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Direct observation of the dead-cone effect in quantum chromodynamics


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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 shower2, 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 mQ and energy E, within a cone of angular size mQ/E around the emitter3. 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 techniques4,5 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. The direct measurement of the QCD dead cone in charm quark fragmentation is reported, using iterative declustering of jets tagged with a fully reconstructed charmed hadron.
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440 | Nature | Vol 605 | 19 May 2022
Direct observation of the dead-cone effect in
quantum chromodynamics
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 shower2, 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 eect, which
predicts a suppression of the gluon spectrum emitted by a heavy quark of mass mQ
and energy E, within a cone of angular size mQ/E around the emitter3. Previously, a
direct observation of the dead-cone eect 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 techniques4,5 to reconstruct the parton shower of charm
quarks. This result conrms 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.
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 pro-
duction 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 jet6. 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.
for the deriva-
tion 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 ± 0.02 GeV/c
) 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 e+e collider meas-
ured 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
mass7, 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 func-
tion of distance from the jet axis was also performed by the ATLAS
collaboration at CERN8, 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 data9. 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 corre-
sponding fraction carried by the leading hadron in light quark-initiated
jets peaks at smaller values1014.
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
Received: 29 June 2021
Accepted: 21 February 2022
Published online: 18 May 2022
Open access
Check for updates
*A list of authors and their afiliations appears at the end of the paper. e-mail:
Nature | Vol 605 | 19 May 2022 | 441
techniques4 enables these aforementioned difficulties to be over
come by reconstructing the evolution of the jet shower, giving access
to the kinematic properties of each individual emission. These tech-
niques reorganize 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 recon-
structed parton shower that are likely to be unmodified by had-
ronization 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
balance1518, which probes the Dokshitzer–Gribov–Lipatov–Altarelli–
Parisi splitting function19, and the Lund plane20, 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 D
meson amongst
their constituents, which has a mass of 1.86 GeV/c
) and is com-
posed of a heavy charm quark and a light anti-up quark. The measure-
ment is performed in proton–proton collisions at a centre-of-mass
energy of
 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.
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 D
mesons and jets need to be
reconstructed in the events. The D
-meson candidates (and their anti-
particles) were reconstructed in the transverse-momentum interval
 GeV/c, through the D0 → Kπ+ (and charged conjugate) had-
ronic decay channel, which has a branching ratio of 3.95 ± 0.03%
). The D
-meson candidates were identified by topological selec-
tions based on the displacement of the D0-meson candidate decay
vertex, in addition to applying particle identification on the D
candidate decay particles. These selection criteria largely suppress
the combinatorial background of Kπ± pairs that do not originate from
the decay of a D
meson. Further details on the selection criteria are
provided in ref. 23.
Tracks (reconstructed charged-particle trajectories) correspond-
ing to the D0-meson candidate decay particles were replaced by the
reconstructed D
-meson candidate in the event, with the D
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 D
-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 D
-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
from the
Fastjet package
, 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.
Reconstructing the jet shower
Once jets containing a D
-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) algorithm26, which clusters these constitu-
ents based solely on their angular distance from one another. A pictorial
representation of this reclustering process, which starts by reconstruct-
ing the smallest angle splittings, is shown in the top panels of Fig.1. As
QCD emissions approximately follow an angular-ordered structure27,
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, θ, the relative transverse momentum of the splitting, k
, and
the sum of the energy of the two prongs, ERadiator, are registered. As the
charm flavour is conserved throughout the showering process, the full
reconstruction of the D
-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 dynami-
cally evolving charm-quark direction. It was verified that in more than
99% of the cases the prong containing the D
-meson candidate at each
splitting coincided with the leading prong. This means that following
the D
-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 lead-
ing 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.
Extracting the true charm splittings
The selected sample of splittings has contributions from jets tagged
with combinatorial Kπ± 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 measure-
ment of the momenta of the K
pairs) with a peak at the true D
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 D
-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
-meson candidates also select a fraction of D
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)
(this generator includes mass effects in the parton shower
and was
used for all MC-based corrections in this work), propagating the gener-
ated particles through a detailed description of the ALICE detector
with GEANT3 (ref.
). The finite efficiency of selecting real D
tagged jets, through the chosen selection criteria on the D
candidates, as well as kinematic selections on the jets, was studied and
accounted for through MC simulations. This efficiency was found to
be strongly
dependent and different for D
mesons originating
442 | Nature | Vol 605 | 19 May 2022
from the hadronization of charm quarks or from the decay of beauty
hadrons. Further details on these analysis steps can be found in the
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 par-
ton shower by mainly adding low-kT splittings32. A selection of
kT > 200 MeV/c ensures that only sufficiently hard splittings are
accepted and is used to suppress such hadronization effects. Other
choices of k
selection were also explored, with stronger k
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 par-
ticles. 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 crea-
tion in the elementary hard scattering, charm quarks can also be pro-
duced in higher-order processes as a result of gluon splitting. Therefore,
the shower history of D
mesons containing such charm quarks will also
have contributions from splittings originating from gluons. Further-
more, 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.
The observable R(θ)
The observable used to reveal the dead cone is built by constructing
the ratio of the splitting angle (θ) distributions for D
-meson tagged
jets and inclusive jets, in bins of ERadiator. This is given by
dln(1/ )/1d
dln(1/ )(1)
where the θ distributions were normalized to the number of jets that
contain at least one splitting in the given ERadiator and kT selection,
denoted by
and Ninclusive jets for the D0-meson tagged and inclu-
sive 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
θkln(1/ )ln()
A selection on the transverse momentum of the leading track in the
leading prong of each registered splitting in the inclusive jet sample,
 GeV/c, was applied. This corresponds to the trans-
verse mass (obtained through the quadrature sum of the rest mass and
transverse momentum) of a 2 GeV/c D
meson and accounts for the
selection in the D
-meson tagged jet sample, enabling a fair comparison
of the two samples.
