2021 107 9 June

Direct observation of the dead-cone effect in QCD

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

In particle collider experiments, elementary particle interactions with large
momentum transfer produce quarks and gluons (known as partons) whose evolution
is governed by the strong force, as described by the theory of quantum
chromodynamics (QCD) [1]. These partons subsequently emit further partons in a
process that can be described as a parton shower [2] which culminates in the
formation of detectable hadrons. Studying the pattern of the parton shower is
one of the key experimental tools for testing QCD. This pattern is expected to
depend on the mass of the initiating parton, through a phenomenon known as the
dead-cone effect, which predicts a suppression of the gluon spectrum emitted
by a heavy quark of mass $m_{\rm{Q}}$ and energy $E$, within a cone of angular
size $m_{\rm{Q}}$/$E$ around the emitter [3]. Previously, a direct observation
of the dead-cone effect in QCD had not been possible, owing to the challenge
of reconstructing the cascading quarks and gluons from the experimentally
accessible hadrons. We report the direct observation of the QCD dead cone by
using new iterative declustering techniques [4, 5] to reconstruct the parton
shower of charm quarks. This result confirms a fundamental feature of QCD.
Furthermore, the measurement of a dead-cone angle constitutes a direct
experimental observation of the non-zero mass of the charm quark, which is a
fundamental constant in the standard model of particle physics.

##  1 Introduction

In particle colliders, quarks and gluons are produced in high-energy
interactions through processes with large momentum transfer, which are
calculable and well described by quantum chromodynamics (QCD). These partons
undergo subsequent emissions, resulting in the production of more quarks and
gluons. This evolution can be described in the collinear limit by a cascade
process known as a parton shower, which transfers the original parton energy
to multiple lower energy particles. This shower then evolves into a multi-
particle final state, with the partons combining into a spray of
experimentally detectable hadrons known as a jet [6]. The pattern of the
parton shower is expected to depend on the mass of the emitting parton,
through a phenomenon known as the dead-cone effect, whereby the radiation from
an emitter of mass $m$ and energy $E$ is suppressed at angular scales smaller
than $m/E$, relative to the direction of the emitter. The dead-cone effect is
a fundamental feature of all gauge field theories (see Ref. [3] for the
derivation of the dead cone in QCD).

The dead-cone effect is expected to have sizeable implications for charm and
beauty quarks, which have masses of $1.28\pm 0.02$ GeV/$\it{c}^{2}$ and
$4.18^{+0.03}_{-0.02}$ GeV/$\it{c}^{2}$ (Ref. [1]) in the minimal subtraction
scheme, respectively, at energies on the GeV scale. The emission probability
in the collinear region, which is the divergent limit of QCD at which the
radiation is most intense, is suppressed with increasing mass of the quark.
This leads to a decrease in the mean number of particles produced in the
parton shower. The DELPHI Collaboration at the LEP $\rm{e}^{+}\rm{e}^{-}$
collider measured the multiplicity difference between events containing jets
initiated by heavy beauty quarks and those containing light quarks (up, down
or strange). They found that the differences depend only on the quark mass
[7], which was attributed to the suppression of collinear gluon radiation from
the heavy quark because of the dead-cone effect. A measurement of the momentum
density of jet constituents as a function of distance from the jet axis was
also performed by the ATLAS collaboration at CERN [8], which pointed to a
depletion of momentum close to the jet axis that was ascribed as a consequence
of the dead-cone effect. The mass of the beauty quark was also estimated
through a phenomenological fit to the measured data [9]. As hard (large
transverse momentum) emissions are preferentially emitted at small angles, and
are therefore suppressed for massive emitters, heavy quarks also retain a
larger fraction of their original momentum compared to lighter quarks, leading
to a phenomenon known as the leading-particle effect. This has been well
established experimentally, with the fraction of the jet momentum carried by
the leading (highest transverse momentum) hadron containing a charm or beauty
quark (heavy-flavour hadron) in jets, peaking at 0.6–0.7 and 0.8–0.9,
respectively, whereas the corresponding fraction carried by the leading hadron
in light quark-initiated jets peaks at smaller values [10, 11, 12, 13, 14].

Until now, a direct experimental measurement of the dead-cone effect has been
subject to two main challenges. First, the dead-cone angular region can
receive contributions from hadronization effects or particles that do not
originate from the gluon radiation from the heavy-flavour quark, such as the
decay products of heavy-flavour hadrons. The second difficulty lies in the
accurate determination of the dynamically evolving direction of the heavy-
flavour quark, relative to which the radiation is suppressed, throughout the
shower process. The development of new experimental declustering techniques
[4] enables these aforementioned difficulties to be overcome by reconstructing
the evolution of the jet shower, giving access to the kinematic properties of
each individual emission. These techniques reorganise the particle
constituents of an experimentally reconstructed jet, to access the building
blocks of the shower and trace back the cascade process. Isolated elements of
the reconstructed parton shower that are likely to be unmodified by
hadronization processes provide a good proxy for real quark and gluon
emissions (splittings). These reclustering techniques have been demonstrated
in inclusive (without tagging the initiating parton flavour) jets to
successfully reconstruct splittings that are connected to or that preserve the
memory of the parton branchings. This is demonstrated by measurements such as
the groomed momentum balance [15, 16, 17, 18], which probes the Dokshitzer-
Gribov-Lipatov-Altarelli-Parisi splitting function [19], and the Lund plane
[20], which exposes the running of the strong coupling with the scale of the
splittings. An experimental method to expose the dead cone in boosted top-
quark events was also proposed in Ref. [21].

Reclustering techniques are extended in this work to jets containing a charm
quark based on the prescription given in Ref. [22]. These jets are tagged
through the presence of a reconstructed D0 meson amongst their constituents,
which has a mass of $1.86$ GeV/$\it{c}^{2}$ (Ref. [1]) and is composed of a
heavy charm quark and a light anti-up quark. The measurement is performed in
proton–proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV at
the Large Hadron Collider (LHC), using the ALICE (A Large Ion Collider
Experiment) detector. Further details of the detector apparatus and data
measured can be found in the Methods. As the charm-quark flavour is conserved
through the shower process, this provides an opportunity to isolate and trace
back the emission history of the charm quark. In this way, by comparing the
emission patterns of charm quarks to those of light quarks and gluons, the QCD
dead cone can be directly revealed.

