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# First measurements of N-subjettiness in central Pb-Pb collisions at sNN = 2.76 TeV

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A bstract The ALICE Collaboration reports the first fully-corrected measurements of the N -subjettiness observable for track-based jets in heavy-ion collisions. This study is performed using data recorded in pp and Pb-Pb collisions at centre-of-mass energies of $$\sqrt{s}$$ s = 7 TeV and $$\sqrt{s_{\mathrm{NN}}}$$ s NN = 2 . 76 TeV, respectively. In particular the ratio of 2-subjettiness to 1-subjettiness, τ 2 /τ 1 , which is sensitive to the rate of two-pronged jet substructure, is presented. Energy loss of jets traversing the strongly interacting medium in heavy-ion collisions is expected to change the rate of two-pronged substructure relative to vacuum. The results are presented for jets with a resolution parameter of R = 0 . 4 and charged jet transverse momentum of 40 ≤ p T , jet ≤ 60 GeV/ c , which constitute a larger jet resolution and lower jet transverse momentum interval than previous measurements in heavy-ion collisions. This has been achieved by utilising a semi-inclusive hadron-jet coincidence technique to suppress the larger jet combinatorial background in this kinematic region. No significant modification of the τ 2 /τ 1 observable for track-based jets in Pb-Pb collisions is observed relative to vacuum PYTHIA6 and PYTHIA8 references at the same collision energy. The measurements of τ 2 /τ 1 , together with the splitting aperture angle ∆ R , are also performed in pp collisions at $$\sqrt{s}$$ s = 7 TeV for inclusive jets. These results are compared with PYTHIA calculations at $$\sqrt{s}$$ s = 7 TeV, in order to validate the model as a vacuum reference for the Pb-Pb centre-of-mass energy. The PYTHIA references for τ 2 /τ 1 are shifted to larger values compared to the measurement in pp collisions. This hints at a reduction in the rate of two-pronged jets in Pb-Pb collisions compared to pp collisions.
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JHEP10(2021)003
Published for SISSA by Springer
Revised:August 2, 2021
Accepted:August 18, 2021
Published:October 1, 2021
First measurements of N-subjettiness in central
Pb-Pb collisions at sNN = 2.76 TeV
The ALICE collaboration
E-mail: ALICE-publications@cern.ch
Abstract: The ALICE Collaboration reports the ﬁrst fully-corrected measurements of
the N-subjettiness observable for track-based jets in heavy-ion collisions. This study is
performed using data recorded in pp and Pb-Pb collisions at centre-of-mass energies of
s= 7 TeV and sNN = 2.76 TeV, respectively. In particular the ratio of 2-subjettiness
to 1-subjettiness, τ21, which is sensitive to the rate of two-pronged jet substructure, is
presented. Energy loss of jets traversing the strongly interacting medium in heavy-ion
collisions is expected to change the rate of two-pronged substructure relative to vacuum.
The results are presented for jets with a resolution parameter of R= 0.4and charged jet
transverse momentum of 40 pT,jet 60 GeV/c, which constitute a larger jet resolution
and lower jet transverse momentum interval than previous measurements in heavy-ion
collisions. This has been achieved by utilising a semi-inclusive hadron-jet coincidence
technique to suppress the larger jet combinatorial background in this kinematic region.
No signiﬁcant modiﬁcation of the τ21observable for track-based jets in Pb-Pb collisions
is observed relative to vacuum PYTHIA6 and PYTHIA8 references at the same collision
energy. The measurements of τ21, together with the splitting aperture angle R, are also
performed in pp collisions at s= 7 TeV for inclusive jets. These results are compared with
PYTHIA calculations at s= 7 TeV, in order to validate the model as a vacuum reference
for the Pb-Pb centre-of-mass energy. The PYTHIA references for τ21are shifted to larger
values compared to the measurement in pp collisions. This hints at a reduction in the rate
of two-pronged jets in Pb-Pb collisions compared to pp collisions.
Keywords: Heavy Ion Experiments
ArXiv ePrint: 2105.04936
for the beneﬁt of the ALICE Collaboration.
Article funded by SCOAP3.
https://doi.org/10.1007/JHEP10(2021)003
JHEP10(2021)003
Contents
1 Introduction 1
2N-subjettiness, aperture angle and axis deﬁnitions 3
2.1 Subjet axes 4
2.1.1 kTclustering 4
2.1.2 Cambridge-Aachen clustering 4
2.1.3 Soft Drop grooming (with C/A) 4
2.1.4 Reclustering metric comparisons 5
3 Data sets, event selection and simulations 6
4 Jet reconstruction and underlying event corrections 8
4.1 Average background subtraction in heavy-ion collisions 9
4.2 Suppression of combinatorial jets via hadron-jet correlations in heavy-ion
collisions 10
4.3 Performance of the heavy-ion underlying event subtraction procedures on
τ2111
5 Detector and background response and two-dimensional unfolding 12
6 Systematic uncertainties 14
7 Results and discussion 16
8 Conclusions 19
The ALICE collaboration 26
1 Introduction
The goal of relativistic heavy-ion physics is to study the behaviour of Quantum Chromo-
Dynamics (QCD) matter in the high energy density and temperature regimes, where a
medium of deconﬁned quarks and gluons, known as the quark-gluon plasma (QGP), is
formed [1,2]. During the initial stages of the collisions, short distance scattering interac-
tions between the constituents of the incoming nucleons produce high-momentum transfer
partons (quarks and gluons), which fragment into collimated showers of particles known
as jets. Jets provide an experimental tool with which to reconstruct the parton shower
and access the kinematics of the initial scattered parton. The production of jets and their
substructure in pp collisions is well described by perturbative QCD [36], which makes
– 1 –
JHEP10(2021)003
them well-calibrated probes to investigate this medium in heavy-ion collisions. The phe-
nomenon of jet quenching, which refers to the modiﬁcation of jet production rates and
jet substructure due to interactions in coloured matter [7], is one of the most important
signatures of QGP formation and has been extensively studied in nuclear collisions at both
the Relativistic Heavy Ion Collider and the Large Hadron Collider, via measurements of
inclusive jet production as well as correlations of jets with high-energy triggers (hadrons,
photons, W and Z bosons and jets) [811]. The observed modiﬁcations are a consequence
of radiative and elastic interactions of the partons with the coloured medium and provide
an opportunity for measuring the transport properties of the QGP, notably the transport
parameter ˆq[12]. However, the dynamical mechanisms underlying such interactions are
still not well understood. Measurements of jet shapes [1318] and more recently, jet sub-
structure [1921] attempt to shed light on these mechanisms. It has also been proposed
that jet-medium interactions might be inﬂuenced by the underlying structure of the jet and
the degree to which the medium can resolve this substructure [22]. Jet substructure ob-
servables can be used to quantify these modiﬁcations and study the responsible energy loss
mechanisms, whilst also being sensitive to the fundamental properties of the medium [23].
In this paper, modiﬁcations to the two-pronged substructure of jets in heavy-ion col-
lisions, compared to those measured in pp collisions, are reported, in order to investigate
the impact of the underlying jet substructure on quenching eﬀects. Two-pronged jets are
composed of exactly two distinct hard or semi-hard substructures and are tagged through
the measurements of the ratio of 2-subjettiness to 1-subjettiness, τ21, which are cal-
culated relative to a variety of diﬀerently deﬁned axes. These are the axes of subjets
obtained by reclustering the jet constituents with jet ﬁnding algorithms. Each algorithm
can operationally reorder the jet shower, in momentum and angular separation, result-
ing in the selection of diﬀerent axes. The reclustering algorithms are also combined with
grooming techniques [24,25] to remove wide-angle soft radiation from the jet and select
speciﬁc regions of the splitting phase space where medium-induced signals are enhanced
(or suppressed) or where jet quenching calculations are under better control [26]. In Pb-
Pb collisions a semi-inclusive data driven approach is used to suppress the combinatorial
background and extend the measurement to larger jet resolution and lower pT,jet . In pp
collisions, comparisons of the measurement with PYTHIA [27] calculations at the same
centre-of-mass energy are used to validate the model as a vacuum reference for the Pb-
Pb centre-of-mass energy. In addition to τ21, the splitting aperture angle, R, is also
reported in pp collisions, providing complementary information on the underlying two-
pronged substructure.
