaboration published the first measurement of inclusive ${\rm
J}/\psi$ production as a function of charged-particle multiplicity, expressed
as the pseudo-rapidity density of charged particles ${\rm d}N_{\rm ch}/{\rm
d}\eta$ at mid-rapidity, in pp collisions at $\sqrt{s}=7$ TeV [40]. An
approximately linear increase of the yield of ${\rm J}/\psi$ with the charged-
particle multiplicity was observed in a multiplicity range reaching four times
the average multiplicity $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$. The
measurements at $|y|<0.9$ and $2.5<y<4.0$ were compatible within the
uncertainties. Both the larger amount of gluon radiation and the contribution
of MPI in collisions where heavy quarks are produced can induce a correlation
between the yield of quarkonia and the charged-particle multiplicity produced
in the collision. The measured rise of ${\rm J}/\psi$ yield with increasing
multiplicity can also be described in the framework of string interaction or
parton saturation models. In particular, in Ref. [41] a stronger–than–linear
trend in the high density domain is anticipated as a consequence of the
interaction (overlap) of strings, which reduces the effective number of
sources for soft-particle production. The increasing trend of ${\rm J}/\psi$
yield with multiplicity is also described in a framework in which high
multiplicities are attained in pp collisions due to the contribution of higher
Fock states in the proton, leading to a larger number of gluons participating
in the collision [37].

It is also worth pointing out that the charged-particle densities attained in
high-multiplicity pp collisions at the LHC are of the same order of magnitude
as those measured in semi-peripheral heavy-ion collisions at lower centre-of-
mass energies [42]. In those heavy-ion collisions, the measured momentum
distributions of light hadrons indicate that the system undergoes a collective
expansion, which can be described in terms of hydrodynamics. Recent
measurements in high-multiplicity p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$
TeV [43, 44, 45, 46, 47, 48] and in high-multiplicity pp collisions at the LHC
[49] indicate that such a collective behaviour could also be at play in these
systems. If charm quarks were to follow a collective motion in high-
multiplicity events, their momentum spectra would be altered, and the heavy-
flavour hadron relative yields at high multiplicity would vary as a function
of $p_{\rm T}$ [50].

The measurements of the $p_{\rm T}$-differential prompt D meson and non-prompt
${\rm J}/\psi$ cross sections in pp collisions at $\sqrt{s}=7$ TeV with the
ALICE experiment at the LHC were published in references [1, 10]. In this
paper, we report the measurement of the relative open heavy-flavour production
yields as a function of the charged-particle multiplicity in pp collisions at
$\sqrt{s}=7$ TeV. Open charm and beauty production is measured by
reconstructing prompt D mesons and non-prompt ${\rm J}/\psi$, i.e. ${\rm
J}/\psi$ mesons coming from the decay of beauty hadrons. The experimental
setup and the multiplicity estimation are described in Secs. 2 and 3,
respectively. Prompt ${\rm D^{0}}$, ${\rm D^{+}}$, ${\rm D^{*+}}$ mesons were
measured at central rapidity, $|y|<0.5$, in six multiplicity intervals and
five $p_{\rm T}$ intervals from 1 $\mathrm{GeV}/c$ to 20 $\mathrm{GeV}/c$
(Sec. 4). The non-prompt fraction of ${\rm J}/\psi$ production was measured in
the rapidity interval $|y|<0.9$ in five multiplicity intervals and for $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ and extrapolated to $p_{\rm T}>0$
(Sec. 5). The relative yields as a function of charged-particle multiplicity
are compared in Sec. 6. Finally, model calculations are discussed and compared
with data in Sec. 7.

##  2 Experimental apparatus and data sample

The ALICE apparatus [51] consists of a central barrel detector covering the
pseudo-rapidity interval $|\eta|<0.9$, a forward muon spectrometer covering
the pseudo-rapidity interval $-4.0<\eta<-2.5$, and a set of detectors at
forward and backward rapidities used for triggering and event
characterization. In the following, the subsystems that are relevant for the D
meson and non-prompt ${\rm J}/\psi$ analyses are described.

The central barrel detectors are located inside a large solenoidal magnet,
which provides a magnetic field of 0.5 T along the beam direction ($z$ axis in
the ALICE reference frame). Tracking and particle identification are performed
using the information provided by the Inner Tracking System (ITS), the Time
Projection Chamber (TPC) and the Time Of Flight (TOF) detectors, that have
full azimuthal coverage in the pseudo-rapidity interval $|\eta|<0.9$. The
detector closest to the beam axis is the ITS, which is composed of six
cylindrical layers of silicon detectors, with radial distances from the beam
axis ranging from 3.9 cm to 43.0 cm. The two innermost layers, with average
radii of 3.9 cm and 7.6 cm, are equipped with Silicon Pixel Detectors (SPD).
The two SPD layers, covering the pseudo-rapidity ranges of $|\eta|<2.0$ and
$|\eta|<1.4$ respectively, have 1200 SPD readout chips. The two intermediate
layers are made of Silicon Drift Detectors (SDD), while Silicon Strip
Detectors (SSD) equip the two outermost layers. The high spatial resolution of
the silicon sensors, together with the low material budget (on average 7.7% of
a radiation length for tracks crossing the ITS perpendicularly to the detector
surfaces, i.e. $\eta=0$) and the small distance of the innermost layer from
the beam vacuum tube, allow for the measurement of the track impact parameter
in the transverse plane ($d_{0}$), i.e. the distance of closest approach of
the track to the primary vertex in the plane transverse to the beam direction,
with a resolution better than 75 $\mu$m for transverse momenta $p_{\rm
T}>1\leavevmode\nobreak\ \mathrm{GeV}/c$ [52]. The SPD provides also a
measurement of the multiplicity of charged particles produced in the collision
based on track segments (tracklets) built by associating pairs of hits in the
two SPD layers.

At larger radii ($85<r<247\leavevmode\nobreak\ \mathrm{cm}$), a 510 cm long
cylindrical TPC [53] provides track reconstruction with up to 159 three-
dimensional space points per track, as well as particle identification via the
measurement of the specific energy deposit ${\rm d}E/{\rm d}x$ in the gas. The
charged particle identification capability of the TPC is supplemented by the
TOF [54], which is equipped with Multi-gap Resistive Plate Chambers (MRPCs)
located at radial distances between 377 and 399 cm from the beam axis. The
overall TOF resolution including the uncertainty on the time at which the
collision took place, and the tracking and momentum resolution was about 160
ps for the data-taking period considered in these analyses.

The V0 detector [55], used for triggering and for estimating the multiplicity
of charged particles in the forward rapidity region, consists of two arrays of
32 scintillators each, placed around the beam vacuum tube on either side of
the interaction region at $z=-90$ cm and $z=+340$ cm. The two arrays cover the
pseudo-rapidity intervals $-3.7<\eta<-1.7$ and $2.8<\eta<5.1$, respectively.

The data from proton–proton (pp) collisions at a centre-of-mass energy of
$\sqrt{s}=7\leavevmode\nobreak\ \mathrm{TeV}$ used for the analyses were
recorded in 2010. The data sample consists of about 314 million minimum-bias
(MB) events, corresponding to an integrated luminosity of $\mathcal{L}_{\rm
int}\simeq 5\leavevmode\nobreak\ {\rm nb^{-1}}$. Minimum-bias collisions were
triggered by requiring at least one hit in either of the V0 counters or in the
SPD ($|\eta|<2$), in coincidence with the arrival time of proton bunches from
both directions. This trigger was estimated to be sensitive to about 85% of
the pp inelastic cross section [56].

To enrich the data sample with high multiplicity events, a High Multiplicity
(HM) trigger based on the multiplicity information provided by the outer SPD
layer was also used. Each readout chip of the SPD promptly asserts a digital
pulse, called FastOR bit, on the presence of at least one firing pixel. A
sample of about 6 million events was collected applying a selection on the
minimum number of readout chips having asserted this digital pulse. The
threshold was configured to select the $\approx 0.7\%$ of the events with
highest number of hits in the outer SPD layer. This HM-trigger sample
($\mathcal{L}_{\rm int}\simeq 14\leavevmode\nobreak\ {\rm nb^{-1}}$) provides
an increase of statistics by a factor of about 2.8 relative to the MB trigger
for events with more than 50 tracklets, corresponding to about six times the
average multiplicity.

Only events with interaction vertex reconstructed from tracks with a
coordinate $|z|<10$ cm along the beam line were used for the analysis. In the
considered data samples, the instantaneous luminosity was limited to
0.6–$1.2\times 10^{29}\leavevmode\nobreak\ \mathrm{cm}^{-2}\mathrm{s}^{-1}$ by
displacing the beams in the transverse plane by 3.8 times the RMS of their
transverse profile. In this way, the interaction probability per bunch
crossing was kept in the range 0.04–0.08, with a probability of collision
pile-up below 4% per triggered event. An algorithm to detect multiple
interaction vertices based on SPD track segments, or tracklets, was used to
further reduce the pile-up contribution. An event is rejected from the
analysed data sample if a second interaction vertex is found, which has at
least three associated tracklets, and is separated from the first one by more
than 0.8 cm along $z$. This removes about $48\%$ of the pile-up events. The
remaining pile-up contamination has two contributions: events with pile-up of
collisions with $\Delta z<0.8$ cm and events in which the piled-up collisions
have low-multiplicity (less than three charged particles reconstructed in the
SPD). In the case of pile-up of collisions with small separation along $z$,
the multiplicity estimation may be biased because some of the tracklets of
charged particles from different interactions may be added together. According
to simulations, the number of tracklets results to be biased when the piled-up
vertices are separated along $z$ by less than 0.6 cm. Combining this result
with the shape of the luminous region along the beam direction and the maximum
pile-up rate of $4\%$, the overall probability that two piled-up events induce
a bias in the determination of multiplicity was found to be lower than
$0.3\%$. The fraction of events with biased number of tracklets increases with
increasing multiplicity and it was estimated to be below $2\%$ at the highest
multiplicities considered in this analysis, while the resulting bias on the
measured number of tracklets was found to be negligible in all the
multiplicity classes.

##  3 Multiplicity definition and corrections

In the present analysis, the experimental estimator of the charged-particle
multiplicity is the number of tracklets in the interval $|\eta|<1.0$ ($N_{\rm
tracklets}$). Tracklets are track segments defined by combining the clusters
in the SPD detector with the reconstructed primary vertex position. Tracklets
are required to point to the primary interaction vertex within $\pm 1$ cm in
the transverse plane and $\pm 3$ cm in the $z$ direction [51, 52]. This
multiplicity estimator is the same as was used in previous studies performed
for inclusive ${\rm J}/\psi$ production [40]. Monte Carlo simulations of the
detector response have shown that $N_{\rm tracklets}$ is proportional to the
pseudo-rapidity density of the generated charged primary particles, ${\rm
d}N_{\rm ch}/{\rm d}\eta$, within $2\%$. Primary particles are defined as
prompt particles produced in the collision and all decay products, except
products from weak decays of strange particles. The pseudo-rapidity coverage
of the SPD detector changes with the position of the interaction vertex along
the beam line, $z_{\rm vtx}$, and with time due to the variation of the number
of inactive channels. The detector response over the analysed data taking
period is equalised by means of a data-based correction, which is applied on
an event-by-event basis depending on $z_{\rm vtx}$ and time.

The measurements in the $N_{\rm tracklets}\in$ [1,49] interval are performed
using minimum-bias triggered data, while those in the [50,80] range exploit
the SPD-based HM trigger described above. The HM trigger is fully efficient
for events with $N_{\rm tracklets}>65$. The number of events and the D-meson
candidate invariant mass distributions were corrected for the HM trigger
inefficiency in the $N_{\rm tracklets}\in$ [50,65] range by means of a data-
driven re-weighting procedure. The $N_{\rm tracklets}$-dependent event weights
were defined from the ratio of the measured distributions of the number of
tracklets in the HM and minimum-bias trigger samples. The effect of this
correction on the per-event raw yield was of about 2.5%. The average ${\rm
d}N_{\rm ch}/{\rm d}\eta$ of events in the highest $N_{\rm tracklets}$
interval was determined from the minimum-bias sample.

The analysis results are presented as a function of the relative charged-
particle multiplicity at central rapidity, $({\rm d}N_{\rm ch}/{\rm
d}\eta)^{j}\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$, where
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle=6.01\pm
0.01\,{\rm(stat.)}\,^{+0.20}_{-0.12}\,{\rm(syst.)}$ is measured in inelastic
pp collisions at $\sqrt{s}=7$ TeV with at least one charged particle in
$|\eta|<1.0$ [57]. The relative quantities are used to minimise the
experimental uncertainties and to facilitate the comparison with other
measurements and models. The considered $N_{\rm tracklets}$ intervals and the
corresponding relative charged-particle multiplicity ranges are summarised in
Table 1. The highest $N_{\rm tracklets}$ interval considered in the analysis
extends to a multiplicity of about 9 times the $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ of inelastic pp collisions and the average multiplicity of
events in this $N_{\rm tracklets}$ interval is about six times the
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$. The uncertainty on $({\rm
d}N_{\rm ch}/{\rm d}\eta)^{j}\big{/}\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ is $6\%$; it includes the influence of (i) the determination of
the $N_{\rm tracklets}$ to ${\rm d}N_{\rm ch}/{\rm d}\eta$ proportionality
factor, $2\%$, (ii) its possible deviation from linearity, $5\%$, (iii) and
the uncertainty on the measured $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$.