Dead-cone effect
Gluon emissions are
suppressed in a cone
with Tdc = mQ/ERadiator
Fully reclustered jet
Reclustering step 1 Reclustering step 2
Reclustering step 3
Emitted gluon
Gluon emission vertex
Charm quark
ERadiator,1 > ... > ERadiator,5
T1!T2 > .... > T5
Fig. 1 | Recon structi on of the showerin g quark. A sketch d etailing the
reconstr uction of the s howering charm qu ark, using itera tive decluster ing, is
presente d. The top pane ls show the initial re clustering pr ocedure with th e C/A
algorithm, i n which the part icles separat ed by the smallest a ngles are brough t
together f irst. Once t he recluster ing is complete, t he decluster ing procedure is
carrie d out by unwinding th e reclusterin g history. Each spli tting node is
numbered a ccording to the de clustering st ep in which it is rec onstructe d. With
each split ting, the char m-quark energ y, ERadiator,n, is reduced and the gl uon is
emitte d at a smaller angle, θn, w ith respec t to previous emi ssions. The m ass of
the heav y quark, mQ, remains constant throughout the showering process. At
each split ting, gluon em issions are supp ressed in the de ad-cone reg ion (shown
by a red cone for the l ast splitting ), which increase s in angle as the qu ark energy
decreases throughout the shower.
Nature | Vol 605 | 19 May 2022 | 443
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
dln(1/ )/1d
dln(1/ ),(2
no dead cone limit
LQ jets
LQ jets
where the superscript LQ refers to light quarks, and the inclusive sample
contains both light-quark and gluon-initiated jets. This indicates that the
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 fragment-
ing at a lower rate and more collinearly than gluons. Therefore, in the limit
of having no dead-cone effect, the ratio of the θ distributions for D
tagged jets and inclusive jets becomes R(θ)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(θ)no dead-cone limit
value dependent on the quark and gluon fractions in the inclusive sam-
ple. 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.
Exposing the dead cone
The measurements of R(θ), in the three radiator (charm-quark) energy
intervals 5 < ERadiator < 10 GeV, 10 < ERadiator < 20 GeV and 20 < ERadiator
< 3  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 extrac-
tion of D0-meson tagged jets, as well as detector inefficiencies in the
reconstruction of charged tracks in both the D
-meson tagged and
inclusive jet samples. More details on the study of systematic uncer-
tainties can be found in the Methods.
A significant suppression in the rate of small-angle splittings is
observed in D
-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 emis-
sions are suppressed. The coloured regions in the plots correspond to
the dead-cone angles in each ERadiator interval, θdc < mQ/ERadiator, where
emissions are suppressed. For a charm-quark mass mQ = 1.275 GeV/c2
), these angles correspond to ln(1/θ
) ≥ 1.37, 2 and 2.75 for the inter-
vals 5 < E
 < 10 GeV, 10 < E
 < 20 GeV and 20 < E
 < 35 GeV,
respectively. These values are in qualitative agreement with the angles
at which the data start 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.
A lower limit for the significance of the small-angle suppression is
estimated by comparing the measured data to R(θ) = 1, which repre-
sents 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(θ) = 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 sig-
nificances of 7.7σ, 3.5σ and 1.0σ, for the 5 < E
 < 10 GeV, 10 < E
< 20 GeV and 20 < ERadiator < 35 GeV intervals, respectively. A σ value
greater than 5 is considered the criteria for a definitive observation,
whereas the value of 1.0 is consistent with the null hypothesis.
1.0 1.5 2.0 2.5
R (T)
5 < ERadiator < 10 GeV
0.37 0.22 0.14 0.08
ALICE data
no dead-cone limit
PYTHIA v.8 LQ/inclusive
no dead-cone limit
SHERPA LQ/inclusive
1.5 2.02.5
proton–proton √s = 13 TeV
Charged jets, anti-kT, R = 0.4
C/A reclustering
0.22 0.14 0.08
1.52.0 2.
2.8 GeV/c
pch,leading track
kT > 200 MeV/c
|Klab|< 0.5
0.22 0.14 0.08 0.05
T,inclusive jet
T (rad)
10 < ERadiator < 20 GeV 20 < ERadiator < 35 GeV
Fig. 2 | Rati os of splitt ing angle pro bability di stributi ons. The rat ios of the
splitting-angle probability distributions for D0-meson t agged jets t o inclusive
jets, R(θ), measured i n proton–proton collisi ons at
TeV, are shown for
5 < ERadiator < 10 GeV (left pan el), 10 < ERadiator < 20 GeV (middle panel) and
20 < ERadiator < 35 GeV (right pa nel). The data are c ompared with PY THIA v.8 and
SHERPA simulat ions, including t he no dead-con e limit given by the rat io of the
angular dis tributions for li ght-quark jets (LQ) to in clusive jets. T he pink shaded
areas corre spond to the ang les within whi ch emissions ar e suppressed by th e
dead-con e effect, as suming a charm-q uark mass of 1. 275 GeV/c2.
444 | Nature | Vol 605 | 19 May 2022
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 POWHEG35
+ PYTHIA v.6.42534 simulations. The non-prompt fraction was found
to be independent of the splitting angle and corresponds to approxi-
mately 10% of the splittings in the 5 < ERadiator < 10 GeV interval and
approximately 15% of the splittings in both the 10 < E
 < 20 GeV
and 20 < E
 < 35 GeV intervals. It was verified through the MC simu-
lations that non-prompt D
-meson tagged jets should exhibit a smaller
suppression at small angles in R(θ) 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(θ), despite the
larger dead-cone angle of the heavier beauty quark.
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 con-
straints 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 confir-
mation of the theoretical understanding of in-medium QCD radiation,
which is a primary tool used to characterize the high-temperature
phase of QCD matter36–38.
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 states39 (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 tech-
nique 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.
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ALICE Collaboration
S. Acharya1, D. Adamova2, A. Adler3, J. Adolfsson4, G. Aglieri Rinella5, M. Agnello6,
N. Agrawal7, Z. Ahammed1, S. Ahmad8, S. U. Ahn9, I. Ahuja10, Z. Akbar11, A. Akindinov12,
M. Al-Turany13, S. N. Alam14, D. Aleksandrov15, B. Alessandro16, H. M. Alfanda17, R. Alfaro
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446 | Nature | Vol 605 | 19 May 2022
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1Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India. 2Nuclear
Physics Institute of the Czech Academy of Sciences, Řežu Prahy, Czech Republic. 3Institut fur
Informatik, Fachbereich Informatik und Mathematik, Johann-Wolfgang-Goethe Universitat
Frankfurt, Frankfurt, Germany. 4Department of Physics, Division of Particle Physics, Lund
University, Lund, Sweden. 5European Organization for Nuclear Research (CERN), Geneva,
Switzerland. 6Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy. 7INFN,
Sezione di Bologna, Bologna, Italy. 8Department of Physics, Aligarh Muslim University,
Aligarh, India. 9Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea. 10Faculty of Science, P.J. Šafarik University, Košice, Slovakia. 11Indonesian Institute of
Sciences, Jakarta, Indonesia. 12NRC Kurchatov Institute – ITEP, Moscow, Russia.
13Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum fur
Schwerionenforschung GmbH, Darmstadt, Germany. 14Fudan University, Shanghai, China.
15National Research Centre Kurchatov Institute, Moscow, Russia. 16INFN, Sezione di Torino,
Turin, Italy. 17Central China Normal University, Wuhan, China. 18Instituto de Fisica, Universidad
Nacional Autonoma de Mexico, Mexico City, Mexico. 19COMSATS University Islamabad,
Islamabad, Pakistan. 20Dipartimento di Fisica e Astronomia dell’Universita and Sezione INFN,
Bologna, Italy. 21University of Houston, Houston, TX, USA. 22Department of Physics and
Technology, University of Bergen, Bergen, Norway. 23Institut fur Kernphysik, Johann Wolfgang
Goethe-Universitat Frankfurt, Frankfurt, Germany. 24St. Petersburg State University, St.
Petersburg, Russia. 25Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania. 26Nikhef, National Institute for Subatomic Physics, Amsterdam, the
Netherlands. 27Institut fur Kernphysik, Westfalische Wilhelms-Universitat Munster, Munster,
Germany. 28Physikalisches Institut, Ruprecht-Karls-Universitat Heidelberg, Heidelberg,
Germany. 29INFN, Sezione di Padova, Padova, Italy. 30Lawrence Berkeley National Laboratory,
Berkeley, CA, USA. 31SUBATECH, IMT Atlantique, Universite de Nantes, CNRS-IN2P3, Nantes,
France. 32Department of Physics, University of Oslo, Oslo, Norway. 33Yale University, New
Haven, CT, USA. 34Laboratoire de Physique des 2 Ininis, Irene Joliot-Curie, Orsay, France.
35INFN, Sezione di Catania, Catania, Italy. 36Gangneung-Wonju National University,
Gangneung, Republic of Korea. 37University of Science and Technology of China, Hefei,
China. 38Indian Institute of Technology Indore, Indore, India. 39Physics Department, University
of Jammu, Jammu, India. 40Department de Physique Nucleaire (DPhN), Universite Paris-Saclay
Centre d’Etudes de Saclay (CEA), IRFU, Saclay, France. 41AGH University of Science and
Technology, Cracow, Poland. 42Helmholtz-Institut fur Strahlen- und Kernphysik, Rheinische
Friedrich-Wilhelms-Universitat Bonn, Bonn, Germany. 43Bose Institute, Department of Physics
and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India.
44Dipartimento di Fisica e Astronomia dell’Universita and Sezione INFN, Catania, Italy. 45Physik
Department, Technische Universitat Munchen, Munich, Germany. 46Dipartimento di Fisica
dell’Universita and Sezione INFN, Turin, Italy. 47Department of Physics, School of Science,
National and Kapodistrian University of Athens,, Athens, Greece. 48Wigner Research Centre
for Physics, Budapest, Hungary. 49Nuclear Physics Group, STFC Daresbury Laboratory,
Daresbury, UK. 50Universite Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France.
51University of Liverpool, Liverpool, UK. 52Dipartimento di Fisica e Astronomia dell’Universita
and Sezione INFN, Padova, Italy. 53Joint Institute for Nuclear Research (JINR), Dubna, Russia.
54Indian Institute of Technology Bombay (IIT), Mumbai, India. 55Seccion Fisica, Departamento
de Ciencias, Pontiicia Universidad Catolica del Peru, Lima, Peru. 56Niels Bohr Institute,
University of Copenhagen, Copenhagen, Denmark. 57Universite de Strasbourg, CNRS, IPHC
UMR 7178, Strasbourg, France. 58NRNU Moscow Engineering Physics Institute, Moscow,
Russia. 59Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Mexico
City, Mexico. 60Petersburg Nuclear Physics Institute, Gatchina, Russia. 61Institute of Space
Science (ISS), Bucharest, Romania. 62Department of Physics, Gauhati University, Guwahati,
India. 63Dipartimento di Fisica dell’Universita and Sezione INFN, Cagliari, Italy. 64INFN,
Laboratori Nazionali di Frascati, Frascati, Italy. 65Faculty of Nuclear Sciences and Physical
Engineering, Czech Technical University in Prague, Prague, Czech Republic. 66The Henryk
Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland.
67The University of Texas at Austin, Austin, TX, USA. 68Dipartimento di Fisica e Nucleare e
Teorica, Universita di Pavia, Pavia, Italy. 69INFN, Sezione di Pavia, Pavia, Italy. 70Oak Ridge
National Laboratory, Oak Ridge, TN, USA. 71Inha University, Incheon, Republic of Korea.
72Universita di Brescia, Brescia, Italy. 73Moscow Institute for Physics and Technology, Moscow,
Russia. 74Universidade de Sao Paulo (USP), Sao Paulo, Brazil. 75Politecnico di Bari and Sezione
INFN, Bari, Italy. 76Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy.
77Russian Federal Nuclear Center (VNIIEF), Sarov, Russia. 78Stefan Meyer Institut fur
Subatomare Physik (SMI), Vienna, Austria. 79iThemba LABS, National Research Foundation,
Somerset West, South Africa. 80University of the Witwatersrand, Johannesburg, South Africa.
81Universidad Autonoma de Sinaloa, Culiacan, Mexico. 82High Energy Physics Group,
Universidad Autonoma de Puebla, Puebla, Mexico. 83Dipartimento di Fisica dell’Universita and
Sezione INFN, Trieste, Italy. 84Saha Institute of Nuclear Physics, Homi Bhabha National
Institute, Kolkata, India. 85Universite de Lyon, CNRS/IN2P3, Institut de Physique des 2 Ininis de
Lyon, Lyon, France. 86Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil.
87University of Tsukuba, Tsukuba, Japan. 88INFN, Sezione di Cagliari, Cagliari, Italy. 89University
of Cape Town, Cape Town, South Africa. 90INFN, Sezione di Bari, Bari, Italy. 91School of Physics
and Astronomy, University of Birmingham, Birmingham, UK. 92Laboratoire de Physique
Subatomique et de Cosmologie, Universite Grenoble-Alpes, CNRS-IN2P3, Grenoble, France.