##  2 Selecting jets containing a D0 meson

To select jets initiated by a charm quark, through the presence of a D0 meson
in their list of constituents, the D0 mesons and jets need to be reconstructed
in the events. The D0-meson candidates (and their anti-particles) were
reconstructed in the transverse-momentum interval $2<p_{\rm T}^{\rm D^{0}}<36$
GeV/$\it{c}$, through the D${}^{0}\rightarrow\rm{K}^{-}\rm{\pi}^{+}$ (and
charged conjugate) hadronic decay channel, which has a branching ratio of
$3.95\pm 0.03\%$ (Ref. [1]). The D0-meson candidates were identified by
topological selections based on the displacement of the D0-meson candidate
decay vertex, in addition to applying particle identification on the D0-meson
candidate decay particles. These selection criteria largely suppress the
combinatorial background of $\rm{K}^{\mp}\rm{\pi}^{\pm}$ pairs that do not
originate from the decay of a D0 meson. Further details on the selection
criteria are provided in Ref. [23].

Tracks (reconstructed charged-particle trajectories) corresponding to the
D0-meson candidate decay particles were replaced by the reconstructed D0-meson
candidate in the event, with the D0-meson candidate four-momentum being the
sum of the decay-particle four-momenta. One benefit of this procedure is to
avoid the case in which the decay products of the D0-meson candidate fill the
dead-cone region. A jet-finding algorithm was then used to cluster the
particles (tracks and the D0-meson candidate) in the event, to reconstruct the
parton shower by sequentially recombining the shower particles into a single
object (the jet). The jet containing the D0-meson candidate was then selected.
The four-momentum of the jet is a proxy for the four-momentum of the charm
quark initiating the parton shower. The jet-finding algorithm used was the
anti-$k_{\rm{T}}$ algorithm [24] from the Fastjet package [25], which is a
standard choice for jet reconstruction because of its high performance in
reconstructing the original parton kinematics. More details on the jet finding
procedure can be found in the Methods.

##  3 Reconstructing the jet shower

Figure 1: Reconstruction of the showering quark. A sketch detailing the
reconstruction of the showering charm quark, using iterative declustering, is
presented. The top panels show the initial reclustering procedure with the C/A
algorithm, in which the particles separated by the smallest angles are brought
together first. Once the reclustering is complete, the declustering procedure
is carried out by unwinding the reclustering history. Each splitting node is
numbered according to the declustering step in which it is reconstructed. With
each splitting, the charm-quark energy, $E_{\rm{Radiator,n}}$, is reduced and
the gluon is emitted at a smaller angle, $\theta_{\rm{n}}$, with respect to
previous emissions. The mass of the heavy quark, $m_{\rm{Q}}$, remains
constant throughout the showering process. At each splitting, gluon emissions
are suppressed in the dead-cone region (shown by a red cone for the last
splitting), which increases in angle as the quark energy decreases throughout
the shower.

Once jets containing a D0-meson candidate amongst their constituents are
selected, the internal cascade process is reconstructed. This is done by
reorganizing (reclustering) the jet constituents according to the Cambridge-
Aachen (C/A) algorithm [26], which clusters these constituents based solely on
their angular distance from one another. A pictorial representation of this
reclustering process, which starts by reconstructing the smallest angle
splittings, is shown in the top panels of Fig. 1. As QCD emissions
approximately follow an angular-ordered structure [27], the C/A algorithm was
chosen as it also returns an angular-ordered splitting tree.

This splitting tree is then iteratively declustered by unwinding the
reclustering history, to access the building blocks of the reconstructed jet
shower. At each declustering step, two prongs corresponding to a splitting are
returned. The angle between these splitting daughter prongs, $\theta$, the
relative transverse momentum of the splitting, $k_{\rm{T}}$, and the sum of
the energy of the two prongs, $E_{\rm{Radiator}}$, are registered. As the
charm flavour is conserved throughout the showering process, the full
reconstruction of the D0-meson candidate enables the isolation of the
emissions of the charm quark in the parton shower, by following the daughter
prong containing the fully reconstructed D0-meson candidate at each
declustering step. This can be seen in the bottom part of Fig. 1, which shows
the evolution of the charm quark reconstructed from the measured final state
particles. Moreover, the kinematic properties of the charm quark are updated
along the splitting tree, enabling an accurate reconstruction of each emission
angle against the dynamically evolving charm-quark direction. It was verified
that in more than $99\%$ of the cases the prong containing the D0-meson
candidate at each splitting coincided with the leading prong. This means that
following the D0-meson candidate or leading prong at each step is equivalent,
and therefore a complementary measurement for an inclusive jet sample, when no
flavour tagging is available, can be made by following the leading prong
through the reclustering history. As the inclusive sample is dominated by
massless gluon and nearly massless light quark-initiated jets, it acts as a
reference to highlight the mass effects present in the charm-tagged sample.

##  4 Extracting the true charm splittings

The selected sample of splittings has contributions from jets tagged with
combinatorial $\rm{K}^{\mp}\rm{\pi}^{\pm}$ pairs, which are not rejected by
the applied topological and particle identification selections. The measured
invariant mass of real D0 mesons, which corresponds to the rest mass, is
distributed in a Gaussian (because of uncertainties in the measurement of the
momenta of the $\rm{K}^{\mp}\rm{\pi}^{\pm}$ pairs) with a peak at the true
D0-meson mass. This enables the implementation of a statistical two-
dimensional side-band subtraction procedure, which characterizes the
background distribution of splittings by sampling the background-dominated
regions of the D0-meson candidate invariant mass distributions, far away from
the signal peak. In this way the combinatorial contribution can be accounted
for and removed. Furthermore, the selections on the D0-meson candidates also
select a fraction of D0 mesons originating as a product of beauty-hadron
decays. These were found to contribute $10$–$15\%$ of the reconstructed
splittings, with only a small influence on the results which will be discussed
later. The studies were performed using Monte-Carlo (MC) PYTHIA 6.425 (Perugia
2011) [28, 29] simulations (this generator includes mass effects in the parton
shower [30] and was used for all MC-based corrections in this work),
propagating the generated particles through a detailed description of the
ALICE detector with GEANT3 (Ref. [31]). The finite efficiency of selecting
real D0-meson tagged jets, through the chosen selection criteria on the
D0-meson candidates, as well as kinematic selections on the jets, was studied
and accounted for through MC simulations. This efficiency was found to be
strongly $p_{\rm T}^{\rm D^{0}}$ dependent and different for D0 mesons
originating from the hadronization of charm quarks or from the decay of beauty
hadrons. Further details on these analysis steps can be found in the Methods.

As the reconstructed jet shower is built from experimentally detectable
hadrons, as opposed to partons, hadronization effects must be accounted for.
As hadronization processes occur at low non-perturbative scales, they are
expected to distort the parton shower by mainly adding low-$k_{\rm{T}}$
splittings [32]. A selection of $k_{\rm{T}}>200$ MeV/$\it{c}$ ensures that
only sufficiently hard splittings are accepted and is used to suppress such
hadronization effects. Other choices of $k_{\rm{T}}$ selection were also
explored, with stronger $k_{\rm{T}}$ selections further removing non-
perturbative effects from the measurement, at the expense of statistical
precision. Other non-perturbative effects, such as the underlying event,
contribute with extra soft splittings primarily at large angles and do not
affect the small-angle region under study.