The paper is organised as follows: section 2describes the observables and the diﬀerent
axis choices (reclustering algorithms). Section 3details the pp and Pb-Pb data sets and
event selection criteria used for the analysis. Section 4describes the jet ﬁnding proce-
dure, including the underlying event and combinatorial background subtraction techniques
used in Pb-Pb collisions. The response of the shapes to detector eﬀects and background
ﬂuctuations are also highlighted. Section 5details the simultaneous correction of the jet
substructure observable and pch
T,jet distributions, via a two-dimensional Bayesian unfolding
procedure, for these detector eﬀects and background ﬂuctuations. Section 6lists the con-
– 2 –
JHEP10(2021)003
tributions to the systematic uncertainties. Finally the fully corrected results are presented
in section 7, alongside a discussion with comparisons to theoretical models.
2N-subjettiness, aperture angle and axis deﬁnitions
This analysis measures the proportion of two-pronged jets in Pb-Pb compared to pp colli-
sions. Track-based jet ﬁnding is performed using the anti-kT[28] algorithm with a jet reso-
lution parameter of R= 0.4(full details of the jet reconstruction are given in section 4). In
order to tag jets as being single-pronged or two-pronged, the N-subjettiness [29] observable
is chosen. N-subjettiness is a jet substructure observable, denoted by τN, which quantiﬁes
the degree to which a jet has a N(or fewer)-pronged substructure. It is measured relative
to Naxes, which are the axes of the subjets returned by unwinding the reclustering history
of a given choice of reclustering algorithm by N1steps, and is deﬁned as,
τN=1
pT,jet ×RX
k
pT,kminimum(∆R1,k,R2,k, . . . ., RN,k),(2.1)
where kruns over the list of jet constituents. The transverse momentum, relative to the
beam, of constituent kis denoted as pT,k and RS,k is the distance in the pseudorapidity-
azimuthal (η-ϕ) plane between the constituent kand the axis of subjet S. The observable
is normalised by the product of the jet resolution parameter, R, and the jet transverse
momentum, pT,jet.
If the bulk of the pT,jet is correlated to at least one of the subjet axes, the jet is
composed of Nor fewer well deﬁned subjets and τNtends to zero. If a sizeable fraction of
the pT,jet is not aligned with any of the subjet axes, the jet is composed of at least N+ 1
subjets and τNtends to unity. The ratio of τNN1is sensitive to exactly N-prongs in
a jet, as an N-pronged jet is expected to have low τNand high τN1values. In this way,
the ratio of the two quantities is more discriminative of N-prongness in jets than either
quantity on its own.
The N-subjettiness observable was originally designed to identify boosted hadronically-
decaying objects such as W bosons and top quarks [29,30] Reconstructed jets containing a
W boson exhibit a distinct two-pronged energy ﬂow due to the two hard subjets produced
by the decay of the W boson to two quarks. The ratio of τ21can be used to discriminate
these jets from quark and gluon-initiated jets, which are primarily single-cored. In this
paper the measured ratio of τ21, on a jet-by-jet basis, is used to identify the two-pronged
subsample of QCD jets in both pp and Pb-Pb collisions. Jets with a clear two-pronged
substructure relative to the subjet axes will have low τ2and high τ1values, resulting in a
small τ21ratio. Various jet quenching mechanisms, such as medium-induced semi-hard
radiation emitted at large angles, are expected to change the rate of two-pronged QCD jets
in heavy-ion collisions relative to the vacuum [31]. Hard medium-induced radiation could
be a signature of the jet interacting with the partonic structure of the QGP, since large
momentum transfers are suppressed for strongly-coupled degrees of freedom [23]. This type
of radiation could create an additional prong in the jet, transforming the predominantly
single-pronged QCD jets, into two-pronged objects. It has also been postulated that colour
– 3 –
JHEP10(2021)003
coherence eﬀects [22], arising from the ﬁnite resolving power of the medium with respect to
jet substructure, could result in a larger degree of quenching for two-pronged jets compared
to single-cored jets. This would result in a decrease in the population of two-pronged jets
in Pb-Pb compared to pp collisions.
In addition to the τ21observable, the aperture angle between the two selected subjet
axes in the N= 2 case, R, is reported in pp collisions. Since the degree to which the jet
substructure is two-pronged depends on the angular separation of the prongs, in addition
to the way the pT,jet is distributed among them, this observable provides complementary
information to τ21. The measurements of the Robservable in pp collisions also provide
an important baseline for measurements of this observable in heavy-ion collisions, where
they can be used to directly probe the angular resolving power of the medium with respect
to coloured structures.
2.1 Subjet axes
The calculation of N-subjettiness requires Nsubjet axes, which are themselves obtained
by unwinding the reclustering history N1steps. The subjet axes are therefore dependent
on the choice of the reclustering algorithm used, with diﬀerent algorithms returning axes
that are sensitive to diﬀerent regions of the splitting phase space. The addition of grooming
techniques can further isolate this probed phase space, allowing for the selection of regions
where calculations are under better theoretical control. The reclustering algorithms em-
ployed in this analysis, which belong to the sequential recombination class of algorithms,
are detailed as follows:
2.1.1 kTclustering
This metric clusters particles based on their pTand angular separation from one an-
other [32]. The clustering begins by combining soft particles, with hard structures only
being brought together in the ﬁnal steps of the clustering history. Therefore unwinding the
2.1.2 Cambridge-Aachen clustering
The C/A algorithm combines particles solely based on their angular separation from one
another, thus maintaining an angular ordered tree in vacuum [33]. Particles closest to
each other in the η-ϕplane are brought together ﬁrst, with the last step of the clustering
combining the furthest separated structures in the jet. Unwinding the reclustering history
one step gives access to the pair of subjets separated by the largest angle.
2.1.3 Soft Drop grooming (with C/A)
The Soft Drop groomer [25] is applied to the C/A reclustered jet. In this case, instead of
selecting the axes returned by unwinding the reclustering history by one step, the splitting
is ﬁrst tested against the Soft Drop condition. This is given by,
minimum(pT,1, pT,2)
pT,1+pT,2
> zcut R
Rβ
,(2.2)
– 4 –
JHEP10(2021)003
where the indices 1and 2label the subjet axes and Rrepresents the jet resolution
parameter. The zcut and βparameters control the grooming behaviour. The former places
a lower limit on the momentum fraction carried by the subleading subjet, which is the subjet
carrying the smaller momentum fraction. The latter quantiﬁes the interplay between the
angular and momentum components of the splitting, with higher βvalues preferentially
removing soft large-angle radiation. If the Soft Drop condition is satisﬁed, the splitting
is accepted and the axes are returned. However, if the splitting does not satisfy the Soft
Drop condition, the subleading subjet is groomed away and the procedure is repeated by
unclustering the leading subjet and testing against the Soft Drop condition. This process
iteratively continues until either a splitting is found which passes the Soft Drop condition
(the axes are returned), or the reclustering history is exhausted and there is only one track
left in which case the jet is discarded.
The purpose of the grooming procedure is to strip away soft radiation from the jet and
uncover a hard substructure. The beneﬁt of using the C/A algorithm for the groomer is
that the splitting tree is angular ordered, which is the expected conﬁguration of the parton
shower in the vacuum. Therefore, the ﬁrst structure that is accepted by the groomer is
expected to be correlated to the earliest hard splitting in the jet. In this work the Soft
Drop condition is deﬁned with values of zcut = 0.1and β= 0, which is equivalent to the
Mass Drop tagger [34]. This removes the angular dependency from eq. 2.2 and reduces
the Soft Drop condition to a test of the hardness of the splitting. In this conﬁguration,
the groomer removes soft large-angle radiation from the jet. The widest hard or semi-hard
splitting that is found in the declustering process, is returned (in vacuum).
