2019 244 28 October

Jet-hadron correlations relative to the event plane

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

The Quark Gluon Plasma (QGP) produced in ultra relativistic heavy-ion
collisions at the Large Hadron Collider (LHC) can be studied by measuring the
modifications of jets formed by hard scattered partons which interact with the
medium. We studied these modifications via angular correlations of jets with
charged hadrons for jets with momenta $20\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\
<\leavevmode\nobreak\ 40$ GeV/$c$ as a function of the associated particle
momentum. The reaction plane fit (RPF) method is used in this analysis to
remove the flow modulated background. The analysis of angular correlations for
different orientations of the jet relative to the second order event plane
allows for the study of the path length dependence of medium modifications to
jets. We present the dependence of azimuthal angular correlations of charged
hadrons with respect to the angle of the axis of a reconstructed jet relative
to the event plane in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV.
The dependence of particle yields associated with jets on the angle of the jet
with respect to the event plane is presented. Correlations at different angles
relative to the event plane are compared through ratios and differences of the
yield. No dependence of the results on the angle of the jet with respect to
the event plane is observed within uncertainties, which is consistent with no
significant path length dependence of the medium modifications for this
observable.

##  1 Introduction

A hot, dense liquid of quarks and gluons is created in high energy collisions
of heavy ions at the Relativistic Heavy Ion Collider (RHIC) [1, 2, 3, 4] and
the Large Hadron Collider (LHC) [5, 6, 7, 8, 9, 10, 11]. This strongly
interacting medium, called the Quark Gluon Plasma (QGP), suppresses colored
probes such as quarks and gluons.

Hard parton scatterings occur early in the collision and lead to the
production of jets, collimated sprays of particles formed from the
fragmentation of the scattered parton. These hard partons lose energy through
induced gluon bremsstrahlung and elastic collisions with medium partons as
they traverse the QGP, leading to a broadening of the resulting jet and
softening of its constituents [12, 13]. This energy loss can be studied with
measurements of high transverse momentum hadrons or reconstructed jets. High
momentum charged hadron production is suppressed by a factor of approximately
five in Au–Au collisions at RHIC [14, 15, 16] and up to a factor of nearly ten
in Pb–Pb collisions at the LHC [7, 17] relative to that in pp collisions.
These measurements are used to constrain the transport coefficient $\hat{q}$,
the squared partonic momentum exchanged with the medium divided by the path
length traversed [18] in the QGP.

An enhancement of particle production at low $p_{\rm T}$ due to medium
interactions has been observed with measurements of fragmentation functions,
the momentum distributions of particles within the jet [19, 20, 21], as well
as through broadening in high momentum dihadron correlations [22, 23] and jet-
hadron correlations [24, 25, 11, 26].

Measurements of correlations allow studies of lower energy jets and of the
soft constituents by means of statistical subtraction of the large
combinatorial background at lower momenta. Studies of correlations have been
limited by methods for background subtraction due to the structures in the
background correlated with the signal because of hydrodynamical flow. The
recent development of the Reaction Plane Fit (RPF) method enables precision
subtraction of the background for both jet-hadron and dihadron correlations
[27].

The path length dependence of partonic energy loss can be constrained through
measurements of the dependence of azimuthal correlations of high momentum
particles or reconstructed jets on the angle of the jet relative to second
order event plane of the collision. Because the overlap region of the incoming
nuclei for non-central collisions is almond shaped, particles traveling
perpendicular to this event plane (out-of-plane) have a longer path length
through the medium on average than those traveling in the direction of the
event plane (in-plane). Therefore, the suppression of high momentum single
particles is expected to be greater in the out-of-plane direction than in-
plane [28]. This is also evident in the azimuthal anisotropy of high-$p_{\rm
T}$ single particle [29, 30, 31, 32] and jet [33, 34] production relative to
the second order event plane. This suppression indicates that there are fewer
jets out-of-plane after interactions with the medium, but is not a measure of
the properties of the surviving jets relative to that plane. Measurements of
dihadron correlations relative to the event plane at RHIC indicate suppression
and some broadening [35, 36], but do not exhibit much event plane dependence
[37]. Some theoretical studies indicate that jet-by-jet fluctuations in the
energy loss may be as important as the path length dependence for some
observables, such as azimuthal anisotropies at high momentum and di-jet
asymmetries [38, 39, 40].

Measurements for the event plane dependence of jet modification can therefore
provide insight into the relative importance of path length for partonic
energy loss. We present measurements of jet-hadron correlations relative to
the event plane in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
using A Large Ion Collider Experiment (ALICE) detector. We first describe the
details of the measurement technique and then present the results. We conclude
with a discussion of the constraints these measurements provide for models.

##  2 The ALICE detector

A detailed description of the ALICE detector and its subdetectors can be found
in [41]. The detectors used for the present analysis are briefly described in
this section. These are the forward scintillator arrays (V0) [42, 43], Inner
Tracking System (ITS) [44], the Time Projection Chamber (TPC) [45], and the
Electromagnetic Calorimeter (EMCal) [46].

The V0 detector is used for centrality estimation and event plane
reconstruction. The V0 system consists of two scintillator arrays located at
asymmetric positions, one at a pseudorapidity range of $2.8<\eta<5.1$ (V0A)
and the other at $-3.7<\eta<-1.7$ (V0C) [42]. Each set of arrays is made of
four radial rings with each ring divided into eight sections in the azimuthal
direction [42].

The ITS and TPC detectors provide tracking of charged particles over the full
range of azimuth with a pseudorapidity range of $|\eta|<0.9$. They are located
inside the central barrel solenoidal magnet which provides a homogenous field
with strength of 0.5 T [47]. The ITS is a cylindrical silicon detector made up
of 6 layers located at the center of the main-barrel. The first two layers are
the Silicon Pixel Detectors (SPD), followed by two layers of Silicon Drift
Detectors (SDD), and two outer layers of Silicon Strip Detectors (SSD) [48].
The TPC surrounds the ITS and is the main detector used for tracking in ALICE.
It is filled with a gas mixture of Ne and CO2 [49]. The transverse momentum
and charge of the particles can be inferred from the curvature of the tracks.
Combining information from the ITS and TPC allows for the momentum
determination of charged particles as low as $p_{\rm T}$ $\approx$ 0.15
GeV/$c$ up to $p_{\rm T}$ $\approx$ 100 GeV/$c$.

Track selection is optimized for track quality, momentum resolution, and
nearly uniform azimuthal acceptance, as in [47]. At least three hits in the
ITS are required. Tracks without a hit in the SPD are refit to include the
primary vertex, reducing the azimuthal dependence of the track reconstruction
efficiency while maintaining good momentum resolution. The tracks used in this
analysis are required to have 80% of the geometrically allowed space points
and at least 70 total space points in the TPC. The tracking efficiency is
determined from simulations of the detector response using tracks simulated
with hijing [50] propagated through the detector using geant3 [51] and ranges
from 80–85% in the momentum range used in this analysis.

The uncertainty on the single track reconstruction efficiency is 4%, with an
additional 1% systematic uncertainty due to contamination from secondary
tracks [52, 47, 53, 54]. This uncertainty is correlated point-to-point and
contributes to the scale uncertainty in the correlation functions and yields.

The EMCal is used for the neutral energy reconstruction and triggering. It is
a lead-scintillator sampling calorimeter with a pseudorapidity coverage of
$|\eta|<0.7$ and an active azimuthal range of $\Delta\phi=107^{\rm o}$ in the
readout in the 2011 configuration [46, 55, 56]. The EMCal had 11520 towers
with transverse size 6 cm $\times$ 6 cm, or approximately twice the effective
Molière radius. The relative energy resolution is
$0.11/\sqrt{E}+0.017+0.051/E$, where the energy $E$ is measured in GeV [55].
Clusters are formed by combining signals from adjacent towers and each cluster
is required to have only one local energy maximum. This analysis uses events
triggered by a high energy deposit in a 4$\times$4 region of towers in the
EMCal. This trigger configuration has less sensitivity to the underlying event
than a trigger configuration with a larger area, often used for jet analyses,
because the contribution of the underlying event to the energy is proportional
to the trigger area. The raw trigger threshold was multiplicity dependent and
corresponded to approximately 4.5–6 GeV in the centrality bin used in this
analysis.