Detector effects also distort the reconstructed parton shower through
inefficiencies and irresolution in the tracking of charged particles. However,
these have been tested and largely cancel in the final observable and any
residual effects are quantified in a data-driven way and included in the
systematic uncertainties.

It should be noted that in addition to direct heavy-flavour pair creation in
the elementary hard scattering, charm quarks can also be produced in higher-
order processes as a result of gluon splitting. Therefore, the shower history
of D0 mesons containing such charm quarks will also have contributions from
splittings originating from gluons. Furthermore, in the case of high
transverse momentum gluons in which the charm quarks are produced close in
angle to each other, the dead-cone region of the charm quark hadronizing into
the reconstructed D0 meson can be populated by particles produced in the
shower, hadronization and subsequent decays of the other (anti-)charm quark.
The influence of such contaminations through gluon splittings was studied with
MC simulations and found to be negligible.

##  5 The observable $R(\theta)$

The observable used to reveal the dead cone is built by constructing the ratio
of the splitting angle ($\theta$) distributions for D0-meson tagged jets and
inclusive jets, in bins of $E_{\rm{Radiator}}$. This is given by,

$R(\theta)=\left.\frac{1}{N^{\rm{D^{0}\,jets}}}\frac{\rm{d}\it{n}^{\rm{D^{0}\,jets}}}{\rm{d}\ln(1/\theta)}{{{/}}}\frac{1}{N^{\rm{inclusive\,\,jets}}}\frac{\rm{d}\it{n}^{\rm{inclusive\,\,jets}}}{\rm{d}\ln(1/\theta)}\right|_{\,k_{\rm
T},\,E_{\rm{Radiator}}}$ (1)

where the $\theta$ distributions were normalized to the number of jets that
contain at least one splitting in the given $E_{\rm{Radiator}}$ and $k_{\rm
T}$ selection, denoted by $N^{\rm{D^{0}\,jets}}$ and
$N^{\rm{inclusive\,\,jets}}$ for the D0-meson tagged and inclusive jet
samples, respectively. Expressing equation (1) in terms of the logarithm of
the inverse of the angle is natural, given that at leading order the QCD
probability for a parton to split is proportional to
$\ln(1/\theta)\ln(k_{\rm{T}})$.

A selection on the transverse momentum of the leading track in the leading
prong of each registered splitting in the inclusive jet sample, $p_{\rm
T,inclusivejets}^{\rm ch,leadingtrack}\geq 2.8$ GeV/$\it{c}$, was applied.
This corresponds to the transverse mass (obtained through the quadrature sum
of the rest mass and transverse momentum) of a $2$ GeV/$\it{c}$ D0-meson and
accounts for the $p_{\rm T}^{\rm D^{0}}$ selection in the D0-meson tagged jet
sample, enabling a fair comparison of the two samples.

In the absence of mass effects, the charm quark is expected to have the same
radiating properties as a light quark. In this limit, equation (1) can be
rewritten as

$R(\theta)_{\rm{no\>dead-
cone\>limit}}=\left.\frac{1}{N^{\rm{LQ\>jets}}}\frac{\rm{d}\it{n}^{\rm{LQ\>jets}}}{\rm{d}\ln(1/\theta)}{{{/}}}\frac{1}{N^{\rm{inclusive\>jets}}}\frac{\rm{d}\it{n}^{\rm{inclusive\>jets}}}{\rm{d}\ln(1/\theta)}\right|_{\,k_{\rm
T},\,E_{\rm{Radiator}}},$ (2)

where the superscript LQ refers to light quarks, and the inclusive sample
contains both light-quark and gluon-initiated jets. This indicates that the
$R(\theta)_{\rm{no\>dead-cone\>limit}}$ ratio depends on the differences
between light-quark and gluon radiation patterns, which originate from the
fact that gluons carry two colour charges (the charge responsible for strong
interactions) whereas quarks only carry one. These differences result in
quarks fragmenting at a lower rate and more collinearly than gluons.
Therefore, in the limit of having no dead-cone effect, the ratio of the
$\theta$ distributions for D0-meson tagged jets and inclusive jets becomes
$R(\theta)_{\rm{no\>dead-cone\>limit}}>1$, at small angles. This was verified
through SHERPA v.2.2.8 (Ref. [33]) and PYTHIA v.8.230 (Tune 4C) [34] MC
generator calculations, with the specific $R(\theta)_{\rm{no\>dead-
cone\>limit}}$ value dependent on the quark and gluon fractions in the
inclusive sample. SHERPA and PYTHIA are two MC generators commonly used in
high-energy particle physics and they use different shower prescriptions and
hadronization models. Both models implement the dead-cone effect.

##  6 Exposing the dead cone

The measurements of $R(\theta)$, in the three radiator (charm-quark) energy
intervals $5<E_{\rm{Radiator}}<10$ GeV, $10<E_{\rm{Radiator}}<20$ GeV and
$20<E_{\rm{Radiator}}<35$ GeV, are presented in Fig. 2. Detector effects
largely cancel out in the ratio and results are compared to particle-level
simulations. Residual detector effects are considered in the systematic
uncertainty together with uncertainties associated with the reconstruction and
signal extraction of D0-meson tagged jets, as well as detector inefficiencies
in the reconstruction of charged tracks in both the D0-meson tagged and
inclusive jet samples. More details on the study of systematic uncertainties
can be found in the Methods.

A significant suppression in the rate of small-angle splittings is observed in
D0-meson tagged jets relative to the inclusive jet population. In Fig. 2, the
data are compared with particle-level SHERPA (green) and PYTHIA v.8.230 (blue)
MC calculations, with SHERPA v.2.2.8 providing a better agreement with the
data. The no dead-cone baseline, as described in equation (2), is also
provided for each MC generator (dashed lines). The suppression of the measured
data points relative to the no dead-cone limit directly reveals the dead cone
within which the charm-quark emissions are suppressed. The coloured regions in
the plots correspond to the dead-cone angles in each $E_{\rm{Radiator}}$
interval, $\theta_{\rm{dc}}<m_{\rm{Q}}/E_{\rm{Radiator}}$, where emissions are
suppressed. For a charm-quark mass $m_{\rm{Q}}=1.275$ GeV/$\it{c}^{2}$ (Ref.
[1]), these angles correspond to $\rm{ln}(1/\theta_{\rm{dc}})\geq 1.37$, $2$
and $2.75$ for the intervals $5<E_{\rm{Radiator}}<10$ GeV,
$10<E_{\rm{Radiator}}<20$ GeV and $20<E_{\rm{Radiator}}<35$ GeV, respectively.
These values are in qualitative agreement with the angles at which the data
starts to show suppression relative to the MC limits for no dead-cone effect.
The magnitude of this suppression increases with decreasing radiator energy,
as expected from the inverse dependence of the dead-cone angle on the energy
of the radiator.