$N_{\rm tracklets}$ | $({\rm d}N_{\rm ch}/{\rm d}\eta)^{j}$ | $({\rm d}N_{\rm ch}/{\rm d}\eta)^{j}\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ | $N_{\rm events}^{{\rm D^{0}}}/10^{6}$ | $N_{\rm events}^{{\rm J}/\psi}/10^{6}$
---|---|---|---|---
$[1,8]$ |  02.7 | $0.45^{+0.03}_{-0.03}$ | 155.1 | –
$[4,8]$ |  03.8 | $0.63^{+0.04}_{-0.04}$ | – | 89.0
$[9,13]$ |  07.1 | $1.18^{+0.07}_{-0.07}$ |  046.2 | 50.5
$[14,19]$ | 10.7 | $1.78^{+0.10}_{-0.11}$ |  032.0 | 35.5
$[20,30]$ | 15.8 | $2.63^{+0.15}_{-0.17}$ |  024.7 | 28.0
$[31,49]$ | 24.1 | $4.01^{+0.23}_{-0.25}$ |  007.9 |  09.5
$[50,80]$ | 36.7 | $6.11^{+0.35}_{-0.39}$ |  001.7 | –
Table 1: Summary of the multiplicity intervals used for the analyses. The
number of reconstructed tracklets $N_{\rm tracklets}$, the average charged-
particle multiplicity $({\rm d}N_{\rm ch}/{\rm d}\eta)^{j}$, and the relative
charged-particle multiplicity $({\rm d}N_{\rm ch}/{\rm
d}\eta)^{j}\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ are detailed.
The number of events analysed in the various multiplicity ranges for both the
D-meson and ${\rm J}/\psi$ analysis are reported. The number of events for the
$N_{\rm tracklets}$ interval $[50,80]$ are corrected for the high multiplicity
trigger efficiency, as explained in Sec. 3.

The analysis of ${\rm D^{0}}$ production is also carried out as a function of
the charged-particle multiplicity in the regions $-3.7<\eta<-1.7$ and
$2.8<\eta<5.1$, as measured with the charge collected by the V0 scintillator
counters, $N_{\rm V0}$, reported in units of the minimum-ionizing-particle
charge. The motivation for studying the multiplicity dependence of charmed-
meson production also with this estimator is that the event multiplicity and
the D-meson yields are evaluated in different pseudorapidity ranges, reducing
the effects of auto-correlations. In contrast, with the $N_{\rm tracklets}$
estimator also the D-meson decay products and the charged particles produced
in the fragmentation of the same charm quark are included in the multiplicity
evaluation. Monte Carlo simulations demonstrate that $N_{\rm V0}$ is
proportional to the charged-particle multiplicity in that pseudo-rapidity
interval. In this paper we report ${\rm D^{0}}$ relative yields as a function
of the relative uncorrected multiplicity in the V0 detector, $N_{\rm
V0}\big{/}\langle N_{\rm V0}\rangle$ (see Sec. 4.4.1).

##  4 D-meson analysis

###  4.1 D-meson reconstruction

Charm production was studied by reconstructing ${\rm D^{0}}$, ${\rm D^{+}}$
and ${\rm D^{*+}}$ mesons, and their antiparticles, via their hadronic decay
channels ${\rm D}^{0}\to{\rm K}^{-}\pi^{+}$ (with branching ratio, BR, of
$3.88\pm 0.05\%$), ${\rm D}^{+}\to{\rm K}^{-}\pi^{+}\pi^{+}$ (BR of $9.13\pm
0.19\%$), and ${\rm D}^{*+}\to{\rm D}^{0}\pi^{+}$ (BR of $67.7\pm 0.05\%$)
with ${\rm D}^{0}\to{\rm K}^{-}\pi^{+}$ [58]. D-meson candidates were selected
with the same strategy as described in [1]. The selection of ${\rm D^{0}}$ and
${\rm D^{+}}$ decays (weak decays with mean proper decay length $c\tau\approx
123$ and $312\leavevmode\nobreak\ \mathrm{\mu m}$, respectively [58]) was
based on the reconstruction of secondary vertices separated by few hundred
microns from the interaction point. In the case of the ${\rm D^{*+}}$ strong
decay, the decay topology of the produced ${\rm D^{0}}$ was reconstructed.
${\rm D^{0}}$ and ${\rm D^{+}}$ candidates were formed using pairs and
triplets of tracks with the proper charge sign combination, $|\eta|<0.8$,
$p_{\rm T}>0.3\leavevmode\nobreak\ \mathrm{GeV}/c$, at least 70 associated
space points (out of a maximum of 159) with $\chi^{2}/{\rm ndf}<2$ of the
momentum fit in the TPC, and at least two hits (out of 6) in the ITS, of which
at least one had to be in either of the two SPD layers. ${\rm D^{*+}}$
candidates were formed by combining ${\rm D^{0}}$ candidates with tracks with
$p_{\rm T}>80\leavevmode\nobreak\ \mathrm{MeV}/c$ and at least 3 hits in the
ITS, out of which at least one should be in the SPD. The selection of tracks
with $|\eta|<0.8$ limits the D-meson acceptance in rapidity. The acceptance
drops steeply to zero for $|y|>0.5$ at low $p_{\rm T}$ and $|y|>0.8$ at
$p_{\rm T}>5\leavevmode\nobreak\ \mathrm{GeV}/c$. A $p_{\rm T}$-dependent
fiducial acceptance cut, $|y_{\rm D}|<y_{\rm fid}(p_{\rm T})$, was therefore
applied on the D-meson rapidity. The cut value, $y_{\rm fid}(p_{\rm T})$,
increases from 0.5 to 0.8 in the transverse momentum range $0<p_{\rm
T}<5\leavevmode\nobreak\ \mathrm{GeV}/c$ according to a second-order
polynomial function and it takes a constant value of 0.8 for $p_{\rm
T}>5\leavevmode\nobreak\ \mathrm{GeV}/c$. The selection of the decay topology
was based on the displacement of the decay tracks from the interaction vertex,
the separation between the secondary and primary vertices, and the pointing
angle of the reconstructed D-meson momentum and its flight line from the
primary to the secondary vertex. The selections were tuned such that a large
statistical significance of the signal and a selection efficiency as high as
possible were achieved, which resulted in cut values that depend on the
D-meson $p_{\rm T}$ and species [1]. The same selections were used in all the
multiplicity intervals in order to minimise the effect of efficiency
corrections in the ratio of the yields. Pion and kaon identification based on
the TPC and TOF detectors were used to obtain a further reduction of the
background. Cuts in units of resolution (at $\pm 3\,\sigma$) were applied
around the expected mean values of energy deposit ${\rm d}E/{\rm d}x$ and
time-of-flight. Tracks without TOF signal were identified using only the TPC
information. Tracks with incompatible TPC and TOF response were considered as
non-identified and were used in the analysis as both pion and kaon candidates.
Particle identification (PID) was not applied to the pion tracks from the
${\rm D^{*+}}$ decay. This selection guarantees a reduction of the background
by a factor of about 2 to 3 at low $p_{\rm T}$, while preserving about $95\%$
of the signal.

Figure 1:  ${\rm D^{0}}$ and ${\rm D^{+}}$ invariant mass and ${\rm D^{*+}}$
mass difference distributions for selected $p_{\rm T}$ and $N_{\rm tracklets}$
intervals for pp collisions at $\sqrt{s}=7$ TeV with $\mathcal{L}_{\rm
int}=5\leavevmode\nobreak\ {\rm nb^{-1}}$. The ${\rm D^{0}}$ distributions are
shown for $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ (top-panels), the
${\rm D^{+}}$ for $4<p_{\rm T}<8\leavevmode\nobreak\ \mathrm{GeV}/c$ (middle-
panels), and the ${\rm D^{*+}}$ for $8<p_{\rm T}<12\leavevmode\nobreak\
\mathrm{GeV}/c$ (bottom-panels). The $N_{\rm tracklets}\in$ [1,8], [14,19] and
[31,49] intervals are shown in the left, middle and right panels respectively.
The fits to the candidate invariant mass distributions are also shown.

The D-meson raw yields were extracted in each $N_{\rm tracklets}$ and $p_{\rm
T}$ interval by means of a fit to the candidate invariant mass distributions
(mass difference $\Delta M=M({\rm K}\pi\pi)-M({\rm K}\pi)$ for ${\rm
D^{*+}}$). Similarly, the multiplicity-integrated raw yields were also
evaluated for each $p_{\rm T}$ interval. The ${\rm D^{0}}$ and ${\rm D^{+}}$
candidate invariant mass distributions were fitted with a function composed of
a Gaussian for the signal and an exponential term that describes the
background shape. The $\Delta M$ distribution of ${\rm D^{*+}}$ candidates,
which features a narrow peak at $\Delta M\simeq 145.4\leavevmode\nobreak\
\mathrm{MeV}/c^{2}$ [58], was fitted with a Gaussian function for the signal
and a threshold function multiplied by an exponential to model the background
$\left(\sqrt{\Delta M-M_{\pi}}\cdot e^{b(\Delta M-M_{\pi})}\right)$. The
centroids of the Gaussians were found to be compatible with the world-average
masses of the D mesons [58] in all multiplicity and $p_{\rm T}$ intervals. The
widths of the Gaussian functions are independent of multiplicity and increase
with increasing D-meson $p_{\rm T}$, ranging between 10 and 20
$\mathrm{MeV}/c^{2}$ for ${\rm D^{0}}$ and ${\rm D^{+}}$ and between 600 and
900 $\mathrm{keV}/c^{2}$ for ${\rm D^{*+}}$ mesons, consistent with the values
obtained in simulations. In order to reduce the influence of statistical
fluctuations, the raw yields were determined by constraining the D-meson line
shape, its mass to the world-average D-meson mass, and its width to the value
obtained from a fit to the invariant mass distribution in the multiplicity-
integrated sample, where the signal statistical significance is larger. Figure
1 shows the ${\rm D^{0}}$ and ${\rm D^{+}}$ candidate invariant mass
distribution, and ${\rm D^{*+}}$ mass difference distributions, for selected
$p_{\rm T}$ and multiplicity intervals. The extraction of the raw signal
yields (sum of particle and antiparticle) was possible in five $p_{\rm T}$
intervals from $1\leavevmode\nobreak\ \mathrm{GeV}/c$ to
$20\leavevmode\nobreak\ \mathrm{GeV}/c$ for the $N_{\rm tracklets}$ ranges
reported in Table 1. The analysis covering the range $N_{\rm
tracklets}\in[1,49]$ exploited the minimum-bias triggered sample and was
possible for the three D-meson species in three $p_{\rm T}$ intervals in the
range between $2$ and $12\leavevmode\nobreak\ \mathrm{GeV}/c$. In addition,
the ${\rm D^{0}}$ signal was extracted in $N_{\rm tracklets}\in[1,49]$ for
$1<p_{\rm T}<2\leavevmode\nobreak\ \mathrm{GeV}/c$, and the ${\rm D^{*+}}$
signal was determined in three multiplicity intervals for $12<p_{\rm
T}<20\leavevmode\nobreak\ \mathrm{GeV}/c$. The highest multiplicity interval
$[50,80]$ was studied with the high multiplicity triggered sample via ${\rm
D^{0}}$ mesons for $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ and the
three D-meson species for $4<p_{\rm T}<8\leavevmode\nobreak\ \mathrm{GeV}/c$.
The raw yield extraction in the remaining $p_{\rm T}$ and multiplicity
intervals for the different D-meson species was not performed due to the
limited statistics in the analysed data sample and/or the large background.

###  4.2 Corrections

The yields of D mesons were evaluated for each multiplicity and $p_{\rm T}$
interval starting from the raw counts, $N_{\rm raw}$, which were divided by
the reconstruction, topological and PID selection efficiencies for prompt D
mesons, $\varepsilon_{\rm prompt\ D}$, and by the number of events analysed in
the considered multiplicity interval, $N^{j}_{\rm event}$. The results are
reported as the ratio of yields in each multiplicity interval, $({\rm
d}^{2}N^{\rm{\rm D^{0}}}/{\rm d}y{\rm d}p_{\rm T})^{j}$, to the multiplicity-
integrated (average) yield, $\langle{\rm d}^{2}N^{\rm{\rm D^{0}}}/{\rm d}y{\rm
d}p_{\rm T}\rangle$,

$\left(\frac{{\rm d}^{2}N^{\rm{\rm D^{0}}}/{\rm d}y{\rm d}p_{\rm
T}}{\langle{\rm d}^{2}N^{\rm{\rm D^{0}}}/{\rm d}y{\rm d}p_{\rm
T}\rangle}\right)^{j}=\left(\frac{1}{N^{j}_{\rm event}}\frac{N_{\rm raw\ {\rm
D^{0}}}^{j}}{\varepsilon^{j}_{\rm prompt\ {\rm
D^{0}}}}\right)\Bigg{/}\left(\frac{1}{N_{\rm MB\,trigger}\ \varepsilon_{\rm
trigger}}\frac{\langle N_{\rm raw\ {\rm
D^{0}}}\rangle}{\langle\varepsilon_{\rm prompt\ {\rm D^{0}}}\rangle}\right),$
(1)

where the index $j$ identifies the multiplicity interval. The acceptance
correction, defined as the fraction of D mesons within a given rapidity and
$p_{\rm T}$ interval whose decay particles are within the detector coverage,
cancels in this ratio. D-meson raw yields have two components: the prompt
D-meson contribution, and the feed-down contribution originating from B hadron
decays. Equation 1 evaluates the yields of prompt D mesons under the
assumption that the relative contribution to the D-meson raw yield due to the
feed-down from B hadron decays does not depend on the multiplicity of the
event, and is therefore cancelling in the ratio to the multiplicity-integrated
values. This assumption is justified by the measurement of the multiplicity
dependence of the B-hadron yields, via the non-prompt ${\rm J}/\psi$ fraction,
presented in Sec. 5 and by PYTHIA simulations. To evaluate the yields per
inelastic collisions, the number of events used for the normalisation of the
multiplicity-integrated yield has to be corrected for the fraction of
inelastic collisions that are not selected by the minimum-bias trigger $N_{\rm
MB\ trigger}/\varepsilon_{\rm trigger}$, with $\varepsilon_{\rm
trigger}=0.85^{+6\%}_{-3\%}$ [56]. The results are also reported in Tables 3
and 5 without this trigger efficiency correction. It was verified with PYTHIA
6.4.21 [30] Monte Carlo simulations that this minimum-bias trigger is 100%
efficient for D mesons in the kinematic range of this measurement.