93Dipartimento di Scienze e Innovazione Tecnologica dell’Universita del Piemonte Orientale
and INFN Sezione di Torino, Alessandria, Italy. 94Universidade Federal do ABC, Santo Andre,
Brazil. 95National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India. 96Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universita and Gruppo
Collegato INFN, Salerno, Italy. 97Frankfurt Institute for Advanced Studies, Johann Wolfgang
Goethe-Universitat Frankfurt, Frankfurt, Germany. 98Warsaw University of Technology,
Warsaw, Poland. 99Department of Physics, University of California, Berkeley, CA, USA.
100Centro de Aplicaciones Tecnologicas y Desarrollo Nuclear (CEADEN), Havana, Cuba.
101Institute for Nuclear Research, Academy of Sciences, Moscow, Russia. 102Physics
Department, Panjab University, Chandigarh, India. 103Comenius University Bratislava, Faculty
of Mathematics, Physics and Informatics, Bratislava, Slovakia. 104Physics Department, Faculty
of Science, University of Zagreb, Zagreb, Croatia. 105NRC Kurchatov Institute IHEP, Protvino,
Russia. 106INFN, Sezione di Trieste, Trieste, Italy. 107Chicago State University, Chicago, IL, USA.
108National Nuclear Research Center, Baku, Azerbaijan. 109University of Kansas, Lawrence, KS,
USA. 110Instituto de Fisica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre,
Brazil. 111Nagasaki Institute of Applied Science, Nagasaki, Japan. 112Wayne State University,
Detroit, MI, USA. 113Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia. 114Institute for Gravitational and Subatomic
Physics (GRASP), Utrecht University/Nikhef, Utrecht, the Netherlands. 115A.I. Alikhanyan
National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia.
116University of Tokyo, Tokyo, Japan. 117Faculty of Engineering and Science, Western Norway
University of Applied Sciences, Bergen, Norway. 118Centro de Investigacion y de Estudios
Avanzados (CINVESTAV), Mexico City and Merida, Mexico. 119Yonsei University, Seoul,
Republic of Korea. 120Creighton University, Omaha, NE, USA. 121University of Tennessee,
Knoxville, TN, USA. 122Ohio State University, Columbus, OH, USA. 123Technical University of
Košice, Košice, Slovakia. 124Suranaree University of Technology, Nakhon Ratchasima, Thailand.
125Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia. 126KTO
Karatay University, Konya, Turkey. 127Hochschule Worms, Zentrum fur Technologietransfer und
Telekommunikation (ZTT), Worms, Germany. 128Department of Physics, Pusan National
University, Pusan, Republic of Korea. 129University of Jyvaskyla, Jyvaskyla, Finland. 130Jeonbuk
National University, Jeonju, Republic of Korea. 131Department of Physics, Sejong University,
Seoul, Republic of Korea. 132California Polytechnic State University, San Luis Obispo, CA, USA.
133National Centre for Nuclear Research, Warsaw, Poland. 134University of South-Eastern
Norway, Tonsberg, Norway. 135China Institute of Atomic Energy, Beijing, China. 136Dipartimento
di Scienze MIFT, Universita di Messina, Messina, Italy. 137Institute of Physics of the Czech
Academy of Sciences, Prague, Czech Republic. 138Universita degli Studi di Foggia, Foggia,
Italy. 139INFN, Sezione di Roma, Rome, Italy. 140Dipartimento di Fisica dell’Universita ‘La
Sapienza’ and Sezione INFN, Rome, Italy. 141Chungbuk National University, Cheongju, Republic
of Korea. 142Hiroshima University, Hiroshima, Japan. 143Budker Institute for Nuclear Physics,
Novosibirsk, Russia. 144Physics Department, University of Rajasthan, Jaipur, India. 145Helsinki
Institute of Physics (HIP), Helsinki, Finland. 146Institute of Physics, Homi Bhabha National
Institute, Bhubaneswar, India. 147Physikalisches Institut, Eberhard-Karls-Universitat Tubingen,
Tubingen, Germany. 148Nara Women’s University (NWU), Nara, Japan. 149Bogolyubov Institute
for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine. 150Present
address: Italian National Agency for New Technologies, Energy and Sustainable Economic
Development, (ENEA), Bologna, Italy. 151Present address: Dipartimento DET del Politecnico di
Torino, Turin, Italy. 152Present address: D.V. Skobeltsyn Institute of Nuclear Physics, M.V.
Lomonosov Moscow State University, Moscow, Russia. 153Present address: Institute of
Theoretical Physics, University of Wroclaw, Wroclaw, Poland. 154Deceased: J. Cleymans.
155Deceased: A. Grigoryan. 156Deceased: M. A. Mazzoni. 157Deceased: V. Samsonov.
Detector setup and data set
The analysis was performed with the ALICE detector at the CERN LHC
The ALICE Inner Tracking System42 and Time Projection Chamber43 were
used for charged-particle reconstruction, and particle identification
(PID) was obtained using the combined information from the Time Pro-
jection Chamber and the Time-Of-Flight detectors
. These detectors
are located in the ALICE central barrel, which has full azimuthal coverage
and a pseudorapidity range of |η| < 0.9. The data set used in this analysis
was collected in 2016, 2017 and 2018 in proton–proton collisions at
 TeV, with a minimum-bias trigger condition defined by the pres-
ence of at least one hit in each of the two V0 scintillators45. This trigger
accepts all events of interest for this analysis and the collected data
sample corresponds to an integrated luminosity of ℒint = 25 nb−1.
Jet finding and tagging
Jet finding was performed using the anti-kT algorithm, with a jet resolu-
tion 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 |η| < 0.5 enforced
on the jet axis, to ensure that the full jet cone was contained in the accept-
ance of the central barrel of the ALICE detector. The ALICE detector
has excellent tracking efficiency down to low pT (approximately 80% at
 = 500 MeV/c), which is homogeneous as a function of pseudorapidity
and azimuthal angle
, within the acceptance. The effect of track density
on the tracking efficiency is also negligible46. 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
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
p5≤ <5
GeV/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 D
-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.