Figure 2: Ratios of splitting angle probability distributions. The ratios of
the splitting-angle probability distributions for D0-meson tagged jets to
inclusive jets, $R(\theta)$, measured in proton–proton collisions at
$\sqrt{s}=13$ TeV, are shown for $5<E_{\rm{Radiator}}<10$ GeV (left panel),
$10<E_{\rm{Radiator}}<20$ GeV (middle panel) and $20<E_{\rm{Radiator}}<35$ GeV
(right panel). The data are compared with PYTHIA v.8 and SHERPA simulations,
including the no dead-cone limit given by the ratio of the angular
distributions for light-quark jets (LQ) to inclusive jets. The pink shaded
areas correspond to the angles within which emissions are suppressed by the
dead-cone effect, assuming a charm-quark mass of $1.275$ GeV/$\it{c}^{2}$.

A lower limit for the significance of the small-angle suppression is estimated
by comparing the measured data to $R(\theta)=1$, which represents the limit of
no dead-cone effect in the case in which the inclusive sample is entirely
composed of light quark-initiated jets. To test the compatibility of the
measured data with the $R(\theta)=1$ limit, a statistical test was performed
by generating pseudodata distributions consistent with the statistical and
systematic uncertainties of the measured data. A chi-square test was then
carried out against this hypothesis for each of the pseudodata distributions.
The mean P values correspond to significances of $7.7\sigma$, $3.5\sigma$ and
$1.0\sigma$, for the $5<E_{\rm{Radiator}}<10$ GeV, $10<E_{\rm{Radiator}}<20$
GeV and $20<E_{\rm{Radiator}}<35$ GeV intervals, respectively. A $\sigma$
value greater than $5$ is considered the criteria for a definitive
observation, whereas the value of $1.0$ is consistent with the null
hypothesis.

The MC distributions shown were generated separately for prompt (charm-quark
initiated) and non-prompt (beauty-quark initiated) D0-meson tagged jet
production and were then combined using the prompt and non-prompt fractions in
data calculated with POWHEG [35]+PYTHIA 6.425 [34] simulations. The non-prompt
fraction was found to be independent of the splitting angle and corresponds to
approximately $10\%$ of the splittings in the $5<E_{\rm{Radiator}}<10$ GeV
interval and approximately $15\%$ of the splittings in both the
$10<E_{\rm{Radiator}}<20$ GeV and $20<E_{\rm{Radiator}}<35$ GeV intervals. It
was verified through the MC simulations that non-prompt D0-meson tagged jets
should exhibit a smaller suppression at small angles in $R(\theta)$ compared
with inclusive jets than their prompt counterparts. This is due to the
additional decay products accompanying non-prompt D0-meson tagged jets that
are produced in the decay of the beauty hadron. These may populate the dead-
cone region, leading to a smaller observed suppression in $R(\theta)$, despite
the larger dead-cone angle of the heavier beauty quark.

##  7 Conclusions

We have reported the direct measurement of the QCD dead cone, using iterative
declustering of jets tagged with a fully reconstructed charmed hadron. The
dead cone is a fundamental phenomenon in QCD, dictated by the non-zero quark
masses, whose direct experimental observation has previously remained elusive.
This measurement provides insight into the influence of mass effects on jet
properties and provides constraints for MC models. These results pave the way
for a study of the mass dependence of the dead-cone effect, by measuring the
dead cone of beauty jets tagged with a reconstructed beauty hadron.

A future study of the dead-cone effect in heavy-ion collisions, in which
partons interact strongly with the hot QCD medium that is formed and undergo
energy loss through (dominantly) medium-induced radiation, is also envisaged.
If a dead cone were observed for these medium-induced emissions, it would be a
confirmation of the theoretical understanding of in-medium QCD radiation,
which is a primary tool used to characterize the high-temperature phase of QCD
matter [36, 37, 38].

The quark masses are fundamental constants of the standard model of particle
physics and needed for all numerical calculations within its framework.
Because of confinement, their values are commonly inferred through their
influence on hadronic observables. An exception is the top quark, which decays
before it can hadronize, as its mass can be constrained experimentally from
the direct reconstruction of the decay final states [39] (see Ref. [40] for a
review of top mass measurements at the Fermilab Tevatron and CERN LHC).

By accessing the kinematics of the showering charm quark, before
hadronization, and directly uncovering the QCD dead-cone effect, our
measurement provides direct sensitivity to the mass of quasi-free charm
quarks, before they bind into hadrons.

Furthermore, future high-precision measurements using this technique on charm
and beauty-tagged jets, potentially in conjunction with machine-learning tools
to separate quark and gluon emissions, could experimentally constrain the
magnitude of the quark masses.

## Acknowledgements

The ALICE Collaboration is grateful to Urs Wiedemann for his valuable
suggestions and fruitful discussions. We are also grateful to Davide
Napoletano for providing the SHERPA configuration files and useful
discussions.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A Methods

###  A.1 Detector setup and data set

The analysis was performed with the ALICE detector at the CERN LHC [1]. The
ALICE Inner Tracking System [2] and Time Projection Chamber [3] were used for
charged-particle reconstruction, whilst particle identification (PID) was
obtained using the combined information from the Time Projection Chamber and
the Time-Of-Flight detectors [4]. These detectors are located in the ALICE
central barrel, which has full azimuthal coverage and a pseudorapidity range
of $|\eta|<0.9$. The data set used in this analysis was collected in 2016,
2017, and 2018 in proton–proton collisions at $\sqrt{s}=13$ TeV, with a
minimum-bias trigger condition defined by the presence of at least one hit in
each of the two V0 scintillators [5]. This trigger accepts all events of
interest for this analysis and the collected data sample corresponds to an
integrated luminosity of $\pazocal{L}_{\rm{int}}=25$ nb-1.