2.1.4 Reclustering metric comparisons
The comparison of the τ21observable for diﬀerent subjet axes choices, using a variety
of reclustering algorithms, is shown in ﬁgure 1for track-based jets at particle level. These
are calculated in simulated pp collisions at s= 7 TeV using the PYTHIA6 Perugia 2011
tune. The angular separation (in the η-ϕplane) of the subjet axes in the τ2case, R, is
also shown in ﬁgure 1(right). The τ21distribution measured for the C/A case tends
towards unity. This is due to the fact that C/A selects soft large-angle subleading prongs,
to which the rest of the jet emissions are not aligned. The addition of the Soft Drop groomer
signiﬁcantly changes the subjet axes, with the τ21distribution in this case peaking at
lower values. This indicates that the subleading axis is correlated to a larger fraction of the
pT,jet. There is also an increase in the population of jets with a value of τ21= 0, due to
an increase of two-track jets after grooming. The distribution obtained with the Soft Drop
groomer is qualitatively similar to the kTcase, where by construction soft particles are
clustered together ﬁrst and the ﬁnal reclustering step brings together any hard structures
present in the jet.
In the “C/A + min” case shown in the plots, a minimisation step is performed, starting
with the axes returned by the C/A reclustering. The process seeks to ﬁnd a local minimum
of N-subjettiness, by geometrically varying the axes [35]. The minimisation was expected
to reduce the sensitivity of the axes to uncorrelated soft radiation. However the impact of
this additional step was found to be minimal, with respect to the C/A case without minimi-
– 5 –
JHEP10(2021)003
0 0.5 1
1
τ
/
2
τ
0
1
2
3
4
5
6
7
8
)
1
τ
/
2
τ
/d(N d
jets
N1/
ALICE Simulation
PYTHIA6 Perugia 2011
= 7 TeVs
pp
= 0.4R charged jets,
T
kAnti-
c < 60 GeV/
part,ch
T,jet
p40 <
R | < 0.9
part
jet
η|
T
k
C/A
C/A + min
Soft Drop
0 0.1 0.2 0.3 0.4 0.5
R
0
2
4
6
8
10
12
R
/dN d
jets
N1/
ALICE Simulation
PYTHIA6 Perugia 2011
= 7 TeVs
pp
= 0.4R charged jets,
T
kAnti-
c < 60 GeV/
part,ch
T,jet
p40 <
R | < 0.9
part
jet
η|
T
k
C/A
C/A + min
Soft Drop
Figure 1. The τ21(left) and R(right) observables are shown for a variety of diﬀerent axis
selection algorithms. Both plots are obtained using a PYTHIA6 Perugia 2011 simulation of pp
collisions at s= 7 TeV, in the particle level charged jet transverse momentum interval of 40
ppart,ch
T,jet 60 GeV/c.
sation, both in the PYTHIA calculations presented here and in measurements made in pp
and Pb-Pb collisions. As such, this particular conﬁguration will not be discussed further.
The Rdistributions, obtained using various reclustering algorithms, show that soft
subleading prongs, selected by the C/A algorithm, are present at large angles from the jet
core (R > 0.3). In contrast, hard subleading prongs, selected by both the kTand Soft
Drop groomer, appear at small angles (R0.1). This indicates that this sample of QCD
jets are predominantly single-cored, with most of the pch
T,jet appearing close to the jet axis.
The pch
T,jet dependence of the τ21and Robservables is shown in ﬁgure 2for the
kTreclustering algorithm, for three consecutive pch
T,jet intervals. The Rshape exhibits a
strong pch
T,jet dependence in accordance with the collimation of jets with increasing pch
T,jet.
However, the τ21shape shows only a mild dependence on the pch
T,jet. The study was
performed for the other algorithms (not shown), with the same conclusion also holding for
C/A with Soft Drop grooming. However, no pch
T,jet dependence is observed for the C/A
reclustering algorithm, with and without minimisation of the τ2and τ1variables. This is
because the presence of large-angle soft particles in the jet cone is largely independent of
pch
T,jet. The weak pch
T,jet dependence observed for the τ21observable facilitates a cleaner
comparison of measurements made in the same pch
T,jet interval in Pb-Pb and pp collisions,
as the reduction in the pch
T,jet scale due to quenching in Pb-Pb collisions has no eﬀect on
the vacuum properties of this observable.
3 Data sets, event selection and simulations
A detailed description of the ALICE detector and its performance can be found in refs. [36,
37]. The analysed pp data were collected during Run 1 of the LHC in 2010 with a collision
centre-of-mass energy of s= 7 TeV using a minimum bias (MB) trigger. The MB trigger
– 6 –
JHEP10(2021)003
0 0.5 1
1
τ
/
2
τ
0
1
2
3
4
5
6
7
8
)
1
τ
/
2
τ
/d(N d
jets
N1/
ALICE Simulation
PYTHIA6 Perugia 2011
= 7 TeVs
pp
= 0.4R charged jets,
T
kAnti-
reclustering
T
kR | < 0.9
part
jet
η|
c < 40 GeV/
part,ch
T,jet
p20 <
c < 60 GeV/
part,ch
T,jet
p40 <
c < 80 GeV/
part,ch
T,jet
p60 <
0 0.1 0.2 0.3 0.4 0.5
R
0
2
4
6
8
10
12
R
/dN d
jets
N1/
ALICE Simulation
PYTHIA6 Perugia 2011
= 7 TeVspp
= 0.4R charged jets,
T
kAnti-
reclustering
T
kR | < 0.9
part
jet
η|
c < 40 GeV/
part,ch
T,jet
p20 <
c < 60 GeV/
part,ch
T,jet
p40 <
c < 80 GeV/
part,ch
T,jet
p60 <
Figure 2. The pch
T,jet dependence of the τ21(left) and R(right) observables are shown, for the
axes obtained using the kTreclustering algorithm. These calculations are made using PYTHIA6
Perugia 2011 simulations of pp collisions at s= 7 TeV.
conﬁguration is the same as described in ref. [38]. The data from heavy-ion collisions were
recorded in 2011 at sNN = 2.76 TeV. This analysis uses the 010% most-central Pb-
Pb collisions selected by the online trigger based on the hit multiplicity measured in the
forward V0 detectors [39]. The data sets and event selections are identical to refs. [8,13].
After oﬄine selection, the pp sample consists of 168 million events (Lint 2.5 nb1), while
the Pb-Pb sample consists of 19 million events (Lint 21.4µb1). In heavy-ion collisions a
semi-inclusive hadron-jet procedure [8] is employed, as described in section 4, which further
restricts the event selection.
The analysis uses primary charged particles reconstructed as tracks in the Inner Track-
ing System (ITS) [40] and Time Projection Chamber (TPC) [41] which both cover the full
azimuth and pseudorapidity |η|<0.9. Tracks are required to have transverse momentum
0.15 < pT<100 GeV/c. Further details of the track selection can be found in ref. [42].
In pp collisions, the tracking eﬃciency is approximately 80% for tracks with pT>
1 GeV/c, decreasing to roughly 56% at pT= 0.15 GeV/c, with a track momentum resolution
of 1% for pT= 1 GeV/c and 4.1% for pT= 40 GeV/c [37,43]. In 010% most-central Pb-
Pb collisions, the tracking eﬃciency is about 2 to 3%lower than in pp at any given pT.
The track pTresolution is about 1% at pT= 1 GeV/c and 2.5% for pT= 40 GeV/c [42].
For both centre-of-mass energies of s= 2.76 TeV and s= 7 TeV used in this
analysis, pp collisions were simulated using PYTHIA6 (Perugia Tune 2011) [44]. These
Monte Carlo (MC) simulations were used to construct the response matrices employed as
part of the unfolding procedures detailed in section 5. These MC simulations were utilised
at three levels which will be discussed in this paper. The ﬁrst is the particle level MC, which
includes primary particles and the decay products from strong and electromagnetic decays.