Clusters with energy above 3 GeV, which exclude minimally ionizing particles
[56], are used in this analysis. Partially formed hadronic showers may still
pass this threshold. To avoid overcounting of charged particle $p_{\rm T}$,
the cluster energies are corrected as in [53]. Tracks are propagated to the
average cluster depth in the EMCal and matched to the nearest cluster. If the
nearest cluster is within $|\Delta\eta|<0.015$ in pseudorapidity and
$|\Delta\phi|<0.025$ in azimuth, the cluster most likely arose from a charged
hadron. If the cluster energy is at or below the track’s momentum, the cluster
is not used in the analysis, while if the cluster energy is above the track’s
momentum, the track momentum is subtracted from the cluster energy [53].

##  3 Method

Figure 1: Jet-hadron correlations are measured for jets in three regions
relative to the $n=2$ event plane, which is transverse to the direction of the
beams. These regions include in-plane ($|\psi-\phi_{\mathrm{jet}}|<\pi/6$)
shown in red, mid-plane ($\pi/6<|\psi-\phi_{\mathrm{jet}}|<\pi/3$) shown in
white, and out-of-plane ($|\psi-\phi_{\mathrm{jet}}|>\pi/3$) shown in blue.

The data used in this analysis were collected during the 2011 run [41] from
0.5M 30–50% central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV.
It was additionally required to be triggered by a high energy deposit in a
4$\times$4 region of towers in the EMCal [56]. Procedures for selection and
reconstruction of tracks from charged particles, identification of calorimeter
clusters, and jet reconstruction are as in [47] and are summarized in Sec.
3.1. Estimates of the distributions of corrected jet energies are also
reported here. The experimentally reconstructed second order symmetry plane is
called the second order event plane, referred to as the “event plane" later in
the text for simplicity. Centrality determination and event plane
reconstruction is discussed in Sec. 3.2. Jets from triggered events are
correlated with all charged tracks in azimuth
($\Delta\phi=\phi_{\mathrm{jet}}-\phi_{\mathrm{assoc}}$) and pseudorapidity
($\Delta\eta=\eta_{\mathrm{jet}}-\eta_{\mathrm{assoc}}$), as discussed in Sec.
3.3. The distributions of these associated tracks relative to the trigger jet
are measured in three bins in the angle between the trigger jet and the event
plane, in-plane ($|\psi-\phi_{\mathrm{jet}}|<\pi/6$), mid-plane
($\pi/6<|\psi-\phi_{\mathrm{jet}}|<\pi/3$), and out-of-plane
($|\psi-\phi_{\mathrm{jet}}|>\pi/3$) bins, as shown in Fig. 1. The analysis is
restricted to 30–50% central Pb–Pb collisions because this is where the event
plane resolution is highest and therefore the analysis will be most sensitive
to any path length dependencies. The subtraction of the combinatorial
background using the RPF method [27] is discussed in Sec. 3.4. The
determination of the yields and the widths is discussed in Sec. 3.5. The
possible impact of the finite event plane resolution on the signal is
discussed in Sec. 3.6.

###  3.1 Jet reconstruction and energy distribution

Tracks and corrected EMCal clusters are clustered into jets using the
anti-$k_{T}$ algorithm with a resolution parameter $R=0.2$ in the FastJet
package [57]. Jet transverse momenta are calculated as the scalar sum of their
constituent transverse momenta using a boost-invariant $p_{\rm T}$
recombination scheme. Tracks are assumed to be pions and clusters to arise
from massless particles. In order to suppress contributions from combinatorial
jets and the contribution of uncorrelated background to the jet energy, jets
are reconstructed with constituents above $p_{\rm T}\leavevmode\nobreak\
>\leavevmode\nobreak\ 3$ GeV/$c$ and are required to have an area of at least
$0.08$ calculated using ghost particles as described in [57]. Jets are
required to be within $|\eta_{\mathrm{jet}}|<0.5$ and
$1.6<\phi_{\mathrm{jet}}<2.9$ so that the entire jet is contained within the
EMCal acceptance.

Small jets are used to reduce the impact of the background, as background
contributions scale with $R^{2}$. Additionally, to further suppress
contributions of the background to the energy and to match trigger conditions
[46], the jets are required to contain a cluster with transverse energy larger
than 6 GeV. We note that this requirement leads to a selection of biased jets,
explicitly biasing the near-side. The away-side, in contrast, is not
explicitly biased, although it is unlikely to be a random sample of the jet
population. With these constituent cuts, the background contribution to the
energy is negligible using estimates of the background per unit area as in
[58]. The background contribution to the energy is therefore not subtracted
from the jets, although any residual contribution would be included in the
energy distribution estimation. The jet energy is not corrected for detector
effects, but the distribution of particle level jet energies in the sample is
estimated using pythia6 [59] Tune A [60] simulations embedded at detector
level into data measured in Pb–Pb collisions and matched back to generator
level.

Detector effects such as the single track reconstruction efficiency, momentum
resolution in the tracking detectors and energy resolution in the calorimeter
combined with contributions from particles which are not directly observed,
such as neutrons and $K^{0}_{\mathrm{L}}$, and contributions from the
background lead to a finite energy resolution. This means that when jet-hadron
correlations are measured at a particular jet $p_{\rm T}$, the distribution of
true jet momenta is broad. A full correction for this effect would require two
dimensional unfolding with jet-hadron correlations measured for several jet
momenta. The current statistics do not allow for such measurements. Instead,
we estimate the distribution of true jet energies and focus on comparisons
between jets at different angles relative to the event plane to enable the
highest precision search for path length dependence allowed by the currently
available data.

The kinematic selection of tracks and clusters used in jet finding is chosen
to suppress contributions from the combinatorial background and reduce
smearing of the jet energy due to the large combinatorial background. With
these kinematic selections, the background density is negligible and showed no
event plane dependence. Given that no event plane dependence is observed in
the signal, this also means that the resolution of the jet axis does not vary
with the angle of the jet relative to the event plane.

pythia6 TuneA [59, 60] simulations of pp collisions with jets are embedded at
detector level into 30-50% Pb–Pb data. The embedded events are analyzed with
the same parameters and cuts as the data analysis, including the jet
constituent and cluster biases, while the generator level jets are measured
for $p_{\rm T}>5$ GeV/$c$. The generator level jets are first matched
geometrically to PYTHIA detector level jets, and then the detector level jets
are geometrically matched to jets found within $R=0.2$ in the embedded event,
with the additional requirement the associated generator level jet
distribution is measured. Each such distribution is normalized within the
region $20\leq p_{\rm T}<100$ GeV/$c$ where fluctuations are minimized and,
assuming that the jet energy distribution in the data is the same as that
provided by PYTHIA6, describes the generator level jet distribution that
corresponds to the measured detector level jet distribution, shown in Fig. 2.
The uncertainty on the jet energy scale is 2.6% and the jet energy resolution,
which is also encoded in the response matrix, is around 20% for the jets
selected in this analysis [53]. There are slight differences in the jets
reconstructed with $p_{\rm T}\leq 20$ GeV/$c$ for jets at different angles
relative to the event plane due to a low momentum embedded jet overlapping
with a another jet in the Pb–Pb data. Since there are more jets in-plane than
out-of-plane in the data, this leads to an apparent difference in the
reconstructed jet spectra. Otherwise there are no significant differences
between jets at different angles relative to the event plane.

Figure 2: The generator level jet probability distribution corresponding to
jets measured with $p_{\rm T}$ between 20-40 GeV/$c$ for PYTHIA events
embedded in 30–50% central Pb–Pb collisions. Generator level jets are required
to have $p_{\rm T}>5$ GeV/$c$. The distribution is measured for each angle
relative to the event plane, as well as the sum of all angles.