###  A.2 Jet finding and tagging

Jet finding was performed using the anti-$k_{\rm{T}}$ algorithm, with a jet
resolution parameter of $R=0.4$. The $E$-scheme recombination strategy was
chosen to combine the tracks of the jet by adding their four-momenta, with a
geometric constraint on the pseudorapidity of $|\eta|<0.5$ enforced on the jet
axis, to ensure that the full jet cone was contained in the acceptance of the
central barrel of the ALICE detector. The ALICE detector has excellent
tracking efficiency down to low $p_{\rm{T}}$ ($\approx 80\%$ at
$p_{\rm{T}}=500$ MeV/$\it{c}$) which is homogeneous as a function of
pseudorapidity and azimuthal angle [1], within the acceptance. The effect of
track density on the tracking efficiency is also negligible [6]. The angular
resolution is about $20\%$ down to splitting angles of 0.05 radians, which
motivated a track-based jet measurement as opposed to a full jet measurement
using calorimetric information. Recent measurements [20, 15] have shown that
track-based jet observables are successful at reconstructing the parton shower
information through declustering techniques, despite missing the information
from the neutral component of the jet.

Jets with a transverse momentum in the interval of $5\leq
p_{\rm{T,jet}}^{\rm{ch}}<50$ GeV/$\it{c}$ were selected for this analysis. To
mitigate against the cases in which two D0-meson candidates share a common
decay track, jet-finding passes were performed independently for each D0-meson
candidate in the event, each time replacing only the decay tracks of that
candidate with the corresponding D0-meson candidate. In each pass the jet
containing the reconstructed D0-meson candidate of that pass was subsequently
tagged as a charm-initiated jet candidate.

###  A.3 Subtraction of the combinatorial background in the D0-meson candidate
sample

To extract the true D0-meson tagged jet $R(\theta)$ distributions and remove
the contribution from combinatorial $\rm{K}^{\mp}\rm{\pi}^{\pm}$ pairs
surviving the topological and PID selections, a side-band subtraction
procedure was used. This involved dividing the sample in $p_{\rm T}^{\rm
D^{0}}$ intervals and fitting the invariant-mass distributions of the D0
candidates in each interval with a Gaussian function for the signal and an
exponential function for the background. The width ($\sigma$) and mean of the
fitted Gaussian were used to define signal and side-band regions, with the
two-dimensional distributions of $\theta$ and $E_{\rm{Radiator}}$ for D0-meson
tagged jet candidates,
$\rho(\theta,E_{\rm{Radiator}})^{\rm{D}^{0}\rm{jet\,candidate}}$, obtained in
each region. The signal region was defined to be within $2\sigma$ on either
side of the Gaussian mean and contained most of the real D0 mesons, with some
contamination present from the combinatorial background. The side-band regions
were defined to be from $4\sigma$ to $9\sigma$ away from the peak in either
direction and were composed entirely of background D0-meson candidates. The
combined $\rho(\theta,E_{\rm{Radiator}})^{\rm{D}^{0}\rm{jet\,candidate}}$
distributions measured in the two side-band regions represent the structural
form of the contribution of background candidates to the
$\rho(\theta,E_{\rm{Radiator}})^{\rm{D}^{0}\rm{jet\,candidate}}$ distribution
measured in the signal region. In this way, the background component of the
total $\rho(\theta,E_{\rm{Radiator}})^{\rm{D}^{0}\rm{jet\,candidate}}$
measured in the signal region can be subtracted, using the following equation,

$\rho(\theta,E_{\rm{Radiator}})^{\rm{D^{0}jet}}=\sum_{i}\frac{1}{\epsilon_{i}}\Big{[}\,(\rho(\theta,E_{\rm{Radiator}})^{\rm{D}^{0}\rm{jet\,candidate}}_{\rm{S}}-\frac{A_{\rm{S}}}{A_{\rm{B}}}\rho(\theta,E_{\rm{Radiator}})^{\rm{D}^{0}\rm{jet\,candidate}}_{\rm{B}}\Big{]}\,$
(3)

where the subscripts S and B denote the signal and side-band regions of the
invariant-mass distributions, respectively. The $A_{\rm{S}}$ and $A_{\rm{B}}$
variables are the areas under the background fit function in the signal and
combined side-band regions, respectively, and were used to normalize the
magnitude of the background in the side-band regions to that in the signal
region. The D0-meson tagged jet selection efficiency (discussed in more detail
in the next section) is denoted by $\epsilon$, with the index $i$ running over
the $p_{\rm T}^{\rm D^{0}}$ bins. As a result of this side-band subtraction,
the true D0-meson tagged jet $\rho(\theta,E_{\rm{Radiator}})^{\rm{D^{0}jet}}$
distributions are obtained, in the different intervals of $p_{\rm T}^{\rm
D^{0}}$.

###  A.4 D0-meson tagged jet reconstruction efficiency correction

The topological and PID selections used to identify the D0 mesons, in the
chosen jet kinematic interval, have a limited efficiency, which exhibits a
strong $p_{\rm{T}}$ dependence. Therefore, before integrating the side-band
subtracted $\rho(\theta,E_{\rm{Radiator}})^{\rm{D^{0}jet}}$ distributions
across the measured $p_{\rm T}^{\rm D^{0}}$ intervals, the
$\rho(\theta,E_{\rm{Radiator}})^{\rm{D^{0}jet}}$ distributions were corrected
for this efficiency. The efficiency, $\epsilon$, was estimated from PYTHIA v.6
MC studies and varies strongly with $p_{\rm T}^{\rm D^{0}}$, from
approximately $0.01$ at $p_{\rm T}^{\rm D^{0}}=2.5$ GeV/$\it{c}$ to
approximately $0.3$ at $p_{\rm T}^{\rm D^{0}}=30$ GeV/$\it{c}$ for prompt
D0-meson tagged jets and from approximately $0.01$ at $p_{\rm T}^{\rm
D^{0}}=2.5$ GeV/$\it{c}$ to approximately $0.2$ at $p_{\rm T}^{\rm{D^{0}}}=30$
GeV/$\it{c}$ for non-prompt D0-meson tagged jets. As the prompt and non-prompt
D0-meson tagged jet reconstruction efficiencies were different, the final
efficiency was obtained by combining the prompt and non-prompt D0-tagged jet
reconstruction efficiencies, evaluated separately. These were combined with
weights derived from simulations, corresponding to the admixture of prompt and
non-prompt D0-meson tagged jets in the reconstructed sample. The fractions of
this admixture were obtained in bins of $p_{\rm T}^{\rm D^{0}}$ by calculating
the prompt and non-prompt D0-meson tagged jet production cross sections with
POWHEG combined with PYTHIA v.6 showering.

###  A.5 Evaluation of systematic uncertainties

Considered sources of systematic uncertainty in the measurement relate to the
reconstruction and signal extraction of D0-meson candidates, with the former
contributing as the leading source. These uncertainties were estimated by
varying the topological and PID selections, as well as the fitting and side-
band subtraction configurations applied to the D0-meson candidate invariant
mass distributions. Variations were chosen that tested the influence of
selected analysis parameters as much as possible, while maintaining a
reasonable significance in the signal extraction. For each of these
categories, the root mean square of all deviations was taken as the final
systematic uncertainty. Theoretical uncertainties in the prompt and non-prompt
D0-meson tagged jet production cross sections from POWHEG were also considered
in the calculation of the reconstruction efficiency, with the largest
variation taken as the uncertainty. For each category, the final systematic
uncertainty was symmetrized before adding up the uncertainties in quadrature
across all categories to obtain the total systematic uncertainty of the
D0-meson tagged jet measurement.