This is used to construct the truth level axes of the response matrices. The second is the
reconstructed level MC, which is obtained by propagating the particle level events through
– 7 –
JHEP10(2021)003
a detailed reconstruction of the ALICE apparatus using GEANT3 [45]. This level includes
both secondaries from interactions in the detector material and the products of weak decays
and is used as the measured axes of the response matrix in pp collisions. To account for
the smearing due to the background in Pb-Pb events, the MC simulated at s= 2.76 TeV
is embedded into real, 010% most-central, Pb-Pb events at reconstructed level to obtain
the measured axes for the response matrices in this collision system. This comprises the
third type of MC in use, referred to as the embedded level. PYTHIA-generated events
are embedded instead of real pp data measured at s= 2.76 TeV, due to the limited
size of the measured data sample. The diﬀerences between PYTHIA and measurements
in pp collisions are studied at s= 7 TeV and are considered when comparing with
measurements in Pb-Pb events.
4 Jet reconstruction and underlying event corrections
In both collisions systems jet reconstruction is performed on all accepted tracks, using
the anti-kTalgorithm with a jet resolution parameter of R= 0.4. This algorithm is the
standard choice for jet ﬁnding at the LHC due to both the stable shape of the resulting
jets as well as the disposition of the algorithm to cluster around hard structures. The
choice of jet clustering algorithm determines the set of jet constituents, with no impact
on the reclustering procedure beyond that. The E-scheme, which simply combines the
four-vectors of two tracks, is used to recombine tracks [46], with the mass of each track
assumed to be that of the charged pion. Jet ﬁnding is done using the FastJet package [46].
The jet area, Ajet, is calculated with a precision in the order of a percent, using so called
ghost particle areas of Ag= 0.005 [47]. In Pb-Pb collisions, a selection on the jet area is
applied, such that jet candidates with an area smaller than 60%of the area of a cone with
a radius of 0.4are rejected. This requirement suppresses background jets whilst preserving
true hard jets with a high eﬃciency [48] (100%in the reported pch
geometric selections are also imposed on the jet candidates, requiring |ηjet|<0.5, where
ηjet is the pseudorapidity of the jet axis. This ensures that the full jet cone is contained
within the acceptance of the ALICE inner barrel. The jet energy instrumental resolution
is similar for pp and Pb-Pb collisions, varying from 15% at pch
T,jet = 20 GeV/c to 25%
at pch
T,jet = 100 GeV/c. The Jet Energy Scale uncertainty is dominated by the tracking
eﬃciency uncertainty which is 4%.
In pp collisions, for the presented jet resolution parameter R= 0.4and jet momentum
interval 40 < pch
T,jet <60 GeV/c, the impact of the underlying event background is minimal.
This, in addition to the low pile-up contamination, means that underlying event corrections
in this collision system are not required. However, for the Pb-Pb analysis, the presence
of the large background due to the underlying event necessitates corrections both for the
smearing of the jet pTand jet substructure observables, as well as to the measured yield of
jets. The smearing of the measured quantities for each jet is corrected for by subtracting
the average underlying background in each event from each jet individually, as described in
section 4.1. Any residual smearing due to local ﬂuctuations of the background are corrected
for using a two-dimensional bayesian unfolding procedure, as described in section 5.
– 8 –
JHEP10(2021)003
The need for a correction to the measured yield of jets arises from a contamination by
jets purely comprised of soft particles not correlated with a given hard scattering, known
as combinatorial jets. This contamination must be corrected for before the unfolding pro-
cedure. Combinatorial jets constitute one of the main challenges for measurements at large
jet resolution parameter and low pch
T,jet in heavy-ion collisions, as the rate of combinatorial
jets is high in this regime. In order to correct for the combinatorial yield without introduc-
ing a bias on the jet fragmentation, a data driven semi-inclusive approach using hadron-jet
coincidences is extended for the ﬁrst time to a substructure measurement. This procedure
is described in detail in section 4.2. The average underlying event is ﬁrst removed on a jet-
by-jet basis, before correcting the resulting yield of jets. Once the impact of combinatorial
jets on the measured sample is suppressed, residual ﬂuctuations of the underlying event
are corrected for via an unfolding procedure.
4.1 Average background subtraction in heavy-ion collisions
The constituent subtraction [49] and area-derivatives [50] methods are applied indepen-
dently to correct the candidate jet pTand shape distributions for the average underlying
event background, with the former used as the default method and the latter used as a
systematic variation. To estimate the background in each event, a separate jet reconstruc-
tion pass is carried out using the kTalgorithm with R= 0.2. This algorithm is sensitive to
soft clusters in the event and allows for the estimation of the density of jet-like transverse
momentum and mass due to the background, ρand ρm. These are deﬁned as
ρ= median
praw,ch,i
T,jet
Ai
jet
, ρm= median mraw,i
jet
Ai
jet !,(4.1)
where the index iruns over all jet candidates in an event, excluding the two with the
highest praw,ch,i
T,jet . The transverse momentum, mass and area of the ith reconstructed jet are
denoted by praw,ch,i
T,jet ,mraw,i
jet and Ai
jet, respectively.
The constituent subtraction method works by uniformly adding ghost particles to each
jet, with the pch
Tand mass of these particles being scaled to represent the event-wise ρand
ρmvalues, respectively. Jet constituents and neighbouring “ghosts” are iteratively paired
up and their pch
Tand mass are subtracted. The pairing and subtraction are done separately
for the pch
T,jet and mass. During this subtraction the pch
T(or mass) of the jet constituent
and “ghost” in each pair are compared and the smaller pch
T(or mass) value is subtracted
from the larger one. The pch
T(or mass) of the smaller one is then set to zero and the jet
constituent or “ghost” that it belonged to is removed from the next iteration of pairing. In
this way, the average underlying event background is removed at a constituent level from
the jets. The area-derivatives method employs a numerical approach to account for the
underlying background. The jet is populated with “ghost” particles and the background
subtracted observable of interest is redeﬁned as an expansion containing the observable
measured in the presence of the background and its derivatives (in this work up to the
second order) with respect to the pch
Tscale of the “ghosts”, which are subtracted from the
ﬁrst term. This series is then numerically solved in the limit that the “ghost” pch
Tscale
– 9 –
JHEP10(2021)003
goes to zero, which represents the case with no underlying event background. A detailed
description of the methods and their application to jet substructure observables in ALICE
can be found in [13].
4.2 Suppression of combinatorial jets via hadron-jet correlations in heavy-ion
collisions
In order to suppress the combinatorial jet yield in the measured sample, a data-driven
method using semi-inclusive hadron-jet correlations, is applied. First, two exclusive classes
of high trigger charged hadron pT, with 15 pT<45 GeV/c(Signal) and 8pT<9GeV/c
(Reference), denoted as TT{15,45}and TT{8,9}(where TT stands for trigger track), are
considered. These intervals are similar to those used in [8] and are chosen so as to optimise
the signal-to-background ratio, as described below. The event sample is split into two
statistically independent samples for the signal and reference measurements. Jet ﬁnding
is then performed in events containing a trigger hadron, with the jets constrained to a
back-to-back (with respect to the trigger hadron) azimuthal window, ϕ=ϕTT ϕjet ,
which is deﬁned such that |π-ϕ|<0.6. This region of azimuthal phase space is chosen
to account for in-medium deﬂections of the recoiling parton. The same pseudorapidity
window of |η|<0.5, as described in section 4, is used for jet selection. The contribution of
combinatorial jets found in the recoiling region of the high transverse momentum trigger
hadrons is expected to be uncorrelated to these hadrons and hence equal for both TT
classes. Therefore, subtracting the per-trigger normalised yield of jets measured in the
recoil regions of the two classes results in a combinatorial-suppressed distribution which
allows for unfolding to particle level. The two trigger classes are of suﬃciently high pT
so that topological, multiplicity and ﬂow biases induced by a trigger hadron saturate and
are removed by the subtraction procedure. In this paper the hadron-jet recoil method is
applied for the ﬁrst time to a jet substructure measurement, where the subtraction involves
the two-dimensional recoil yields of pch
T,jet and the τ21substructure observable (deﬁned in
section 2) measured for each trigger hadron class. The subtraction procedure is given by,
τ21
recoil =1
Ntrig,Sig
d2N
dpch
T,jetdτ21pT,trig TTSig
1
Ntrig,Ref
d2N
dpch
T,jetdτ21pT,trig TTRef
,(4.2)
where TTSig and TTRef represent TT{15,45}and TT{8,9}, respectively. The vari-
ables Ntrig,Sig and Ntrig,Ref represent the number of trigger hadrons selected in the signal
and reference classes, respectively. It should be noted that the scale factor term found
in [8], which corrects the reference trigger class yield for eﬀects of ﬁnite phase-space in the
recoil region, is omitted. The impact of this scale factor is found to be negligible through
tests in data. This follows from the fact that this correction mostly aﬀects the absolute
yield of the subtracted distribution and has a smaller impact on the shape of the distri-
bution. As the PYTHIA distributions are compared with inclusive measurements in pp
collisions, only the descriptions of the shapes of the distributions are validated. As the
descriptions in PYTHIA of the magnitudes of the semi-inclusive yields of the observables
are not validated, the presented measurements in Pb-Pb collisions are self normalised for
– 10 –
JHEP10(2021)003
comparisons to PYTHIA. As such, the scale factor correction has a negligible impact on
the results.