The D-meson efficiency corrections were determined with Monte Carlo
simulations using the PYTHIA 6.4.21 event generator [30] with Perugia-0 tune
[59], and the GEANT3 transport code [60]. The detector configuration and the
LHC beam conditions were included, taking into account their evolution with
time during the data taking period. The $\varepsilon^{j}_{\rm prompt\ D}$
depends on the D-meson species and on $p_{\rm T}$. For prompt ${\rm D^{0}}$
mesons it is 3–4% in the $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$
interval and it increases up to 25–35% for $p_{\rm T}>8\leavevmode\nobreak\
\mathrm{GeV}/c$, because less stringent topological selections were used at
high $p_{\rm T}$, where the combinatorial background is smaller. The
efficiency for feed-down D mesons is larger by about 20–30% than for prompt D
mesons. This is due to the fact that feed-down D mesons decay further away
from the interaction vertex and are therefore more efficiently selected by the
topological requirements. The D-meson selection efficiency depends also on the
multiplicity of charged particles produced in the collision, because the
resolution on the position of primary vertex improves with increasing
multiplicity, providing a better resolution of the variables used for the
topological selections. For example, the ${\rm D^{0}}$ selection efficiency in
$2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ increases by about 40% from
the lowest to the highest multiplicity intervals considered in this analysis.

###  4.3 Systematic uncertainties

Several sources of systematic uncertainty that could affect the relative
yields as expressed in Eq. 1 were studied. Only the raw yield extraction and
the feed-down subtraction contribution were found to have an influence on the
relative yields. The influence of the raw signal extraction from the invariant
mass distribution was evaluated by using the raw yields obtained with
different approaches to separate the signal from the combinatorial background.
The contribution to the ${\rm D^{0}}$ line shape of mis-identified K and $\pi$
pairs from ${\rm D^{0}}$ decays, e.g. a ${\rm D^{0}}\to{\rm K}^{-}\,\pi^{+}$
that passes the selection criteria as $\overline{{\rm D^{0}}}\to\pi^{-}\,{\rm
K}^{+}$, was assumed to be the same in all multiplicity intervals and was
neglected in this analysis. Different background fit functions were considered
(exponential, polynomial, linear for ${\rm D^{0}}$ and ${\rm D^{+}}$;
threshold, $(\Delta M-M_{\pi})^{b}$, for ${\rm D^{*+}}$); the centroid and
width of the Gaussians were left as free parameters in the fit instead of
keeping them fixed to the values obtained from the multiplicity-integrated
distribution; the raw yield was also extracted by counting the invariant mass
histogram entries in a $\pm 3\sigma$ interval around the peak after
subtracting the background evaluated by fitting the distribution side bands
(i.e. excluding the $\pm 3\sigma$ interval around the centroid). The
uncertainty was estimated from the stability of the ratio of the raw yields
$N_{\rm raw\ {\rm D^{0}}}^{j}/\langle N_{\rm raw\ {\rm D^{0}}}\rangle$, where
the same raw yield extraction method was used in the multiplicity interval $j$
and for the multiplicity-integrated result. The assigned systematic
uncertainty varies from 3% to 15% depending on the meson species, $p_{\rm T}$
and multiplicity interval.

The efficiency corrections were calculated independently for each multiplicity
interval. The multiplicity distribution of primary charged particles in the
Monte Carlo simulation, $P(N_{\rm ch})$, was tuned to reproduce the measured
charged-particle multiplicity [57]. The efficiencies obtained with different
Monte Carlo setups, that generate different initial multiplicity
distributions, showed a good agreement in all multiplicity intervals. This
effect was not considered as a source of systematic uncertainty.

The D-meson decay tracks can be included or not in (i) the counting of the
number of tracklets, resulting in a shift of the estimated multiplicity, and
in (ii) the determination of the primary vertex position, which leads to a
different resolution on the vertex position and of the geometrical variables
used for the D-meson selection. In the default configuration, the analysis was
done excluding the D-meson decay tracks from the primary vertex determination
and without excluding them from the multiplicity estimation. To check for
possible systematic effects due to the multiplicity determination, the
analysis was repeated excluding the D-meson decay tracks from the multiplicity
estimation, obtaining compatible results. Furthermore, the relative yields
were determined without excluding the D-meson decay tracks from the primary
vertex determination. The influence of such variation is properly reproduced
by Monte Carlo simulations, leading to a null effect on the corrected relative
yields. Therefore this effect was not considered as a source of systematic
uncertainty.

The analysis was repeated for all D-meson species with different sets of
topological selection criteria. It was verified that the corrected relative
D-meson yields as defined in Eq. 1 are not sensitive to this variation. This
confirmed that the systematic uncertainty related to the topological selection
description in the Monte Carlo cancels in the ratio. The influence of the PID
strategy, which is based on the information of TPC and TOF detectors, was
studied by also extracting the D-meson raw yields without PID selection
criteria, which could be done only for D-meson $p_{\rm
T}>2\leavevmode\nobreak\ \mathrm{GeV}/c$. The ratios of the relative raw
yields, $N_{\rm raw\ {\rm D^{0}}}^{j}/\langle N_{\rm raw\ {\rm
D^{0}}}\rangle$, with and without PID selections were found to be compatible
with unity. As a consequence, this effect was not considered as a source of
systematic uncertainty.

As mentioned above, Eq. 1 describes the prompt corrected yields under the
assumption that the fraction of prompt D mesons, $f_{\rm prompt}$, does not
vary with the event multiplicity. To estimate the uncertainty related to this
assumption, the multiplicity integrated $f_{\rm prompt}$ factor was evaluated
with the FONLL B-hadron production cross sections [7], the B $\rightarrow$
D+$X$ decay kinematics from EvtGen [61], and the acceptance, reconstruction
and selection efficiency of D mesons from B decays as described in [1]. The
resulting $f_{\rm prompt}$ values are about 85–95% depending on the D-meson
$p_{\rm T}$ and the applied selection criteria. The uncertainty due to the B
feed-down contribution to the relative yields, $f_{\rm B}=1-f_{\rm prompt}$,
was evaluated assuming a linear increase of the fraction $f_{\rm
B}^{j}/\langle f_{\rm B}\rangle$ from $1/2$ to $2$ from the lowest to the
highest multiplicity interval. The resulting uncertainties vary with the
$p_{\rm T}$ and multiplicity range and are different for the three mesons.
Typical values for intermediate $p_{\rm T}$ at low multiplicity are
${}^{+5}_{-0}\%$, and at high multiplicity ${}^{+0}_{-20}\%$.

###  4.4 Results

The results of the ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ meson
relative yields for each $p_{\rm T}$ interval are presented in Figs. 2 and 3
as a function of the relative charged-particle multiplicity. The relative
yields are presented in the top panels with their statistical (vertical bars)
and systematic (boxes) uncertainties except the uncertainty on the feed-down
fraction, which is drawn separately in the bottom panels in the form of
relative uncertainties. The position of the points on the abscissa is the
average value of the relative charged-particle multiplicity, $({\rm d}N_{\rm
ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$, for every
$N_{\rm tracklets}$ interval. The ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm
D^{*+}}$ meson relative yields are compatible in all $p_{\rm T}$ intervals
within uncertainties.

(a) D meson with $1<p_{\rm T}<2\leavevmode\nobreak\ \mathrm{GeV}/c$

(b) D meson with $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$

Figure 2: ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ meson relative
yields for each $p_{\rm T}$ interval as a function of charged-particle
multiplicity at central rapidity. The relative yields are presented on the top
panels with their statistical (vertical bars) and systematic (boxes)
uncertainties, except for the feed-down fraction uncertainty that is drawn
separately in the bottom panels. ${\rm D^{0}}$ mesons are represented by red
circles, ${\rm D^{+}}$ by green squares, and ${\rm D^{*+}}$ by blue triangles.
The position of the points on the abscissa is the average value of $({\rm
d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$.
For ${\rm D^{+}}$ and ${\rm D^{*+}}$ mesons the points are shifted
horizontally by $1.5\%$ to improve the visibility. The diagonal (dashed) line
is also shown to guide the eye.

(a) D meson with $4<p_{\rm T}<8\leavevmode\nobreak\ \mathrm{GeV}/c$

(b) D meson with $8<p_{\rm T}<12\leavevmode\nobreak\ \mathrm{GeV}/c$

(c) D meson with $12<p_{\rm T}<20\leavevmode\nobreak\ \mathrm{GeV}/c$

Figure 3: ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ meson relative
yields for each $p_{\rm T}$ interval as a function of charged-particle
multiplicity at central rapidity. The relative yields are presented on the top
panels with their statistical (vertical bars) and systematic (boxes)
uncertainties, except for the feed-down fraction uncertainty that is drawn
separately in the bottom panels. ${\rm D^{0}}$ mesons are represented by red
circles, ${\rm D^{+}}$ by green squares, and ${\rm D^{*+}}$ by blue triangles.
The position of the points on the abscissa is the average value of $({\rm
d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$.
For ${\rm D^{+}}$ and ${\rm D^{*+}}$ mesons the points are shifted
horizontally by $1.5\%$ to improve the visibility. The diagonal (dashed) line
is also shown to guide the eye.

The average of ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ relative yields
was computed for each $p_{\rm T}$ interval using as weights the inverse square
of their relative statistical uncertainties. The yield extraction uncertainty
was considered as uncorrelated systematic uncertainty. The feed-down fraction
systematic uncertainty was treated as a correlated systematic uncertainty. The
average of the D-meson relative yields for all $p_{\rm T}$ intervals is
summarised in Tables 3 and 4, and presented in Fig. 4(a). The relative D-meson
yields increase with the charged-particle multiplicity by about a factor of 15
in the range between 0.5 and six times $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$. Figure 4(b) shows the ratios of the average of the D-meson
relative yields in various $p_{\rm T}$ intervals with respect to the $2<p_{\rm
T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ interval values. The yield
enhancement is independent of transverse momentum within the uncertainties of
the measurement.

(a) $p_{\rm T}$ dependence.

(b) Ratios of $p_{\rm T}$ intervals vs the $2<p_{\rm T}<4\leavevmode\nobreak\
\mathrm{GeV}/c$.

Figure 4: Average of ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ relative
yields as a function of the relative charged-particle multiplicity at central
rapidity. (a) Average of D-meson relative yields in $p_{\rm T}$ intervals. (b)
Ratio of the average relative yields in all $p_{\rm T}$ intervals with respect
to that of the $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ interval.
The results are presented in the top panels with their statistical (vertical
bars) and systematic (boxes) uncertainties, except for the feed-down fraction
uncertainty that is drawn separately in the bottom panels. The position of the
points on the abscissa is the average value of $({\rm d}N_{\rm ch}/{\rm
d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$. For some $p_{\rm
T}$ intervals the points are shifted horizontally by $1.5\%$ to improve the
visibility. The dashed lines are also shown to guide the eye, a diagonal on
(a) and a constant on (b).

####  4.4.1 Studies with the charged-particle multiplicity at forward rapidity

In the analysis described above, D-meson yields were measured in the same
rapidity interval as the charged-particle multiplicity. This could lead to a
bias if the particles produced in the charm-quark fragmentation and in the
D-meson decay would amount to a large fraction of the measured charged
particles. In order to study this possible bias, the measurement of the ${\rm
D^{0}}$ yields at central rapidity was also performed as a function of the
relative charged-particle multiplicity at forward-rapidity. The charge
collected by the V0 scintillator counters, covering $-3.7<\eta<-1.7$ and
$2.8<\eta<5.1$, was used as multiplicity estimator in this case. The
multiplicity value $N_{\rm V0}$ was evaluated by dividing the collected charge
by the expected average minimum-ionizing-particle charge. The ${\rm D^{0}}$
yields were evaluated in intervals of $N_{\rm V0}$, and corrected as
previously described and summarised in Eq. 1. The relative yields of ${\rm
D^{0}}$ mesons are presented in Fig. 5 as a function of the relative mean
multiplicity measured with the V0 counters, $N_{\rm V0}\big{/}\langle N_{\rm
V0}\rangle$. The statistical (systematic) uncertainties are represented by the
vertical bars (empty boxes). The systematic uncertainties due to the raw yield
extraction and the B feed-down contribution were determined as explained in
Sec. 4.3. The uncertainty due to the unknown feed-down fraction evolution with
the charged-particle multiplicity is drawn separately in the bottom panels.
The points are located on the $x$-axis at the average value of the relative
mean multiplicity, $N_{\rm V0}\big{/}\langle N_{\rm V0}\rangle$. The
uncertainty on the mean multiplicity values, $N_{\rm V0}$, was determined by
comparing the mean and median values of the distributions. It was found to be
below 3% for each multiplicity interval, and about $24\%$ for the multiplicity
integrated value. The uncertainty on $N_{\rm V0}\big{/}\langle N_{\rm
V0}\rangle$ is not displayed on this figure. These results are also summarised
in Tables 5 and 6. The ${\rm D^{0}}$ relative yields increase with the
relative uncorrected multiplicity at forward rapidity, as measured with the V0
detector. The results in the $2<p_{\rm T}<4\leavevmode\nobreak\
\mathrm{GeV}/c$ and $4<p_{\rm T}<8\leavevmode\nobreak\ \mathrm{GeV}/c$
intervals are compatible within uncertainties. The results with the V0
multiplicity estimator indicate that the increase of the D-meson yield with
the event multiplicity observed with the mid-rapidity estimator is not related
to the fact that charmed mesons, originating from the fragmentation of charm
quarks produced in hard partonic scattering processes, and the charged
particle multiplicity are measured in the same pseudo-rapidity range. A
qualitatively similar increasing trend of D-meson yield with multiplicity is
indeed observed also when an $\eta$ gap is introduced between the regions
where the D-mesons and the multiplicity are measured.

Figure 5: ${\rm D^{0}}$ meson relative yields at $|y|<0.5$ for two $p_{\rm T}$
intervals as a function of the relative charged-particle multiplicity, $N_{\rm
V0}$, measured at $-3.7<\eta<-1.7$ and $2.8<\eta<5.1$. The relative yields are
presented on the top panels with their statistical (vertical bars) and
systematic (boxes) uncertainties, except the uncertainty on the feed-down
fraction which is drawn separately in the bottom panels. The position of the
points on the abscissa is at the average value of $N_{\rm V0}\big{/}\langle
N_{\rm V0}\rangle$, shifted by $1.5\%$ to improve the visibility. The diagonal
(dashed) line is also shown to guide the eye.