###  3.2 Centrality determination and event plane reconstruction

Centrality is determined from the sum of the energy deposition [42] in the V0
scintillator tiles, as described in [61]. The centrality of the collision is
reported as percent ranges of the total hadronic cross section, with lower
percentiles referring to the most central (largest multiplicity) events [61].
The second order event plane $\Psi_{\mathrm{EP},2}$ is reconstructed using the
V0 following the procedure in [33] by combining signals from the V0A and V0C
arrays [43]. The separation in pseudorapidity between the measurement of the
signal and the measurement of the event plane suppresses the contribution from
the jet signal to the event plane determination [33].

The reaction plane is defined by the beam axis and the vector between the
centers of the two incoming nuclei. Additional asymmetries in the distribution
of nucleons within the overlap region, generally quantified by a harmonic
decomposition, generate symmetry planes at all orders ($n>0$) [62, 63]. If the
nucleons were in their average positions and there were no fluctuations in
interactions between nucleons, the reaction plane would correspond to the
second order symmetry plane, $\Psi_{EP,2}$. The experimentally reconstructed
symmetry planes are called event planes. For simplicity, we refer here to the
experimentally reconstructed second order event plane as the event plane. As
explained below, we do not correct the signal for the difference between the
event and symmetry planes because no event plane dependence is observed in
this measurement. Corrections for the event plane resolution will increase
differences between results at different angles relative to the event plane
but will not induce any event plane dependence if there is none in the
uncorrected results. We discuss the impact of the event plane resolution in
Sec. 3.6. The impact of the dijets on the event plane reconstruction was
studied in [33] and found to be negligible.

The event plane is also extracted using TPC tracks in order to determine the
event plane resolution. The $n$-th order event plane can be calculated from
the charged particle azimuthal distribution by [64]:

$\Psi_{n,EP}=\left(\arctan\frac{\sum_{i}w_{i}\sin(n\phi_{i})}{\sum_{i}w_{i}\cos(n\phi_{i})}\right)/n,$
(1)

where the sum is over all particles in the event, $\phi_{i}$ is the azimuthal
angle of the $i$-th particle, and $w_{i}$ is the weight of the $i$-th
particle. For measurement of the event plane with the V0, the sum is over all
of its sectors and the weights are equal to the amplitude of the respective
sector in the V0, which is proportional to the local multiplicity. A
calibration and recentering procedure following [33] is applied to remove any
bias introduced by non-uniform acceptance of the V0 system. For measurement in
the TPC, tracks are given equal weights ($w_{i}$ = 1) and the acceptance is
nearly uniform. Track selection is the same as that described in Sec. 3 except
the transverse momentum range is restricted to 0.15 $<p_{\rm T}<$ 5.0 GeV/$c$.
More details of the procedure can be found in [33].

Due to the finite multiplicity of each event, there will be a difference
between the symmetry plane and the reconstructed event plane. This difference
is quantified by the event plane resolution

$\Re_{n}=\langle\cos(n[\Psi_{\mathrm{n,EP}}-\Psi_{n}])\rangle.$ (2)

where $\Psi_{n}$ is the true angle and $\Psi_{n,EP}$ is the measured angle of
the $n$th order event plane. To evaluate the event plane resolution directly
from data, this analysis uses three sub-events, comparing the event planes
measured in the full V0, measured in the TPC using tracks at positive
pseudorapidities, and measured in the TPC using tracks at negative
pseudorapidities. We can express the $n$th order resolution of the full V0,
$\Re^{V0}_{n}$ [65, 64], of the second order event plane by

$\Re^{\mathrm{V0}}_{n}=\langle\cos(n[\Psi^{\mathrm{V0}}_{2,\mathrm{EP}}-\Psi_{2}])\rangle=\sqrt{\frac{\langle\cos(n[\Psi^{V0}_{2,\mathrm{EP}}-\Psi^{\mathrm{TPC},\eta>0}_{2,\mathrm{EP}}])\rangle\langle\cos(n[\Psi^{\mathrm{V0}}_{2,\mathrm{EP}}-\Psi^{\mathrm{TPC},\eta<0}_{2,\mathrm{EP}}])\rangle}{\langle\cos(n[\Psi^{\mathrm{TPC},\eta>0}_{2,\mathrm{EP}}-\Psi^{\mathrm{TPC},\eta<0}_{2,\mathrm{EP}}])\rangle}}$
(3)

where $\Psi^{V0}_{2,\mathrm{EP}}$,
$\Psi^{\mathrm{TPC},\eta>0}_{2,\mathrm{EP}}$, and
$\Psi^{\mathrm{TPC},\eta<0}_{2,\mathrm{EP}}$ are the second order event planes
calculated using the three different sub-events, and $\Psi_{2}$ is the true
angle of the second order symmetry plane. Fits to the Fourier decomposition of
the correlated background are performed up to $n=4$ and are measured relative
to the event plane. Thus, event plane resolution corrections
$\Re_{2}(\psi_{2})$ and $\Re_{4}(\psi_{2})$ are needed to correct these terms
for the finite precision of the second order event plane measured in the V0
system, as discussed in Sec. 3.4. The event plane resolution for the 30-40%
and 40-50% centrality ranges are combined by weighting the two samples by the
number of corresponding events of each. The event plane resolutions
$\Re_{2}(\psi_{2})$ and $\Re_{4}(\psi_{2})$ for the analyzed 30-50% event
sample are 0.73 and 0.44, respectively, with negligible uncertainties.

###  3.3 Jet-hadron correlations

The distribution of charged particles relative to $20\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\rm jet}\leavevmode\nobreak\
<\leavevmode\nobreak\ 40$ GeV/$c$ reconstructed jets is measured in azimuth
($\Delta\phi$) and pseudorapidity ($\Delta\eta$) as

$\frac{1}{N_{\mathrm{trig}}}\frac{d^{2}N_{\mathrm{assoc}}}{d\Delta\phi
d\Delta\eta}=\frac{1}{N_{\mathrm{trig}}}\frac{1}{a(\Delta\phi,\Delta\eta)\epsilon(p_{\rm
T}^{\mathrm{assoc}},\eta^{\mathrm{assoc}})}\frac{d^{2}N_{\mathrm{meas}}}{d\Delta\phi
d\Delta\eta}$ (4)

where $N_{\mathrm{trig}}$ is the number of trigger jets, $\epsilon(p_{\rm
T}^{\mathrm{assoc}},\eta^{\mathrm{assoc}})$ is the product of the single track
reconstruction efficiency and acceptance, and $a(\Delta\phi,\Delta\eta)$
dominantly corrects for the pair acceptance. The distributions are determined
in bins of centrality, associated hadron transverse momentum ($\it{p}_{\rm
T}^{\mathrm{assoc}}$), and bins of the trigger jet angle relative to the event
plane.

The correction $a(\Delta\phi,\Delta\eta)$ is calculated as a function of
centrality and associated particle momentum by mixed events using a trigger
jet from an EMCal-triggered event and associated hadrons from minimum bias
events or semi-central triggered events. The mixed event procedure will also
remove the trivial correlation due to an $\eta$ dependence in the single
particle and track distributions. However, since there is little $\eta$
dependence in either tracks or jets within the acceptance used in this
analysis, the dominant effect is the pair acceptance. Mixed events are
constructed separately for 30–40% and 40–50% centrality classes. The mixed
events are required to be within the same 10% centrality class and have vertex
positions within 2 cm along the direction of the beam, $z_{\mathrm{vtx}}$.
There is no difference in the correction within uncertainties for different
orientations of the jet relative to the event plane, and therefore the same
correction $a(\Delta\phi,\Delta\eta)$ is applied for all angles relative to
the event plane. All associated momentum bins for $p_{\rm
T}\leavevmode\nobreak\ >\leavevmode\nobreak\ 2.0$ GeV/$c$ are combined to
increase statistics because $a(\Delta\phi,\Delta\eta)$ has little momentum
dependence at high momenta. The correction $a(\Delta\phi,\Delta\eta)$ is
normalized to one at its maximum with the systematic uncertainty in the
normalization determined by using different regions in $\Delta\phi$ and
$\Delta\eta$, with a systematic uncertainty below 0.5% for all $\it{p}_{\rm
T}^{\mathrm{assoc}}$ bins used in this analysis. There is an additional shape
uncertainty due to slight changes in the correlation function at large
$\Delta\eta$ in the acceptance with $z_{\mathrm{vtx}}$ position. Since the
background level is determined from the level of the correlation function at
large $\Delta\eta$, this leads to a scale uncertainty in the background
subtraction. This uncertainty is determined by varying the binning of the
mixed events in $z_{\mathrm{vtx}}$ and is correlated for different angles
relative to the event plane and for different bins in
$p_{\mathrm{T}}^{\mathrm{assoc}}$. This scale uncertainty is used later for
determining a systematic uncertainty on the background subtraction and is
dependent on $p_{\mathrm{T}}^{\mathrm{assoc}}$.