4.3 Performance of the heavy-ion underlying event subtraction procedures on
τ21
The performances of the constituent subtraction and area-derivatives methods for the τ21
observable are studied by embedding simulated PYTHIA MB events, propagated to recon-
structed level, into the 010% most central, real Pb-Pb events. Jet ﬁnding is then performed
at the embedded level and the constituent subtraction and area-derivatives methods are
applied. The particle level jets are then matched to their embedded level counterparts
to assess the impact of these underlying event subtraction methods. In addition to de-
termining a geometric correspondence between the particle level and embedded level jet
axes, the matching condition also requires that tracks pertaining to half of the transverse
momentum of the particle level jet are included in the matched embedded level jet. These
will be the matching criteria used in all cases between jets at particle and embedded levels.
Figure 3(left) shows the τ21distributions, measured using the kTreclustering algorithm,
for unsubtracted embedded jets (diamonds), average background-subtracted embedded jets
(squares and triangles for the two methods), and PYTHIA particle level jets (full circles).
The heavy-ion background has a large impact on the PYTHIA distribution, promoting
the unsubtracted embedded distribution to signiﬁcantly larger values compared to parti-
cle level. The background subtraction techniques do a fairly good job of correcting the
distribution back to particle level. The comparison is performed in the particle level mo-
mentum, ppart,ch
T,jet , interval of 4060 GeV/c. Similar performances are obtained for all subjet
axes choices. After applying these methods to the measured data, any remaining residual
diﬀerences between the particle level and background subtracted distributions, which are
due to background ﬂuctuations and detector eﬀects, are corrected using an unfolding pro-
cedure (see section 5). Since the embedded MC jets are matched to particle level, no yield
correction to suppress combinatorial jets is required for this performance check.
Figure 3(right) shows the residual distributions for τ21, simulated for both pp and
Pb-Pb (via embedding) collisions, for 40 < ppart,ch
T,jet <60 GeV/c. As expected, the dis-
tributions measured in Pb-Pb collisions exhibit a larger width compared to those in pp
collisions, as the residuals are inﬂuenced by background ﬂuctuations in addition to instru-
mental eﬀects.
The impact of employing the semi-inclusive hadron-jet coincidence technique to sup-
press the combinatorial yield is shown for the measured data in ﬁgure 4, where the τ21
distributions measured in the recoil region of each trigger hadron class, along with the diﬀer-
ence of these two distributions, are presented in three intervals of pch
T,jet. It can be seen that
the signal-to-background ratio, which can be inferred from the separation of the two TT
classes, increases with increasing pch
T,jet, as the contribution of combinatorial jets decreases.
For 20 < pch
T,jet <40 GeV/c, combinatorial jets are dominant and the diﬀerence between the
recoil shape yields of the two trigger classes is small. As expected, this diﬀerence, which is
the combinatorial-suppressed distribution, increases relative to the TT{15,45}distribution
– 11 –
JHEP10(2021)003
0 0.2 0.4 0.6 0.8 1 1.2 1.4
1
τ
/
2
τ
6
10
4
10
2
10
1
2
10
4
10
)
1
τ
/
2
τ
/d(N d
jets
N1/
ALICE Simulation
= 2.76 TeV
NN
s
0-10% Pb-Pb
= 0.4R charged jets,
T
kAnti-
c < 60 GeV/
part,ch
T,jet
p40 <
reclustering
T
k
R | < 0.9
part
jet
η|
PYTHIA Part.
PYTHIA Emb. Const. Sub.
PYTHIA Emb. Area-Deriv. Sub.
PYTHIA Emb. Unsubtracted
1.510.50 0.5 1 1.5
part
)
1
τ
/
2
τ
-(
rec
)
1
τ
/
2
τ
(
0
0.1
0.2
0.3
0.4
0.5
0.6
Probability per bin
ALICE Simulation
= 0.4R charged jets,
T
kAnti-
c < 60 GeV/
part,ch
T,jet
p40 <
reclustering
T
k
R | < 0.9
part
jet
η|
= 7 TeVsPYTHIA
= 2.76 TeV
NN
sPYTHIA Embedded
Figure 3. Left: the performances of the constituent (squares) and area-derivatives (triangles)
subtraction methods on the τ21observable, measured with the kTreclustering algorithm, are
evaluated by embedding PYTHIA MC events into real Pb-Pb data. The ﬁlled circles represent the
case with no heavy-ion background and the diamonds represent the case with background but no
subtraction. Right: the τ21residual distributions characterising the observable resolution due to
detector eﬀects and uncorrelated background. Both plots are shown for 40 < ppart,ch
T,jet <60 GeV/c.
with increasing pch
T,jet. It is now possible to unfold this distribution to particle level, as the
combinatorial entries are heavily suppressed through this semi-inclusive correction.
5 Detector and background response and two-dimensional unfolding
The measured distributions are unfolded to simultaneously correct the reconstructed pch
T,jet
and shape distributions back to particle level. The corrections account for detector ef-
fects (pp and Pb-Pb collisions) and residual background ﬂuctuations (Pb-Pb collisions).
As shown in ﬁgure 3, the background subtraction techniques applied in Pb-Pb collisions
perform well for the measured τ21distributions. Therefore, the unfolding procedure does
not induce large correction factors.
– 12 –
JHEP10(2021)003
0 0.2 0.4 0.6 0.8 1 1.2
1
τ
/
2
τ
4
10
3
10
2
10
1
10
1
10
2
10
)
1
τ
/
2
τ
/d(N d
trig
N1/
= 2.76 TeV
NN
s0-10% Pb-Pb
= 0.4R charged jets,
T
kAnti-
| < 0.6ϕ π|
c < 40 GeV/
ch
T,jet
p20 <
reclustering
T
k
TT{15,45}
TT{8,9}
TT{8,9} TT{15,45}
0 0.2 0.4 0.6 0.8 1 1.2
1
τ
/
2
τ
4
10
3
10
2
10
1
10
1
10
2
10
)
1
τ
/
2
τ
/d(N d
trig
N1/
= 2.76 TeV
NN
s0-10% Pb-Pb
= 0.4R charged jets,
T
kAnti-
| < 0.6ϕ π|
c < 60 GeV/
ch
T,jet
p40 <
reclustering
T
k
TT{15,45}
TT{8,9}
TT{8,9} TT{15,45}
0 0.2 0.4 0.6 0.8 1 1.2
1
τ
/
2
τ
5
10
4
10
3
10
2
10
1
10
1
10
2
10
)
1
τ
/
2
τ
/d(N d
trig
N1/
= 2.76 TeV
NN
s0-10% Pb-Pb
= 0.4R charged jets,
T
kAnti-
| < 0.6ϕ π|
c < 80 GeV/
ch
T,jet
p60 <
reclustering
T
k
TT{15,45}
TT{8,9}
TT{8,9} TT{15,45}
Figure 4. The uncorrected τ21distributions of the jets recoiling from a trigger hadron, mea-
sured in Pb-Pb collisions at sNN = 2.76 TeV, are presented. For each trigger hadron class, three
consecutive uncorrected pch
T,jet bins of 20 pch
T,jet <40,40 pch
T,jet <60 and 60 pch
T,jet <80 GeV/c
are measured. The red, blue and black data points represent the signal trigger class, the reference
trigger class and the diﬀerence between the two classes, respectively.