##  5 Non-prompt ${\rm J}/\psi$ analysis

###  5.1 Non-prompt ${\rm J}/\psi$ reconstruction

The fraction of non-prompt ${\rm J}/\psi$ in the inclusive ${\rm J}/\psi$
yields, $f_{\rm B}$, was measured as a function of the charged-particle
multiplicity by studying displaced ${\rm J}/\psi$ mesons that decay into
electron pairs in the rapidity range $|y|<0.9$. This measurement, combined
with the inclusive ${\rm J}/\psi$ relative yield [40], provides the
multiplicity dependence of the production of beauty hadrons. ${\rm J}/\psi$
candidates were formed by combining pairs of opposite-sign electron tracks.
The tracks were required to have $p_{\rm T}>1\leavevmode\nobreak\
\mathrm{GeV}/c$, at least 70 (out of a maximum of 159) associated space points
in the TPC with a $\chi^{2}/{\rm ndf}$ of the momentum fit lower than 2, and
to point back to the primary interaction vertex within $1$ cm in the
transverse plane. The tracks were also required to have at least one
associated hit in the SPD detector, with the constraint that one of the two
tracks should have a hit in the first SPD layer. Electron identification was
based only on the TPC information. A selection of $\pm 3\sigma$ around the
expected mean values of the specific energy deposit ${\rm d}E/{\rm d}x$ for
electrons was used. To further reduce the background, a $\pm 3.5\sigma$ ($\pm
3\sigma$) exclusion band around the expected mean specific energy deposit for
pions (protons) was also applied. In order to reduce the combinatorial
background, electron candidates compatible, together with a positron
candidate, with being products of $\gamma$-conversions (invariant mass below
$100\leavevmode\nobreak\ \mathrm{MeV}/c^{2}$) were removed.

The measurement of $f_{\rm B}$ is based on a statistical discrimination of
${\rm J}/\psi$ mesons produced at a secondary vertex displaced from the
primary pp collision vertex. The signed projection of the ${\rm J}/\psi$
flight distance onto its transverse momentum vector, $\vec{p_{\rm T}}$, was
constructed as $L_{\rm xy}=\left(\vec{L}\cdot\vec{p_{\rm T}}\right)/p_{\rm
T}$, where $\vec{L}$ is the vector from the primary vertex to the ${\rm
J}/\psi$ decay vertex. The pseudo-proper decay length $x=\left(c\cdot L_{\rm
xy}\cdot m\right)\big{/}p_{\rm T}$ was calculated from the observed decay
length using the world-average ${\rm J}/\psi$ mass $m({\rm
J}/\psi)=3096.916\pm 0.011\leavevmode\nobreak\ \mathrm{MeV}/c^{2}$ [58]. The
fraction of non-prompt ${\rm J}/\psi$ can be determined from a 2-dimensional
un-binned log-likelihood fit to $x$ and the unlike-sign di-electron invariant
mass distributions. The fit procedure and the functions used to describe the
invariant mass and the pseudo-proper decay length distributions were
introduced in [10].

The fraction of non-prompt ${\rm J}/\psi$ as a function of the relative
charged-particle multiplicity was determined for $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ in five multiplicity intervals in
the $N_{\rm tracklets}$ range $[4,49]$. The $N_{\rm tracklets}\in[1,3]$ range
was excluded from this analysis due to the poor pseudo-proper decay length
resolution, $R(x)$, and the presence of a bias in the determination of $x$ in
the case of non-prompt candidates. The resolution of the pseudo-proper decay
length is determined with Monte Carlo simulations evaluating the RMS of the
$x$ distributions of reconstructed promptly produced ${\rm J}/\psi$ mesons.
The event primary vertex can be computed with or without removing the decay
tracks of the ${\rm J}/\psi$ candidates. The removal of the decay tracks
causes a degradation of the resolution on $x$, especially in the low-
multiplicity intervals, as a consequence of the lower precision in the
determination of the primary vertex with a reduced number of tracks. For
simulated events with non-prompt ${\rm J}/\psi$, the removal of the decay
tracks also results in a shift of the primary vertex position away from the
secondary decay vertex of the beauty hadrons, which is reflected in a
systematic shift of the mean of the $x$ distribution. However, one should
consider that beauty quarks are always produced in pairs: the two decay tracks
from the non-prompt-${\rm J}/\psi$, when included, pull the primary vertex
towards the beauty hadron decay vertex, but the charged tracks from the decay
of the second beauty quark, which enter in the barrel acceptance, pull the
primary vertex in the opposite direction. The shift is larger in the lowest
multiplicity bin where it reaches about 35 $\mu$m. This bias is reduced when
the ${\rm J}/\psi$ decay tracks are kept in the evaluation of the primary
vertex.

Figure 6:  ${\rm J}/\psi$ invariant mass and pseudo-proper decay length
distributions in several multiplicity intervals with superimposed the
likelihood fit results. The contributions of the signal, the background and
their sum are represented with dashed, dot-dashed and full lines,
respectively. In addition, the pseudo-proper decay length figures include the
prompt and non-prompt contributions to the inclusive yields with dotted and
long-dashed lines.

The effect of the bias, estimated with Monte Carlo simulations, is a reduction
of the measured $f_{\rm B}$111 This shift would be greater than 50 $\mu$m in
the $N_{\rm tracklets}$ interval $[1,3]$, leading to a large bias on the
extracted $f_{\rm B}$ value (up to 35%). The correction for this bias would
introduce a large systematic uncertainty.  by about 20% for events with
$N_{\rm tracklets}$ = 4, and it becomes negligible for $N_{\rm tracklets}>10$.
Therefore, the primary vertex was computed considering all reconstructed
tracks. To correct for the remaining bias, a modification in the resolution
function, $R(x)$, used to describe the non-prompt ${\rm J}/\psi$ in the
likelihood fit function was introduced, which depends on $N_{\rm tracklets}$.
In particular, the shape of the resolution function was adjusted to obtain a
good matching between the function used to describe the non-prompt ${\rm
J}/\psi$ in the likelihood fit (a convolution of a template of the $x$
distribution of ${\rm J}/\psi$ from beauty hadron decays with the resolution
function [10]) and the pseudo-proper decay length distribution of
reconstructed secondary ${\rm J}/\psi$ from Monte Carlo simulations.

Figure 6 presents the invariant mass and pseudo-proper decay length
distributions for $p_{\rm T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ for each
multiplicity interval together with a projection of the result of the log-
likelihood fit.

###  5.2 Corrections

For all multiplicity intervals, the measured fraction of non-prompt ${\rm
J}/\psi$, $f_{\rm B}^{\prime}$, was corrected using the acceptance and
reconstruction efficiency of prompt, $\langle Acc\times\varepsilon\rangle_{\rm
prompt}$, and non-prompt ${\rm J}/\psi$, $\langle
Acc\times\varepsilon\rangle_{\rm B}$, as

$f_{\rm B}=\left(1+\frac{1-f_{\rm B}^{\prime}}{f_{\rm
B}^{\prime}}\cdot\frac{\langle Acc\times\varepsilon\rangle_{\rm B}}{\langle
Acc\times\varepsilon\rangle_{\rm prompt}}\right)^{-1}.$ (2)

Here all terms refer to non-prompt ${\rm J}/\psi$ with $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$. The corrections for acceptance and
efficiency were computed using Monte Carlo simulations using the GEANT3
transport code [60]. Prompt ${\rm J}/\psi$ were generated with a $p_{\rm T}$
distribution extrapolated from CDF measurements [16] and a $y$ distribution
parameterised with the Colour Evaporation Model (CEM) [62, 63]. Beauty hadrons
were generated using the PYTHIA 6.4.21 event generator [30] with Perugia-0
tune [64]. The acceptance times efficiency values for prompt and non-prompt
${\rm J}/\psi$ have a minimum of 8% at $p_{\rm T}=2\leavevmode\nobreak\
\mathrm{GeV}/c$ and a broad maximum of 12% at $p_{\rm T}=7\leavevmode\nobreak\
\mathrm{GeV}/c$ [65]. The relative difference in efficiency between prompt and
non-prompt ${\rm J}/\psi$ is only about 3%. The ratio $\langle
Acc\times\varepsilon\rangle_{\rm B}/\langle Acc\times\varepsilon\rangle_{\rm
prompt}$ is assumed to be independent of multiplicity. The uncertainty related
to this assumption is discussed in the next section.

The measured non-prompt ${\rm J}/\psi$ fractions were extrapolated from
$p_{\rm T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ down to $p_{\rm T}=0$ using

$f_{\rm B}^{\rm extr}(p_{\rm T}>0)=\alpha^{\rm extr}\cdot f_{\rm B}(p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c);\qquad\alpha^{\rm
extr}=\frac{f_{\rm B}^{\rm model}(p_{\rm T}>0)}{f_{\rm B}^{\rm model}(p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c)},$ (3)

where $f_{\rm B}^{\rm model}$ represents a functional form modelled on
existing data. It was calculated as the ratio of the differential cross
section of non-prompt ${\rm J}/\psi$, as obtained with FONLL calculations [7],
to that of inclusive ${\rm J}/\psi$, parameterised by the phenomenological
function defined in [66]:

$f_{\rm B}^{\rm model}(p_{\rm T})=\frac{{\rm d}^{2}\sigma^{\rm FONLL}_{{\rm
J}/\psi\leftarrow h_{B}}}{{\rm d}y{\rm d}p_{\rm T}}\,\Big{/}\,\frac{{\rm
d}^{2}\sigma_{{\rm J}/\psi}^{\rm phenom}}{{\rm d}y{\rm d}p_{\rm T}}.$ (4)

A combined fit to the existing results of $f_{\rm B}$ in pp collisions at 7
TeV [10, 67, 13, 68] in the rapidity bin closest to central rapidity was
performed to determine the parameters of the phenomenological
parameterisation. The extrapolation factor obtained is $\alpha^{\rm
extr}=0.99^{+0.01}_{-0.03}$. Its uncertainties were determined by repeating
the fit by (i) excluding the LHCb data points at forward rapidities, and (ii)
using for the non-prompt ${\rm J}/\psi$ cross section the upper and lower
uncertainty bands of the FONLL predictions, obtained by varying the
factorisation and renormalisation scales, instead of the central values. The
uncertainties were determined by the maximum and minimum $\alpha^{\rm extr}$
values obtained from these fit variations. The $f_{\rm B}$ fractions in all
multiplicity intervals were extrapolated using the same $\alpha^{\rm extr}$
value, evaluated from the fit of the multiplicity integrated measurements.

###  5.3 Systematic uncertainties

The systematic uncertainty introduced by the experimental resolution on the
primary vertex position was evaluated by repeating the fitting procedure in
two alternative ways: (i) the primary vertex was evaluated without removing
the decay tracks of the ${\rm J}/\psi$ candidates. The fit was performed using
the standard resolution function for non-prompt ${\rm J}/\psi$, that does not
depend on multiplicity, but the $x$ distribution of the non-prompt ${\rm
J}/\psi$ was shifted by a multiplicity-dependent value, which was determined
by the Monte Carlo simulation. (ii) The event primary vertex was computed
after removing the decay tracks of the ${\rm J}/\psi$ candidates and the fit
was performed using the corresponding degraded resolution function $R(x)$ and
without any shift. The resulting uncertainties decrease with increasing
multiplicity, ranging from 19% in the lowest multiplicity interval to 3% at
the highest multiplicities.

The uncertainty related to the extrapolation of $f_{\rm B}$ from $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ to $p_{\rm T}>0$ was estimated with
the method discussed above and it is about 3%. This uncertainty was assumed to
be uncorrelated among the multiplicity intervals.

The resolution function used in the fits is based on Monte Carlo simulations,
which might introduce systematic effects. These were estimated by repeating
the log-likelihood fits modifying the resolution function, $R(x)$, according
to $\left(1/(1+\delta)\right)\cdot R\left(x/(1+\delta)\right)$, where $\delta$
is the relative variation of the RMS of the resolution function, and it was
varied from $-0.1$ to $+0.1$ to take into account the uncertainties in the
Monte Carlo description. The systematic uncertainty due to the resolution
function increases with multiplicity from $8\%$ to $20\%$.

The $p_{\rm T}$ distribution of the signal candidates (prompt and non-prompt
${\rm J}/\psi$) could depend on the event multiplicity which could affect the
shape of the resolution function which depends on the ${\rm J}/\psi$ $p_{\rm
T}$. The average $p_{\rm T}$ of the signal candidates was estimated from data
in each multiplicity interval and found to be constant as a function of event
multiplicity within statistical uncertainties about $\pm 10\%$. The influence
of a $\langle p_{\rm T}\rangle$ variation on the resolution function was
determined using Monte Carlo simulations: the $p_{\rm T}$ distribution was
changed, considering softer or harder $p_{\rm T}$ distributions, in order to
obtain a $\pm 10\%$ variation of the $\langle p_{\rm T}\rangle$. The
corresponding variations obtained for the RMS of the resolution function are
$+7\%$ and $-8.5\%$ for the softer and harder $p_{\rm T}$ distribution,
respectively. The latter variations are within those quoted for the resolution
function ($\pm$10%), therefore no additional uncertainty was included.

The acceptance times efficiency values of prompt and non-prompt ${\rm J}/\psi$
reconstructed for $p_{\rm T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ are of
the order of 10% and differ by 3%. The influence of the $p_{\rm T}$ shape
assumed in the simulation on the ratio $\langle
Acc\times\varepsilon\rangle_{\rm B}/\langle Acc\times\varepsilon\rangle_{\rm
prompt}$ was evaluated by varying the average $p_{\rm T}$ of the simulated
${\rm J}/\psi$ distributions within $\pm$50%. A $1\%$ variation in the
acceptance was obtained both for prompt and non-prompt ${\rm J}/\psi$. The
corresponding variation obtained on $f_{\rm B}$ through the Eq. 2 is about 1%.

The pseudo-proper decay length shape of the combinatorial background was
determined by a fit to the $x$ distribution of the candidates in the sidebands
of the invariant mass [10]. By varying the fit parameters within their errors
an envelope of distributions was obtained, whose extremes were used in the
likelihood fit to estimate the systematic uncertainty. It increases slightly
with multiplicity, ranging from $1\%$ to $5\%$.