Subtraction of the combinatorial background in the D0-meson
candidate sample
To extract the true D0-meson tagged jet R(θ) distributions and remove
the contribution from combinatorial K
pairs surviving the topo-
logical and PID selections, a side-band subtraction procedure was
used. This involved dividing the sample into p
intervals and fitting
the invariant-mass distributions of the D
candidates in each interval
with a Gaussian function for the signal and an exponential function
for the background. The width (σ) and mean of the fitted Gaussian
were used to define signal and side-band regions, with the two-dimen
sional distributions of θ and E
for D
-meson tagged jet candi-
ρθE(, )
Djet candidat
, obtained in each region. The signal
region was defined to be within 2σ on either side of the Gaussian mean
and contained most of the real D
mesons, with some contamination
present from the combinatorial background. The side-band regions
were defined to be from 4σ to 9σ away from the peak in either direc-
tion and were composed entirely of background D0-meson candidates.
The combined
ρθE(, )
Djet candidat
distributions measured in
the two side-band regions represent the structural form of the con-
tribution of background candidates to the
ρθE(, )
Djet candidat
distribution measured in the signal region. In this way, the background
component of the total
ρθE(, )
Djet candidat
measured in the
signal region can be subtracted, using the following equation:
(, )
=1[((, )−(, )(3
Radiator Djet
Radiator S
Radiator B
where the subscripts S and B denote the signal and side-band regions
of the invariant-mass distributions, respectively. The A
and A
are the areas under the background fit function in the signal and com-
bined 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 ε, with the index i run-
ning over the
bins. As a result of this side-band subtraction, the true
-meson tagged jet
θE(, )
distributions are obtained, in
the different intervals of
D0-meson tagged jet reconstruction efficiency correction
The topological and PID selections used to identify the D
in the chosen jet kinematic interval, have a limited efficiency, which
exhibits a strong p
dependence. Therefore, before integrating the
side-band subtracted
ρθE(, )
distributions across the meas-
intervals, the
θE(, )
distributions were corrected
for this efficiency. The efficiency, ε, was estimated from PYTHIA v.6
MC studies and varies strongly with
, from approximately 0.01 at
 = 2.5 GeV/c to approximately 0.3 at
 = 30 GeV/c for prompt
-meson tagged jets and from approximately 0.01 at
 = 2.5 GeV/c
to approximately 0.2 at
 = 30 GeV/c for non-prompt D
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-meson tagged
jet reconstruction efficiencies, evaluated separately. These were
combined with weights derived from simulations, corresponding to
the admixture of prompt and non-prompt D
-meson tagged jets in
the reconstructed sample. The fractions of this admixture were
obtained in bins of
by calculating the prompt and non-prompt
D0-meson tagged jet production cross sections with POWHEG com-
bined with PYTHIA v.6 showering.
Evaluation of systematic uncertainties
Considered sources of systematic uncertainty in the measurement
relate to the reconstruction and signal extraction of D0-meson candi-
dates, with the former contributing as the leading source. These uncer-
tainties were estimated by varying the topological and PID selections,
as well as the fitting and side-band subtraction configurations applied
to the D
-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. Theo-
retical uncertainties in the prompt and non-prompt D
-meson tagged
jet production cross sections from POWHEG were also considered in
the calculation of the reconstruction efficiency, with the largest vari-
ation 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 uncer-
tainty of the D0-meson tagged jet measurement.
For the inclusive jet results, the minimum p
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 D
meson with
 = 2 GeV/c, which was found to be 0.06 GeV/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 D
-meson tagged jet and inclusive jet samples equally, and
they largely cancelled in the R(θ) ratio. Therefore, the systematic uncer
tainty of R(θ) 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 D
-meson tagged jets and inclusive jets. The
ratio of the resulting R(θ) distribution to the case with no track removal
was taken, to obtain the uncertainty, which was symmetrized.
The relative uncertainty of R(θ) resulting from the separate D
tagged jet and inclusive jet uncertainties was calculated, with the result-
ing absolute uncertainty added in quadrature to the detector effects
uncertainty to obtain the total systematic uncertainty of the R(θ)
measurement. The magnitude of each of these sources of systematic
uncertainty is shown in Table1, for the smallest-angle splittings cor-
responding to the interval 2 ≤ ln (1/θ) < 3, in which the uncertainties
are largest.
Data availability
All data shown in histograms and plots are publicly available on the
HEPdata repository (
Code availability
The source code utilized in this study is publicly available under the
names AliPhysics and AliRoot. Further information can be provided
by the authors upon reasonable request.
41. ALICE Collaboration, Abelev, B. etal. Performance of the ALICE experiment at the CERN
LHC. Int. J. Mod. Phys. A29, 1430044 (2014).
42. ALICE Collaboration, Aamodt, K. etal. Alignment of the ALICE inner tracking system with
cosmic-ray tracks. J. Instrum. 5, P03003 (2010).
43. Alme, J. etal. The ALICE TPC, a large 3-dimensional tracking device with fast readout for
ultra-high multiplicity events. Nucl. Instrum. Meth. A 622, 316–367 (2010).
44. Akindinov, A. etal. Performance of the ALICE time-of-light detector at the LHC. Eur. Phys.
J. Plus 128, 44 (2013).
45. ALICE Collaboration, Abbas, E. etal. Performance of the ALICE VZERO system. J. Instrum.
8, P10016 (2013).
46. ALICE Collaboration, Abelev, B. etal. Performance of the ALICE experiment at the CERN
LHC. Int. J. Mod. Phys. A 29, 1430044 (2014).
Acknowledgements The ALICE Collaboration is grateful to U. Wiedemann for his valuable
suggestions and fruitful discussions. We are also grateful to D. Napoletano for providing the
SHERPA coniguration iles 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 Cientíico 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), Institut National
de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National dela
Recherche Scientiique (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 Ofice, 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 Scientiic 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), the Netherlands; The Research Council of Norway, Norway; Commission on
Science and Technology for Sustainable Development in the South (COMSATS), Pakistan;
Pontiicia 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
Scientiic 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 Ofice 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, Ofice of Nuclear Physics (DOE NP), United
States of America.
Author contributions All authors have contributed to the publication, being variously involved
in the design and the construction of the detectors, in writing software, calibrating
subsystems, operating the detectors and acquiring data, and inally analysing the processed
data. The ALICE Collaboration members discussed and approved the scientiic results. The
manuscript was prepared by a subgroup of authors appointed by the collaboration and
subject to an internal collaboration-wide review process. All authors reviewed and approved
the inal version of the manuscript.
Competing interests The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material available at
Correspondence and requests for materials should be addressed to the ALICE Collaboration.