– 13 –
JHEP10(2021)003
A two-dimensional Bayesian unfolding procedure, as implemented in the RooUnfold
package [51], is used. To guarantee statistical stability of the correction procedure, the 2D
correlation (prec,ch
T,jet , shaperec,ch
jet ), which is the input to the unfolding, is binned such that
there are no empty bins. This sets the upper limit of the input prec,ch
T,jet range at 80 GeV/cin
both pp and Pb-Pb collisions. The response matrix is constructed with matched particle
and embedded (reconstructed) level jets for the unfolding of Pb-Pb (pp) collisions and
contains no entries for combinatorial jets. As the raw input data in Pb-Pb collisions also
has a negligible contribution from combinatorial background jets, it can in principle be
unfolded down to arbitrarily low jet prec,ch
T,jet . In practice, however, the minimum accepted
jet momentum is set at 20GeV/cto maintain the statistical stability of the unfolding. The
same lower limit is also applied in pp collisions. The reconstructed range supplied to the
response matrix must also mirror that of the input.
A particle level ppart,ch
T,jet interval of 0-160 GeV/cwas supplied to the response matrices.
The particle level ranges were extended relative to the input ranges, to account for jet
migrations into the reconstructed level range due to background ﬂuctuations and instru-
mental eﬀects. The unfolding procedure cannot account for the feed-in from reconstructed
level jets outside the truncated (reconstructed level) range which at particle level are within
the given range. These must be corrected for independently. This correction is calculated
using MC simulations at particle and reconstructed levels and is limited by choosing re-
ported unfolded bins far away from the truncation thresholds. Therefore, our ﬁnal results
are presented for the jet momentum interval 4060 GeV/c.
For the Pb-Pb analysis, the entries into the response matrices are weighted according
to their particle level ppart,ch
T,jet values, to transform the shape of the particle level embedded
spectrum from that of inclusive to recoil jets. This is to ensure the response matrix is more
representative of the underlying input data distribution. These weights are calculated in
bins of particle level ppart,ch
T,jet by taking the ratio of a particle level PYTHIA recoil jet ppart,ch
T,jet
distribution and a (scaled) PYTHIA inclusive jet ppart,ch
T,jet distribution.
The unfolded solutions converge after a few iterations in both collision systems. The
stability of each unfolding procedure is tested by refolding the unfolded solutions back
and checking the agreement with the input distributions. In Pb-Pb (pp) collisions, both
distributions agree within 5%(1%) after the third (second) iteration. A closure test is also
performed, where two statistically independent MC samples are used to ﬁll the response
matrix (particle and reconstructed levels) and provide the input data to the unfolding
(reconstructed level). In this case, the unfolded solutions agree with the particle level MC
corresponding to the pseudo input samples within 10%in pp and Pb-Pb collisions.
6 Systematic uncertainties
The systematic uncertainties for the jet substructure distributions are determined by vary-
ing the analysis settings for instrumental responses and method induced selections. The
sources of systematic uncertainty considered are:
The tracking eﬃciency uncertainty for the track selection used is ±4% in both pp and
Pb-Pb collisions. The unfolding procedure is repeated with a response matrix con-
– 14 –
JHEP10(2021)003
structed with 4% worse tracking eﬃciency. This represents the largest contribution
to the jet energy scale uncertainty [17].
A series of systematic variations of the unfolding procedure are considered. The vari-
ation giving the largest uncertainty in each bin is chosen as the unfolding systematic
uncertainty. These include the following:
1. The prior in the two-dimensional Bayesian implementation of RooUnfold is taken
as the projection of the response matrix onto the particle level axis. The default
prior is PYTHIA6 Perugia 0. A variation to the prior, which re-weights the
response matrix such that the prior coincides with the unfolded solution, is
considered.
2. The unfolding is regularised by controlling the number of iterations performed,
which is four for pp and Pb-Pb collisions in the default solutions. The uncer-
tainty in the regularisation is estimated by considering the diﬀerences to solu-
tions for iterations that are one lower and three higher than the default number
of iterations.
3. In both collision systems, the minimum accepted jet pch
T,jet as input to the un-
folding is 20 GeV/c. As a variation, this truncation threshold is lowered by
10 GeV/c. For Pb-Pb collisions, the τ21shape input is also truncated at 1.0
to preserve statistical stability in the default unfolding case. The upper bound
of this input is extended to 1.2 as a variation.
4. The binning of the input data is varied arbitrarily (whilst keeping the statistical
requirements of no empty bins) in both the pch
T,jet and shape dimensions.
The choice of the background subtraction method in Pb-Pb collisions, which primar-
ily aﬀects the tails of the distributions, is varied. The default solution is obtained
using the constituent subtraction method, whereas the systematic uncertainty is cal-
culated using the area-based derivatives subtraction method. This uncertainty is
not available for the distribution calculated using the Soft Drop algorithm as the
numerical subtraction procedure does not produce stable results.
The diﬀerent components of the systematic uncertainties, for the observables calculated
using the kTreclustering algorithm, are summarised in tables 1and 2, for pp and Pb-
Pb collisions, respectively. All sources of systematic uncertainty are considered to be
uncorrelated and each is symmetrised before being added in quadrature to obtain the
overall systematic uncertainty.
The relative contribution and magnitude of the uncertainties are similar for all the
reclustering algorithms considered, with the exception of the ﬁrst two bins of the R
distribution measured with the C/A algorithm in pp collisions, where the tracking eﬃciency
uncertainty has a larger impact.
– 15 –
JHEP10(2021)003
Observable τ21R
Interval 0.2–0.4 0.5–0.6 0.8–0.9 0.0–0.1 0.1–0.2 0.2–0.3
Tracking 7.5% 5.2% 11.2% 4.4% 0.8% 0.9%
Unfolding 1.5% 4.4% 5.7% 3.7% 2.8% 3.9%
Total 7.6% 6.8% 12.6% 5.7% 2.9% 4.0%
Table 1. Relative systematic uncertainties of the measured observables, using kTreclustering, in
pp collisions at s= 7 TeV are shown for three selected intervals of the observables in the jet pch
T,jet
range of 4060 GeV/c. All sources of systematic uncertainty are considered to be uncorrelated.
Shape τ21
Shape interval 0.2–0.4 0.4–0.6 0.8–1
Tracking 3.9% 1.5% 1.4%
Unfolding 11.6% 2.0% 3.2%
Bkg. Sub 2.4% 2.6% 0.9%
Total 12.5% 4.1% 3.6%
Table 2. Relative systematic uncertainties on the τ21shape, measured using kTreclustering,
are shown in 010% most central Pb-Pb collisions at sNN = 2.76 TeV for three selected intervals
of the observables in the jet pch
T,jet range 4060 GeV/c. All sources of systematic uncertainty are
considered to be uncorrelated.
7 Results and discussion
The fully corrected Rand τ21distributions, measured in pp collisions at s= 7 TeV
in the pch
T,jet interval 4060 GeV/c, are presented in ﬁgures 5and 6, respectively. The C/A
algorithm appears highly sensitive to the underlying event, with the axis of the subleading
prong being strongly correlated to large angle (large R) soft (high τ21) radiation in the
jet cone. The addition of the Soft Drop groomer modiﬁes the subjet axes dramatically,
with the axes being qualitatively similar to the kTcase. The lower τ21values obtained
with these reclustering algorithms, compared to the C/A case, show that both axes are
aligned with a more signiﬁcant fraction of the transverse momentum inside the jet. The R
distributions for these two algorithms peak at small values, showing that the jets measured
in this sample are strongly single-cored. This is responsible for the τ21distributions
peaking at intermediate values, as the two hard substructures found in the jet are often
not well separated and deﬁned.
The results are compared with PYTHIA6 Perugia 2011 and PYTHIA8 Monash dis-
tributions obtained at the same collision energy. The opening angle between the subjet
axes (R) is well described by the MC for all three reclustering algorithms. The frag-
mentation of particles around these axes (τ21) is less well described by the MC models.