The uncertainty on the background invariant mass shape, which was determined
by fits to the invariant mass distributions of opposite-sign candidates in
each multiplicity bin, was evaluated by using like-sign distributions instead,
adopting the same procedure as described in [10]. The systematic uncertainty
is about $7\%$, independent of the charged-particle multiplicity.

The shape of the $x$ distribution of ${\rm J}/\psi$ from b-hadrons was
evaluated using PYTHIA 6.4.21 [30]. The systematic uncertainty on its shape
was computed by (i) changing the b-hadron decay kinematic, using EvtGen [61]
instead of PYTHA 6.4.21 or (ii) by assuming a harder and a softer b-hadron
$p_{\rm T}$ distribution, resulting in a $\langle p_{\rm T}\rangle$ variation
of about $\pm 15\%$. The resulting systematic uncertainty is about $3\%$,
constant with multiplicity.

The signal invariant mass shape was fixed from the Monte Carlo simulation
which includes the detector resolution effects and the radiative decays using
the EvtGen [61] package. The effect on the invariant mass signal shape due to
the uncertainty on the detector material was studied with dedicated Monte
Carlo simulations, where the detector material budget was varied by $\pm 6\%$
with respect to the nominal values [69, 70]. The resulting systematic
uncertainty on $f_{\rm B}$ is $3\%$ in the lowest event multiplicity interval
and $5\%$ in the highest one.

The systematic uncertainties on the pseudo-proper decay length of the
combinatorial background, on the $p_{\rm T}$-extrapolation uncertainty
$\alpha^{\rm extr}$ and on the invariant mass shape of background are found
or, in the case of $\alpha^{\rm extr}$, assumed to be uncorrelated among
multiplicity intervals. The remaining systematic uncertainties are (fully or
partially) correlated in different multiplicity intervals.

###  5.4 Results

The relative yield of ${\rm J}/\psi$ from beauty hadron decays as a function
of the charged-particle multiplicity was evaluated from the inclusive ${\rm
J}/\psi$ yield and the fraction of non-prompt ${\rm J}/\psi$ per multiplicity
interval:

$\frac{{\rm d}N_{{\rm J}/\psi}^{\rm non-prompt}/{\rm d}y}{\left\langle{\rm
d}N_{{\rm J}/\psi}^{\rm non-prompt}/{\rm d}y\right\rangle}=\frac{{\rm
d}N_{{\rm J}/\psi}/{\rm d}y}{\left\langle{\rm d}N_{{\rm J}/\psi}/{\rm
d}y\right\rangle}\cdot\frac{f_{\rm B}}{\left\langle f_{\rm B}\right\rangle}.$
(5)

$f_{\rm B}$ is the fraction of non-prompt ${\rm J}/\psi$ in each multiplicity
interval, $\langle f_{\rm B}\rangle$ is the fraction in the multiplicity
integrated sample [10], and $({\rm d}N_{{\rm J}/\psi}/{\rm
d}y)\big{/}\langle{\rm d}N_{{\rm J}/\psi}/{\rm d}y\rangle$ is the inclusive
${\rm J}/\psi$ relative yield measured for $p_{\rm T}>0$ in each multiplicity
interval normalized to its value in inelastic pp collisions [40]. All these
quantities were measured using the same data sample and the statistical
correlations were taken into account. In the first charged-particle
multiplicity class $N_{\rm tracklets}\in[4,8]$, which is used for the non-
prompt ${\rm J}/\psi$ analysis presented here, the relative yield of inclusive
${\rm J}/\psi$ normalized to the inelastic cross section is $({\rm d}N_{{\rm
J}/\psi}/{\rm d}y)\big{/}\langle{\rm d}N_{{\rm J}/\psi}/{\rm
d}y\rangle=0.41\pm 0.07\,{\rm(stat)}\pm 0.01\,{\rm(syst)}$. The values of
$f_{\rm B}$ extrapolated to $p_{\rm T}>0$ were used in Eq. 5, providing the
non-prompt ${\rm J}/\psi$ relative yields for $p_{\rm T}>0$. The relative
yields of inclusive ${\rm J}/\psi$ were also recomputed for $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$ and no difference was observed with
respect to those for $p_{\rm T}>0$ within the uncertainties.

The results for the fraction of non-prompt ${\rm J}/\psi$ for both $p_{\rm
T}>0$ and $p_{\rm T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$, the relative
yields of prompt and non-prompt ${\rm J}/\psi$ in each multiplicity bin for
$p_{\rm T}>0$ are summarized in Tables 7 and 8 and shown in Fig. 7.

Figure 7: Non-prompt ${\rm J}/\psi$ fraction as a function of the relative
charged-particle multiplicity at central rapidity for $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$. The vertical bars represent the
statistical uncertainties, while the empty boxes stand for the systematic
uncertainties. The width and the height of these empty boxes indicate the
measurement uncertainty on the horizontal and vertical axis respectively. The
dashed line shows the value of $f_{\rm B}$ measured in the same $p_{\rm T}$
range and integrated over multiplicity [10]. The shaded area represents the
statistical and systematic uncertainties on the multiplicity-integrated result
added in quadrature.

##  6 Comparison of charm and beauty production

Figure 8(a) presents prompt D meson and inclusive ${\rm J}/\psi$ results to
compare open and hidden charm production. The average prompt D-meson results
are shown in the $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ interval
with the $p_{\rm T}$-integrated inclusive ${\rm J}/\psi$ measurement222 After
the inclusive ${\rm J}/\psi$ measurement was published in reference [40],
there was an improvement of the ALICE measurement of the inelastic cross
section in pp collisions at $\sqrt{s}=7$ TeV. The improved evaluation of the
inelastic cross section does not rely on Monte Carlo, hence the systematic
uncertainty is larger [56]. To allow a proper comparison with the results
reported here, we updated the published inclusive ${\rm J}/\psi$ measurement
by the corresponding change of the trigger efficiency for inelastic collisions
0.864/0.85. The normalisation uncertainties were also changed from $1.5\%$ to
${}^{+6}_{-3}\%$.  at central and forward-rapidity by the ALICE experiment
[40]. The results for prompt ${\rm J}/\psi$ at central rapidity from this
paper ($p_{\rm T}>0$) and for prompt D mesons ($2<p_{\rm
T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$) are compared in Fig. 8(b). A similar
increase of the relative yield with the charged-particle multiplicity is
observed for open and hidden charm production both at central and forward
rapidities.

Figure 8(c) superimposes the open charm and beauty production measurements
reported in this paper showing the average prompt D-meson results in the
$2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ interval and the $p_{\rm
T}$-integrated non-prompt ${\rm J}/\psi$ measurement at central rapidity. The
results are compatible within the measurement uncertainties.

(a) D meson with $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ and
inclusive ${\rm J}/\psi$

(b) D meson with $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ and prompt
${\rm J}/\psi$

(c) D meson with $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$ and non-
prompt ${\rm J}/\psi$

Figure 8: Average D meson and ${\rm J}/\psi$ relative yields as a function of
the relative charged-particle multiplicity at central rapidity. D-meson yields
are shown for $2<p_{\rm T}<4\leavevmode\nobreak\ \mathrm{GeV}/c$, while ${\rm
J}/\psi$ yields are for $p_{\rm T}>0$. (a) Inclusive ${\rm J}/\psi$ results
for $|y|<0.9$ are represented by empty black circles [40], inclusive ${\rm
J}/\psi$ results for $2.5<y<4.0$ by black filled symbols [40], and prompt D
mesons by red filled circles. (b) Prompt ${\rm J}/\psi$ results for $|y|<0.9$
are represented by green filled crosses, and prompt D mesons by red filled
circles. (c) Non-prompt ${\rm J}/\psi$ results for $|y|<0.9$ are represented
by blue filled squares, and prompt D mesons by red filled circles. The
relative yields are presented on the top panels with their statistical
(vertical bars) and systematic (boxes) uncertainties except the uncertainty on
the feed-down fraction for D mesons, which is drawn separately on the bottom
panels. The points are located on the x-axis at the average value of $({\rm
d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$.
The diagonal (dashed) line is drawn to guide the eye.

Open charm, open beauty and hidden charm hadron relative yields present a
similar increase with charged-particle multiplicity. The comparison of open
and hidden heavy flavour production suggests that this behaviour is most
likely related to the ${\rm c}\bar{\rm c}$ and ${\rm b}\bar{\rm b}$ production
processes, and is not significantly influenced by hadronisation. The
enhancement of the heavy-flavour relative yields with the charged-particle
multiplicity is qualitatively consistent with the calculations of the
contribution from MPIs to particle production at LHC energies [27, 28, 29]. It
could also be explained by the naive picture that processes with large
momentum exchange might be associated to a larger amount of gluon-radiation at
LHC energies, but no specific model implementation of this effect exists yet.
The comparison of the results with model calculations is shown in the next
section.

##  7 Comparison to theoretical calculations

Figures 4, 7 and 8 evidence a correlation between heavy-flavour and charged-
particle multiplicities. Heavy-flavour production is dominated by hard
processes, while charged-particle yields are associated to the soft momentum
scale processes. It is then interesting to compare our results with
calculations of event generators, designed to be as close as possible to real
events in their description of the hard and soft components. Even though
several event generators are available, few of them include heavy quarks in a
consistent way. One of these is PYTHIA [30, 31], which will be discussed in
more detail in Sec. 7.1. In Sec. 7.2 a comparison to PYTHIA 8 [31], to the
EPOS 3 [71, 72] event generator results and to a percolation model [41, 73]
calculation are presented.

###  7.1 PYTHIA 8 simulations

PYTHIA 8 [31] is the C++ successor of PYTHIA 6 [30]. One of the major
improvements in PYTHIA 8 with respect to PYTHIA 6 concerns the treatment of
the MPI scenario, where the c and b quarks can be involved in MPI $2\to 2$
hard subprocesses. This model improvement is fundamental for an understanding
of heavy-flavour production as a function of multiplicity, as MPI can
contribute to the observed phenomena. Here PYTHIA 8.157 simulations with the
”SoftQCD” process selection including colour reconnection and diffractive
processes 333 In this simulation, single- and double-diffractive processes
contribute to about $20\%$ of the cross section.  are discussed, which will be
referred to as PYTHIA 8.

Heavy-flavour production in PYTHIA 8 proceeds via four main mechanisms: (i)
The first (hardest) hard process, where the initial c/b quarks originate from
the first $2\to 2$ hard process, mostly by gluon fusion ($gg\to{\rm c}\bar{\rm
c}$) or involving a c/b sea-quark (e.g. ${\rm c}{\rm u}\to{\rm c}{\rm u}$).
(ii) The subsequent hard processes in MPI, produced via the same mechanisms as
the first hard process but in consecutive interactions, that we refer to as
hard process in MPI. Each produced gluon has a probability to split into a
${\rm c}\bar{\rm c}$ or ${\rm b}\bar{\rm b}$ pair contributing to heavy-
flavour production. When the initial gluon originates from a hard process,
either the first one or a subsequent process (in MPI), we refer to this
process as (iii) gluon splitting from hard process. When the initial gluon
originates from initial or final state radiation, we refer to this process as
(iv) ISR/FSR.

The contribution of the various production processes to the total D- and
B-meson production in PYTHIA 8 for pp collisions at $\sqrt{s}=7$ TeV is
summarised in Table 2. In the following, D mesons refer to the average of
${\rm D^{0}}$, ${\rm D^{+}}$, and ${\rm D^{*+}}$, while B mesons represent the
average of $\rm B^{0}$, $\rm B^{+}$, and $\rm B^{*+}$. Initial and final state
radiation are the main contributors to open heavy-flavour production in PYTHIA
8, corresponding to $\sim 62\%$ for D mesons and $\sim 40\%$ for B mesons. MPI
correspond to $\sim 21\%$ ($\sim 24\%$) of the D-meson (B-meson) production,
while the first hard process is contributing $\sim 11\%$ for D mesons and
$\sim 36\%$ for B mesons. It should be noted that in PYTHIA 8 the largest
contribution to hard processes comes from c sea-quarks and not from gluon
fusion [74].

Origin of c and b quark content | D mesons | B mesons
---|---|---
First hard process |  | 11% |  | 36% |
| gluon fusion |  | 2% |  | 15%
| c/b sea |  | 9% |  | 21%
Hard process in MPI |  | 21% |  | 24% |
Gluon splitting from hard process | 6% |  | included in ISR/FSR |
ISR/FSR |  | 62% |  | 40% |
Remnant |  | $<0.2\%$ |  | $<0.4\%$ |
Table 2:  Contribution of the different production processes to the total D-
and B-meson production in PYTHIA 8.157 [31] for pp collisions at $\sqrt{s}=7$
TeV.  Figure 9:  D- and B-meson relative yield as a function of the relative
charged-particle multiplicity at central rapidity calculated with the PYTHIA
8.157 event generator [31]. The different c and b quark production processes
are separated on the top panels: first hard process, hard process in multiple
interactions (MPI), gluon splitting from hard processes and initial/final
state radiation (ISR/FSR). The bottom panels present the multiplicity
dependence in several $p_{\rm T}$ intervals for prompt D-meson production, on
the left for all contributions and on the right for first hard process only.
The coloured lines represent the calculation distributions, whereas the shaded
bands represent their statistical uncertainties at given values of $({\rm
d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$.
The diagonal (dashed) line is drawn to guide the eye.

Figure 9 (top panels) shows the D and B-meson production as a function of the
relative charged-particle multiplicity calculated with PYTHIA 8. The
distributions for the main production processes are shown independently. The
top-left panel presents results for D mesons, revealing an increasing trend of
the relative yields as a function of the relative charged-particle
multiplicity for MPI, the gluon splitting from hard processes, and the ISR/FSR
contributions. This is consistent with the fact that in PYTHIA 8 MPI and
ISR/FSR contribute both to the total multiplicity and to heavy-flavour
production. The first hard process contribution instead shows a weaker
dependence on the multiplicity: a slight increase is observed at low
multiplicities (${\rm d}N_{\rm ch}/{\rm d}\eta\big{/}\langle{\rm d}N_{\rm
ch}/{\rm d}\eta\rangle<1$) followed by a saturation. The picture for B mesons,
on the top-right panel, presents similar features as that of D mesons. The
trend for the first hard process contribution shows an increase at low
multiplicities and then saturates. The relative charged-particle multiplicity
at which the plateau sets in is higher for B than for D mesons. The other
contributions to particle production increase faster with multiplicity for B
than for D mesons. These differences can be understood as being due to the
larger B-meson mass, allowing a larger event activity in MPI and ISR/FSR
processes.

Figure 9 (bottom panels) presents the D-meson relative yields as a function of
the relative charged-particle multiplicity in PYTHIA 8 for five $p_{\rm T}$
intervals. The bottom-left panel shows the trend for the sum of all
contributions, where an overall linear behaviour is observed, the slope of
which increases with $p_{\rm T}$. The bottom-right panel shows the $p_{\rm T}$
evolution for the first hard processes only. The relative D-meson yield
decreases with multiplicity at low $p_{\rm T}$ ($1<p_{\rm
T}<2\leavevmode\nobreak\ \mathrm{GeV}/c$), while at high $p_{\rm T}$
($12<p_{\rm T}<20\leavevmode\nobreak\ \mathrm{GeV}/c$) it exhibits a linear
increase. This feature is caused in PYTHIA 8 by the fact that MPI are ordered
by their hardness, i.e. the $p_{\rm T}$ of the first hard scattering is an
upper limit for the subsequent hard scatterings and the related ISR/FSR. Thus,
charm and beauty production at low $p_{\rm T}$ is associated mostly with low
multiplicity events, whereas heavy-flavour hadron production in high $p_{\rm
T}$ intervals is associated to higher multiplicity events. For completeness,
the contribution of MPI to the total charged-particle multiplicity was
studied. Only events with a small number of MPI contribute to the low
multiplicity intervals, while high multiplicity events are dominated by a
large number of MPI, e.g. events with about five times the average
multiplicity can have more than 16 parton–parton interactions in the event.

In the following, the multiplicity dependence for D and B-meson production
including all contributions in a given $p_{\rm T}$ interval, as shown in Fig.
9 (bottom-left panel) for D-mesons, is compared to the measurements.

###  7.2 Comparison of data with models

Figure 10 shows the comparison between D-meson (average of ${\rm D^{0}}$,
${\rm D^{+}}$ and ${\rm D^{*+}}$) production and theoretical calculations in
four $p_{\rm T}$ intervals. The results of the PYTHIA 8 [30, 31] and the EPOS
3 [71, 72] event generators, and of percolation calculations [41, 73] are
represented by the red dotted line, green dashed or long-dashed and dotted
line, and the blue dot-dashed line, respectively. The description of the
PYTHIA 8 setup was discussed in Sec. 7.1. Figure 11 presents $p_{\rm
T}$-integrated non-prompt ${\rm J}/\psi$ results together with PYTHIA 8 [30,
31] calculations.

Figure 10:  Average D-meson relative yield as a function of the relative
charged-particle multiplicity at central rapidity in different $p_{\rm T}$
intervals. The systematic uncertainties on the data normalisation
($+6\%/-3\%$), on the $({\rm d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm
d}N_{\rm ch}/{\rm d}\eta\rangle$ values ($\pm 6\%$), and on the feed down
contribution are not shown in this figure. Different calculations are
presented: PYTHIA 8.157 [30, 31], EPOS 3 with and without hydro [71, 72] and a
$p_{\rm T}$-integrated percolation model [41, 73]. The coloured lines
represent the calculation curves, whereas the shaded bands represent their
statistical uncertainties at given values of $({\rm d}N_{\rm ch}/{\rm
d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$. The diagonal
(dashed) line is shown to guide the eye.  Figure 11:  Non-prompt ${\rm
J}/\psi$ relative yield as a function of the relative charged-particle
multiplicity at central rapidity for $p_{\rm T}>0$. The systematic
uncertainties on the data normalisation ($+6\%/-3\%$) and on the $({\rm
d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$
values ($\pm 6\%$) are not shown in this figure. PYTHIA 8.157 [31] calculation
for B mesons is also presented. The coloured line represents the calculation
curve, whereas the shaded band represents its uncertainty at given values of
$({\rm d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$. The diagonal (dashed) line is shown to guide the eye.

The percolation model assumes that high-energy hadronic collisions are driven
by the exchange of colour sources between the projectile and target in the
collision [41, 73]. These colour sources have a finite spatial extension and
can interact. In a high-density environment, the coherence among the sources
leads to a reduction of their effective number. The source transverse mass
determines its transverse size ($\propto 1/m_{\rm T}$), and allows to
distinguish between soft (light) and hard (heavy) sources. As a consequence,
at high densities the total charged-particle multiplicity, which originates
from soft sources, is reduced. In contrast, hard particle production is less
affected due to the smaller transverse size of hard sources. The percolation
model predicts a faster-than-linear increase of heavy flavour relative
production with the relative charged-particle multiplicity. The D-meson
$p_{\rm T}$-integrated percolation calculation is represented in all panels of
Fig. 10, even though in this scenario a $p_{\rm T}$ dependence of the results
is expected, such that the higher the $p_{\rm T}$ of the particle the stronger
the deviation from the linear expectation.

EPOS 3 [71, 72] is an event generator for various colliding systems: pp, p–A
and A–A. This event generator imposes the same theoretical scheme in all the
systems, i.e. it assumes initial conditions followed by a hydrodynamical
evolution. Initial conditions are generated in the Gribov-Regge multiple
scattering framework, using the ”Parton based Gribov-Regge” formalism [71].
Individual scatterings are referred to as Pomerons, and are identified with
parton ladders. Each parton ladder is composed of a pQCD hard process with
initial and final state radiation. Non-linear effects are considered by means
of a saturation scale. The hadronisation is performed with a string
fragmentation procedure. Based on these initial conditions, a hydrodynamical
evolution can be applied on the dense core of the collision (3+1D viscous
hydrodynamics) [72]. An evaluation within the EPOS 3 model shows that the
energy density reached in pp collisions at $\sqrt{s}=7$ TeV is high enough to
apply such hydrodynamic evolution [72]. Here we discuss the results of an EPOS
3.099 calculation without jet-bulk interaction, which is a process that
produces hadrons from hard partons and quarks from the fluid. EPOS 3 without
the hydro component (green dashed line in Fig. 10) predicts an approximately
linear increase of D-meson production as a function of the charged-particle
multiplicity. This linear scaling shows a $p_{\rm T}$ dependence, as observed
in PYTHIA 8 with the colour reconnection scenario (red dotted line in Fig.
10), although the results differ in magnitude. In EPOS 3, a consequence of the
Parton based Gribov-Regge approach is that the number of MPIs is directly
related to the multiplicity, i.e. $N_{\rm hard\ process}\propto N_{\rm
ch}\propto N_{\rm MPI}$. When the hydrodynamic evolution is considered (green
long-dashed and dotted line in Fig. 10), one observes a departure from a
linear multiplicity dependence which is qualitatively comparable to that of
the $p_{\rm T}$-integrated percolation calculation.

The measurements, see Fig. 10 and Fig. 11, provide evidence for an increase of
the relative heavy-flavour yields with the relative charged-particle
multiplicity which proceeds faster than linearly for high multiplicities. This
result tends to favour calculations with a substantial deviation from
linearity at high multiplicities such as EPOS 3.099 with hydrodynamics or the
percolation model.

##  8 Summary

Charm and beauty hadron production as a function of the charged-particle
multiplicity was studied in pp collisions at $\sqrt{s}=7$ TeV. Charged-
particle multiplicity at central rapidity was evaluated for events with at
least a charged particle in the interval $|\eta|<1.0$. Prompt ${\rm D^{0}}$,
${\rm D^{+}}$ and ${\rm D^{*+}}$ meson yields were measured at central
rapidity ($|y|<0.5$) in their hadronic decay channels in five $p_{\rm T}$
intervals, from $1\leavevmode\nobreak\ \mathrm{GeV}/c$ to
$20\leavevmode\nobreak\ \mathrm{GeV}/c$. The increase of the relative yield
with increasing charged-particle multiplicity was found to be similar for
D-meson species in all investigated $p_{\rm T}$ intervals. The average of the
${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ relative yields increase with
the relative charged-particle multiplicity faster than linearly at high
multiplicities. No $p_{\rm T}$ dependence is observed within the current
statistical and systematic uncertainties. The lack of quantitative model
estimates of the $p_{\rm T}$ dependence together with the measurement
uncertainties prevent to conclude on a possible $p_{\rm T}$ dependence. A
relative yield enhancement of about a factor of 15 with respect to the
multiplicity integrated value is observed for events with six times the
average charged-particle multiplicity. Prompt ${\rm D^{0}}$ relative yields
were also measured as a function of the relative charged-particle multiplicity
determined in the pseudo-rapidity intervals $-3.7<\eta<-1.7$ and
$2.8<\eta<5.1$. The results were found to be consistent with those obtained
using the charged-particle multiplicity measured at central rapidity. ${\rm
J}/\psi$ inclusive yields were measured earlier at central rapidity
($|y|<0.9$) in their di-electron decay channel [40]. The non-prompt ${\rm
J}/\psi$ contribution was evaluated for $p_{\rm T}>1.3\leavevmode\nobreak\
\mathrm{GeV}/c$, and extrapolated to $p_{\rm T}>0$. The non-prompt ${\rm
J}/\psi$ fraction does not show a dependence on the charged-particle
multiplicity at central rapidity.

Open charm, open beauty, and hidden charm hadron yields exhibit a similar
increase with the charged-particle multiplicity at central rapidity. This
suggests that heavy-flavour relative yields enhancement is not significantly
influenced by hadronisation, but more likely directly related to the ${\rm
c}\bar{\rm c}$ and ${\rm b}\bar{\rm b}$ production processes. The heavy-
flavour relative yield enhancement as a function of the charged-particle
multiplicity is qualitatively described by: (a) PYTHIA 8.157 calculations
including the MPI contributions to particle production [31], (b) percolation
model estimates of the influence of colour charge exchanges during the
interaction [41, 73], (c) predictions by the EPOS 3 event generator which
provides a description of the initial conditions followed by a hydrodynamical
evolution [71, 72]. However, the PYTHIA 8.157 [31] event generator seems to
under-estimate the increase of heavy flavour yields with the charged-particle
multiplicity at high multiplicities.

## Acknowledgements

We would like to thank P. Skands, co-author of PYTHIA 8, and K. Werner and B.
Guiot, co-authors of EPOS 3, for fruitful discussions and for providing their
theoretical calculations.

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: State
Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds
Kidagan, Armenia, 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); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; Danish Natural Science Research Council, the
Carlsberg Foundation and the Danish National Research Foundation; The European
Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und
Technologie (BMBF) and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; Hungarian Orszagos
Tudomanyos Kutatasi Alappgrammok (OTKA) and National Office for Research and
Technology (NKTH); Department of Atomic Energy and Department of Science and
Technology of the Government of India; Istituto Nazionale di Fisica Nucleare
(INFN) and Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
”Enrico Fermi”, Italy; MEXT Grant-in-Aid for Specially Promoted Research,
Japan; Joint Institute for Nuclear Research, Dubna; National Research
Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT),
Direccion General de Asuntos del Personal Academico(DGAPA), México, Amerique
Latine Formation academique - European Commission (ALFA-EC) and the EPLANET
Program (European Particle Physics Latin American Network); Stichting voor
Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway
(NFR); National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and National Council of Scientific
Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Education
and Science of Russian Federation, Russian Academy of Sciences, Russian
Federal Agency of Atomic Energy, Russian Federal Agency for Science and
Innovations and The Russian Foundation for Basic Research; Ministry of
Education of Slovakia; Department of Science and Technology, South Africa;
Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas
(CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA),
Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia
(Consellería de Educación), Centro de Aplicaciones Tecnológicas y Desarrollo
Nuclear (CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy
Agency); Swedish Research Council (VR) and Knut $\&$ Alice Wallenberg
Foundation (KAW); Ukraine Ministry of Education and Science; United Kingdom
Science and Technology Facilities Council (STFC); The United States Department
of Energy, the United States National Science Foundation, the State of Texas,
and the State of Ohio; Ministry of Science, Education and Sports of Croatia
and Unity through Knowledge Fund, Croatia. Council of Scientific and
Industrial Research (CSIR), New Delhi, India

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##  Appendix A Tables of the results

Table 4 reports the results of the relative average D-meson yields per
inelastic collision as a function of the relative charged-particle
multiplicity at mid-rapidity in several D-meson transverse momentum intervals,
see Fig. 4. The corresponding relative average D-meson yields normalised to
the visible cross section instead of the inelastic one are presented in Table
3.

Table 6 summarises the relative ${\rm D^{0}}$ yields per inelastic collision
as a function of the relative raw multiplicity measured with the V0 detector
at forward rapidity, see Fig. 5. These relative ${\rm D^{0}}$ yields are also
presented in Table 5 normalised to the visible cross section.

Table 7 reports the fraction of non-prompt ${\rm J}/\psi$ to the inclusive
${\rm J}/\psi$ yields as a function of the relative charged-particle
multiplicity at mid-rapidity, see Fig 7. The relative prompt and non-prompt
${\rm J}/\psi$ yields per inelastic collision are reported in Table 8, while
Table 7 presents these yields normalised to the visible cross section.

|  $N_{\rm tracklets}$ interval
---|---
| [1,8] | [9,13] | [14,19] | [20,30] | [31,49] | [50,80]
$p_{\rm T}$ ($\mathrm{GeV}/c$) | $({\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T})\big{/}\langle{\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T}\rangle\times\epsilon_{\rm trigger}$
1–2 | $0.39\pm 0.09\pm 0.05_{-0}^{+0.07}$ | $0.94\pm 0.21\pm 0.11_{-0.07}^{+0.14}$ | $1.45\pm 0.36\pm 0.15_{-0.22}^{+0.16}$ | $3.60\pm 0.66\pm 0.40_{-0.82}^{+0.27}$ | $5.33\pm 1.59\pm 0.62_{-2.01}^{+0}$ | –
2–4 | $0.18\pm 0.01\pm 0.01_{-0}^{+0.02}$ | $0.91\pm 0.05\pm 0.06_{-0.03}^{+0.07}$ | $1.94\pm 0.10\pm 0.11_{-0.14}^{+0.10}$ | $3.64\pm 0.16\pm 0.15_{-0.40}^{+0.13}$ | $7.67\pm 0.48\pm 0.40_{-1.42}^{+0}$ | $14.04\pm 2.21\pm 1.79_{-3.28}^{+0}$
4–8 | $0.15\pm 0.01\pm 0.01_{-0}^{+0.01}$ | $1.01\pm 0.04\pm 0.06_{-0.03}^{+0.06}$ | $1.95\pm 0.08\pm 0.10_{-0.12}^{+0.09}$ | $4.13\pm 0.12\pm 0.22_{-0.35}^{+0.12}$ | $9.36\pm 0.39\pm 0.45_{-1.49}^{+0}$ | $16.94\pm 1.60\pm 1.45_{-3.15}^{+0}$
8–12 | $0.14\pm 0.02\pm 0.01_{-0}^{+0.01}$ | $0.69\pm 0.07\pm 0.05_{-0.02}^{+0.04}$ | $2.41\pm 0.15\pm 0.15_{-0.15}^{+0.11}$ | $4.27\pm 0.25\pm 0.26_{-0.42}^{+0.14}$ | $8.74\pm 0.72\pm 0.57_{-1.48}^{+0}$ | –
12–20 | – | – | $2.14\pm 0.30\pm 0.26_{-0.10}^{+0.07}$ | $4.15\pm 0.51\pm 0.43_{-0.28}^{+0.09}$ | $11.60\pm 1.59\pm 1.18_{-1.31}^{+0}$ | –
Table 3: Average of ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ mesons relative yields for the sum of particle and antiparticle in several multiplicity and $p_{\rm T}$ intervals for pp collisions at $\sqrt{s}=7$ TeV as a function of the relative charged-particle multiplicity at central rapidity. The values are reported together with their uncertainties, which are quoted in the the order: statistical, systematic and feed-down contribution uncertainties. The yields reported here are not corrected by the trigger selection efficiency, they are normalised to the visible cross section.  | $({\rm d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$
---|---
| $0.45^{+0.03}_{-0.03}$ | $1.18^{+0.07}_{-0.07}$ | $1.78^{+0.10}_{-0.11}$ | $2.63^{+0.15}_{-0.17}$ | $4.01^{+0.23}_{-0.25}$ | $6.11^{+0.35}_{-0.39}$
$p_{\rm T}$ ($\mathrm{GeV}/c$) | $({\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T})\big{/}\langle{\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T}\rangle$
1–2 | $0.45\pm 0.11\pm 0.05_{-0}^{+0.09}$ | $1.11\pm 0.25\pm 0.13_{-0.08}^{+0.17}$ | $1.70\pm 0.43\pm 0.18_{-0.26}^{+0.19}$ | $4.24\pm 0.78\pm 0.47_{-0.96}^{+0.32}$ | $6.27\pm 1.87\pm 0.73_{-2.37}^{+0}$ | –
2–4 | $0.21\pm 0.02\pm 0.01_{-0}^{+0.02}$ | $1.08\pm 0.06\pm 0.06_{-0.04}^{+0.08}$ | $2.28\pm 0.12\pm 0.13_{-0.16}^{+0.12}$ | $4.28\pm 0.19\pm 0.17_{-0.48}^{+0.16}$ | $9.02\pm 0.57\pm 0.47_{-1.67}^{+0}$ | $16.51\pm 2.60\pm 2.11_{-3.86}^{+0}$
4–8 | $0.18\pm 0.01\pm 0.01_{-0}^{+0.01}$ | $1.18\pm 0.05\pm 0.07_{-0.04}^{+0.07}$ | $2.30\pm 0.09\pm 0.12_{-0.14}^{+0.11}$ | $4.85\pm 0.15\pm 0.26_{-0.42}^{+0.14}$ | $11.02\pm 0.46\pm 0.53_{-1.75}^{+0}$ | $19.92\pm 1.89\pm 1.71_{-3.71}^{+0}$
8–12 | $0.16\pm 0.02\pm 0.01_{-0.00}^{+0.01}$ | $0.81\pm 0.08\pm 0.06_{-0.03}^{+0.05}$ | $2.84\pm 0.17\pm 0.18_{-0.17}^{+0.13}$ | $5.02\pm 0.29\pm 0.31_{-0.50}^{+0.17}$ | $10.28\pm 0.85\pm 0.67_{-1.74}^{+0}$ | –
12–20 | – | – | $2.52\pm 0.35\pm 0.30_{-0.11}^{+0.09}$ | $4.88\pm 0.61\pm 0.51_{-0.33}^{+0.11}$ | $13.65\pm 1.87\pm 1.38_{-1.54}^{+0}$ | –
Table 4: Average of ${\rm D^{0}}$, ${\rm D^{+}}$ and ${\rm D^{*+}}$ mesons relative yields for the sum of particle and antiparticle in several multiplicity and $p_{\rm T}$ intervals for pp collisions at $\sqrt{s}=7$ TeV as a function of the relative charged-particle multiplicity at central rapidity. The values are reported together with their uncertainties, which are quoted in the the order: statistical, systematic and feed-down contribution uncertainties. The yields reported here are per inelastic event.  | $N_{\rm V0}\big{/}\langle N_{\rm V0}\rangle$
---|---
| 0.43 | 1.0 | 1.5 | 2.2 | 3.3
$p_{\rm T}$ ($\mathrm{GeV}/c$) | $({\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T})\big{/}\langle{\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T}\rangle\times\epsilon_{\rm trigger}$
2–4 | $0.15\pm 0.02\pm 0.01^{+0.02}_{-0}$ | $0.65\pm 0.07\pm 0.03^{+0.06}_{-0.03}$ | $1.28\pm 0.11\pm 0.07^{+0.09}_{-0.12}$ | $2.81\pm 0.15\pm 0.11^{+0.13}_{-0.39}$ | $4.22\pm 0.33\pm 0.24^{+0}_{-0.99}$
4–8 | $0.17\pm 0.02\pm 0.01^{+0.02}_{-0}$ | $0.80\pm 0.07\pm 0.04^{+0.07}_{-0.04}$ | $1.50\pm 0.12\pm 0.08^{+0.10}_{-0.13}$ | $2.57\pm 0.15\pm 0.14^{+0.11}_{-0.34}$ | $4.53\pm 0.34\pm 0.24^{+0}_{-1.00}$
Table 5: ${\rm D^{0}}$ meson relative yields for the sum of particle and antiparticle in several multiplicity and $p_{\rm T}$ intervals for pp collisions at $\sqrt{s}=7$ TeV as a function of the relative average multiplicity in the V0 detector, $N_{\rm V0}\big{/}\langle N_{\rm V0}\rangle$. The yields reported here are not corrected by the trigger selection efficiency, they are normalised to the visible cross section.  | $N_{\rm V0}\big{/}\langle N_{\rm V0}\rangle$
---|---
| 0.43 | 1.0 | 1.5 | 2.2 | 3.3
$p_{\rm T}$ ($\mathrm{GeV}/c$) | $({\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T})\big{/}\langle{\rm d}^{2}N/{\rm d}y{\rm d}p_{\rm T}\rangle$
2–4 | $0.18\pm 0.02\pm 0.01^{+0.02}_{-0}$ | $0.76\pm 0.08\pm 0.04^{+0.07}_{-0.04}$ | $1.50\pm 0.13\pm 0.08^{+0.11}_{-0.14}$ | $3.31\pm 0.18\pm 0.13^{+0.15}_{-0.46}$ | $4.96\pm 0.38\pm 0.28^{+0}_{-1.16}$
4–8 | $0.20\pm 0.02\pm 0.01^{+0.02}_{-0}$ | $0.94\pm 0.09\pm 0.05^{+0.08}_{-0.04}$ | $1.76\pm 0.14\pm 0.09^{+0.12}_{-0.16}$ | $3.02\pm 0.18\pm 0.16^{+0.13}_{-0.40}$ | $5.33\pm 0.40\pm 0.29^{+0}_{-1.18}$
Table 6: ${\rm D^{0}}$ meson relative yields for the sum of particle and
antiparticle in several multiplicity and $p_{\rm T}$ intervals for pp
collisions at $\sqrt{s}=7$ TeV as a function of the relative average
multiplicity in the V0 detector, $N_{\rm V0}\big{/}\langle N_{\rm V0}\rangle$.
The yields reported here are normalised to the inelastic cross section.

$N_{\rm tracklets}$ |  $f_{\rm B}$(%) |  $f_{\rm B}^{\rm extr}$(%) | $({\rm d}N_{{\rm J}/\psi}^{\rm prompt}/{\rm d}y)\big{/}\langle{\rm d}N_{{\rm J}/\psi}^{\rm prompt}/{\rm d}y\rangle\times\epsilon_{\rm trigger}$ | $({\rm d}N_{{\rm J}/\psi}^{\rm non-prompt}/{\rm d}y)\big{/}\langle{\rm d}N_{{\rm J}/\psi}^{\rm non-prompt}/{\rm d}y\rangle\times\epsilon_{\rm trigger}$
---|---|---|---|---
[4,8] | $10.1\pm 7.8\pm 2.5$ | $10.2\pm 7.9\pm 2.5$ | $0.37\pm 0.07\pm 0.01$ | $0.24\pm 0.20^{+0.05}_{-0.04}$
[9,13] | $20.8\pm 6.9\pm 2.7$ | $20.9\pm 6.9\pm 2.7$ | $0.80\pm 0.14\pm 0.04$ | $1.20\pm 0.39^{+0.19}_{-0.14}$
[14,19] | $15.6\pm 6.3\pm 2.0$ | $15.7\pm 6.3\pm 2.0$ | $1.95\pm 0.31\pm 0.24$ | $2.06\pm 0.84^{+0.37}_{-0.35}$
[20,30] | $16.7\pm 6.7\pm 3.3$ | $16.8\pm 6.7\pm 3.3$ | $2.61\pm 0.46\pm 0.27$ | $2.99\pm 1.23^{+0.51}_{-0.47}$
[31,49] | $19.0\pm 11.9\pm 4.2$ | $19.0\pm 12.0\pm 4.2$ | $6.50\pm 1.50\pm 0.31$ | $8.70\pm 5.75^{+1.41}_{-1.24}$

Table 7: Fraction of non-prompt ${\rm J}/\psi$ measured for $p_{\rm
T}>1.3\leavevmode\nobreak\ \mathrm{GeV}/c$, $f_{\rm B}$(%), and extrapolated
down to $p_{\rm T}>0$, $f_{\rm B}^{\rm extr}$(%) in the various $N_{\rm
tracklets}$ intervals. Prompt and non-prompt ${\rm J}/\psi$ relative yields
for $p_{\rm T}>0$ are also reported in the different multiplicity intervals.
The first and second uncertainties correspond to the statistical and
systematic uncertainties, respectively. The yields reported here are not
corrected by the trigger selection efficiency, they are normalised to the
visible cross section.

$({\rm d}N_{\rm ch}/{\rm d}\eta)\big{/}\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ | $({\rm d}N_{{\rm J}/\psi}^{\rm prompt}/{\rm d}y)\big{/}\langle{\rm d}N_{{\rm J}/\psi}^{\rm prompt}/{\rm d}y\rangle$ | $({\rm d}N_{{\rm J}/\psi}^{\rm non-prompt}/{\rm d}y)\big{/}\langle{\rm d}N_{{\rm J}/\psi}^{\rm non-prompt}/{\rm d}y\rangle$
---|---|---
$0.63^{+0.4}_{-0.4}$ | $0.44\pm 0.08\pm 0.01$ | $0.28\pm 0.23^{+0.06}_{-0.05}$
$1.18^{+0.07}_{-0.07}$ | $0.94\pm 0.17\pm 0.05$ | $1.41\pm 0.46^{+0.22}_{-0.17}$
$1.78^{+0.10}_{-0.11}$ | $2.29\pm 0.36\pm 0.28$ | $2.42\pm 0.99^{+0.44}_{-0.41}$
$2.63^{+0.15}_{-0.17}$ | $3.07\pm 0.54\pm 0.32$ | $3.52\pm 1.45^{+0.60}_{-0.55}$
$4.01^{+0.23}_{-0.25}$ | $7.65\pm 1.76\pm 0.36$ | $10.24\pm 6.76^{+1.66}_{-1.46}$

Table 8:  Prompt and non-prompt relative ${\rm J}/\psi$ relative yields for
$p_{\rm T}>0$ in different multiplicity bins. The first and second
uncertainties correspond to the statistical and systematic uncertainties
respectively. The yields reported here are normalised to the inelastic cross
section.

##  Appendix B The ALICE Collaboration

J. Adamorg40&D. Adamováorg83&M.M. Aggarwalorg87&G. Aglieri Rinellaorg36&M.
Agnelloorg111&N. Agrawalorg48&Z. Ahammedorg131&I. Ahmedorg16&S.U. Ahnorg68&I.
Aimoorg94,org111&S. Aiolaorg136&M. Ajazorg16&A. Akindinovorg58&S.N.
Alamorg131&D. Aleksandrovorg100&B. Alessandroorg111&D. Alexandreorg102&R.
Alfaro Molinaorg64&A. Aliciorg105,org12&A. Alkinorg3&J. Almeorg38&T.
Altorg43&S. Altinpinarorg18&I. Altsybeevorg130&C. Alves Garcia Pradoorg119&C.
Andreiorg78&A. Andronicorg97&V. Anguelovorg93&J. Anielskiorg54&T.
Antičićorg98&F. Antinoriorg108&P. Antonioliorg105&L. Aphecetcheorg113&H.
Appelshäuserorg53&S. Arcelliorg28&N. Armestoorg17&R. Arnaldiorg111&T.
Aronssonorg136&I.C. Arseneorg22&M. Arslandokorg53&A. Augustinusorg36&R.
Averbeckorg97&M.D. Azmiorg19&M. Bachorg43&A. Badalàorg107&Y.W. Baekorg44&S.
Bagnascoorg111&R. Bailhacheorg53&R. Balaorg90&A. Baldisseriorg15&M.
Ballorg92&F. Baltasar Dos Santos Pedrosaorg36&R.C. Baralorg61&A.M.
Barbanoorg111&R. Barberaorg29&F. Barileorg33&G.G. Barnaföldiorg135&L.S.
Barnbyorg102&V. Barretorg70&P. Bartaliniorg7&J. Bartkeorg116&E.
Bartschorg53&M. Basileorg28&N. Bastidorg70&S. Basuorg131&B. Bathenorg54&G.
Batigneorg113&A. Batista Camejoorg70&B. Batyunyaorg66&P.C. Batzingorg22&I.G.
Beardenorg80&H. Beckorg53&C. Beddaorg111&N.K. Beheraorg48&I. Belikovorg55&F.
Belliniorg28&H. Bello Martinezorg2&R. Bellwiedorg121&R. Belmontorg134&E.
Belmont-Morenoorg64&V. Belyaevorg76&G. Bencediorg135&S. Beoleorg27&I.
Berceanuorg78&A. Bercuciorg78&Y. Berdnikovorg85&D. Berenyiorg135&R.A.
Bertensorg57&D. Berzanoorg36,org27&L. Betevorg36&A. Bhasinorg90&I.R.
Bhatorg90&A.K. Bhatiorg87&B. Bhattacharjeeorg45&J. Bhomorg127&L.
Bianchiorg27,org121&N. Bianchiorg72&C. Bianchinorg134,org57&J. Bielčíkorg40&J.
Bielčíkováorg83&A. Bilandzicorg80&S. Biswasorg79&S. Bjelogrlicorg57&F.
Blancoorg10&D. Blauorg100&C. Blumeorg53&F. Bockorg74,org93&A. Bogdanovorg76&H.
Bøggildorg80&L. Boldizsárorg135&M. Bombaraorg41&J. Bookorg53&H. Borelorg15&A.
Borissovorg96&M. Borriorg82&F. Bossúorg65&M. Botjeorg81&E. Bottaorg27&S.
Böttgerorg52&P. Braun-Munzingerorg97&M. Bregantorg119&T. Breitnerorg52&T.A.
Brokerorg53&T.A. Browningorg95&M. Brozorg40&E.J. Bruckenorg46&E.
Brunaorg111&G.E. Brunoorg33&D. Budnikovorg99&H. Bueschingorg53&S.
Bufalinoorg36,org111&P. Buncicorg36&O. Buschorg93&Z. Butheleziorg65&J.T.
Buxtonorg20&D. Caffarriorg36,org30&X. Caiorg7&H. Cainesorg136&L. Calero
Diazorg72&A. Calivaorg57&E. Calvo Villarorg103&P. Cameriniorg26&F.
Carenaorg36&W. Carenaorg36&J. Castillo Castellanosorg15&A.J.
Castroorg124&E.A.R. Casulaorg25&C. Cavicchioliorg36&C. Ceballos Sanchezorg9&J.
Cepilaorg40&P. Cerelloorg111&B. Changorg122&S. Chapelandorg36&M.
Chartierorg123&J.L. Charvetorg15&S. Chattopadhyayorg131&S.
Chattopadhyayorg101&V. Chelnokovorg3&M. Cherneyorg86&C. Cheshkovorg129&B.
Cheynisorg129&V. Chibante Barrosoorg36&D.D. Chinellatoorg120&P.
Chochulaorg36&K. Choiorg96&M. Chojnackiorg80&S. Choudhuryorg131&P.
Christakoglouorg81&C.H. Christensenorg80&P. Christiansenorg34&T.
Chujoorg127&S.U. Chungorg96&C. Cicaloorg106&L. Cifarelliorg12,org28&F.
Cindoloorg105&J. Cleymansorg89&F. Colamariaorg33&D. Colellaorg33&A.
Colluorg25&M. Colocciorg28&G. Conesa Balbastreorg71&Z. Conesa del
Valleorg51&M.E. Connorsorg136&J.G. Contrerasorg11,org40&T.M. Cormierorg84&Y.
Corrales Moralesorg27&I. Cortés Maldonadoorg2&P. Corteseorg32&M.R.
Cosentinoorg119&F. Costaorg36&P. Crochetorg70&R. Cruz Albinoorg11&E.
Cuautleorg63&L. Cunqueiroorg36&T. Dahmsorg92,org37&A. Daineseorg108&A.
Danuorg62&D. Dasorg101&I. Dasorg51,org101&S. Dasorg4&A. Dashorg120&S.
Dashorg48&S. Deorg131,org119&A. De Caroorg31,org12&G. de Cataldoorg104&J. de
Cuvelandorg43&A. De Falcoorg25&D. De Gruttolaorg12,org31&N. De Marcoorg111&S.
De Pasqualeorg31&A. Delofforg77&E. Dénesorg135&G. D’Erasmoorg33&D. Di
Bariorg33&A. Di Mauroorg36&P. Di Nezzaorg72&M.A. Diaz Corcheroorg10&T.
Dietelorg89&P. Dillensegerorg53&R. Diviàorg36&Ø. Djuvslandorg18&A.
Dobrinorg57,org81&T. Dobrowolskiorg770&D. Domenicis Gimenezorg119&B.
Dönigusorg53&O. Dordicorg22&A.K. Dubeyorg131&A. Dublaorg57&L. Ducrouxorg129&P.
Dupieuxorg70&R.J. Ehlersorg136&D. Eliaorg104&H. Engelorg52&B.
Erazmusorg113,org36&D. Eschweilerorg43&B. Espagnonorg51&M. Estienneorg113&S.
Esumiorg127&D. Evansorg102&S. Evdokimovorg112&G. Eyyubovaorg40&L.
Fabbiettiorg37,org92&D. Fabrisorg108&J. Faivreorg71&A. Fantoniorg72&M.
Faselorg74&L. Feldkamporg54&D. Feleaorg62&A. Felicielloorg111&G.
Feofilovorg130&J. Ferenceiorg83&A. Fernández Téllezorg2&E.G. Ferreiroorg17&A.
Ferrettiorg27&A. Festantiorg30&J. Figielorg116&M.A.S. Figueredoorg123&S.
Filchaginorg99&D. Finogeevorg56&F.M. Fiondaorg104&E.M. Fioreorg33&M.G.
Fleckorg93&M. Florisorg36&S. Foertschorg65&P. Fokaorg97&S. Fokinorg100&E.
Fragiacomoorg110&A. Francesconorg36,org30&U. Frankenfeldorg97&U. Fuchsorg36&C.
Furgetorg71&A. Fursorg56&M. Fusco Girardorg31&J.J. Gaardhøjeorg80&M.
Gagliardiorg27&A.M. Gagoorg103&M. Gallioorg27&D.R. Gangadharanorg74&P.
Ganotiorg88&C. Gaoorg7&C. Garabatosorg97&E. Garcia-Solisorg13&C.
Gargiuloorg36&P. Gasikorg37,org92&M. Germainorg113&A. Gheataorg36&M.
Gheataorg62,org36&P. Ghoshorg131&S.K. Ghoshorg4&P. Gianottiorg72&P.
Giubellinoorg36&P. Giubilatoorg30&E. Gladysz-Dziadusorg116&P. Glässelorg93&A.
Gomez Ramirezorg52&P. González-Zamoraorg10&S. Gorbunovorg43&L.
Görlichorg116&S. Gotovacorg115&V. Grabskiorg64&L.K. Graczykowskiorg133&A.
Grelliorg57&A. Grigorasorg36&C. Grigorasorg36&V. Grigorievorg76&A.
Grigoryanorg1&S. Grigoryanorg66&B. Grinyovorg3&N. Grionorg110&J.F. Grosse-
Oetringhausorg36&J.-Y. Grossiordorg129&R. Grossoorg36&F. Guberorg56&R.
Guernaneorg71&B. Guerzoniorg28&K. Gulbrandsenorg80&H. Gulkanyanorg1&T.
Gunjiorg126&A. Guptaorg90&R. Guptaorg90&R. Haakeorg54&Ø. Haalandorg18&C.
Hadjidakisorg51&M. Haiducorg62&H. Hamagakiorg126&G. Hamarorg135&L.D.
Hanrattyorg102&A. Hansenorg80&J.W. Harrisorg136&H. Hartmannorg43&A.
Hartonorg13&D. Hatzifotiadouorg105&S. Hayashiorg126&S.T. Heckelorg53&M.
Heideorg54&H. Helstruporg38&A. Herghelegiuorg78&G. Herrera Corralorg11&B.A.
Hessorg35&K.F. Hetlandorg38&T.E. Hildenorg46&H. Hillemannsorg36&B.
Hippolyteorg55&P. Hristovorg36&M. Huangorg18&T.J. Humanicorg20&N.
Hussainorg45&T. Hussainorg19&D. Hutterorg43&D.S. Hwangorg21&R. Ilkaevorg99&I.
Ilkivorg77&M. Inabaorg127&C. Ionitaorg36&M. Ippolitovorg76,org100&M.
Irfanorg19&M. Ivanovorg97&V. Ivanovorg85&P.M. Jacobsorg74&C. Jahnkeorg119&H.J.
Jangorg68&M.A. Janikorg133&P.H.S.Y. Jayarathnaorg121&C. Jenaorg30&S.
Jenaorg121&R.T. Jimenez Bustamanteorg63&P.G. Jonesorg102&H. Jungorg44&A.
Juskoorg102&P. Kalinakorg59&A. Kalweitorg36&J. Kaminorg53&J.H. Kangorg137&V.
Kaplinorg76&S. Karorg131&A. Karasu Uysalorg69&O. Karavichevorg56&T.
Karavichevaorg56&E. Karpechevorg56&U. Kebschullorg52&R. Keidelorg138&D.L.D.
Keijdenerorg57&M. Keilorg36&K.H. Khanorg16&M.M. Khanorg19&P. Khanorg101&S.A.
Khanorg131&A. Khanzadeevorg85&Y. Kharlovorg112&B. Kilengorg38&B.
Kimorg137&D.W. Kimorg68,org44&D.J. Kimorg122&H. Kimorg137&J.S. Kimorg44&M.
Kimorg44&M. Kimorg137&S. Kimorg21&T. Kimorg137&S. Kirschorg43&I. Kiselorg43&S.
Kiselevorg58&A. Kisielorg133&G. Kissorg135&J.L. Klayorg6&C. Kleinorg53&J.
Kleinorg93&C. Klein-Bösingorg54&A. Klugeorg36&M.L. Knichelorg93&A.G.
Knospeorg117&T. Kobayashiorg127&C. Kobdajorg114&M. Kofaragoorg36&M.K.
Köhlerorg97&T. Kolleggerorg97,org43&A. Kolojvariorg130&V. Kondratievorg130&N.
Kondratyevaorg76&E. Kondratyukorg112&A. Konevskikhorg56&M. Kourorg90&C.
Kouzinopoulosorg36&V. Kovalenkoorg130&M. Kowalskiorg36,org116&S. Koxorg71&G.
Koyithatta Meethaleveeduorg48&J. Kralorg122&I. Králikorg59&A.
Kravčákováorg41&M. Krelinaorg40&M. Kretzorg43&M. Krivdaorg102,org59&F.
Krizekorg83&E. Kryshenorg36&M. Krzewickiorg97,org43&A.M. Kuberaorg20&V.
Kučeraorg83&Y. Kucheriaevorg1000&T. Kugathasanorg36&C. Kuhnorg55&P.G.
Kuijerorg81&I. Kulakovorg43&A. Kumarorg90&J. Kumarorg48&L. Kumarorg79,org87&P.
Kurashviliorg77&A. Kurepinorg56&A.B. Kurepinorg56&A. Kuryakinorg99&S.
Kushpilorg83&M.J. Kweonorg50&Y. Kwonorg137&S.L. La Pointeorg111&P. La
Roccaorg29&C. Lagana Fernandesorg119&I. Lakomovorg51,org36&R. Langoyorg42&C.
Laraorg52&A. Lardeuxorg15&A. Lattucaorg27&E. Laudiorg36&R. Leaorg26&L.
Leardiniorg93&G.R. Leeorg102&S. Leeorg137&I. Legrandorg36&J. Lehnertorg53&R.C.
Lemmonorg82&V. Lentiorg104&E. Leograndeorg57&I. León Monzónorg118&M.
Leoncinoorg27&P. Lévaiorg135&S. Liorg7,org70&X. Liorg14&J. Lienorg42&R.
Lietavaorg102&S. Lindalorg22&V. Lindenstruthorg43&C. Lippmannorg97&M.A.
Lisaorg20&H.M. Ljunggrenorg34&D.F. Lodatoorg57&P.I. Loenneorg18&V.R.
Logginsorg134&V. Loginovorg76&C. Loizidesorg74&X. Lopezorg70&E. López
Torresorg9&A. Loweorg135&X.-G. Luorg93&P. Luettigorg53&M. Lunardonorg30&G.
Luparelloorg26,org57&A. Maevskayaorg56&M. Magerorg36&S. Mahajanorg90&S.M.
Mahmoodorg22&A. Maireorg55&R.D. Majkaorg136&M. Malaevorg85&I. Maldonado
Cervantesorg63&L. Malininaidp3748880,org66&D. Mal’Kevichorg58&P.
Malzacherorg97&A. Mamonovorg99&L. Manceauorg111&V. Mankoorg100&F.
Mansoorg70&V. Manzariorg104,org36&M. Marchisoneorg27&J. Marešorg60&G.V.
Margagliottiorg26&A. Margottiorg105&J. Marguttiorg57&A. Marínorg97&C.
Markertorg117&M. Marquardorg53&I. Martashviliorg124&N.A. Martinorg97&J. Martin
Blancoorg113&P. Martinengoorg36&M.I. Martínezorg2&G. Martínez Garcíaorg113&M.
Martinez Pedreiraorg36&Y. Martynovorg3&A. Masorg119&S. Masciocchiorg97&M.
Maseraorg27&A. Masoniorg106&L. Massacrierorg113&A. Mastroserioorg33&A.
Matyjaorg116&C. Mayerorg116&J. Mazerorg124&M.A. Mazzoniorg109&D.
Mcdonaldorg121&F. Meddiorg24&A. Menchaca-Rochaorg64&E. Meninnoorg31&J. Mercado
Pérezorg93&M. Meresorg39&Y. Miakeorg127&M.M. Mieskolainenorg46&K.
Mikhaylovorg58,org66&L. Milanoorg36&J. Milosevicorg22,org132&L.M.