###  3.4 Background subtraction

The signal in equation 4 has a large combinatorial background from particles
created by processes other than the hard process which created the jet. The
jet signal may be correlated with the second order event plane because of jet
quenching, and soft hadrons are correlated with the second order event plane
due to hydrodynamical flow. The Fourier expansion of this background can be
expressed by:

$\frac{dN}{\pi
d\Delta\phi}=B\bigg{(}1+\sum_{n=1}^{\infty}2\tilde{v}_{n}^{\mathrm{trig}}\tilde{v}_{n}^{\mathrm{assoc}}\cos(n\Delta\phi)\bigg{)},$
(5)

where $\tilde{v}_{n}^{\mathrm{trig}}$ and $\tilde{v}_{n}^{\mathrm{assoc}}$
refer to the effective Fourier coefficients for the azimuthal anisotropy of
the trigger jet and associated hadron, respectively, to the background. For
inclusive measurements, if the background is dominantly due to flow, the
$\tilde{v}_{n}$ of this background will be equal to the $v_{n}$ due to flow.
The exact values may be slightly different due to differences in the event
samples, varying sensitivity in the method to fluctuations in the $v_{n}$ and
non-flow, the difference between the average over all pairs
$\langle\tilde{v}_{n}^{\mathrm{trig}}\tilde{v}_{n}^{\mathrm{assoc}}\rangle$
and the product of the averages over all events
$\langle\tilde{v}_{n}^{\mathrm{trig}}\rangle\langle\tilde{v}_{n}^{\mathrm{assoc}}\rangle$,
differences in the $v_{n}$ for particles in jets and from the bulk, and
decorrelations between symmetry planes for hard and soft processes.

The contribution from these soft processes is subtracted using the RPF method
[27]. This method avoids contamination by the near- and away-side jets by
focusing on the near-side only at large $\Delta\eta$ and instead using the
dependence of the flow-modulated background on the angle of the trigger jet
relative to the event plane to constrain the background shape and level. For
in-plane jets, background particles are more likely to be near the trigger jet
than $\pi$ away in azimuth, leading to a higher $\cos(2\Delta\phi)$ term, and
the background level is higher because there are more jets in-plane. For out-
of-plane jets, background particles are less likely to be near the trigger
jet, leading to a negative $\cos(2\Delta\phi)$ term, and the background is
lower because there are fewer jets. Because the second and fourth order event
planes are correlated, a similar argument holds for the fourth order terms.
These effects help constrain the even $n$ terms and help distinguish them from
the odd $n$ terms and constrain the background level while avoiding
contamination from the near- and away-side jets.

The event plane dependence can be used to determine the background shape and
level. When the angle of the jet is fixed relative to the event plane, the
effective size and shape of the background is given by

$\displaystyle\tilde{B}$
$\displaystyle=\frac{N_{t}N_{a}c}{\pi^{2}}\Big{(}1+2\sum_{k=1}^{\infty}\frac{v_{2k}^{\mathrm{trig}}}{2kc}\sin(2kc)\Re_{2k}C_{2k,0}\cos(2k\phi_{s})\Big{)},$
(6) $\displaystyle\tilde{v}_{n}^{\mathrm{trig}}$
$\displaystyle=\frac{v_{n}+\frac{\delta_{n,\mathrm{mult}\
2}}{nc}\sin(nc)\Re_{n}C_{n,0}\cos(n\phi_{s})+\sum_{k=1}^{\infty}(v_{2k+n}^{\mathrm{trig}}C_{|2k+n|,n}+v_{|2k-n|}^{\mathrm{trig}}C_{|2k-n|,n})\frac{\sin(2kc)\cos(2k\phi_{s})\Re_{2k}}{2kc}}{1+2\sum_{k=1}^{\infty}\frac{v_{2k}^{\mathrm{trig}}}{2kc}\sin(nc)\Re_{2k}C_{2k,0}\cos(2k\phi_{s})}$
$\displaystyle C_{n,m}$
$\displaystyle=\langle\cos(n\psi_{n}+m\psi_{m}-(n+m)\psi_{2})\rangle$

where $\phi_{s}$ is the center of the azimuthal range of the trigger particle
relative to the event plane, $c$ is the width of that range, $N_{t}$ is the
number of triggers, $N_{a}$ is the number of associated particles,
$v_{n}^{\mathrm{assoc}}$ are the $v_{n}$ of the associated particles,
$v_{n}^{\mathrm{trig}}$ are the $v_{n}$ of the triggers, and $\Re_{n}$ is the
event plane resolution given in equation 3 [66, 67]. Terms $v_{n}$ with $n<1$
are zero. The $C_{n,m}$ terms are a measure of how correlated event planes of
different orders are with the second order event plane and are approximately
zero when either $n$ or $m$ is odd. This is consistent with the weak
correlation between the $n=2$ participant plane and odd order participant
planes [68] because the odd $\tilde{v}_{n}$ arise mainly due to fluctuations
in the initial state. In this case, the even $\tilde{v}_{n}$ will change when
the angle of the jet relative to the event plane is changed while the odd
$\tilde{v}_{n}$ remain constant. The equation is expanded to include terms up
to $v_{4}$. The term $C_{2,0}$ = 1 and the terms $C_{4,0}$ and $C_{4,2}$ are
approximated to be one. The latter assumption will lead to an inconsistency
between the $v_{4}$ from independent measurements and from the fit, but the
fit will still provide a valid description of the background.

The shape of the background depends on the $\Re_{n}$, which are fixed at the
measured values. The fourth order event plane resolution is calculated
relative to the second order event plane, consistent with the shape described
in equation 6. The uncertainties on the event plane resolution are negligible
relative to the statistical and background fit uncertainties of the final
results.

The jet signal in equation 4 can be decomposed into a near-side and an away-
side. The near-side is a peak which is narrow in both $\Delta\phi$ and
$\Delta\eta$, meaning that it is negligible at large $\Delta\eta$, while the
away-side is narrow in $\Delta\phi$ but broad in $\Delta\eta$. The correlation
function at large $\Delta\eta$ ($0.8<|\Delta\eta|<1.2$) and small $\Delta\phi$
($|\Delta\phi|<\pi/2$) is fit simultaneously for $\tilde{v}_{n}$ up to $n=4$
for trigger jets in-plane ($|\psi-\phi_{\mathrm{j}et}|<\pi/6$), mid-plane
($\pi/6<|\psi-\phi_{\mathrm{j}et}|<\pi/3$), and out-of-plane
($|\psi-\phi_{\mathrm{j}et}|>\pi/3$), shown in Fig. 1, to determine the
background shape and level. Because the even $\tilde{v}_{n}$ depend on the
angle of the jet relative to the event plane, as shown in equation 6, the
$\tilde{v}_{2}$ and $\tilde{v}_{4}$ of both the trigger jet and the associated
particle are determined in the fit while only the product
$\tilde{v}_{3}^{\mathrm{jet}}\tilde{v}_{3}^{\mathrm{assoc}}$ is extracted from
the fit. A rapidity-even $\tilde{v}_{1}$ term can arise due to both momentum
conservation and fluctuations in the initial state. This rapidity-even
$\tilde{v}_{1}$ has been measured for single hadrons and is comparable in
magnitude to $\tilde{v}_{2}$ and $\tilde{v}_{3}$ [69, 70]. This term does not
change when the angle of the trigger jet is varied relative to the event plane
so the product $\tilde{v}_{1}^{\mathrm{jet}}\tilde{v}_{1}^{\mathrm{assoc}}$
contributes to the background. When the fit function is varied to include this
$n=1$ term, it is zero within uncertainties and did not lead to significant
differences in the correlation function. Since
$\tilde{v}_{1}^{\mathrm{assoc}}$ is known to be non-zero, this likely means
that $\tilde{v}_{1}^{\mathrm{jet}}$ is near zero. For associated particles
above $p_{\rm T}\leavevmode\nobreak\ >\leavevmode\nobreak\ 2$ GeV/$c$, the
background is low and the statistics for the region which is background-
dominated on the near-side are therefore also low, so the fit is restricted up
to $n=3$. The fits used in this analysis therefore have six parameters below 2
GeV/$c$, $B$, $\tilde{v}_{2}^{\rm jet}$, $\tilde{v}_{2}^{\mathrm{assoc}}$,
$\tilde{v}_{3}^{\mathrm{jet}}\tilde{v}_{3}^{\mathrm{assoc}}$,
$\tilde{v}_{4}^{\mathrm{jet}}$, and $\tilde{v}_{4}^{\rm assoc}$, and four
above. The event plane resolution is fixed and variations within the
uncertainties lead to negligible differences in the correlation functions.