Peer review information Nature thanks Benjamin Nachman and the other, anonymous,
reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are
Reprints and permissions information is available at
Table 1 | R(θ) systematic uncertainties
Source ERadiator
5−10GeV 10−20GeV 20−35GeV
Invariant-mass itting 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 pT selection 2.0 3.2 0.2
Detector effects 0.7 5.2 0.9
Total 5.6 8.9 8.1
The percentage magnitude of the systematic uncertainties of each source considered, and
the total systematic uncertainty, for the R(θ) variable are shown for the smallest splitting-angle
interval 2≤ln(1/θ)<3.
... Correlators involving heavy quarks are also particularly interesting in the medium, since they introduce another intrinsic scale, and are not often pair produced, allowing them to be tracked through the medium (for recent interesting uses of heavy quarks, see e.g. [7,[93][94][95]). Finally, we have focused on the perturbative region of the EEC, but it would be also interesting to study medium modifications to the hadronisation transition, which has already been analysed in vacuum [52]. ...
Jets provide us with ideal probes of the quark-gluon plasma (QGP) produced in heavy-ion collisions, since its dynamics at its different scales is imprinted into the multi-scale substructure of the final state jets. We present a new approach to jet substructure in heavy-ion collisions based on the study of correlation functions of energy flow operators. By analysing the two-point correlator of an in-medium quark jet, we demonstrate that the spectra of correlation functions robustly identify the scales defined by the properties of the QGP, particularly those associated with the onset of colour coherence.
... In principle, one can expect a spectacular effect known as "dead cone" [93]. The dead cone effect was recently observed experimentally for the first time by the ALICE Collaboration [94]. Energy loss due to emission outside of the jet cone can then be written as ...
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We calculate differential cross sections for cc¯- and bb¯-dijet production in pp scattering at s=13 TeV in the kT-factorization and hybrid approaches with different unintegrated parton distribution functions (uPDFs). We present distributions in the transverse momentum and pseudorapidity of the leading jet, the rapidity difference between the jets and the dijet invariant mass. Our results are compared to recent LHCb data on forward production of heavy-flavor dijets, measured recently for the first time individually for both charm and bottom flavors. We find that an agreement between the predictions and the data within the full kT factorization is strongly related to the modeling of the large-x behavior of the gluon uPDFs, which is usually not well constrained. The problem may be avoided following the hybrid-factorization approach. Then, we obtain a good description of the measured distributions with the parton-branching, Kimber-Martin-Ryskin, Kutak-Sapeta, and Jung setA0 models for the gluon uPDF. We also calculate differential distributions for the ratio of the cc¯ and bb¯ cross sections. In all cases we obtain a ratio close to 1, which is caused by the condition on the minimal jet transverse momentum (pTjet>20 GeV) introduced in the experiment, that makes the role of the heavy-quark mass almost negligible. The LHCb experimental ratio seems a bit larger than the theoretical predictions. We discuss potentially important for the ratio effect of c- or b-quark gluon radiative corrections related to emission outside of the jet cone. The found effect seems rather small. A more refined calculation requires full simulation of c and b jets, which goes beyond of the scope of this paper.
... Dedicated phenomenological strategies have been designed to expose and study this effect, e.g. [14][15][16], which has been recently measured by the ALICE collaboration at the LHC [17]. Furthermore, the possibility of exploiting the imprint that quark masses leave on colour correlations has been recently investigated in the context of b-tagging [18]. ...
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A bstract Observables involving heavy quarks can be computed in perturbative QCD in two different approximation schemes: either the quark mass dependence is fully retained, or it is retained only where needed to regulate the collinear singularity. The two schemes have different advantages and drawbacks. In particular, it is known that the structure of large logarithms arising from soft emissions is different in the two approaches. We investigate the origin of this difference in some detail, focussing on a few specific processes. We show that it is related to the non-commutativity of the small-mass and soft-emission limits. Finally, we perform the resummation of soft-emission logarithms to next-to-leading accuracy in the case of Higgs decay into a b $$ \overline{b} $$ b ¯ pair, in the scheme in which the quark mass dependence is fully accounted for.
... This pattern depends on the mass of the initiating parton through the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a HQ of mass m and energy E, within a cone of angular size θ ≈ m/E around the emitter. The observable used to reveal the dead-cone effect is built by constructing the ratio R(θ) of the splitting angle distributions for D 0 -tagged jets and inclusive jets in intervals of the energy of the radiator [10]. In Fig. 2 the measured R(θ) is reported in three different energy intervals and it shows a significant suppression at small-splitting angles for D 0 -tagged jets with respect to inclusive jets. ...
The early production of heavy-flavor (HF, charm and beauty) quarks makes them an excellent probe of the dynamical evolution of quantum chromodynamics (QCD) systems. Jets tagged by the presence of a HF hadron give access to the kinematics of the heavy quarks, and along with correlation measurements involving HF hadrons allow for comparisons of their production, propagation and fragmentation across different systems. In this contribution the latest results on HF jets and correlations measured with the ALICE detector in pp, p--Pb and Pb--Pb collisions from the LHC Run 2 data are reported.
... Recent experimental advances in techniques pertaining to the substructure of heavy-flavour jets [9,10] have allowed for the isolation and study of gluon emissions from heavy quarks. This technique has been used to perform a first direct measurement [11] of the dead-cone effect [12] in charm-quark jets. The dead cone corresponds to an angular region along the flight direction of the emitter, with an opening proportional to the ratio of mass to energy of the emitter, within which the probability of emissions is suppressed. ...
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Understanding the role of parton mass and Casimir colour factors in the quantum chromodynamics parton shower represents an important step in characterising the emission properties of heavy quarks. Recent experimental advances in jet substructure techniques have provided the opportunity to isolate and characterise gluon emissions from heavy quarks. In this work, the first direct experimental constraint on the charm-quark splitting function is presented, obtained via the measurement of the groomed shared momentum fraction of the first splitting in charm jets, tagged by a reconstructed ${\rm D}^0$ meson. The measurement is made in proton--proton collisions at $\sqrt{s}$ = 13 TeV, in the low jet transverse-momentum interval of $15 \leq p_{\rm T}^{\rm jet~ch} < 30$ GeV/$c$ where the emission properties are sensitive to parton mass effects. In addition, the opening angle of the first perturbative emission of the charm quark, as well as the number of perturbative emissions it undergoes, are reported. Comparisons to measurements of an inclusive-jet sample show a steeper splitting function for charm quarks compared to gluons and light quarks. Charm quarks also undergo fewer perturbative emissions in the parton shower, with a reduced probability of large-angle emissions.
