[]Antonio Palasciano

# First measurements of in-jet fragmentation and correlations of charmed
mesons and baryons in pp collisions with ALICE

###### Abstract

Fragmentation functions are one of the key components of the factorisation
theorem used to calculate heavy-flavour hadron production cross sections. The
non-perturbative nature of fragmentation functions necessitates that they are
constrained through experimental measurements, commonly performed in the clean
environments of $\mathrm{e}^{+}\mathrm{e}^{-}$ and ep collisions. However,
recent measurements of charm-hadron transverse-momentum spectra and the ratios
of charmed-hadron abundances in pp collisions have questioned the universality
of fragmentation functions between leptonic and hadronic collision systems in
the baryon sector. In this contribution, we present measurements of
differential observables of heavy-flavour hadrons that also consider the
hadronic density surrounding the hadron. These measurements provide additional
information to the previously reported baryon-to-meson results and allow us
closer access to the charm fragmentation functions. We report the fraction of
longitudinal momentum carried by $\mathrm{D^{0}}$ and $\mathrm{D^{+}_{s}}$
mesons as well as $\Lambda^{+}_{\mathrm{c}}$ baryons. We also report the
azimuthal correlation distributions between heavy-flavour decay electrons and
charged particles in pp and p–Pb collisions, as well as between
$\Lambda^{+}_{\mathrm{c}}$ baryons and charged particles in pp collisions,
which provide quantitative access to the angular profile, $p_{\mathrm{T}}$ and
multiplicity distributions of the jets produced by the heavy-quark
fragmentation.

##  1 Introduction

Heavy-flavour (HF) measurements in ultra-relativistic hadronic collisions play
a crucial role in probing and testing our current understanding of the
perturbative Quantum Chromodynamics (pQCD). In this theoretical framework, the
factorization theorem, used to compute HF hadron production cross-section,
foresees the separation of perturbative quantities, as the partonic cross-
sections, from non-perturbative quantities as the parton distribution
functions (PDFs) and the fragmentation functions (FF), which are evaluated by
exploiting measurements. The recently observed enhancement of baryon-to-meson
ratios with respect to measurements in $\mathrm{e^{+}e^{-}}$,
$\mathrm{e^{-}p}$ collisions [1, 2] has questioned the fragmentation
universality across colliding systems, exposing discrepancies between
experimental measurements in hadronic collisions and models relying on FF
constrained to $\mathrm{e^{+}e^{-}}$ and $\mathrm{e^{-}p}$ data. Charm-tagged
jets measurements and azimuthal correlations between charm-origin particles
and other charged particles, differently from single-particle studies,
directly access complementary aspects of the charm fragmentation, providing a
tool for the description of the charm shower.

##  2 Heavy-flavour tagged jets

The study of charm-baryon production in jets can provide additional insights
into the charm hadronisation mechanisms in pp collisions. Charm-tagged jets
were identified by the presence of prompt charmed hadrons, such as D mesons or
charmed baryons, among their constituents. In events where at least one charm
hadron candidate was reconstructed, an anti-$k_{\mathrm{T}}$ clustering
algorithm as implemented in the FastJet [3] package was applied to the
reconstructed charged particles to define the jet produced by the charm
showering process. Corrections accounting for the D-meson reconstruction
efficiency, acceptance, and beauty-hadron feed-down contribution were applied
and an unfolding procedure was performed to account for detector effects such
as non-reconstructed particles and limited resolution on the jet momentum.

The ALICE Collaboration has measured the $p_{\mathrm{T}}$-differential cross
section of $\mathrm{D^{0}}$-tagged charm jets [4]. In Fig. 1, the results for
three different values of the jet resolution parameter $R$ are compared to
PYTHIA 8 simulations with Monash-2013 tune and with color reconnection beyond-
leading-colour (CR-BLC) Mode 2 [5, 7] tune, as well as with POWHEG + PYTHIA 8
[6] simulations, in pp collisions at $\sqrt{s}=$ 5.02 and 13 TeV. The two
PYTHIA 8 predictions correctly reproduce the measured
$p^{\mathrm{ch~{}jet}}_{\mathrm{T}}$ -differential cross sections for both
collision energies. A good agreement within the experimental and theoretical
uncertainties is also observed in POWHEG + PYTHIA 8 predictions.