Figure 3 shows a sample correlation function in the region which is
background-dominated on the near-side compared to the fit for in-plane (a),
mid-plane (b), and out-of-plane (c) jets and all jets combined (d) for
associated particles with momenta $1.5\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\mathrm{assoc}}\leavevmode\nobreak\
<\leavevmode\nobreak\ 2.0$ GeV/$c$. Correlation functions for other
$p_{\mathrm{T}}^{\mathrm{assoc}}$ ranges used in this analysis are given in
[71]. The ratio of the difference between the data and the fit to the fit is
shown in Fig. 3(e-h), showing that the fit describes the data well. The
background subtracted correlation functions in the region $|\Delta\eta|<0.6$
are shown in Fig. 3(i-l). The uncertainties from the background subtraction
are propagated using the covariance matrix from the fit. These uncertainties
are non-trivially correlated point-to-point and between different bins
relative to the event plane and are shown as a blue band. The scale
uncertainties on the background are shown as a green band and are correlated
point-to-point and between different bins relative to the event plane. The
uncertainties due to the single track reconstruction efficiency,
contamination, and the normalization of the acceptance correction are
uncorrelated with each other but correlated for all points. These
uncertainties are combined and listed as the scale uncertainty. The
$\tilde{v}_{2}^{\mathrm{jet}}$ and $\tilde{v}_{2}^{\mathrm{assoc}}$ extracted
from the fits are in agreement with other ALICE results [33, 30].

Figure 3: The signal plus background region, $|\Delta\eta|<0.6$ (green
points), the region which is background-dominated on the near-side,
$0.8<|\Delta\eta|<1.2$ (black points), and the RPF fit to $|\Delta\phi|<\pi/2$
(blue band) to the region which is background-dominated on the near-side for
$20\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{jet}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 40$ GeV/$c$ jets
correlated with $1.5\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 2.0$ GeV/$c$
hadrons from 30-50% centrality collisions on the top panel. The middle panel
shows the quality of the RPF fit to the region which is background-dominated
on the near-side, (data$-$fit)/fit. On the bottom panel are the RPF corrected
correlation functions, with the uncertainty from the background fit (red
band), and the correlated uncertainty (green band).

Finite event plane resolution reduces the event plane dependence of the signal
because the measurement in one bin relative to the event plane will have
contributions from other bins as well. Techniques for correcting for this
effect increase the event plane dependence observed in the uncorrected data
[72], but if there is no event plane dependence in the uncorrected data, these
corrections will not reveal an event plane dependence. Since no event plane
dependence is observed within uncertainties and corrections would increase the
complexity of the measurement and the systematic uncertainties, no correction
is applied for the finite event plane resolution. The impact of the finite
event plane resolution is discussed in Sec. 3.6.

###  3.5 Associated track yields and peak widths

The yield of tracks associated with jets is calculated by integrating the
associated yield:

$Y=\frac{1}{N_{\mathrm{trig}}}\int_{\eta_{1}}^{\eta_{2}}\int_{\phi_{1}}^{\phi_{2}}\frac{d(N_{meas}-N_{bkgd})}{d\Delta\phi}d\Delta\phi
d\Delta\eta.$ (7)

The integration limits of $\phi_{1}=-\pi/3$ and $\phi_{2}=\pi/3$ for the near-
side, $\phi_{1}=2\pi/3$ and $\phi_{2}=4\pi/3$ for the away-side, and
$\eta_{1}=-0.6$ and $\eta_{2}=0.6$ for both are part of the definition of the
measurement. The systematic uncertainties due to the extraction of the
background from the RPF are propagated using the covariance matrix from the
fit. This uncertainty is non-trivially correlated between yields for different
angles of the jet relative to the event plane and for the near- and away-side
and uncorrelated for points at different $p_{\mathrm{T}}^{\mathrm{assoc}}$.
The shape uncertainty in the acceptance correction at large $\Delta\eta$ leads
to an additional scale uncertainty when propagating the background determined
in the region $0.8<|\Delta\eta|<1.2$ to the region ($|\Delta\eta|<0.6$). This
uncertainty is 100% correlated for all data points. The single track
reconstruction efficiency uncertainty, the uncertainty due to normalization of
the acceptance correction, and the uncertainty due to contamination from
secondary particles are 100% correlated for all points and affect the scale of
the correlation functions and the yields.

The ratios and differences of yields are calculated in order to investigate
possible event plane dependent modifications. The systematic uncertainties
from the background largely cancel out in the ratio and the difference. The
track reconstruction efficiency, mixed event normalization, and secondary
contamination systematic uncertainties cancel out in the ratio.

The widths are quantified by fitting the correlation functions to a Gaussian,
$A\rm e^{(\Delta\phi-\Delta\phi_{0})^{2}/2\sigma^{2}}$ where
$\Delta\phi_{0}\leavevmode\nobreak\ =\leavevmode\nobreak\ 0$ on the near-side
and $\Delta\phi_{0}\leavevmode\nobreak\ =\leavevmode\nobreak\ \pi$ on the
away-side, in the range $|\Delta\phi|\leavevmode\nobreak\
<\leavevmode\nobreak\ \pi/3$ on the near-side and
$|\Delta\phi-\pi|\leavevmode\nobreak\ <\leavevmode\nobreak\ \pi/3$ on the
away-side. The near- and away-side are fit separately. The Gaussian fit is
repeated with different values of the background parameters and the covariance
matrix is used to propagate the uncertainties.

The systematic uncertainties are summarized in Tab. 1 and Tab. 2. Table 1
lists the sources of systematic uncertainties which are independent of the
angle relative to the event plane and the momentum, including the single track
reconstruction efficiency (Sec. 2), contamination from secondaries (Sec. 2),
uncertainties in the mixed events due to their normalization and shape in
$\Delta\phi$ (Sec. 3.3), and uncertainties in the event plane resolution (Sec.
3.2). The uncertainties in the single track reconstruction efficiency,
normalization of the acceptance correction determined from mixed events, and
secondary contamination lead to a 5% uncertainty in the scale of the
correlation functions and yields. This uncertainty is uncorrelated for
different associated particle momenta.

Table 2 lists uncertainties which are dependent on the angle of the jet
relative to the event plane and the associated particle’s momentum on the
yields due to the scale uncertainty in the mixed events (Sec. 3.3) and in the
background fit (Sec. 3.4) for a few representative associated particle
momenta. The uncertainty of the acceptance correction determined from mixed
events in $\Delta\eta$ and the uncertainty due to the background subtraction
are different for different $p_{\mathrm{T}}^{\mathrm{assoc}}$ bins and
therefore shown separately for each data point. The uncertainty due to the
shape uncertainty of the acceptance correction determined from mixed events in
$\Delta\eta$ is correlated for different angles relative to the event plane
and uncorrelated between different $p_{\mathrm{T}}^{\mathrm{assoc}}$ bins. The
uncertainty due to the background subtraction is non-trivially correlated for
different angles of the jet relative to the event plane but uncorrelated
between different $p_{\mathrm{T}}^{\mathrm{assoc}}$ bins.