The PYTHIA distributions appear shifted towards less 2-prong jets compared to the data.
Measurements of τ21for top-tagged jets, made by the CMS collaboration [5], show the
same relation to MC models in a complementary jet momentum range. The results ob-
– 16 –
JHEP10(2021)003
served in pp collisions are used to validate the MC for comparisons with Pb-Pb. However,
there are two caveats to consider during this validation. The ﬁrst is the diﬀerence in s
between the two collision systems. Due to the slow change in the underlying event in pp
collisions, this is expected to be negligible. The second caveat is that measurements in pp
collisions were performed on an inclusive jet sample, whilst those in Pb-Pb collisions were
performed on jets recoiling from high-pTtrigger hadrons. These methods are incorporated
into the respective MC calculations for each centre-of-mass energy. However, the recoiling
sample of jets are expected to have no fragmentation biases, which would be the main
concern when comparing the PYTHIA performances, on the two diﬀerent samples, for the
observable measured.
Figure 7presents the fully corrected τ21distributions measured in Pb-Pb collisions at
sNN = 2.76 TeV in the pch
T,jet interval 4060 GeV/c. The results are compared with vacuum
PYTHIA6 Perugia 2011 and PYTHIA8 Monash distributions obtained at the same collision
energy. The ratio plots in the lower panels indicate an agreement of about 20% between
the data and MC. Since in pp collisions the MC seems to produce fewer jets with a distinct
two-pronged substructure than data, the better agreement in Pb-Pb collisions alludes to
the possibility that fewer two-prong jets are measured in heavy-ion collisions relative to
pp, at the same reconstructed energy. This conclusion is most relevant for the kTand Soft
Drop algorithms, where the axes are aligned to hard substructures in the jet.
The measurement of the Rshape is not presented for Pb-Pb collisions. This is due to
the non-diagonal nature of the Rresponse which arises from the presence of combinatorial
subleading prongs, to which the Rshape is very sensitive. These prongs persist in a sig-
niﬁcant fraction of jets after the background subtraction procedure and contribute strongly
in the region of phase space where the area is maximal, RR. This oﬀ-diagonality of
the response renders the unfolding unstable and a fully corrected measurement cannot be
presented. This response to the underlying event can be understood through the nature of
the substructure observable in question, which can be broadly placed in one of two distinct
classes. The ﬁrst of these are observables which isolate a particular set of constituents or
structures in the jet, such as a subjet, and then measure the properties of this isolated
structure. Such observables are prone to non-continuous deformations by the underlying
event, which in some cases are not possible to correct for through unfolding. Ris one
such observable as it is a measure of the geometrical placement of subjets within the jet.
The second class of observables are those which do not isolate any part of the jet,
but instead use all the tracks in the jet to statistically calculate a value, based on a given
deﬁnition. The deformation of these observables by the background has a continuous
characteristic and as such can be handled by the unfolding procedure. τ21is one such
observable and is therefore not very sensitive to these combinatorial subleading prongs. In
fact, a signiﬁcant redistribution in the jet momentum is required to signiﬁcantly alter the
value of τ21. As the majority of the measured jet sample have a single-cored substructure,
any potential displacement of the subleading axis, by a soft combinatorial axis, has minimal
eﬀect on the observable. In the τ2case, the leading axis remains in the jet core, where the
majority of the momentum is situated, and thus does not signiﬁcantly alter the measured
value. The τ1value is also not signiﬁcantly impacted as the axis remains close to the
– 17 –
JHEP10(2021)003
Figure 5. Fully corrected Rdistributions, measured with the kT, C/A and C/A with Soft Drop
grooming algorithms, in pp collisions at s= 7 TeV for jets with R= 0.4in the jet pch
T,jet interval
of 4060 GeV/c, are shown. The systematic uncertainties are given by the grey boxes. The results
are compared with PYTHIA6 Perugia 2011 and PYTHIA8 Monash. The uncertainties presented
for the PYTHIA distributions are purely statistical.
core and the contribution from the soft background to the calculation is small. Only the
addition of a hard second prong has the potential to signiﬁcantly alter the observable, by
increasing the value of the τ1variable. In this way, the τ21observable is resilient to
soft combinatorial prongs and can therefore be unfolded due to he diagonal nature of the
response matrix.
– 18 –
JHEP10(2021)003
Figure 6. Fully corrected τ21distributions, measured with the kT, C/A and C/A with Soft Drop
grooming algorithms, in pp collisions at s= 7 TeV for jets with R= 0.4in the jet pch
T,jet interval
of 4060 GeV/c, are shown. The systematic uncertainties are given by the grey boxes. The results
are compared with PYTHIA6 Perugia 2011 and PYTHIA8 Monash. The uncertainties presented
for the PYTHIA distributions are purely statistical.
8 Conclusions
The ﬁrst measurements of τ21in heavy-ion collisions have been presented, as a means to
explore a possible change in the degree to which the internal structure of jets are composed
of two distinct substructures. This two-prongness of jets might be sensitive to coherence
eﬀects in the QGP, where jets with distinct substructures that are resolved by the medium,
are expected to lose more energy compared to jets where the energy ﬂow is concentrated
in a single core. The measurements are made relative to a variety of axes choices, selected
– 19 –
JHEP10(2021)003
Figure 7. Fully corrected τ21distributions, measured with the kT, C/A and C/A with Soft
Drop grooming algorithms, in Pb-Pb collisions at sNN = 2.76 TeV for jets with R= 0.4in the
jet pch
T,jet interval of 4060 GeV/c, are shown. The systematic uncertainties are given by the grey
boxes. The results are self normalised and compared with PYTHIA6 Perugia 2011 and PYTHIA8
Monash. The uncertainties presented for the PYTHIA distributions are purely statistical.
through the use of diﬀerent reclustering metrics and grooming procedures, which are in
turn potentially sensitive to diﬀerent aspects of in-medium jet modiﬁcation. In order to
extend this substructure measurement to low jet transverse momentum and large jet res-
olution, where the impact of the underlying heavy-ion background on the yield of jets is
large, a semi-inclusive hadron-jet coincidence technique was extended for the ﬁrst time to
a substructure observable, allowing for a fully corrected measurement in this unexplored
regime. This sets the foundation for further such measurements in the future. Measure-
– 20 –
JHEP10(2021)003
ments reported in pp collisions provide both information on the alignment of QCD jet
radiation relative to the diﬀerent axes choices, as well as validating MC calculations for
comparison with the Pb-Pb measurements. The aperture angle between the subjet axes,
R, is also presented in pp collisions, providing complementary information on the spacial
distinctness of the subjets returned by the diﬀerent axes choices. This measurement also
serves as a baseline for future measurements in heavy-ion collisions, which can be used to
directly probe the coherence angle in the QGP.
In pp collisions, the MC calculations underestimate the two-prongness of jets (MC
distributions of τ21are shifted to larger values) whilst the aperture angle between the
subjet axes remains well described. In Pb-Pb collisions, the measured two-prongness of
jets is found to not be signiﬁcantly modiﬁed relative to the MC reference, for a variety
of diﬀerent reclustering algorithms. These two ﬁndings hint at a reduction in the two-
prongness of jets in heavy-ion collisions relative to pp collisions in the same measured jet
momentum interval.
Correlation studies performed by the CMS collaboration at particle level [5] indicate
that the τ21observable is weakly correlated with the majority of other substructure ob-
servables, measured at particle level, so far by the ALICE collaboration. These include
the jet width, the jet momentum dispersion and the (Soft Drop) groomed jet radius. In
this way, the presented τ21measurements can provide extra constraints for jet quench-
ing calculations and models. A relatively stronger correlation is observed between the
τ21observable and both the groomed momentum imbalance and the number of subjet
prongs passing the Soft Drop condition. Detector-level measurements by the ALICE col-
laboration indicate a modiﬁcation of the groomed momentum imbalance for wide-angle
splittings [21]. Future fully corrected measurements of these observables can explore the
three-dimensional correlations between the jet momentum, the groomed momentum imbal-
ance and the groomed radius. In the same way, the correlation between the jet momentum,
two-prongness of jets measured via τ21and the apeture angle between the axes, can be
used to understand the interplay between colour coherence and energy loss.
Acknowledgments
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 ac-
knowledges the following funding agencies for their support in building and running the
ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Insti-
tute) 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
– 21 –
JHEP10(2021)003
(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 Tecnológi-
cas 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 Foun-
dation (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 Technol-
ogy, Ministry of Education, Research and Religions, Greece; National Research, Develop-
ment 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, Sci-
ence 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 Gen-
eral de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Nor-
way; Commission on Science and Technology for Sustainable Development in the South
(COMSATS), Pakistan; Pontiﬁcia Universidad Católica del Perú, Peru; Ministry of Edu-
cation 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, Roma-
nia; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the
Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foun-
dation 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 Facil-
ities 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.
– 22 –
JHEP10(2021)003
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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The ALICE collaboration
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JHEP10(2021)003
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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,
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. Lee136, 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
– 27 –
JHEP10(2021)003
Torres8, J.R. Luhder146 , M. Lunardon28 , G. Luparello62, Y.G. Ma41 , A. Maevskaya65,
M. Mager35, T. Mahmoud44 , A. Maire139 , M. Malaev101, Q.W. Malik20 , L. Malinina77,iv ,
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. Mazzoni60 ,
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 , C.J. Myers127 , 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 ,
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. Redlich88,v, 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. Samsonov101,96,i ,
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 ,
– 28 –
JHEP10(2021)003
J.E. Seger15, Y. Sekiguchi135, D. Sekihata135, I. Selyuzhenkov110,96 , S. Senyukov139, J.J. Seo63 ,
D. Serebryakov65 , L. Šerkšnyt˙e108, 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 , 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 , R.C. Torres82 , 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,
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. Yano47,140 , 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 , D. Zhou7, Y. Zhou92 , J. Zhu7,110,
Y. Zhu7, A. Zichichi26, G. Zinovjev3, N. Zurlo142,59
iDeceased
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
vAlso at: Institute of Theoretical Physics, University of Wroclaw, Poland
1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan,
Armenia
2AGH University of Science and Technology, Cracow, Poland
3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev,
Ukraine
4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science
(CAPSS), Kolkata, India
– 29 –
JHEP10(2021)003
5Budker Institute for Nuclear Physics, Novosibirsk, Russia
6California Polytechnic State University, San Luis Obispo, California, United States
7Central China Normal University, Wuhan, China
8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba
9Centro 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
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
– 30 –
JHEP10(2021)003
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
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
– 31 –
JHEP10(2021)003
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
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
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
– 32 –
JHEP10(2021)003
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
– 33 –
... Another substructure observable of interest is the N -subjettiness, denoted by τ N , which quantifies the degree to which a jet has a N (or fewer)-pronged substructure [163] The ratio of τ 2 /τ 1 is used to tag boosted hadronically-decaying objects such as the W and top quarks, which are typically 2-prong objects as compared to QCD jets, which are mostly 1-pronged. ALICE measured τ 2 /τ 1 [164] using several declustering metrics, including exclusive k T and CA+SD. The results do not reveal a significant change in the prong-structure of the jet relative to Pythia, which describes the observable well in pp collisions. ...
Preprint
We review the current status of jet measurements in heavy-ion collisions at the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC). We discuss how the current measurements provide information about the quark-gluon plasma and discuss near future opportunities at both RHIC and the LHC.
Article
Full-text available
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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Measurements of fragmentation functions for jets associated with an isolated photon are presented for the first time in pp and Pb-Pb collisions. The analysis uses data collected with the CMS detector at the CERN LHC at a nucleon-nucleon center-of-mass energy of 5.02 TeV. Fragmentation functions are obtained for jets with pTjet>30 GeV/c in events containing an isolated photon with pTγ>60 GeV/c, using charged tracks with transverse momentum pTtrk>1 GeV/c in a cone around the jet axis. The association with an isolated photon constrains the initial pT and azimuthal angle of the parton whose shower produced the jet. For central Pb-Pb collisions, modifications of the jet fragmentation functions are observed when compared to those measured in pp collisions, while no significant differences are found in the 50% most peripheral collisions. Jets in central Pb-Pb events show an excess (depletion) of low (high) pT particles, with a transition around 3 GeV/c. This measurement shows for the first time the in-medium shower modifications of partons (quark dominated) with well-defined initial kinematics. It constitutes a new well-controlled reference for testing theoretical models of the parton passage through the quark-gluon plasma.
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A measurement of jet substructure observables is presented using tt¯ events in the lepton+jets channel from proton-proton collisions at s=13 TeV recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb−1. Multiple jet substructure observables are measured for jets identified as bottom, light-quark, and gluon jets, as well as for inclusive jets (no flavor information). The results are unfolded to the particle level and compared to next-to-leading-order predictions from powheg interfaced with the parton shower generators pythia 8 and herwig 7, as well as from sherpa 2 and Dire 2. A value of the strong coupling at the Z boson mass, αS(mZ)=0.115−0.013+0.015, is extracted from the substructure data at leading-order plus leading-log accuracy.
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A bstract A measurement of the groomed jet mass in PbPb and pp collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV with the CMS detector at the LHC is presented. Jet grooming is a recursive procedure which sequentially removes soft constituents of a jet until a pair of hard subjets is found. The resulting groomed jets can be used to study modifications to the parton shower evolution in the presence of the hot and dense medium created in heavy ion collisions. Predictions of groomed jet properties from the pythia and herwig ++ event generators agree with the measurements in pp collisions. When comparing the results from the most central PbPb collisions to pp data, a hint of an increase of jets with large jet mass is observed, which could originate from additional medium-induced radiation at a large angle from the jet axis. However, no modification of the groomed mass of the core of the jet is observed for all PbPb centrality classes. The PbPb results are also compared to predictions from the jewel and q - pythia event generators, which predict a large modification of the groomed mass not observed in the data.
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A bstract We present the measurement of a new set of jet shape observables for track-based jets in central Pb-Pb collisions at $$\sqrt{s_{\mathrm{NN}}}=2.76$$ s N N = 2.76 TeV. The set of jet shapes includes the first radial moment or angularity, g ; the momentum dispersion, p T D ; and the difference between the leading and sub-leading constituent track transverse momentum, LeSub . These observables provide complementary information on the jet fragmentation and can constrain different aspects of the theoretical description of jet-medium interactions. The jet shapes were measured for a small resolution parameter R = 0 . 2 and were fully corrected to particle level. The observed jet shape modifications indicate that in-medium fragmentation is harder and more collimated than vacuum fragmentation as obtained by PYTHIA calculations, which were validated with the measurements of the jet shapes in proton-proton collisions at $$\sqrt{s}=7$$ s = 7 TeV. The comparison of the measured distributions to templates for quark and gluon-initiated jets indicates that in-medium fragmentation resembles that of quark jets in vacuum. We further argue that the observed modifications are not consistent with a totally coherent energy loss picture where the jet loses energy as a single colour charge, suggesting that the medium resolves the jet structure at the angular scales probed by our measurements ( R = 0 . 2). Furthermore, we observe that small- R jets can help to isolate purely energy loss effects from other effects that contribute to the modifications of the jet shower in medium such as the correlated background or medium response.
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Book
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.
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2020 IOP Publishing Ltd. Studies of fully-reconstructed jets in heavy-ion collisions aim at extracting thermodynamical and transport properties of hot and dense QCD matter. Recently, a plethora of new jet substructure observables have been theoretically and experimentally developed that provide novel precise insights on the modifications of the parton radiation pattern induced by a QCD medium. This report, summarizing the main lines of discussion at the 5th Heavy Ion Jet Workshop and CERN TH institute 'Novel tools and observables for jet physics in heavy-ion collisions' in 2017, presents a first attempt at outlining a strategy for isolating and identifying the relevant physical processes that are responsible for the observed medium-induced jet modifications. These studies combine theory insights, based on the Lund parton splitting map, with sophisticated jet reconstruction techniques, including grooming and background subtraction algorithms.