... The fragmentation function formalism was initially developed for light quarks, where the initial conditions to the evolution equations are purely non-perturbative. In the case of heavy quarks, the quark mass acts as an infrared regulator that prevents exactly collinear emissions in the fragmentation process (dead-cone effect, [24,25]). By introducing a perturbative contribution to the heavy-quark fragmentation functions [26], it is possible to incorporate the heavy quark mass effects for observables including identified heavy hadrons (or identified heavy quark jets, [27]) into otherwise fully massless calculations at higher orders, and resum large logarithms of collinear origin [28]. ...
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We extend the antenna subtraction method to include hadron fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD in $e^+e^-$ collisions. To handle collinear singularities associated with the fragmentation process, we introduce fragmentation antenna functions in final-final kinematics with associated phase space mappings. These antenna functions are integrated over the relevant phase spaces, retaining their dependence on the momentum fraction of the fragmenting parton. The integrated antenna functions are cross-checked against the known NNLO coefficient functions for identified hadron production from $\gamma^*/Z^* \to q\bar{q}$ and $H \to gg$ processes.
... The most relevant perturbative QCD processes that contribute to the production cross section are leading-order (LO) flavor creation, and next-to-leading order (NLO) gluon splitting as well as flavor excitation [14]. The parton shower and fragmentation of heavy-flavor jets is different from light-flavor jets due to two main reasons: the color charge effect, that is, heavy flavor jets are initiated by quarks as opposed to light-flavor jets that are mostly gluon-initiated [15]; and the dead-cone effect, meaning that small-angle gluon radiations off a massive parton are forbidden in QCD, and as a consequence, heavy-flavor fragmentation is harder and results in different jet substructures [16][17][18][19]. ...
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It has recently been shown that a KNO-like scaling is fulfilled inside the jets, which indicates that the KNO scaling is violated by complex vacuum-QCD processes outside the jet development, such as single and double parton scattering or softer multiple-parton interactions. In the current work we investigated the scaling properties of heavy-flavor jets using Monte-Carlo simulations. We found that while jets from leading-order flavor-creation processes exhibit a flavor-dependent pattern, heavy-flavor jets from production in the parton shower follow the inclusive-jet pattern. This suggests that the KNO-like scaling is driven by initial hard parton production and not by processes in the later stages of the reaction.
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We present a systematic analysis of heavy-flavour production in the underlying event in connection to a leading hard process in pp collisions at s=13 TeV, using the PYTHIA 8 Monte Carlo event generator. We compare results from events selected by triggering on the leading hadron, as well as those triggered with reconstructed jets. We show that the kinematics of heavy-flavour fragmentation complicates the characterisation of the underlying event, and the usual method which uses the leading charged final-state hadron as a trigger may wash away the connection between the leading process and the heavy-flavour particle created in association with that. Events triggered with light or heavy-flavour jets, however, retain this connection and bring more direct information on the underlying heavy-flavour production process, but may also import unwanted sensitivity to gluon radiation. The methods outlined in the current work provide means to verify model calculations for light and heavy-flavour production in the jet and the underlying event in great details.
Full-text available
Jet substructure observables have been used by experiments at the Large Hadron Collider (LHC) as instruments to search for new physics as well as to study perturbative and nonperturbative processes in quantum chromodynamics (QCD). Some observables are infrared and collinear safe and thus easily comparable to first-principles calculations, while others offer direct insight into specific physical phenomena such as the quark-gluon plasma formed in heavy-ion collisions. The high-precision capability of the ALICE tracking system allows a unique opportunity at LHC energies to measure tracks with low transverse momentum, permitting high precision access to the softer components inside jets with an excellent angular resolution. We present some recent charged-particle jet substructure measurements in pp collisions with ALICE, including the generalized jet angularities, the angular jet axes differences, and the direct observation of the dead-cone effect in QCD using the primary Lund Plane. These results provide new insights into the evolution of jets by comparing ALICE measurements to predictions from different event generators and perturbative QCD calculations.
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A bstract The Lund-jet plane has recently been proposed as a powerful jet substructure tool with a broad range of applications. In this paper, we provide an all-order single logarithmic calculation of the primary Lund-plane density in Quantum Chromodynamics, including contributions from the running of the coupling, collinear effects for the leading parton, and soft logarithms that account for large-angle and clustering effects. We also identify a new source of clustering logarithms close to the boundary of the jet, deferring their resummation to future work. We then match our all-order results to exact next-to-leading order predictions. For phenomenological applications, we supplement our perturbative calculation with a Monte Carlo estimate of non-perturbative corrections. The precision of our final predictions for the Lund-plane density is 5 − 7% at high transverse momenta, worsening to about 20% at the lower edge of the perturbative region, corresponding to transverse momenta of about 5 GeV. We compare our results to a recent measurement by the ATLAS collaboration at the Large-Hadron Collider, revealing good agreement across the perturbative domain, i.e. down to about 5 GeV.
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The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,324 new measurements from 878 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 120 reviews are many that are new or heavily revised, including a new review on High Energy Soft QCD and Diffraction and one on the Determination of CKM Angles from B Hadrons. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 98 review articles. Volume 2 consists of the Particle Listings and contains also 22 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group ( and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print and as a web version optimized for use on phones as well as an Android app.
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The prevalence of hadronic jets at the LHC requires that a deep understanding of jet formation and structure is achieved in order to reach the highest levels of experimental and theoretical precision. There have been many measurements of jet substructure at the LHC and previous colliders, but the targeted observables mix physical effects from various origins. Based on a recent proposal to factorize physical effects, this Letter presents a double-differential cross-section measurement of the Lund jet plane using 139 fb−1 of s=13 TeV proton-proton collision data collected with the ATLAS detector using jets with transverse momentum above 675 GeV. The measurement uses charged particles to achieve a fine angular resolution and is corrected for acceptance and detector effects. Several parton shower Monte Carlo models are compared with the data. No single model is found to be in agreement with the measured data across the entire plane.