Table 1: Summary of systematic uncertainties which are independent of the angle relative to the event plane and the momentum for $20\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 40$ GeV/$c$ in 30-50$\%$ central Pb–Pb collisions. Source | Uncertainty $\%$
---|---
Single particle reconstruction efficiency | 4
Contamination | 1
Mixed event (shape $\Delta\phi$) | negligible
Mixed event normalization |  $<$ 0.5
event plane resolution | negligible
Table 2: Summary of systematic uncertainties on the yields and widths calculated from the correlation functions due to the shape uncertainty coming from the shape of the acceptance correction in $\Delta\eta$ and the correlated background fit uncertainty, both varying with event plane orientation bins. They are displayed for $20\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 40$ GeV/$c$ in 30-50$\%$ central Pb–Pb collisions for $1.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 1.5$ GeV/$c$ and $3.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 4.0$ GeV/$c$ bins. The values are expressed as a percent of the nominal value. Source | Result | Orientation | Uncertainty $\%$
---|---|---|---
Near-side: $\it{p}_{\rm{}_{T}}^{\mathrm{assoc}}$ (GeV/$c$) | Away-side: $\it{p}_{\rm{}_{T}}^{\mathrm{assoc}}$ (GeV/$c$)
1.0-1.5 | 3.0-4.0 | 1.0-1.5 | 3.0-4.0
| Yield | in-plane | 20 | 2.8 | 33 | 7.9
mid-plane | 13 | 2.7 | 25 | 9.2
Acceptance | out-of-plane | 10 | 2.5 | 22 | 6.3
shape | Width | in-plane | 14 | 1.5 | - | 5.0
| mid-plane | 9.8 | 1.4 | - | 7.1
| out-of-plane | 5.9 | 0.9 | - | 4.6
| Yield | in-plane | 16 | 6.3 | 50 | 18
mid-plane | 9.3 | 3.9 | 37 | 13
Background | out-of-plane | 7.9 | 6.0 | 35 | 15
fit | Width | in-plane | 23 | 4.2 | - | 12
| mid-plane | 25 | 2.7 | - | 23
| out-of-plane | 10 | 3.0 | - | 11

###  3.6 Impact of event plane resolution

To understand the impact of a possible event plane dependence in the signal,
we consider the Fourier decomposition approach to correcting for the event
plane resolution as in [72]. We can quantify the true azimuthal anistropy of
the signal by a Fourier decomposition as

$S(\Delta\phi)\big{(}1+2\sum_{n=1}^{\infty}v_{n}^{\mathrm{quench}}\cos(\phi^{\mathrm{trig}}-\psi)\big{)},$
(8)

where $S(\Delta\phi)$ is the correlation function of the signal averaged over
all angles relative to the event plane, the $v_{n}^{\mathrm{quench}}$ are due
to jet quenching, and $\phi^{\mathrm{trig}}$ is the azimuthal angle of the
trigger particle. The $v_{n}^{\mathrm{quench}}$ could also be a function of
$\Delta\phi$. The measured azimuthal anisotropy of the signal is then given by

$S\big{(}1+2\sum_{n=1}^{\infty}\Re_{n}v_{n}^{\mathrm{quench}}\cos(\phi^{\mathrm{trig}}-\psi)\big{)}.$
(9)

Note that the $v_{n}^{\mathrm{quench}}$ are distinct from both the $v_{n}$
from flow and the jet $v_{n}$. The jet $v_{n}$ measured in [33, 34] are
anisotropies in the number of jets relative to the event plane while the
$v_{n}^{\mathrm{quench}}$ are a measure of the anisotropies of the
constituents of those jets. Precision extraction of the
$v_{n}^{\mathrm{quench}}$ would require measurements of the signal in several
bins of $\phi^{\mathrm{trig}}-\psi$ and is not feasible for this measurement.
Equation 9 shows that the impact of the finite event plane resolution is
small, since for this analysis $\Re_{2}=0.73$.

If we assume that the $v_{n}^{\mathrm{quench}}$ do not depend on $\Delta\phi$,
the yields are given by integrating the equation 9 over the same angles of the
trigger particle relative to the event plane. The in-plane
($Y_{\mathrm{IP}}$), mid-plane ($Y_{\mathrm{MP}}$), and out-of-plane
($Y_{\mathrm{OP}}$) yields up to $n=3$ in terms of the average yield ($Y$) are
then given by

$\displaystyle Y_{\mathrm{IP}}$
$\displaystyle=Y(1+\frac{6}{\pi}\Re_{1}v_{1}^{\mathrm{quench}}+\frac{3\sqrt{3}}{\pi}\Re_{2}v_{2}^{\mathrm{quench}}+\frac{4}{\pi}\Re_{3}v_{3}^{\mathrm{quench}})$
(10) $\displaystyle Y_{\mathrm{MP}}$
$\displaystyle=Y(1+\frac{6(\sqrt{3}-1)}{\pi}\Re_{1}v_{1}^{\mathrm{quench}}-\frac{4}{\pi}\Re_{3}v_{3}^{\mathrm{quench}})$
$\displaystyle Y_{\mathrm{OP}}$
$\displaystyle=Y(1-\frac{3\sqrt{3}}{\pi}\Re_{2}v_{2}^{\mathrm{quench}}).$

The differences and ratios of the yields up to $n=3$ are then

$\displaystyle\frac{Y_{\mathrm{OP}}}{Y_{\mathrm{IP}}}$
$\displaystyle\approx\frac{Y_{\mathrm{OP}}-Y_{\mathrm{IP}}}{Y}\approx
1-\frac{6}{\pi}\Re_{1}v_{1}^{\mathrm{quench}}-\frac{6\sqrt{3}}{\pi}\Re_{2}v_{2}^{\mathrm{quench}}-\frac{4}{\pi}\Re_{3}v_{3}^{\mathrm{quench}}$
(11) $\displaystyle\frac{Y_{\mathrm{MP}}}{Y_{\mathrm{IP}}}$
$\displaystyle\approx\frac{Y_{\mathrm{MP}}-Y_{\mathrm{IP}}}{Y}\approx
1-\frac{6\sqrt{3}-12}{\pi}\Re_{1}v_{1}^{\mathrm{quench}}-\frac{3\sqrt{3}}{\pi}\Re_{2}v_{2}^{\mathrm{quench}}-\frac{8}{\pi}\Re_{3}v_{3}^{\mathrm{quench}}.$

Since the coefficients of the $v_{n}^{\mathrm{quench}}$ are on the order of
one, the deviations of these ratios from one are on the order of the
$v_{n}^{\mathrm{quench}}$. The odd $v_{n}^{\mathrm{quench}}$ will partially
cancel out because they will have opposite signs on different sides of the
event plane and in the absence of surface bias, they will cancel out
completely. The $n=2$ term is therefore likely the dominant term. We use this
expression to evaluate the approximate effect of the event plane resolution.
The allowed range of ${v}_{n}^{\mathrm{quench}}$ is
$-0.5<{v}_{2}^{\mathrm{quench}}<0.5$, with positive (negative) values
indicating suppression (enhancement) of the constituents. While the
${v}_{n}^{\mathrm{quench}}$ is a measure of the asymmetry of modifications of
jets relative to the event plane rather than the distribution of jets, we
consider the asymmetry in the number of jets [33, 34],
$v_{2}^{\mathrm{jet}}=0.1$, as a reasonable value of
${v}_{n}^{\mathrm{quench}}$. This would lead to
$\frac{Y_{\mathrm{OP}}}{Y_{\mathrm{IP}}}\approx\frac{Y_{\mathrm{OP}}-Y_{\mathrm{IP}}}{Y}\approx
0.67$ and
$\frac{Y_{\mathrm{MP}}}{Y_{\mathrm{IP}}}\approx\frac{Y_{\mathrm{MP}}-Y_{\mathrm{IP}}}{Y}\approx
0.83$ with perfect event plane resolution ($\Re_{2}=1.0$) and
$\frac{Y_{\mathrm{OP}}}{Y_{\mathrm{IP}}}\approx\frac{Y_{\mathrm{OP}}-Y_{\mathrm{IP}}}{Y}\approx
0.75$ and
$\frac{Y_{\mathrm{MP}}}{Y_{\mathrm{IP}}}\approx\frac{Y_{\mathrm{MP}}-Y_{\mathrm{IP}}}{Y}\approx
0.88$ with the event plane resolution in this analysis, $\Re_{2}=0.73$.