Figure 1: $\mathrm{D^{0}}$-jet production cross-section measurements in pp
collisions at $\sqrt{s}=$ 5.02 and 13 TeV for three different resolution
parameter $R$ = 0.2, 0.4, 0.6, compared to POWHEG + PYTHIA 8 and PYTHIA 8
Monte Carlo predictions.

The hardness of the fragmentation of charm quarks into hadrons can be accessed
by investigating the relation between the hadron momentum in the jet direction
with respect to the momentum of the charged jets by introducing the parallel
jet momentum fraction, defined as:

$z_{||}^{\mathrm{ch}}=\dfrac{\vec{p}^{\mathrm{HF}}\cdot\vec{p}^{\mathrm{ch~{}jet}}}{\vec{p}^{\mathrm{ch~{}jet}}\cdot\vec{p}^{\mathrm{ch~{}jet}}}.$
(1)

In order to detail the charm-quark fragmentation and to understand possible
modifications induced by different hadronisation mechanisms on the charm
shower products, the $z_{||}^{\mathrm{ch}}$ distributions of prompt
$\mathrm{D}^{+}_{\mathrm{s}}$ mesons and $\Lambda^{+}_{\mathrm{c}}$ baryons in
pp collisions at $\sqrt{s}$ = 13 TeV in the kinematic region 7
$<p_{\mathrm{T}}^{\mathrm{ch~{}j}}<$ 15 GeV/$c$ and 3
$<p_{\mathrm{T}}^{\mathrm{trigger}}<$ 15 GeV/$c$ with $R$ = 0.4 have been
measured and compared with previously released $\mathrm{D^{0}}$ meson-tagged
jets measurements [4]. An overall good agreement is observed between the
$\mathrm{D^{+}_{s}}$ and the $\mathrm{D^{0}}$ parallel jet momentum fraction
distributions (Fig. 2, left), with some tensions for large value of
$z_{||}^{\mathrm{ch}}$, that could be interpreted as the
$\mathrm{D}_{\mathrm{s}}$ carrying, on average, slightly more jet-momentum
than the $\mathrm{D^{0}}$ meson. The peak at intermediate values of
$z_{||}^{\mathrm{ch}}$ measured for $\Lambda^{+}_{\mathrm{c}}$-jets (Fig. 2,
right), suggests a possible softer fragmentation of charm quarks in baryons
than in mesons. The comparison with Monte Carlo predictions are represented in
the bottom panels of Fig. 2 as the ratio of the $z_{||}^{\mathrm{ch}}$
distributions, $\mathrm{D}^{+}_{\mathrm{s}}$/$\mathrm{D^{0}}$ and
$\Lambda^{+}_{\mathrm{c}}$/$\mathrm{D^{0}}$. In the first case, no significant
differences are observed between model predictions, overall providing a good
description of the data. In the $\Lambda^{+}_{\mathrm{c}}$/$\mathrm{D^{0}}$
ratio, the introduction of color reconnection mechanisms beyond leading color,
expected to enhance the baryon production, significantly modifies the expected
fragmentation function trend with respect to the Monash tune, providing a
qualitatively better description of the measurement.

Figure 2: $\mathrm{D}^{+}_{\mathrm{s}}$ and $\Lambda^{+}_{\mathrm{c}}$
parallel jet momentum fraction distributions compared to $\mathrm{D^{0}}$
measurements in the same kinematic region. In the bottom panels, the ratio of
the $z_{||}^{\mathrm{ch}}$ distribution for $\mathrm{D}^{+}_{\mathrm{s}}$ and
$\Lambda^{+}_{\mathrm{c}}$ over $\mathrm{D^{0}}$, compared to PYTHIA Monte
Carlo predictions, is shown.