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The ALICE collaboration at the CERN LHC reports novel measurements of jet substructure in pp collisions at s=7 TeV and central Pb–Pb collisions at sNN=2.76 TeV. Jet substructure of track-based jets is explored via iterative declustering and grooming techniques. We present the measurement of the momentum sharing of two-prong substructure exposed via grooming, the zg, and its dependence on the opening angle, in both pp and Pb–Pb collisions. We also present the measurement of the distribution of the number of branches obtained in the iterative declustering of the jet, which is interpreted as the number of its hard splittings. In Pb–Pb collisions, we observe a suppression of symmetric splittings at large opening angles and an enhancement of splittings at small opening angles relative to pp collisions, with no significant modification of the number of splittings. The results are compared to predictions from various Monte Carlo event generators to test the role of important concepts in the evolution of the jet in the medium such as colour coherence.
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Sherpa is a general-purpose Monte Carlo event generator for the simulation of particle collisions in high-energy collider experiments. We summarise essential features and improvements of the Sherpa 2.2 release series, which is heavily used for event generation in the analysis and interpretation of LHC Run 1 and Run 2 data. We highlight a decade of developments towards ever higher precision in the simulation of particle-collision events.
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A bstract The production of charm jets in proton-proton collisions at a center-of-mass energy of $$ \sqrt{s}=7 $$ s = 7 TeV was measured with the ALICE detector at the CERN Large Hadron Collider. The measurement is based on a data sample corresponding to a total integrated luminosity of 6 . 23 nb ⁻¹ , collected using a minimum-bias trigger. Charm jets are identified by the presence of a D ⁰ meson among their constituents. The D ⁰ mesons are reconstructed from their hadronic decay D ⁰ →K ⁻ π ⁺ . The D ⁰ -meson tagged jets are reconstructed using tracks of charged particles (track-based jets) with the anti- k T algorithm in the jet transverse momentum range $$ 5 5 < p T , jet ch < 30 GeV /c and pseudorapidity | η jet | < 0 . 5. The fraction of charged jets containing a D ⁰ -meson increases with $$ {p}_{{\mathrm{T}}_{,\mathrm{jet}}}^{\mathrm{ch}} $$ p T , jet ch from 0 . 042 ± 0 . 004 (stat) ± 0 . 006 (syst) to 0 . 080 ± 0 . 009 (stat) ± 0 . 008 (syst). The distribution of D ⁰ -meson tagged jets as a function of the jet momentum fraction carried by the D ⁰ meson in the direction of the jet axis $$ \left({z}_{\parallel}^{\mathrm{ch}}\right) $$ z ∥ ch is reported for two ranges of jet transverse momenta, $$ 5 5 < p T , jet ch < 15 GeV /c and $$ 15 15 < p T , jet ch < 30 GeV /c in the intervals $$ 0.2 0.2 < z ‖ ch < 1.0 and $$ 0.4 0.4 < z ‖ ch < 1.0 , respectively. The data are compared with results from Monte Carlo event generators (PYTHIA 6, PYTHIA 8 and Herwig 7) and with a Next-to-Leading-Order perturbative Quantum Chromodynamics calculation, obtained with the POWHEG method and interfaced with PYTHIA 6 for the generation of the parton shower, fragmentation, hadronisation and underlying event.
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We present a new method to expose the dead-cone effect at colliders using iterative declustering techniques. Iterative declustering allows one to unwind the jet clustering and to access the subjets or branches at different depths of the jet tree. Our method consists of declustering the heavy flavor-tagged jet using the Cambridge-Achen algorithm following the branch containing the heavy flavor at each step and registering the kinematics of the complementary untagged prong. The kinematics of the complementary untagged prong fill a Lund map representing the gluon radiation off the heavy-flavor quark at each step of the vacuum shower. Using Pythia8 Monte Carlo, we show that a simple cut on the Lund plane introduced by ln(kT)>0 suppresses hadronization effects and the angular separation between the jet prongs becomes very sensitive to flavor effects. A clear suppression for heavy-flavor jets relative to inclusive jets in the region of splitting angles delimited by the relation θ<mQ/E is observed, where mQ is the mass of the heavy quark and E is the energy of the radiator or splitting prong.
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A bstract Lund diagrams, a theoretical representation of the phase space within jets, have long been used in discussing parton showers and resummations. We point out that they can be created for individual jets through repeated Cambridge/Aachen declustering, providing a powerful visual representation of the radiation within any given jet. Concentrating here on the primary Lund plane, we outline some of its analytical properties, highlight its scope for constraining Monte Carlo simulations and comment on its relation with existing observables such as the z g variable and the iterated soft-drop multiplicity. We then examine its use for boosted electroweak boson tagging at high momenta. It provides good performance when used as an input to machine learning. Much of this performance can be reproduced also within a transparent log-likelihood method, whose underlying assumption is that different regions of the primary Lund plane are largely decorrelated. This suggests a potential for unique insight and experimental validation of the features being used by machine-learning approaches.
This concise primer reviews the latest developments in the field of jets. Jets are collinear sprays of hadrons produced in very high-energy collisions, e.g. at the LHC or at a future hadron collider. They are essential to and ubiquitous in experimental analyses, making their study crucial. At present LHC energies and beyond, massive particles around the electroweak scale are frequently produced with transverse momenta that are much larger than their mass, i.e., boosted. The decay products of such boosted massive objects tend to occupy only a relatively small and confined area of the detector and are observed as a single jet. Jets hence arise from many different sources and it is important to be able to distinguish the rare events with boosted resonances from the large backgrounds originating from Quantum Chromodynamics (QCD). This requires familiarity with the internal properties of jets, such as their different radiation patterns, a field broadly known as jet substructure. This set of notes begins by providing a phenomenological motivation, explaining why the study of jets and their substructure is of particular importance for the current and future program of the LHC, followed by a brief but insightful introduction to QCD and to hadron-collider phenomenology. The next section introduces jets as complex objects constructed from a sequential recombination algorithm. In this context some experimental aspects are also reviewed. Since jet substructure calculations are multi-scale problems that call for all-order treatments (resummations), the bases of such calculations are discussed for simple jet quantities. With these QCD and jet physics ingredients in hand, readers can then dig into jet substructure itself. Accordingly, these notes first highlight the main concepts behind substructure techniques and introduce a list of the main jet substructure tools that have been used over the past decade. Analytic calculations are then provided for several families of tools, the goal being to identify their key characteristics. In closing, the book provides an overview of LHC searches and measurements where jet substructure techniques are used, reviews the main take-home messages, and outlines future perspectives.