##  4 Results

The near-side and away-side jet yields as a function of
$p_{\mathrm{T}}^{\mathrm{assoc}}$ for $20\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\
<\leavevmode\nobreak\ 40$ GeV/$c$ full jets in 30-50% central Pb–Pb collisions
are shown in Fig. 4 for jets reconstructed in-plane, mid-plane, and out-of
plane for $1.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 1.5$ GeV/$c$,
$1.5\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 2.0$ GeV/$c$,
$2.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 3.0$ GeV/$c$,
$3.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 4.0$ GeV/$c$,
$4.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 5.0$ GeV/$c$,
$5.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 6.0$ GeV/$c$,
and $6.0\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm
T}^{\mathrm{assoc}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 10.0$ GeV/$c$.
The dominant feature is the decrease in the yield with increasing
$p_{\mathrm{T}}^{\mathrm{assoc}}$. Note that yields with
$p_{\mathrm{T}}^{\mathrm{assoc}}$ $>3$ GeV/$c$ include jet constituents,
complicating the interpretation of these data points. We therefore focus on
lower momentum on the near-side and on the away-side.

Figure 4: The (a) near-side and (b) away-side yield vs
$p_{\mathrm{T}}^{\mathrm{assoc}}$ for $20\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\
<\leavevmode\nobreak\ 40$ GeV/$c$ full jets of 30-50% centrality in Pb–Pb
collisions. The wider band corresponds to the background uncertainty, which is
non-trivially correlated point-to-point [27, 37]. The narrower bands are the
systematic uncertainties coming from the shape uncertainty of the acceptance
correction. There is an additional 5% global scale uncertainty. Points are
displaced for visibility.

Jet-hadron correlations can be used to measure changes in the momentum balance
within the jet, as in [24]. Partonic energy loss will shift energy in the jet
from higher momentum constituents to lower momentum constituents, so if jets
in-plane interact less with the medium, the differences
$Y_{\mathrm{MP}}-Y_{\mathrm{IP}}$ and $Y_{\mathrm{OP}}-Y_{\mathrm{IP}}$ will
be negative at high momenta and positive at low momenta. For these
differences, the systematic uncertainties partially cancel out. Figure 5 shows
the yield differences $Y_{\mathrm{MP}}-Y_{\mathrm{IP}}$ and
$Y_{\mathrm{OP}}-Y_{\mathrm{IP}}$ for the near- and away-side. There is no
event plane dependence within uncertainties, consistent with expectations if
$v_{2}^{\mathrm{quench}}\approx 0.1$ as observed for inclusive jet production.
Comparisons between yields in jet-hadron correlations in Au–Au and pp
collisions demonstrated suppression at high momenta and an enhancement at low
momenta in Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV [24]. The
lack of an event plane dependence therefore indicates that any dependence of
these modifications on the average path length is less than our experimental
uncertainties.

Figure 5:  The (a) near-side and (b) away-side yield differences vs
$p_{\mathrm{T}}^{\mathrm{assoc}}$ for $20\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\
<\leavevmode\nobreak\ 40$ GeV/$c$ full jets of 30-50% centrality in Pb–Pb
collisions. The narrower band corresponds to the background uncertainty, which
is non-trivially correlated point-to-point [27, 37]. The wider bands are the
systematic uncertainties coming from the shape uncertainty of the acceptance
correction. There is an additional 5% global scale uncertainty. Points are
displaced for visibility. Data are compared to calculations from JEWEL [73]
with and without recoil particles.

To better quantify and examine the event plane dependence of the yields,
ratios of mid-plane yields relative to in-plane yields
$Y_{\mathrm{MP}}/Y_{\mathrm{IP}}$ and out-of-plane yields relative to in-plane
yields $Y_{\mathrm{OP}}/Y_{\mathrm{IP}}$ as a function of
$p_{\mathrm{T}}^{\mathrm{assoc}}$ are shown in Fig. 6 for both the near- and
away-sides. As for the yield differences, a substantial fraction of the
systematic uncertainties cancel out for the ratios. If medium modifications
increase with increasing path length traversed by the parton, these ratios
will be less than one at high momenta and greater than one at low momenta.
These ratios are consistent with one for all
$p_{\mathrm{T}}^{\mathrm{assoc}}$. In contrast, $R_{\mathrm{AA}}$ can be as
low as 0.1 [7], indicating partonic energy loss.

The modification of the correlated yield ratios
$Y_{\mathrm{OP}}/Y_{\mathrm{IP}}$ and $Y_{\mathrm{MP}}/Y_{\mathrm{IP}}$ due to
jet quenching can be estimated from equation 11 as approximately
$1-3.3\times\Re_{2}v_{2}^{\mathrm{quench}}$ for out-of-plane to in-plane
ratios and $1-1.7\times\Re_{2}v_{2}^{\mathrm{quench}}$ for mid-plane to in-
plane ratios following the logic in Sec. 3.6. Since $\Re_{2}=0.73$, the ratios
in Fig. 6 can be used to constrain a hypothetical $v_{2}^{\mathrm{quench}}$.
While $v_{2}^{\mathrm{quench}}$ is a measure of the azimuthal asymmetry in jet
modifications rather than the number of jets, we use the asymmetry in the
number of jets, $v_{2}^{\mathrm{jet}}=0.1$ [33, 34], as a reasonable value for
$v_{2}^{\mathrm{quench}}$. If $v_{2}^{\mathrm{quench}}=0.1$, the out-of-plane
to in-plane ratios would be 0.75 and the mid-plane to in-plane ratios would be
0.88. The data in Fig. 6 are therefore consistent both with
$v_{2}^{\mathrm{quench}}$ comparable to the inclusive jet asymmetry and with
no asymmetry.

To investigate whether or not there is a systematic change in the ratio of
yields with the angle of the jet relative to the event plane, we fit the data
in Fig. 6 to a constant. The systematic uncertainties are treated as
uncorrelated point-to-point and added in quadrature to the statistical
uncertainties. The results are given in Tab. 3 and are consistent with yield
ratios of one. We note that medium modifications could result in a
$p_{\mathrm{T}}^{\mathrm{assoc}}$ dependence and this could be exacerbated by
kinematic biases on the near side because associated particles with momenta
above 3 GeV/$c$ are included in jet reconstruction. The $\chi^{2}$ per degree
of freedom may be large either because this procedure averages over different
physical effects which change with momentum or because of point-to-point
correlations in the uncertainties.

Figure 6:  The (a) near-side and (b) away-side yield ratios vs $p_{\mathrm{T}}^{\mathrm{assoc}}$ for $20\leavevmode\nobreak\ <\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\ <\leavevmode\nobreak\ 40$ GeV/$c$ full jets of 30-50% centrality in Pb–Pb collisions. The bands correspond to the background uncertainty, which is non-trivially correlated point-to-point [27, 37]. The systematic uncertainties coming from the shape uncertainty of the acceptance correction cancel out for the ratios. Points are displaced for visibility. Data are compared to calculations from JEWEL [73] with and without recoil particles.  Table 3: Results of fits to Fig. 6 to a constant $c$, the $\chi^{2}$ over the number of degrees of freedom (NDF), the number of standard deviations $\sigma$ of $c$ from one, and the range of $c$ within a 90% confidence limit (CL). | Near-side | Away-side
---|---|---
parameter | $Y_{\mathrm{OP}}/Y_{\mathrm{IP}}$ | $Y_{\mathrm{MP}}/Y_{\mathrm{IP}}$ | $Y_{\mathrm{OP}}/Y_{\mathrm{IP}}$ | $Y_{\mathrm{MP}}/Y_{\mathrm{IP}}$
$c$ | 0.972 $\pm$ 0.037 | 0.960 $\pm$ 0.036 | 0.885 $\pm$ 0.079 | 0.835 $\pm$ 0.078
$\chi^{2}$/NDF | 2.5 | 2.4 | 2.4 | 0.8
$\sigma$ | -0.8 | -1.1 | -1.5 | -2.1
90% CL | 0.91 – 1.03 | 0.90 – 1.02 | 0.75 – 1.02 | 0.71 – 0.96

Figure 7 shows the widths from a fit to the Gaussian for the near- and away-
side. Broadening would be expected from either collisional energy loss or
gluon bremsstrahlung and path length dependent energy loss would lead to a
greater width for jets out-of-plane than in-plane. No event plane dependence
is observed within uncertainties, indicating that any effect is smaller than
the precision of the data.