For the inclusive-jet results, the minimum $p_{\rm{T}}$ requirement on the
track with the highest transverse momentum within the leading prong of each
splitting was varied. The magnitude of the variation was taken to be the
resolution of the transverse momentum of a D0-meson with $p_{\rm T}^{\rm
D^{0}}=2$ GeV/$\it{c}$, which was found to be $0.06$ GeV/$\it{c}$. Variations
above and below the nominal selection value were made and the largest
deviation was symmetrized. Systematic detector effects are dominated by the
tracking efficiency and were shown in detector simulations to affect both the
D0-meson tagged jet and inclusive-jet samples equally, and they largely
cancelled in the $R(\theta)$ ratio. Therefore, the systematic uncertainty of
$R(\theta)$ because of detector effects was estimated directly on the ratio by
randomly removing $15\%$ of the reconstructed tracks, as given by the tracking
efficiency of the ALICE detector, in the track samples used for clustering
both the D0-tagged jets and inclusive jets. The ratio of the resulting
$R(\theta)$ distribution to the case with no track removal was taken, to
obtain the uncertainty, which was symmetrized.

The relative uncertainty of $R(\theta)$ resulting from the separate D0-meson
tagged jet and inclusive-jet uncertainties was calculated, with the resulting
absolute uncertainty added in quadrature to the detector effects uncertainty
to obtain the total systematic uncertainty of the $R(\theta)$ measurement. The
magnitude of each of these sources of systematic uncertainty is shown in Table
1, for the smallest-angle splittings corresponding to the interval
$2\leq\ln(1/\theta)<3$, in which the uncertainties are largest.

Table 1: The percentage magnitude of the systematic uncertainties of each
source considered, and the total systematic uncertainty, for the $R(\theta)$
variable are shown for the smallest splitting-angle interval
$2\leq\ln(1/\theta)<3$ $R(\theta)$ systematic uncertainties ($\%$)
---
|  $E_{\rm{Radiator}}$ (GeV)
Source | $5-10$ | $10-20$ | $20-35$
Invariant-mass fitting | $2.3$ | $1.4$ | $3.0$
Side-band subtraction | $2.0$ | $1.8$ | $1.4$
D0-jet selection stability | $4.1$ | $5.0$ | $7.2$
Non-prompt contribution | $1.0$ | $3.5$ | $1.1$
Leading hadron $p_{\rm{T}}$ selection | $2.0$ | $3.2$ | $0.2$
Detector effects | $0.7$ | $5.2$ | $0.9$
Total | $5.6$ | $8.9$ | $8.1$

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Giubilato28, A.M.C. Glaenzer140, P. Glässel107, D.J.Q. Goh85, V. Gonzalez145,
L.H. González-Trueba73, S. Gorbunov40, M. Gorgon2, L. Görlich120, S.
Gotovac36, V. Grabski73, L.K. Graczykowski144, L. Greiner82, A. Grelli64, C.
Grigoras35, V. Grigoriev96, A. GrigoryanI,1, S. Grigoryan77,1, O.S.
Groettvik21, F. Grosa35,61, J.F. Grosse-Oetringhaus35, R. Grosso110, G.G.
Guardiano124, R. Guernane81, M. Guilbaud117, K. Gulbrandsen92, T. Gunji135, A.
Gupta104, R. Gupta104, S.P. Guzman46, L. Gyulai147, M.K. Habib110, C.
Hadjidakis80, G. Halimoglu70, H. Hamagaki85, G. Hamar147, M. Hamid7, R.
Hannigan121, M.R. Haque144,89, A. Harlenderova110, J.W. Harris148, A.
Harton10, J.A. Hasenbichler35, H. Hassan99, D. Hatzifotiadou55, P. Hauer44,
L.B. Havener148, S. Hayashi135, S.T. Heckel108, E. Hellbär70, H. Helstrup37,
T. Herman38, E.G. Hernandez46, G. Herrera Corral9, F. Herrmann146, K.F.
Hetland37, H. Hillemanns35, C. Hills130, B. Hippolyte139, B. Hofman64, B.
Hohlweger93,108, J. Honermann146, G.H. Hong149, D. Horak38, S. Hornung110, A.
Horzyk2, R. Hosokawa15, P. Hristov35, C. Hughes133, P. Huhn70, T.J.
Humanic100, H. Hushnud112, L.A. Husova146, A. Hutson127, D. Hutter40, J.P.
Iddon35,130, R. Ilkaev111, H. Ilyas14, M. Inaba136, G.M. Innocenti35, M.
Ippolitov91, A. Isakov38,98, M.S. Islam112, M. Ivanov110, V. Ivanov101, V.
Izucheev94, M. Jablonski2, B. Jacak82, N. Jacazio35, P.M. Jacobs82, S.
Jadlovska119, J. Jadlovsky119, S. Jaelani64, C. Jahnke124,123, M.J.
Jakubowska144, A. Jalotra104, M.A. Janik144, T. Janson76, M. Jercic102, O.
Jevons113, F. Jonas99,146, P.G. Jones113, J.M. Jowett 35,110, J. Jung70, M.
Jung70, A. Junique35, A. Jusko113, J. Kaewjai118, P. Kalinak66, A. Kalweit35,
V. Kaplin96, S. Kar7, A. Karasu Uysal79, D. Karatovic102, O. Karavichev65, T.
Karavicheva65, P. Karczmarczyk144, E. Karpechev65, A. Kazantsev91, U.
Kebschull76, R. Keidel48, D.L.D. Keijdener64, M. Keil35, B. Ketzer44, Z.
Khabanova93, A.M. Khan7, S. Khan16, A. Khanzadeev101, Y. Kharlov94, A.
Khatun16, A. Khuntia120, B. Kileng37, B. Kim17,63, C. Kim17, D. Kim149, D.J.
Kim128, E.J. Kim75, J. Kim149, J.S. Kim42, J. Kim107, J. Kim149, J. Kim75, M.
Kim107, S. Kim18, T. Kim149, S. Kirsch70, I. Kisel40, S. Kiselev95, A.
Kisiel144, J.P. Kitowski2, J.L. Klay6, J. Klein35, S. Klein82, C. Klein-
Bösing146, M. Kleiner70, T. Klemenz108, A. Kluge35, A.G. Knospe127, C.
Kobdaj118, M.K. Köhler107, T. Kollegger110, A. Kondratyev77, N. Kondratyeva96,
E. Kondratyuk94, J. Konig70, S.A. Konigstorfer108, P.J. Konopka35,2, G.
Kornakov144, S.D. Koryciak2, L. Koska119, A. Kotliarov98, O. Kovalenko88, V.
Kovalenko115, M. Kowalski120, I. Králik66, A. Kravčáková39, L. Kreis110, M.
Krivda113,66, F. Krizek98, K. Krizkova Gajdosova38, M. Kroesen107, M.
Krüger70, E. Kryshen101, M. Krzewicki40, V. Kučera35, C. Kuhn139, P.G.
Kuijer93, T. Kumaoka136, D. Kumar143, L. Kumar103, N. Kumar103, S. Kundu35,89,
P. Kurashvili88, A. Kurepin65, A.B. Kurepin65, A. Kuryakin111, S. Kushpil98,
J. Kvapil113, M.J. Kweon63, J.Y. Kwon63, Y. Kwon149, S.L. La Pointe40, P. La
Rocca27, Y.S. Lai82, A. Lakrathok118, M. Lamanna35, R. Langoy132, K.
Lapidus35, P. Larionov53, E. Laudi35, L. Lautner35,108, R. Lavicka38, T.
Lazareva115, R. Lea142,24,59, J. Lehrbach40, R.C. Lemmon97, I. León Monzón122,
E.D. Lesser19, M. Lettrich35,108, P. Lévai147, X. Li11, X.L. Li7, J. Lien132,
R. Lietava113, B. Lim17, S.H. Lim17, V. Lindenstruth40, A. Lindner49, C.
Lippmann110, A. Liu19, J. Liu130, I.M. Lofnes21, V. Loginov96, C. Loizides99,
P. Loncar36, J.A. Lopez107, X. Lopez137, E. López Torres8, J.R. Luhder146, M.
Lunardon28, G. Luparello62, Y.G. Ma41, A. Maevskaya65, M. Mager35, T.
Mahmoud44, A. Maire139, M. Malaev101, N.M. Malik104, Q.W. Malik20, L.
MalininaIV,77, D. Mal’Kevich95, N. Mallick51, P. Malzacher110, G.
Mandaglio33,57, V. Manko91, F. Manso137, V. Manzari54, Y. Mao7, J. Mareš68,
G.V. Margagliotti24, A. Margotti55, A. Marín110, C. Markert121, M. Marquard70,
N.A. Martin107, P. Martinengo35, J.L. Martinez127, M.I. Martínez46, G.
Martínez García117, S. Masciocchi110, M. Masera25, A. Masoni56, L.
Massacrier80, A. Mastroserio141,54, A.M. Mathis108, O. Matonoha83, P.F.T.
Matuoka123, A. Matyja120, C. Mayer120, A.L. Mazuecos35, F. Mazzaschi25, M.
Mazzilli35, M.A. MazzoniI,60, J.E. Mdhluli134, A.F. Mechler70, F. Meddi22, Y.
Melikyan65, A. Menchaca-Rocha73, E. Meninno116,30, A.S. Menon127, M. Meres13,
S. Mhlanga126,74, Y. Miake136, L. Micheletti61,25, L.C. Migliorin138, D.L.
Mihaylov108, K. Mikhaylov77,95, A.N. Mishra147, D. Miśkowiec110, A. Modak4,
A.P. Mohanty64, B. Mohanty89, M. Mohisin Khan16, Z. Moravcova92, C.
Mordasini108, D.A. Moreira De Godoy146, L.A.P. Moreno46, I. Morozov65, A.
Morsch35, T. Mrnjavac35, V. Muccifora53, E. Mudnic36, D. Mühlheim146, S.
Muhuri143, J.D. Mulligan82, A. Mulliri23, M.G. Munhoz123, R.H. Munzer70, H.
Murakami135, S. Murray126, L. Musa35, J. Musinsky66, J.W. Myrcha144, B.
Naik134,50, R. Nair88, B.K. Nandi50, R. Nania55, E. Nappi54, M.U. Naru14, A.F.
Nassirpour83, A. Nath107, C. Nattrass133, A. Neagu20, L. Nellen71, S.V.
Nesbo37, G. Neskovic40, D. Nesterov115, B.S. Nielsen92, S. Nikolaev91, S.
Nikulin91, V. Nikulin101, F. Noferini55, S. Noh12, P. Nomokonov77, J.
Norman130, N. Novitzky136, P. Nowakowski144, A. Nyanin91, J. Nystrand21, M.
Ogino85, A. Ohlson83, V.A. Okorokov96, J. Oleniacz144, A.C. Oliveira Da
Silva133, M.H. Oliver148, A. Onnerstad128, C. Oppedisano61, A. Ortiz
Velasquez71, T. Osako47, A. Oskarsson83, J. Otwinowski120, K. Oyama85, Y.
Pachmayer107, S. Padhan50, D. Pagano142,59, G. Paić71, A. Palasciano54, J.
Pan145, S. Panebianco140, P. Pareek143, J. Park63, J.E. Parkkila128, S.P.
Pathak127, R.N. Patra104,35, B. Paul23, J. Pazzini142,59, H. Pei7, T.
Peitzmann64, X. Peng7, L.G. Pereira72, H. Pereira Da Costa140, D. Peresunko91,
G.M. Perez8, S. Perrin140, Y. Pestov5, V. Petráček38, M. Petrovici49, R.P.
Pezzi117,72, S. Piano62, M. Pikna13, P. Pillot117, O. Pinazza55,35, L.
Pinsky127, C. Pinto27, S. Pisano53, M. Płoskoń82, M. Planinic102, F.
Pliquett70, M.G. Poghosyan99, B. Polichtchouk94, S. Politano31, N. Poljak102,
A. Pop49, S. Porteboeuf-Houssais137, J. Porter82, V. Pozdniakov77, S.K.
Prasad4, R. Preghenella55, F. Prino61, C.A. Pruneau145, I. Pshenichnov65, M.
Puccio35, S. Qiu93, L. Quaglia25, R.E. Quishpe127, S. Ragoni113, A.
Rakotozafindrabe140, L. Ramello32, F. Rami139, S.A.R. Ramirez46, A.G.T.
Ramos34, T.A. Rancien81, R. Raniwala105, S. Raniwala105, S.S. Räsänen45, R.
Rath51, I. Ravasenga93, K.F. Read99,133, A.R. Redelbach40, K. RedlichV,88, A.
Rehman21, P. Reichelt70, F. Reidt35, H.A. Reme-ness37, R. Renfordt70, Z.
Rescakova39, K. Reygers107, A. Riabov101, V. Riabov101, T. Richert83,92, M.
Richter20, W. Riegler35, F. Riggi27, C. Ristea69, S.P. Rode51, M. Rodríguez
Cahuantzi46, K. Røed20, R. Rogalev94, E. Rogochaya77, T.S. Rogoschinski70, D.
Rohr35, D. Röhrich21, P.F. Rojas46, P.S. Rokita144, F. Ronchetti53, A.
Rosano33,57, E.D. Rosas71, A. Rossi58, A. Rotondi29,59, A. Roy51, P. Roy112,
S. Roy50, N. Rubini26, O.V. Rueda83, R. Rui24, B. Rumyantsev77, P.G. Russek2,
A. Rustamov90, E. Ryabinkin91, Y. Ryabov101, A. Rybicki120, H. Rytkonen128, W.
Rzesa144, O.A.M. Saarimaki45, R. Sadek117, S. Sadovsky94, J. Saetre21, K.
Šafařík38, S.K. Saha143, S. Saha89, B. Sahoo50, P. Sahoo50, R. Sahoo51, S.
Sahoo67, D. Sahu51, P.K. Sahu67, J. Saini143, S. Sakai136, S. Sambyal104, V.
SamsonovI,101,96, D. Sarkar145, N. Sarkar143, P. Sarma43, V.M. Sarti108,
M.H.P. Sas148, J. Schambach99,121, H.S. Scheid70, C. Schiaua49, R.
Schicker107, A. Schmah107, C. Schmidt110, H.R. Schmidt106, M.O. Schmidt107, M.
Schmidt106, N.V. Schmidt99,70, A.R. Schmier133, R. Schotter139, J.
Schukraft35, Y. Schutz139, K. Schwarz110, K. Schweda110, G. Scioli26, E.
Scomparin61, J.E. Seger15, Y. Sekiguchi135, D. Sekihata135, I.
Selyuzhenkov110,96, S. Senyukov139, J.J. Seo63, D. Serebryakov65, L.
Šerkšnytė108, A. Sevcenco69, T.J. Shaba74, A. Shabanov65, A. Shabetai117, R.
Shahoyan35, W. Shaikh112, A. Shangaraev94, A. Sharma103, H. Sharma120, M.
Sharma104, N. Sharma103, S. Sharma104, U. Sharma104, O. Sheibani127, K.
Shigaki47, M. Shimomura86, S. Shirinkin95, Q. Shou41, Y. Sibiriak91, S.
Siddhanta56, T. Siemiarczuk88, T.F. Silva123, D. Silvermyr83, G. Simonetti35,
B. Singh108, R. Singh89, R. Singh104, R. Singh51, V.K. Singh143, V.
Singhal143, T. Sinha112, B. Sitar13, M. Sitta32, T.B. Skaali20, G.
Skorodumovs107, M. Slupecki45, N. Smirnov148, R.J.M. Snellings64, C.
Soncco114, J. Song127, A. Songmoolnak118, F. Soramel28, S. Sorensen133, I.
Sputowska120, J. Stachel107, I. Stan69, P.J. Steffanic133, S.F.
Stiefelmaier107, D. Stocco117, I. Storehaug20, M.M. Storetvedt37, C.P.
Stylianidis93, A.A.P. Suaide123, T. Sugitate47, C. Suire80, M. Suljic35, R.
Sultanov95, M. Šumbera98, V. Sumberia104, S. Sumowidagdo52, S. Swain67, A.
Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi108, G. Taillepied137, J.
Takahashi124, G.J. Tambave21, S. Tang137,7, Z. Tang131, M. Tarhini117, M.G.
Tarzila49, A. Tauro35, G. Tejeda Muñoz46, A. Telesca35, L. Terlizzi25, C.
Terrevoli127, G. Tersimonov3, S. Thakur143, D. Thomas121, R. Tieulent138, A.
Tikhonov65, A.R. Timmins127, M. Tkacik119, A. Toia70, N. Topilskaya65, M.
Toppi53, F. Torales-Acosta19, T. Tork80, S.R. Torres38, A. Trifiró33,57, S.
Tripathy55,71, T. Tripathy50, S. Trogolo35,28, G. Trombetta34, V. Trubnikov3,
W.H. Trzaska128, T.P. Trzcinski144, B.A. Trzeciak38, A. Tumkin111, R.
Turrisi58, T.S. Tveter20, K. Ullaland21, A. Uras138, M. Urioni59,142, G.L.
Usai23, M. Vala39, N. Valle59,29, S. Vallero61, N. van der Kolk64, L.V.R. van
Doremalen64, M. van Leeuwen93, P. Vande Vyvre35, D. Varga147, Z. Varga147, M.
Varga-Kofarago147, A. Vargas46, M. Vasileiou87, A. Vasiliev91, O. Vázquez
Doce108, V. Vechernin115, E. Vercellin25, S. Vergara Limón46, L. Vermunt64, R.
Vértesi147, M. Verweij64, L. Vickovic36, Z. Vilakazi134, O. Villalobos
Baillie113, G. Vino54, A. Vinogradov91, T. Virgili30, V. Vislavicius92, A.
Vodopyanov77, B. Volkel35, M.A. Völkl107, K. Voloshin95, S.A. Voloshin145, G.
Volpe34, B. von Haller35, I. Vorobyev108, D. Voscek119, N. Vozniuk65, J.
Vrláková39, B. Wagner21, C. Wang41, D. Wang41, M. Weber116, R.J.G.V.
Weelden93, A. Wegrzynek35, S.C. Wenzel35, J.P. Wessels146, J. Wiechula70, J.
Wikne20, G. Wilk88, J. Wilkinson110, G.A. Willems146, B. Windelband107, M.
Winn140, W.E. Witt133, J.R. Wright121, W. Wu41, Y. Wu131, R. Xu7, S. Yalcin79,
Y. Yamaguchi47, K. Yamakawa47, S. Yang21, S. Yano47, Z. Yin7, H. Yokoyama64,
I.-K. Yoo17, J.H. Yoon63, S. Yuan21, A. Yuncu107, V. Zaccolo24, A. Zaman14, C.
Zampolli35, H.J.C. Zanoli64, N. Zardoshti35, A. Zarochentsev115, P. Závada68,
N. Zaviyalov111, H. Zbroszczyk144, M. Zhalov101, S. Zhang41, X. Zhang7, Y.
Zhang131, V. Zherebchevskii115, Y. Zhi11, N. Zhigareva95, D. Zhou7, Y. Zhou92,
J. Zhu7,110, Y. Zhu7, A. Zichichi26, G. Zinovjev3, N. Zurlo142,59

Affiliation Notes

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

Collaboration Institutes

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