##  3 Azimuthal correlations between charm hadrons and charged particles

Angular correlations of prompt charm hadrons with charged particles in small
systems can provide additional details on the charm fragmentation in small
systems with respect to charm-tagged jets. The typical structure of two-
dimensional correlation functions between “trigger” charm particles and
“associated” charged particles is expressed in terms of pseudorapidity and
azimuthal angle difference, featuring a near-side (NS) peak at
($\Delta\varphi$, $\Delta\eta$) = (0,0), and an away-side (AS) peak at
$\Delta\varphi$ = $\pi$ extending over a wide pseudorapidity range. The shape
and associated particle yields of the near-side peak unveils the internal
composition of the charm jet in term of $p_{\mathrm{T}}$ distribution and
multiplicity of its constituents. Moreover, studies of the peak features as a
function of the associated charged particle $p_{\mathrm{T}}$ provide insight
into the redistribution of the charm-quark momentum among the other particles
produced by its fragmentation in association to the heavy-flavour trigger, as
well as their radial displacement from the jet axis.

$\Lambda^{+}_{\mathrm{c}}$-hadron azimuthal correlation distributions were
measured for the first time in pp collisions at $\sqrt{s}$ = 13 TeV. The
comparison with the D meson-charged particles measurements in the same
collision system [9] can shed light on possible modifications to the charm
fragmentation and provide hints about the different hadronisation mechanisms
at play when the final state is a meson or a baryon. A large discrepancy is
observed at 3 $<p_{\mathrm{T}}^{\mathrm{D,\Lambda_{\mathrm{c}}^{+}}}<$ 5
GeV/$c$ and 0.3 $<p_{\mathrm{T}}^{\mathrm{assoc}}<$ 1.0 GeV/$c$, both in the
NS and in the AS region, as shown from the comparison of the azimuthal
correlations distribution in Fig. 3, suggesting a larger multiplicity of
small-momentum associated particle produced, respectively, collimated or in
the opposite direction to the $\Lambda^{+}_{\mathrm{c}}$ baryon. In addition
to different charm hadronisation mechanisms at play, the peaks enhancement
could also be possibly explained by assuming a softer fragmentation of the
charm baryons than into D mesons, as observed in charm-jet measurements,
translating to a larger initial energy of the charm parton, and consequently
in more phase space available for the production of other fragmenting
particles. Additionally, also the decay of known and unknown heavier charm-
baryon states into $\Lambda^{+}_{\mathrm{c}}$ baryons could possibly cause the
enhancement of the NS. PYTHIA 8 simulations, both with the Monash tune and
implementing CR-BLC, are not able to reproduce the
$\Lambda^{+}_{\mathrm{c}}$-hadron distributions, significantly underestimating
the NS yields, as illustrated in Fig. 3 for 0.3
$<p_{\mathrm{T}}^{\mathrm{assoc}}<$ 1.0 GeV/$c$. Similarly, also AS yields are
underestimated by the Monte Carlo simulations.

Figure 3: Left: comparison between $\Lambda^{+}_{\mathrm{c}}$-hadron and D
mesons-hadron azimuthal correlation distributions for 3
$<p_{\mathrm{T}}^{\mathrm{D,\Lambda_{\mathrm{c}}^{+}}}<$ 5 GeV/$c$ and 0.3
$<p_{\mathrm{T}}^{\mathrm{assoc}}<$ 1.0 GeV/$c$. Right: comparison between the
measured $\Lambda^{+}_{\mathrm{c}}$-hadron near-side yields and PYTHIA 8
predictions for 0.3 $<p_{\mathrm{T}}^{\mathrm{assoc}}<$ 1.0 GeV/$c$.

More insights about the heavy-flavour quark fragmentation were introduced by
studying the azimuthal correlations between electrons from semileptonic decays
of HF hadrons and other charged particle in pp and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV in the integrated transverse momentum
range 4 $<p^{\mathrm{e}}_{\mathrm{T}}<$ 12 GeV/$c$, shown in Fig.4. A good
compatibility was observed between the two colliding systems, suggesting
negligible impact with current uncertainties of cold nuclear matter effects on
the measurements, as it was also observed in D meson-hadron correlation in
p–Pb collisions [11].

Figure 4: Comparison between NS and AS yields (top row) and widths (bottom
row) of HF electron-hadron azimuthal correlations in pp and p–Pb collisions.

##  4 Conclusion

Charm-jets and azimuthal correlations of charm-origin particles provide a
benchmark for studying the fragmentation of charm quarks. Charm-baryon
measurements in pp collisions at $\sqrt{s}=$ 13 TeV suggest a softer charm
fragmentation with respect to D meson measurements. While PYTHIA 8 Monash
tune, relying on FF constrained to $\mathrm{e^{+}e^{-}}$ and $\mathrm{e^{-}p}$
data, correctly reproduced D mesons measurements, some tensions are observed
in the description of $\Lambda^{+}_{\mathrm{c}}$-jets: including mechanisms
sensitive to the surrounding partonic density (color reconnections) improves
the description of the parallel jet momentum fraction distributions, but is
not sufficient to explain the $\Lambda_{\mathrm{c}}$-hadron azimuthal
correlation distributions with respect to D-hadron correlations.

The larger data samples collected during the LHC Run 3 data taking and the
improved detector performances in tracking and vertexing will allow ALICE to
provide more accurate and precise measurements in the charm baryon sector.
Thus, measurements of the observables proposed here as function of the event
multiplicity from small to large collision systems will be accessible,
enabling the study of possible modifications to the charm fragmentation and
hadronisation mechanisms induced by the presence of a deconfined medium.

## References

  * [1] ALICE Collaboration, “Measurement of prompt $\mathrm{D}^{0}$, $\Lambda_{\rm c}^{+}$, and $\Sigma_{\rm c}^{0,++}$(2455) production in pp collisions at $\sqrt{s}$=13 TeV”, PLB 128 (2022) 012001
  * [2] ALICE Collaboration, “Observation of a multiplicity dependence in the $p_{\mathrm{T}}$-differential charm baryon-to-meson ratios in proton–proton collisions at $\sqrt{s}$=13 TeV”, PLB 829 (2022) 137065
  * [3] M. Cacciari, G. P. Salam, and G. Soyez, “FastJet User Manual”, EPJC 72 (2012) 1896
  * [4] ALICE Collaboration, “Measurement of the production of charm jets tagged with $\mathrm{D}^{0}$ mesons in pp collisions at $\sqrt{s}$ = 5.02 and 13 TeV”, arXiv:2204.10167.
  * [5] Torbjörn Sjöstrand et al., “An introduction to PYTHIA 8.2”, arXiv:1410.3012[hep-ph]
  * [6] S. Frixione, P. Nason and C. Oleari, “Matching NLO QCD computations with Parton Shower simulations: the POWHEG method”, JHEP 11 (2007), 070
  * [7] Jesper R. Christiansen and Peter Z. Skands, “String Formation Beyond Leading Colour”, JHEP 2015, 3 (2015)
  * [8] ALICE Collaboration, “Exploring the non-universality of charm hadronisation through the measurement of the fraction of jet longitudinal momentum carried by $\Lambda_{\rm c}^{+}$ baryons in pp collisions”, arXiv:2301.13798 [nucl-ex].
  * [9] ALICE Collaboration, “Investigating charm production and fragmentation via azimuthal correlations of prompt D mesons with charged particles in pp collisions at $\sqrt{s}$=13 TeV”, EPJC 82 (2022) 335.
  * [10] ALICE Collaboration, “Azimuthal correlations of heavy-flavor hadron decay electrons with charged particles in pp and p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV”, arXiv:2303.00591 [nucl-ex].
  * [11] ALICE Collaboration, “Azimuthal correlations of prompt D mesons with charged particles in pp and p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV”, EPJC 80, 979 (2020).