The data in Fig. 5 and Fig. 6 are compared to calculations from JEWEL, a jet
energy loss model based on radiative and collisional energy loss in connection
with partons sampled from a longitudinally expanding medium [73]. An important
setting in the model is the choice of whether or not to keep the recoiled
partons sampled from the medium in the simulation. With no recoils, the lost
jet momentum vanishes from the entire system, while including the recoils
conserves the jet’s overall momentum, but adds energy and background particles
(from the medium) to the simulated dijet. We compare to JEWEL with both
recoils off and recoils on. Results with recoils off are useful for modeling
energy loss in the hard part of the jet. Results with recoils on show where
the jet’s lost momentum goes. Any experimental analysis would likely include
some but not all of the recoil particles in JEWEL, as some proportion of the
recoil particles are indistinguishable from background.

JEWEL only predicts a slight event plane dependence, despite the path length
dependence of partonic energy loss, due to the dominant impact of jet-by-jet
fluctuations in partonic energy loss over path length dependence [74, 38]. The
slight event plane dependence predicted by JEWEL is well below the systematic
uncertainty in the measurement. The agreement of JEWEL with the data is
therefore consistent with path length dependence having an insignificant
impact compared to jet-by-jet fluctuations in energy loss, although
fluctuations in the density of the medium (not included in the JEWEL model)
may also suppress observable path length dependence.

Figure 7:  The (a) near-side and (b) away-side widths vs
$p_{\mathrm{T}}^{\mathrm{assoc}}$ for $20\leavevmode\nobreak\
<\leavevmode\nobreak\ p_{\rm T}^{\mathrm{jet}}\leavevmode\nobreak\
<\leavevmode\nobreak\ 40$ GeV/$c$ full jets of 30-50% centrality in Pb–Pb
collisions. The wider band corresponds the background uncertainty, which is
non-trivially correlated point-to-point [27, 37]. The narrower bands are the
systematic uncertainties coming from the shape uncertainty of the acceptance
correction. Points are displaced for visibility.

##  5 Conclusions

Partonic interactions depend on the length traversed in the medium, so any
medium modifications of the jet are expected to be path length dependent. The
path length traversed by a jet is correlated on average with the angle of the
jet with respect to the event plane. The use of the RPF method for background
subtraction reduces the assumptions required for background subtraction and
since the determination of the background is currently limited by statistics,
it is likely that future studies could reduce these systematic uncertainties.
Measurements of jet-hadron correlations relative to the event plane in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV are presented. Results are
consistent with no dependence in the yields or the widths on the angle of the
jet relative to the event plane within uncertainties. This may indicate that
jet-by-jet fluctuations in partonic energy loss are important for a full
description of medium modifications of jets.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&A. Adlerorg73&J. Adolfssonorg79&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N. Agrawalorg10,org53&Z.
Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg75&A. Akindinovorg90&M. Al-
Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D. Aleksandrovorg86&B.
Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B. Aliorg17&Y.
Aliorg15&A. Aliciorg10,org27,org53&A. Alkinorg2&J. Almeorg22&T. Altorg68&L.
Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C. Andreiorg47&D.
Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M. Angelettiorg34&V.
Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F. Antinoriorg56&P.
Antonioliorg53&R. Anwarorg125&N. Apadulaorg78&L. Aphecetcheorg114&H.
Appelshäuserorg68&S. Arcelliorg27&R. Arnaldiorg58&M. Arratiaorg78&I.C.
Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R. Averbeckorg105&S.
Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S. Bagnascoorg58&X.
Baiorg105&R. Bailhacheorg68&R. Balaorg99&A. Baldisseriorg137&M. Ballorg42&S.
Balouzaorg103&R. Barberaorg28&L. Barioglioorg26&G.G. Barnaföldiorg145&L.S.
Barnbyorg92&V. Barretorg134&P. Bartaliniorg6&K. Barthorg34&E. Bartschorg68&F.
Baruffaldiorg29&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg74&D. Bauriorg48&J.L. Bazo Albaorg110&I.G. Beardenorg87&C.
Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&A.D.C. Bell Hechavarriaorg144&F.
Belliniorg34&R. Bellwiedorg125&V. Belyaevorg91&G. Bencediorg145&S.
Beoleorg26&A. Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg58&M.G. Besoiuorg67&L. Betevorg34&A.
Bhasinorg99&I.R. Bhatorg99&M.A. Bhatorg3&H. Bhattorg48&B.
Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg26&N. Bianchiorg51&J.
Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg103,org117&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg86&C. Blumeorg68&G.
Bocaorg139&F. Bockorg34,org94&A. Bogdanovorg91&L. Boldizsárorg145&A.
Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H. Borelorg137&A.
Borissovorg91,org144&H. Bossiorg146&E. Bottaorg26&L. Bratrudorg68&P. Braun-
Munzingerorg105&M. Bregantorg121&T.A. Brokerorg68&M. Brozorg37&E.J.
Bruckenorg43&E. Brunaorg58&G.E. Brunoorg104&M.D. Bucklandorg127&D.
Budnikovorg107&H. Bueschingorg68&S. Bufalinoorg31&O. Bugnonorg114&P.
Buhlerorg113&P. Buncicorg34&Z. Butheleziorg72,org131&J.B. Buttorg15&J.T.
Buxtonorg95&S.A. Bysiakorg118&D. Caffarriorg88&A. Calivaorg105&E. Calvo
Villarorg110&R.S. Camachoorg44&P. Cameriniorg25&A.A. Caponorg113&F.
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## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIIIDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org3Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

org5California Polytechnic State University, San Luis Obispo, California,
United States

org6Central China Normal University, Wuhan, China

org7Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org10Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

org14Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Pusan National University, Pusan, Republic of
Korea

org19Department of Physics, Sejong University, Seoul, Republic of Korea

org20Department of Physics, University of California, Berkeley, California,
United States

org21Department of Physics, University of Oslo, Oslo, Norway

org22Department of Physics and Technology, University of Bergen, Bergen,
Norway

org23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34European Organization for Nuclear Research (CERN), Geneva, Switzerland

org35Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org36Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org37Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org38Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

org42Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

org44High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org45Hiroshima University, Hiroshima, Japan

org46Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org47Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

org61Institut de Physique Nucléaire d’Orsay (IPNO), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3/CNRS), Université de
Paris-Sud, Université Paris-Saclay, Orsay, France

org62Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org63Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

org64Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org65Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org66Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org67Institute of Space Science (ISS), Bucharest, Romania

org68Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org69Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org70Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org71Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org72iThemba LABS, National Research Foundation, Somerset West, South Africa

org73Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org74Joint Institute for Nuclear Research (JINR), Dubna, Russia

org75Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org76KTO Karatay University, Konya, Turkey

org77Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org78Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org79Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org80Nagasaki Institute of Applied Science, Nagasaki, Japan

org81Nara Women’s University (NWU), Nara, Japan

org82National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org83National Centre for Nuclear Research, Warsaw, Poland

org84National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org85National Nuclear Research Center, Baku, Azerbaijan

org86National Research Centre Kurchatov Institute, Moscow, Russia

org87Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org88Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org89NRC Kurchatov Institute IHEP, Protvino, Russia

org90NRC «Kurchatov Institute» - ITEP, Moscow, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

org92Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org93Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org94Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

org97Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

org101Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org102Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

org105Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org108Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org109School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org110Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

org113Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org114SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

org117Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org118The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org119The University of Texas at Austin, Austin, Texas, United States

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

org121Universidade de São Paulo (USP), São Paulo, Brazil

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Techonology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

org134Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org135Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org136Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org137Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU,
Départment de Physique Nucléaire (DPhN), Saclay, France

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

org141Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

org144Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org145Wigner Research Centre for Physics, Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea