2023 180 24 August

Search for jet quenching effects in HM pp collisions at $\sqrt{\textit{s}}=13$
TeV

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

The ALICE Collaboration reports a search for jet quenching effects in high-
multiplicity (HM) proton–proton collisions at $\sqrt{s}$ = 13 TeV, using the
semi-inclusive azimuthal-difference distribution $\Delta\varphi$ of charged-
particle jets recoiling from a high transverse momentum
(high-$p_{\mathrm{T,trig}}$) trigger hadron. Jet quenching may broaden the
$\Delta\varphi$ distribution measured in HM events compared to that in minimum
bias (MB) events. The measurement employs a $p_{\mathrm{T,trig}}$-differential
observable for data-driven suppression of the contribution of multiple
partonic interactions, which is the dominant background. While azimuthal
broadening is indeed observed in HM compared to MB events, similar broadening
for HM events is observed for simulations based on the PYTHIA 8 Monte Carlo
generator, which does not incorporate jet quenching. We elucidate the origin
of the broadening by comparing biases induced by HM selection in the data and
simulations, and discuss its implications for the study of jet quenching in
small collision systems.

##  1 Introduction

Strongly-interacting matter at extreme temperature and density forms
quark–gluon plasma (QGP), a state in which the dominant degrees of freedom are
sub-hadronic [1, 2]. The QGP filled the early universe, and it is generated
today in the collision of heavy atomic nuclei at the Relativistic Heavy Ion
Collider (RHIC) at Brookhaven National Laboratory and at the Large Hadron
Collider (LHC) at CERN. Measurements at these facilities, and their comparison
with theoretical calculations based on viscous relativistic hydrodynamics,
show that the QGP exhibits complex collective behavior, flowing with very low
specific shear viscosity [3].

A key question in the experimental study of the QGP is the limit of its
formation in terms of the size of the colliding nuclei. To explore this
question, measurements have been carried out for “small collision systems”, in
which one of the projectiles is a proton or light nucleus and the other a
heavy nucleus, additionally with selection of high event activity (EA) such as
produced particle multiplicity or forward neutron production (see e.g. Ref.
[4]). Final-state hadronic distributions in small systems exhibit experimental
signatures which are associated with production of the QGP in heavy-ion
collisions [5], including collective flow [6, 7, 8, 9] and enhancement in the
production of strange hadrons [10].

Jets are the hadronic remnants of hard (high momentum transfer $Q^{2}$)
interactions of quarks and gluons from the hadronic projectiles. Measurements
of jet production and jet structure in elementary collisions are well
described by theoretical calculations based on perturbative QCD (pQCD) [11,
12, 13]. In heavy-ion collisions, jets interact with the QGP, resulting in
modifications of jet production rates, structure, and angular distributions,
which provide incisive probes of the QGP (“jet quenching”) [14, 15].

Jet quenching is a necessary consequence of QGP formation in small systems,
though its effects are expected to be small [16, 17, 18, 19, 20, 21, 22]. A
common signature of jet quenching is the suppression of inclusive hadron or
jet yield measured in heavy-ion collisions compared to that expected by
scaling the corresponding yield measured in minimum-bias (MB) pp collisions,
using a Glauber modeling of the collision geometry [23, 14, 15]. Inclusive jet
yield suppression has been reported using this approach in EA-selected d–Au
collisions at RHIC (EA based on forward multiplicity) [24] and in p–Pb
collisions at the LHC (EA based on forward transverse energy $E_{\mathrm{T}}$)
[25]. However, Glauber modeling using these EA metrics in small systems is
subject to significant non-geometric bias [26, 4, 27, 28, 29, 30, 31, 22, 32].
An alternative choice for the EA metric, based on zero-degree neutron
measurements (nZDC), is found to be less biased, though the scaling still has
model-dependent assumptions and uncertainties [4]. Such biases and
uncertainties limit the sensitivity of the measurement of jet quenching
effects in small systems using Glauber-scaled inclusive yield observables. At
present there is no significant evidence, beyond experimental uncertainties,
of jet quenching in small systems using this approach [33, 34, 35].

The PHENIX Collaboration has recently searched for jet quenching in d–Au
collisions at a center-of-mass energy per nucleon–nucleon collision
$\sqrt{s_{\rm NN}}=200$ GeV by the measurement of both $\pi^{0}$ and direct
photon ($\gamma_{\mathrm{dir}}$) inclusive yields in collisions selected by EA
[32]. Jet quenching is studied using the $\gamma_{\mathrm{dir}}$ inclusive
yield to estimate empirically the rate of hard processes, which does not
depend upon Glauber scaling. Strong suppression in the ratio of $\pi^{0}$ and
$\gamma_{\mathrm{dir}}$ inclusive yields is observed for high-EA relative to
MB collisions, though with absolute value that is consistent with unity within
the normalization uncertainty.

An alternative approach has been proposed to search for medium-induced
inclusive yield suppression in small systems utilizing MB collisions of light
nuclei [20, 19], which likewise does not require Glauber modeling for the
yield scaling. However, this approach cannot be applied to EA-selected event
populations in small collision systems, where the strongest signals
characteristic of collective flow have been observed [6, 7, 8, 9, 10].

The comprehensive search for jet quenching effects in small collision systems
therefore also requires approaches based on coincidence observables, which are
self-normalized and likewise do not require a Glauber model calculation of
nuclear geometry for an EA-selected population. The measurement of jets
recoiling from a high-$p_{\mathrm{T}}$ hadron trigger in p–Pb collisions at
$\sqrt{s_{\rm NN}}=5.02$ TeV has set a limit of 0.4 $\mathrm{GeV/}c$ (90%
confidence) for medium-induced energy transport to angles greater than 0.4
radians relative to the jet axis, for high-EA collisions selected with
criteria based both on forward multiplicity and on nZDC [36]. Measurement of
the distribution of hadrons recoiling from a high-$p_{\mathrm{T}}$ jet trigger
in EA-selected (nZDC) p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV likewise
finds no significant jet quenching signal within uncertainties [37]. The
measurement of azimuthal anisotropy of high-$p_{\mathrm{T}}$ hadrons finds
small but non-zero second Fourier coefficient $v_{2}$ for events selected by
EA based on forward $E_{\mathrm{T}}$ [38], though such effects cannot be
attributed solely to jet quenching.

It therefore remains an open question whether the collective effects observed
in small systems are indeed due to QGP formation, or whether they arise from
other phenomena [39, 40, 41, 22]. New searches for jet quenching effects in
small systems are required to resolve this issue.

In this article we present a novel search for jet quenching effects in EA-
selected high-multiplicity (HM) pp collisions at $\sqrt{s}=13$ TeV. Since
“collision geometry” is ill-defined for EA-selected pp collisions, inclusive
observables are not appropriate for such a search. Rather, we utilize the
semi-inclusive hadron+jet acoplanarity observable [42, 43, 36], i.e. the
distribution of the azimuthal angle $\Delta\varphi$ between a
high-$p_{\mathrm{T}}$ hadron trigger and correlated recoil jets, comparing
$\Delta\varphi$ measurements in HM-selected and MB populations. Jets are
reconstructed from charged particles using the anti-$k_{\mathrm{T}}$ algorithm
[44] with resolution parameter $R=0.4$. Jet quenching in the QGP is expected
to broaden the $\Delta\varphi$ distribution relative to that in vacuum, due to
in-medium multiple scattering [45, 46, 47, 48, 49, 50]. However, at present
there is no theoretical guidance for the magnitude of the jet transport
parameter $\hat{q}$ [14] or alternative characterizations of jet quenching in
EA-selected pp collisions, and this is therefore entirely an experiment-driven
search.

The analysis is based on the $\Delta_{\mathrm{recoil}}$ observable developed
for semi-inclusive measurements in [42], which provides data-driven
suppression of uncorrelated background yield through the difference of trigger
hadron-normalised recoil jet distributions in two exclusive trigger
$p_{\mathrm{T}}$ intervals (Sec. 5). Precise suppression of uncorrelated
background yield is crucial in this analysis, since the yield of uncorrelated
recoil jets generated by multiple partonic interactions (MPI) from independent
high-$Q^{2}$ processes can mimic azimuthal broadening arising from jet
quenching. For the HM population we utilize a large data sample recorded by
ALICE with an online HM trigger during the 2016–2018 LHC pp runs at
$\sqrt{s}=13$ TeV. The $\Delta\varphi$ distributions from the HM-selected and
MB event populations are compared. The results are also compared to
theoretical calculations.

The paper is organized as follows: Sec. 2 presents the data set and offline
analysis; Sec. 3 presents characterization of event activity using forward
multiplicity; Sec. 4 presents jet reconstruction; Sec. 5 presents the
coincidence observable $\Delta_{\mathrm{recoil}}$; Sec. 6 presents data
corrections; Sec. 7 presents systematic uncertainties; and Sec. 8 presents the
physics results and their interpretation.

##  2 Data set and offline analysis

The ALICE detector and its performance are described in Refs. [51, 52]. Data
for this analysis were recorded during the 2016, 2017, and 2018 LHC runs with
pp collisions at $\sqrt{s}=13$ TeV. Events were selected online using signals
in the V0 detectors [53], which are plastic scintillator arrays covering the
pseudorapidity ranges $2.8<\eta<5.1$ (V0A) and $-3.7<\eta<-1.7$ (V0C). The V0
signal is proportional to the total number of charged particles (multiplicity)
in the detector acceptance. Two different V0 trigger configurations were
employed, called minimum bias (labelled “MB”) and high multiplicity (“HM”).
The MB trigger required the in-time coincidence of V0A and V0C signals, while
the HM trigger required the sum of V0A and V0C signal amplitudes (denoted as
V0M) to be at least five times larger than the mean signal amplitude in MB
events (denoted as $\left<{\rm V0M}\right>$). The HM trigger selected 0.1% of
MB events with the largest value of V0M.

The EA is characterized offline by the scaled V0 signal,
$\text{V0M}/\langle\text{V0M}\rangle=(\text{V0A~{}+~{}V0C})/\left<\text{V0A~{}+~{}V0C}\right>$,
which is insensitive to changes in V0 gain in the different data-taking
periods due to scintillator aging. It also provides ordering of events in
terms of EA without the need for precise calculation of the absolute V0 signal
in model calculations, for a well-defined comparison of such models with data.
The value of $\left<{\rm V0M}\right>$ is calculated separately for each data-
taking run lasting a few hours, as a function of the collision vertex position
along the beam axis. The HM selection is further constrained in the offline
analysis to the range $5<\text{V0M}/\langle\text{V0M}\rangle<9$. The lower
bound of 5 is determined by the online HM trigger threshold, while the upper
bound of 9 is determined by the range over which the
$\text{V0M}/\langle\text{V0M}\rangle$ distributions for the three different
measurement periods are consistent; higher values may be affected by residual,
uncorrected pileup effects.

In the offline analysis, jets are measured at midrapidity using charged
particles reconstructed with the ALICE central barrel detectors, covering the
range $|\eta|<0.9$. Track reconstruction is based on space points measured by
the Inner Tracking System (ITS) and Time Projection Chamber (TPC) [52].
Primary event vertices are reconstructed offline based on global tracks, which
are required to have space points in the Silicon Pixel Detector (SPD) forming
the two innermost layers of the ITS. Accepted events are required to have the
primary vertex within $\left|z_{\mathrm{vtx}}\right|<10$ cm, where
$z_{\mathrm{vtx}}$ is the location of the vertex along the beam axis relative
to the nominal center of the ALICE detector.

For MB-triggered events, the pileup rate due to multiple hadronic pp
collisions in the same LHC bunch crossing is less than 3.5%. The pile-up
contribution is suppressed offline by rejecting events with multiple
reconstructed event vertices. As discussed in Sec. 5, the observable
$\Delta_{\mathrm{recoil}}$ used in the analysis provides data-driven
suppression of uncorrelated background yield, which also includes residual
pileup events that are not rejected by the multiple-vertex algorithm. After
event selection, the data sets have an integrated luminosity of 32 nb-1 for
the MB trigger and 10 pb-1 for the HM trigger.

During the data taking the ITS had non-uniform efficiency, and the analysis
therefore utilizes hybrid tracks [54, 13] to achieve azimuthally uniform
tracking response. Hybrid tracks consist of good quality global tracks with at
least one hit in the SPD, and complementary tracks without SPD signals. To
ensure good momentum resolution, the momentum of these complementary tracks is
determined using the primary vertex as a constraint. Reconstructed tracks with
$|\eta|<0.9$ and $p_{\mathrm{T}}>0.15$ $\mathrm{GeV/}c$ are accepted for the
analysis. Hybrid track reconstruction efficiency is 0.85 at $p_{\mathrm{T}}=1$
$\mathrm{GeV/}c$, 0.82 at $p_{\mathrm{T}}=10$ $\mathrm{GeV/}c$, and 0.74 at
$p_{\mathrm{T}}=50$ $\mathrm{GeV/}c$. Tracking efficiencies for MB and HM
events are similar. Primary-track momentum resolution is 0.7% at
$p_{\mathrm{T}}=1$ $\mathrm{GeV/}c$, 1.3% at $p_{\mathrm{T}}=10$
$\mathrm{GeV/}c$, and 3.7% at $p_{\mathrm{T}}=50$ $\mathrm{GeV/}c$.

Simulations are utilized for data corrections and for comparison to
theoretical calculations. The simulations are based on the PYTHIA 8 event
generator [55] with Monash tune [56], and a detailed GEANT3 model [57] of the
ALICE detector response, which includes production of secondary particles and
realistic hit digitization. Events generated by PYTHIA 8 without detector
effects are denoted “particle-level,” and such events passed through GEANT3
are denoted “detector-level.”

For particle-level events, the V0A and V0C responses are determined by
counting the number of charged particles in their acceptance. The coincidence
requirement of the online trigger is modeled by requiring particle-level
events to have particles in both V0A and V0C, while detector-level events are
required to have GEANT-generated hits in both V0A and V0C. The MB events are
used to calculate the $\mathrm{V0M}$ distributions at both detector and
particle level.

##  3 $\text{V0M}/\langle\text{V0M}\rangle$ distributions

Figure 1: Probability distribution of $\text{V0M}/\langle\text{V0M}\rangle$ in
MB pp collisions measured at $\sqrt{s}=13$ TeV, and in simulated MB pp events
generated by PYTHIA 8 at the particle and detector level. The vertical dashed
lines indicate the lower bound for HM selection for data and particle-level
simulations.

Figure 1 shows the $\text{V0M}/\langle\text{V0M}\rangle$ probability
distribution for MB pp collisions at $\sqrt{s}=13$ TeV. The lower limit for HM
event selection, $\text{V0M}/\langle\text{V0M}\rangle=5$, is indicated by the
red dashed-dotted line. The figure also shows the
$\text{V0M}/\langle\text{V0M}\rangle$ probability distribution at the particle
and detector level for PYTHIA 8-generated events for MB pp collisions at
$\sqrt{s}=13$ TeV. These distributions differ because of a large contribution
at forward angles of secondary particles generated in detector material [58].
The particle-level distribution falls more rapidly than that observed in data
in the range $\text{V0M}/\langle\text{V0M}\rangle>4$. However, the detector-
level distribution qualitatively reproduces that observed in data, with
probability densities which lie within a factor $\sim 2$ of each other over a
range of nine orders of magnitude in $\text{V0M}/\langle\text{V0M}\rangle$.

In order to compare PYTHIA 8 particle-level HM-selected distributions to data,
we assume that the secondary particle yield due to interactions in detector
material is on average proportional to the primary multiplicity in the V0
acceptance. The HM selection for the particle-level distribution is therefore
chosen to select the same fraction of the MB cross section (0.1%) as the HM
selection $\text{V0M}/\langle\text{V0M}\rangle>5.0$ used for data. This
selection corresponds to particle-level
$\text{V0M}/\langle\text{V0M}\rangle>4.4$, as indicated by the dark dashed
line in Fig. 1.

##  4 Jet reconstruction

Several types of reconstructed jets are used in the analysis, which are
distinguished using the notation defined in Refs. [42, 36]. For data,
$p_{\mathrm{T,jet}}^{\mathrm{raw,ch}}$ refers to the raw output of the jet
reconstruction algorithm; $p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$ refers to
$p_{\mathrm{T,jet}}^{\mathrm{raw,ch}}$ after subtraction of the background
contribution estimated as $\rho\times A_{\mathrm{jet}}$, the product of median
jet $p_{\mathrm{T}}$ density in the event and the jet area (Eq. 1); and
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$ refers to the fully corrected jet
transverse momentum. For simulations, $p_{\mathrm{T,jet}}^{\mathrm{part}}$
refers to charged-particle jets at the particle level, and
$p_{\mathrm{T,jet}}^{\mathrm{det}}$ charged-particle jets at the detector
level; both quantities are corrected by $\rho\times A_{\mathrm{jet}}$ using
the following procedure.

Jets are reconstructed from accepted charged-particle tracks. Particles are
assumed to be massless and their four-momenta are combined with the boost-
invariant $p_{\mathrm{T}}$ recombination scheme [59]. Jet reconstruction is
carried out twice for each event. The first reconstruction pass uses the
$k_{\mathrm{T}}$ algorithm [59] with $R=0.4$ and accepts jets with
$|\eta_{\mathrm{jet}}|<0.9-R$. The first-pass jet population is used to
determine $\rho$, the event-wise estimate of the background energy density
[60],

$\rho=\mathrm{median}\left\\{\frac{p_{\mathrm{T,jet}}^{\mathrm{raw,i}}}{A_{\mathrm{jet}}^{\mathrm{i}}}\right\\},$
(1)

where $p_{\mathrm{T,jet}}^{\mathrm{raw,i}}$ and
$A_{\mathrm{jet}}^{\mathrm{i}}$ are the raw jet $p_{\mathrm{T}}$ and the area
[61] of the $i^{\mathrm{th}}$ jet in the event. Jet area is calculated using
the ghost area method of FastJet, with a ghost area of 0.005 [61]. The two
hardest jets in the event are excluded from the median calculation. The most
probable value of $\rho$ is zero in both the MB and HM populations, while the
mean value of $\rho$ is 0.09 $\mathrm{GeV/}c$ for MB and 1.24 $\mathrm{GeV/}c$
for HM-selected events. For events containing a charged track in $|\eta|<0.9$
with $20<p_{\mathrm{T}}<30$ $\mathrm{GeV/}c$, the mean value of $\rho$ is 0.39
$\mathrm{GeV/}c$ for MB and 1.62 $\mathrm{GeV/}c$ for HM events.

The second reconstruction pass uses the anti-$k_{\mathrm{T}}$ algorithm [59]
with $R=0.4$. The acceptance for the second pass is likewise
$|\eta_{\mathrm{jet}}|<0.9-R$ over the full azimuth.

The jet $p_{\mathrm{T}}$ obtained from the second pass is then adjusted for
the median background $p_{\mathrm{T}}$ density $\rho$ according to [60]

$p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}=p_{\mathrm{T,jet}}^{\mathrm{raw,ch}}-\rho\times
A_{\mathrm{jet}}.$ (2)

The jet $p_{\mathrm{T}}$ scale and jet $p_{\mathrm{T}}$ resolution are the
same as in Ref. [62].

##  5 Observables and raw data

The analysis utilizes a differential observable based on the semi-inclusive
distribution of charged-particle jets recoiling from a high-$p_{\mathrm{T}}$
trigger (“h+jet”) [42] (see also [43, 36]). The key components of this
approach are summarized in this section.

The goal of the analysis is the search for broadening of the $\Delta\varphi$
distribution in HM-selected events due to medium-induced jet scattering, by
comparison to the MB population. A significant source of background yield to
this process arises from MPIs, in which multiple uncorrelated high-$Q^{2}$
partonic interactions occur in the same pp collision, with one such
interaction generating a trigger hadron and another generating a recoil jet in
the acceptance. The $\Delta\varphi$ distribution of such MPI pairs is by
definition uniform on average, thereby limiting the measurement sensitivity to
broadening of the $\Delta\varphi$ distribution from medium-induced scattering
of correlated recoil jets.

Precise background yield correction must be carried out in a fully data-driven
way, without model dependence. We therefore employ the
$\Delta_{\mathrm{recoil}}$ observable [42], which is the difference between
semi-inclusive recoil jet distributions for two ranges of
$p_{\mathrm{T,trig}}$, both normalized to the number of trigger hadrons,

$\Delta_{\mathrm{recoil}}(p_{\mathrm{T}},\Delta\varphi)=\frac{1}{N_{\rm{trig}}}\frac{{\rm
d}^{2}N_{\rm
jet}}{\mathrm{d}p_{\mathrm{T,jet}}^{\mathrm{ch}}\mathrm{d}\Delta\varphi}\Bigg{|}_{p_{\mathrm{T,trig}}\in{\mathrm{TT}_{\mathrm{Sig}}}}-c_{\mathrm{Ref}}\times\frac{1}{N_{\rm{trig}}}\frac{{\rm
d}^{2}N_{\rm
jet}}{\mathrm{d}p_{\mathrm{T,jet}}^{\mathrm{ch}}\mathrm{d}\Delta\varphi}\Bigg{|}_{p_{\mathrm{T,trig}}\in{\mathrm{TT}_{\mathrm{Ref}}}},$
(3)

where TT denotes “trigger track.” In this analysis,
$\mathrm{TT}_{\mathrm{Sig}}=\mathrm{TT}\\{20,30\\}$ specifies the range
$20<p_{\mathrm{T,trig}}<30$ $\mathrm{GeV/}c$ for the Signal trigger
distribution, and $\mathrm{TT}_{\mathrm{Ref}}=\mathrm{TT}\\{6,7\\}$ specifies
the range $6<p_{\mathrm{T,trig}}<7$ $\mathrm{GeV/}c$ for the Reference trigger
distribution. These intervals were chosen to optimize the opposing
requirements of obtaining high statistical precision and limiting the
kinematic range for more precise comparison of the same observables with
different EA selections. The number of trigger hadrons measured in each TT
class is denoted $N_{\rm{trig}}$. The azimuthal difference $\Delta\varphi$
between TT and recoil jet is defined to have the range $[0,\pi]$ radians.

The $\Delta_{\mathrm{recoil}}$ distribution is a two-dimensional function of
$p_{\mathrm{T,jet}}$ and $\Delta\varphi$ [42, 36]. We define its one-
dimensional projections, $\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}$) and
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$), onto the
$p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$ and $\Delta\varphi$ axes respectively,
for restricted ranges in the other kinematic variable. These projections are
shown in Figs. 2 and 3 both prior to and after corrections, as indicated by
the functional argument (e.g.
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$) or
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$)).

The scaling factor $c_{\mathrm{Ref}}$, which is applied to the Reference
distribution (second term in Eq. 3), accounts for the different phase space
available to observe uncorrelated yield in the Signal and Reference
distributions [42, 43]. In this analysis, the value of $c_{\mathrm{Ref}}$ is
determined from the ratio of trigger-normalized Signal and Reference recoil
jet yields in the bin $0<p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}<1$
$\mathrm{GeV/}c$, which is expected to be dominated by background. This gives
values $c_{\mathrm{Ref}}=0.95\pm{0.03}~{}\text{(syst.)}$ in MB events and
$c_{\mathrm{Ref}}=0.94\pm{0.03}~{}\text{(syst.)}$ in HM events.

Since the uncorrelated yield is by definition independent of TT, it therefore
contributes with equal magnitude to the two terms in Eq. 3 and is therefore
removed by the subtraction. While $\Delta_{\mathrm{recoil}}$ is a differential
observable and not an absolutely normalized yield, its two terms are
nevertheless calculable perturbatively [63]. Measurements of
$\Delta_{\mathrm{recoil}}$ in minimum-bias pp collisions are well described by
PYTHIA 8 [42, 36].

In the analysis of both MB and HM-selected events, the dataset is divided into
two statistically independent subsets, with the Signal distribution determined
using 95% of all events, and the Reference distribution determined using the
remaining 5%. These fractions were chosen to provide an equal number of
trigger hadrons in the two TT classes, in order to optimize the statistical
precision of $\Delta_{\mathrm{recoil}}$. The statistical error due to the
$N_{\rm{trig}}$ normalization is negligible.

If two hadrons in an event satisfy the TT condition, one is chosen at random.
This selection ensures that the $p_{\mathrm{T}}$-differential TT distribution
has the same shape as the inclusive charged-hadron yield, which is an
essential requirement for a semi-inclusive measurement [42].

Figure 2: The Signal ($\mathrm{TT}\\{20,30\\}$) and Reference
($\mathrm{TT}\\{6,7\\}$) trigger-normalized recoil jet distributions and the
corresponding $\Delta_{\mathrm{recoil}}$ distribution for MB and HM pp
collisions at $\sqrt{s}=13$ TeV. Left panels: projection onto
$p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$ for $|\Delta\varphi-\pi|<0.6$. Middle
and right panels: projection onto $\Delta\varphi$ in two
$p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$ intervals.

Figure 2 shows selected
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$) and
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$) distributions, together with their
corresponding Signal and Reference distributions. The Signal and Reference
distributions have similar magnitude only in the region
$p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}<20$ $\mathrm{GeV/}c$, while at larger
values of $p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$ the Reference distribution
falls below the Signal distribution and $\Delta_{\mathrm{recoil}}$ is similar
in magnitude to the Signal distribution.

##  6 Corrections

Subtraction of the scaled Reference distribution in Eq. 3 accurately removes
the uncorrelated jet yield [42]. However, the resulting
$\Delta_{\mathrm{recoil}}$ distribution is still subject to instrumental
effects which smear $p_{\mathrm{T,jet}}$ and $\Delta\varphi$, whose correction
is discussed in this section. These smearing effects are encoded in the four-
dimensional response matrix $R_{\mathrm{instr}}$, which maps the true
(particle-level) distribution of $\Delta_{\mathrm{recoil}}$ onto the measured
distribution,

$\Delta_{\mathrm{recoil}}^{\mathrm{Meas}}\left({\Delta\varphi}^{\mathrm{det}},p_{\mathrm{T,jet}}^{\mathrm{det}}\right)=R_{\mathrm{instr}}\left({\Delta\varphi}^{\mathrm{det}},p_{\mathrm{T,jet}}^{\mathrm{det}};{\Delta\varphi}^{\mathrm{part}},p_{\mathrm{T,jet}}^{\mathrm{part}}\right)\otimes\Delta_{\mathrm{recoil}}^{\mathrm{True}}\left({\Delta\varphi}^{\mathrm{part}},p_{\mathrm{T,jet}}^{\mathrm{part}}\right).$
(4)

Particle-level jets are clustered from all final-state charged particles
generated with PYTHIA 8 as described in Sec. 2, except for weak decay
daughters [64, 65], while detector-level jets are reconstructed from charged-
particle tracks in the corresponding detector-level simulated events.

The $p_{\mathrm{T,jet}}$ and angular smearing due to instrumental effects is
very similar in the inclusive and recoil jet populations in these simulations.
In addition, the inclusive population has a substantially larger sample in the
simulated dataset. The matrix $R_{\mathrm{instr}}$ is therefore constructed
using the inclusive jet population, by matching particle-level and detector-
level jets in phase space within $\Delta
R=\sqrt{(\Delta\eta)^{2}+(\Delta\varphi)^{2}}<0.3$. The response matrix has
$p_{\mathrm{T}}$ bins of width 1 $\mathrm{GeV/}c$, so that the difference in
the spectrum shape of the inclusive and recoil jet populations has negligible
effect on this procedure.

Track reconstruction efficiency, which is the dominant instrumental effect, is
found to be the same for MB and HM events. The MB and HM analyses therefore
use the same response matrix, obtained using MB events. Unmatched particle-
level jets are tabulated and their rate is applied as an efficiency
correction, following the unfolding correction discussed below. Jet matching
efficiency for both MB and HM events is 0.98 at
$p_{\mathrm{T,jet}}^{\mathrm{ch}}=10$ $\mathrm{GeV/}c$ and consistent with
unity at higher $p_{\mathrm{T,jet}}^{\mathrm{ch}}$.

The corrected $\Delta_{\mathrm{recoil}}$ distribution is calculated by
regularized inversion of Eq. 4, using two-dimensional iterative Bayesian
unfolding [66] implemented in the RooUnfold package [67]. The input
distribution $\Delta_{\mathrm{recoil}}^{\mathrm{Meas}}$ is specified in the
range $10<p_{\mathrm{T,jet}}^{\mathrm{det}}<100$ $\mathrm{GeV/}c$ and
$\pi/2<{\Delta\varphi}^{\mathrm{det}}<\pi$ rad. The prior distribution for
initiating the unfolding is the $\Delta_{\mathrm{recoil}}$ particle-level
spectrum calculated using PYTHIA 8 simulations. For unfolding the MB dataset,
the prior is calculated using MB PYTHIA 8 events, whereas for unfolding the HM
dataset the detector-level HM selection is applied to the simulated data, as
shown in Fig. 1.

Regularization is optimized by requiring that the unfolded distributions from
successive iterations exhibit a mean change of less than 2%, averaged over all
$p_{\mathrm{T}}$ bins. The optimum number of iterations using this criterion
is found to be 5, for both the MB and HM analyses.

While correction of the $\Delta_{\mathrm{recoil}}$ distribution for
instrumental effects is carried out by regularized unfolding using the full
instrumental response matrix $R_{\mathrm{instr}}$, insight into the unfolding
procedure can also be gained by numerical characterization of the main
smearing effects. Since the goal of this analysis is the search for broadening
of the acoplanarity distribution in HM events, we focus here on azimuthal
angular smearing, which is calculated event-by-event by the difference between
particle-level and detector-level quantities. The observable $\Delta\varphi$
is the azimuthal angular difference between the trigger track momentum vector
and recoil jet centroid, both of which are smeared by instrumental effects.
The angular smearing is found to have the same magnitude in MB and HM events.
Azimuthal smearing of tracks contributing to $\mathrm{TT}\\{20,30\\}$ has
$\text{RMS}\approx 2\times 10^{-3}$ rad, while azimuthal smearing of the jet
axis has $\text{RMS}\approx 26\times 10^{-3}$ rad for
$10<p_{\mathrm{T,jet}}^{\mathrm{ch}}<15$ $\mathrm{GeV/}c$ and $11\times
10^{-3}$ rad for $60<p_{\mathrm{T,jet}}^{\mathrm{ch}}<80$ $\mathrm{GeV/}c$.
The corresponding distributions of $\Delta\varphi$ have RMS of $34\times
10^{-3}$ rad for $10<p_{\mathrm{T,jet}}^{\mathrm{ch}}<15$ $\mathrm{GeV/}c$ and
$13\times 10^{-3}$ rad for $60<p_{\mathrm{T,jet}}^{\mathrm{ch}}<80$
$\mathrm{GeV/}c$.

Subtraction of the reference distribution in the $\Delta_{\mathrm{recoil}}$
observable corrects the uncorrelated background yield. However, the resulting
two-dimensional distribution as a function of
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$ and $\Delta\varphi$ is still smeared by
residual fluctuations of the uncorrelated background component. Correction for
such fluctuations requires model assumptions (see e.g. Refs. [62, 35]) and is
therefore not included in the unfolding; rather, its magnitude is assessed for
two common model choices and the variation in unfolded distributions is
included in the systematic uncertainty, as discussed in Sec. 7.4.

The unfolding procedure is validated by a closure test in which the input is
PYTHIA 8 detector-level events, the full analysis chain including unfolding is
carried out, and the output is compared to the particle-level PYTHIA 8
spectrum. Good agreement between both distributions is found within
statistical uncertainties, thereby confirming the robustness of the applied
corrections.

##  7 Systematic uncertainties

The main sources of systematic uncertainty in the measurement of
$\Delta_{\mathrm{recoil}}$ are related to track reconstruction efficiency;
track $p_{\mathrm{T}}$ resolution; the unfolding procedure; the determination
of the scaling factor $c_{\mathrm{Ref}}$; and residual background
fluctuations. The systematic uncertainty due to each source is estimated by
varying the appropriate parameters and rerunning the full analysis chain.

However, the finite statistical precision of the data imposes a limit on the
precision with which the spectrum can be unfolded. This limit is taken into
account in the determination of the systematic uncertainties by using the
following procedure, which is described in detail in Ref. [36]. For each
parameter variation the spectrum is unfolded 10 times, with the central values
of the spectrum varied randomly and independently using a Poisson distribution
corresponding to the statistical error of each data point [36]. The ratio of
the unfolded spectrum from each iteration to that of the primary analysis is
calculated, and at each point the median of this set of ratios is assigned as
the systematic uncertainty from this source. Tables 1 and 2 show
representative values of the systematic uncertainty in
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$) and
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$) measurements for MB and HM-
selected event populations, respectively.

Table 1: Main sources of systematic uncertainty and total uncertainty in $\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$) and $\Delta_{\mathrm{recoil}}$($\Delta\varphi$) in representative bins, for MB events. | Relative systematic uncertainty (%)
---|---
Projection |  $\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$) |  $\Delta_{\mathrm{recoil}}$($\Delta\varphi$) |  $\Delta_{\mathrm{recoil}}$($\Delta\varphi$)
$|\Delta\varphi-\pi|<0.6$ |  $p_{\mathrm{T,jet}}^{\mathrm{ch}}\in(20,40)$ $\mathrm{GeV/}c$ |  $p_{\mathrm{T,jet}}^{\mathrm{ch}}\in(40,60)$ $\mathrm{GeV/}c$
Bin |  10–20 $\mathrm{GeV/}c$ |  60–80 $\mathrm{GeV/}c$ | $2\pi/3$ | $\pi$ | $2\pi/3$ | $\pi$
Tracking efficiency | 0.2 | 7.1 | 3.7 | 1.9 | 8.4 | 5.6
Track $p_{\text{T}}$ resolution | 0.3 | 0.3 | 0.2 | 0.2 | $\sim 0$ | 0.3
Unfolding procedure | 0.6 | 0.7 | 3.9 | 0.3 | 3.4 | 0.9
$c_{\mathrm{Ref}}$ variation | $(-1.7,1.9)$ | $(-0.2,0.2)$ | $(-0.6,0.7)$ | $(-0.4,0.4)$ | $(-0.5,0.5)$ | $(-0.1,0.2)$
Bkgd fluctuations | $(-1.6,0)$ | $(-2.4,0)$ | $(-4.7,0)$ | $(-1.6,0)$ | $(-5.0,0)$ | $(-2.7,0)$
Total uncertainty | $(-2.5,~{}2.0)$ | $(-7.6,7.2)$ | $(-7.2,5.4)$ | $(-2.5,2.0)$ | $(-10.4,9.0)$ | $(-6.3,5.7)$
Table 2: Same as Tab. 1, for HM-selected events. | Relative systematic uncertainty (%)
---|---
Projection | $\Delta_{\mathrm{recoil}}(p_{\mathrm{T,jet}}^{\mathrm{ch}})$ | $\Delta_{\mathrm{recoil}}(\Delta\varphi)$ | $\Delta_{\mathrm{recoil}}(\Delta\varphi)$
$|\Delta\varphi-\pi|<0.6$ |  $p_{\mathrm{T,jet}}^{\mathrm{ch}}\in(20,40)$ $\mathrm{GeV/}c$ |  $p_{\mathrm{T,jet}}^{\mathrm{ch}}\in(40,60)$ $\mathrm{GeV/}c$
Bin |  10–20 $\mathrm{GeV/}c$ |  60–80 $\mathrm{GeV/}c$ | $2\pi/3$ | $\pi$ | $2\pi/3$ | $\pi$
Tracking efficiency | 0.6 | 7.6 | 4.2 | 1.9 | 7.1 | 5.2
Track $p_{\text{T}}$ resolution | 0.3 | 0.1 | 0.4 | 0.2 | 0.1 | 0.3
Unfolding procedure | 0.9 | 0.7 | 5.7 | 1.6 | 2.6 | 1.2
$c_{\mathrm{Ref}}$ variation | $(-4.5,3.2)$ | $(-0.3,0.2)$ | $(-1.5,1.1)$ | $(-0.6,0.5)$ | $(-1.3,0.9)$ | $(-0.3,0.2)$
Bkgd fluctuations | $(-1.5,0)$ | $(-3.0,0)$ | $(-7.4,0)$ | $(-2.1,0)$ | $(-4.5,0)$ | $(-3.2,0)$
Total uncertainty | $(-4.6,3.7)$ | $(-8.2,7.6)$ | $(-10.3,7.2)$ | $(-3.3,2.5)$ | $(-8.9,7.6)$ | $(-6.3,5.4)$

###  7.1 Tracking efficiency and track $\mathbf{\textit{p}_{\mathrm{\bf T}}}$
resolution

The tracking efficiency uncertainty is 3% [54]. To assess the corresponding
uncertainty in the $\Delta_{\mathrm{recoil}}$ distribution, a variation of
$R_{\mathrm{instr}}$ is constructed in which 3% of all tracks are randomly
discarded. While it is in practice not possible to generate
$R_{\mathrm{instr}}$ with 3% higher tracking efficiency, this uncertainty is
expected to be symmetric. The resulting uncertainty ranges from $<1$% at low
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$ to 7% at high
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$, with only minor dependence on EA.

To assess the systematic uncertainty due to track $p_{\mathrm{T}}$ resolution,
two different instances of $R_{\mathrm{instr}}$ are generated, with
$p_{\mathrm{T}}$-resolution corresponding to that of either real data or
detector-level MC data hybrid tracks. This source makes negligible
contribution to the total systematic uncertainty.

###  7.2 Unfolding

The unfolding procedure has several parameters whose values influence the
corrected $\Delta_{\mathrm{recoil}}$ distribution: number of iterations;
choice of prior spectrum; and range and binning of the raw input distribution.
Each source was varied independently:

  * •

The regularization condition was varied by $\pm 1$ iterations with respect to
the optimized value of 5. The corresponding uncertainty is found to be small,
since unfolding converges rapidly to a stable result.

  * •

Variations in the prior spectrum were obtained using the particle-level
$\Delta_{\mathrm{recoil}}$ spectra generated by the POWHEG MC event generator
[68, 69] matched to PYTHIA 8 for parton shower and hadronization, and with
different choices of regularization and factorization scale.

  * •

The $p_{\mathrm{T,jet}}$ binning was varied by shifting the bin boundaries by
1–2 $\mathrm{GeV/}c$, and by changing the lower bound of the input spectrum
from 10 $\mathrm{GeV/}c$ to 6 $\mathrm{GeV/}c$. The binning in $\Delta\varphi$
was not varied, since $\Delta\varphi$ smearing effects are small.

The systematic uncertainty attributed to unfolding is the maximum deviation in
the $\Delta_{\mathrm{recoil}}$ spectrum from varying these parameters,
relative to the $\Delta_{\mathrm{recoil}}$ spectrum using the primary analysis
parameters. For
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$), the resulting
relative systematic uncertainty is about 0.6% for MB and 0.9% for HM events,
with a weak dependence on $p_{\mathrm{T,jet}}^{\mathrm{ch}}$. For
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$), the relative systematic
uncertainty is smallest at $\Delta\varphi=\pi$ and increases monotonically
towards $\Delta\varphi=\pi/2$, for both MB and HM events.

###  7.3 Scaling factor $\mathbf{\textit{c}_{\mathrm{\bf Ref}}}$

The value of the $c_{\mathrm{Ref}}$ scaling factor in Eq. 3 was varied in the
range $[0.9,1]$. This range brackets the $c_{\mathrm{Ref}}$ values obtained by
changing the $p_{\mathrm{T,jet}}^{\mathrm{reco,ch}}$ bin in which it is
evaluated from $(0,1)$ $\mathrm{GeV/}c$ to $(-1,0)$ $\mathrm{GeV/}c$, and by
its variation with $\Delta\varphi$. Different choices of $c_{\mathrm{Ref}}$
modify the $\Delta_{\mathrm{recoil}}$ spectrum relative to that of the primary
analysis result, with uncertainty decreasing as a function of
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$. Representative values are provided in
Tables 1 and 2.

###  7.4 Background fluctuations

As discussed in Sec. 6, no correction is applied directly for the effect of
residual background fluctuations; rather, a model-dependent estimate of its
magnitude contributes to the systematic uncertainty. For this estimate, a
response matrix which encodes the effect of residual background fluctuations,
$R_{\mathrm{bkgd}}$, is convoluted with the instrumental response matrix
$R_{\mathrm{instr}}$ in Eq. 4. The matrix $R_{\mathrm{bkgd}}$ is determined
for events selected with $\mathrm{TT}\\{20,30\\}$, using two methods:

  * •

Calculate the sum of track $p_{\mathrm{T}}$ in a cone $R$ = 0.4 placed
randomly in the acceptance, excluding overlap with the leading and sub-leading
jets, and the TT. This sum is corrected for the median background density,

$\delta
p_{\mathrm{T}}^{\text{RC}}=\sum_{\text{tracks}~{}\in~{}\text{RC}}p_{\text{T,
track}}-\rho\times\pi R^{2},$ (5)

where $\pi R^{2}$ is the cone area and $\rho$ is defined in Eq. 1. The matrix
$R_{\mathrm{bkgd}}$ is the distribution of $\delta
p_{\mathrm{T}}^{\text{RC}}$.

  * •

Embed a high-$p_{\mathrm{T}}$ track perpendicular in azimuth to the TT and at
the same value of $\eta$, with $p_{\mathrm{T}}$ distributed uniformly in the
range 0–20 $\mathrm{GeV/}c$. Jet reconstruction is then carried out, the jet
candidate containing the embedded track is identified, and the quantity
$\delta p_{\mathrm{T}}^{\text{ET}}$ is calculated as

$\delta p_{\mathrm{T}}^{\text{ET}}=p_{\text{T, jet}}^{\text{ch,
emb}}-\rho\times A_{\text{jet}}^{\text{emb}}-p_{\mathrm{T}}^{\text{emb}},$ (6)

where $p_{\mathrm{T}}^{\text{emb}}$ is transverse momentum of the embedded
track. The matrix $R_{\mathrm{bkgd}}$ is the distribution of $\delta
p_{\mathrm{T}}^{\text{ET}}$.

Unfolding is then carried out for both choices, and the assigned systematic
uncertainty is the maximum difference of the two unfolded
$\Delta_{\mathrm{recoil}}$ distributions from that of the primary analysis.

###  7.5 Total systematic uncertainty

The total systematic uncertainty of the unfolded $\Delta_{\mathrm{recoil}}$
distribution is the quadrature sum of the contribution from each source. The
systematic uncertainties from all sources except unfolding are correlated
between the HM and MB analyses. This correlation is accounted for in the
systematic uncertainty of ratios of $\Delta_{\mathrm{recoil}}$ distributions
by estimating the systematic uncertainty directly from the spread of the
ratios calculated for each variation of the analysis configuration.

##  8 Results

###  8.1 Fully corrected distributions

Figure 3: Fully-corrected $\Delta_{\mathrm{recoil}}$ distributions measured in
MB and HM-selected events in pp collisions at $\sqrt{s}=13$ TeV. Left panel:
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$) in
$|\Delta\varphi-\pi|<0.6$; middle and right panels:
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$) for
$20<p_{\mathrm{T,jet}}^{\mathrm{ch}}<40$ $\mathrm{GeV/}c$ and
$40<p_{\mathrm{T,jet}}^{\mathrm{ch}}<60$ $\mathrm{GeV/}c$. Also shown are
particle-level simulated distributions calculated with PYTHIA 8 Monash tune,
and a pQCD calculation at LO with Sudakov broadening [70, 71, 49] (MB
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$) only). The width of the PYTHIA 8
HM band represents the statistical uncertainty. Top row:
$\Delta_{\mathrm{recoil}}$ distributions; middle row: ratio of
$\Delta_{\mathrm{recoil}}$ distributions for HM/MB from data; bottom row:
Data/PYTHIA 8 separately for MB and HM event selections.

Figure 3 shows fully-corrected distributions of
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$) and
$\Delta_{\mathrm{recoil}}$($\Delta\varphi$) measured in MB and HM-selected pp
collisions at $\sqrt{s}=13$ TeV, together with calculations based on PYTHIA 8,
Monash tune, and a pQCD calculation at LO with Sudakov broadening [70, 71, 49]
(the latter only for $\Delta_{\mathrm{recoil}}$($\Delta\varphi$) in MB
collisions). Since the pQCD calculation is LO, there are large uncertainties
in its normalization; the $\Delta_{\mathrm{recoil}}$($\Delta\varphi$)
distributions from the calculation are therefore scaled to the integrated
yield of the data in the same $p_{\mathrm{T,jet}}^{\mathrm{ch}}$ bin in order
to compare their shapes. Both PYTHIA 8 and the pQCD calculation
($\Delta_{\mathrm{recoil}}$($\Delta\varphi$) shape only) are consistent with
the distributions measured in MB events, within experimental uncertainties.

Comparison of the MB and HM
$\Delta_{\mathrm{recoil}}$($p_{\mathrm{T,jet}}^{\mathrm{ch}}$) distributions
reveals a yield suppression in HM collisions that is largely independent of
$p_{\mathrm{T,jet}}$, though there is a hint of a harder recoil jet spectrum
for HM events. The mean value of the yield ratio HM/MB in the left panel of
Fig. 3 is 0.78. The $\Delta_{\mathrm{recoil}}$($\Delta\varphi$) distributions
show that the jet-yield suppression in HM events occurs predominantly in the
back-to-back configuration, with the yield ratio HM/MB in the bin
$\Delta\varphi\sim\pi$ measured to be 0.69 for
$20<p_{\mathrm{T,jet}}^{\mathrm{ch}}<40$ $\mathrm{GeV/}c$ (Fig. 3, middle
panel) and 0.78 for $40<p_{\mathrm{T,jet}}^{\mathrm{ch}}<60$ $\mathrm{GeV/}c$
(Fig. 3, left panel). The total yield is suppressed, while the azimuthal
distribution is broadened; such broadening could arise from jet quenching,
i.e. medium-induced jet scattering occurs preferentially in HM events.
Notably, however, PYTHIA 8 particle-level distributions likewise exhibit jet
yield suppression and azimuthal broadening for HM-selected events, accurately
reproducing the measured distributions. Since PYTHIA 8 does not incorporate
jet quenching, this disfavors jet quenching as the predominant effect
generating the broadening seen in data.

###  8.2 Origin of HM induced TT-jet acoplanarity in PYTHIA 8

Figure 4: PYTHIA 8 particle-level simulation of the probability distribution
of the yield of charged-particle jets ($R=0.4$) recoiling from a
high-$p_{\mathrm{T}}$ hadron ($\mathrm{TT}\\{20,30\\}$) as a function of
$\eta_{\mathrm{jet}}$ for various $p_{\mathrm{T,jet}}^{\mathrm{ch}}$
intervals, in pp collisions at $\sqrt{s}=13$ TeV. Left: MB events; right: HM
events. V0A and V0C acceptances are also shown.

To clarify the origin of the broadening, a more detailed investigation is
carried out of the particle-level distributions from PYTHIA 8 simulations.
Figure 4 shows the calculated pseudorapidity ($\eta_{\mathrm{jet}}$)
distribution of charged-particle jets recoiling from a high-$p_{\mathrm{T}}$
trigger hadron with $\mathrm{TT}\\{20,30\\}$ in MB and HM-selected event
populations, for various lower thresholds in
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$. Since the per-trigger yield varies with
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$, these distributions are normalized to unit
integral to enable a direct comparison of their shapes. The acceptances of V0A
and V0C are also shown; note that V0C covers smaller values of $|\eta|$ than
V0A. While the $\eta_{\mathrm{jet}}$ distribution for MB events is symmetric,
the $\eta_{\mathrm{jet}}$ distribution for HM events is highly asymmetric,
with significant enhancement in the relative rate of recoil jets in the V0C
acceptance. The enhancement is largest for the highest value of
$p_{\mathrm{T,jet}}^{\mathrm{ch}}$.

Figure 5: Same as Fig. 4, but for recoil jets with
$p_{\mathrm{T,jet}}^{\mathrm{ch}}>25$ $\mathrm{GeV/}c$ for various intervals
in $\mathrm{V0M}/\left<\mathrm{V0M}\right>$. Distributions are normalized per
trigger.

Figure 5 shows similar distributions for recoil jets with
$p_{\mathrm{T,jet}}^{\mathrm{ch}}>25$ $\mathrm{GeV/}c$, in various intervals
of $\mathrm{V0M}/\left<\mathrm{V0M}\right>$. A striking enhancement is
observed in the per-trigger jet yield within the V0C acceptance for the
largest values of $\mathrm{V0M}/\left<\mathrm{V0M}\right>$. Since HM events
are selected based on the value of $\mathrm{V0M}/\left<\mathrm{V0M}\right>$,
it is evident that the HM selection induces a bias which enhances the rate of
hard recoil jets in the V0C acceptance.

Figure 6: Distribution of probability per trigger hadron of number of jets
with $R=0.4$ and $p_{\mathrm{T,jet}}^{\mathrm{ch}}>15$ $\mathrm{GeV/}c$
recoiling from a high-$p_{\mathrm{T}}$ hadron ($\mathrm{TT}\\{20,30\\}$) at
midrapidity ($|\eta_{\mathrm{jet}}|<0.5$), for MB and HM pp collisions at
$\sqrt{s}=13$ TeV. Left panels: ALICE data; right panels: simulations at the
particle level with PYTHIA 8 Monash tune. Lower panels show the ratio HM/MB.
The insert in the lower panels has magnified vertical scale to show the ratio
of probabilities to observe a single jet.

Figure 6 provides additional insight into the bias induced by the HM event
selection. The figure shows the probability to observe a specific number of
jets with $R=0.4$ and $p_{\mathrm{T,jet}}^{\mathrm{ch}}>15$ $\mathrm{GeV/}c$
recoiling against a high-$p_{\mathrm{T}}$ hadron trigger
($\mathrm{TT}\\{20,30\\}$) in the ALICE central barrel acceptance
($|\eta_{\mathrm{jet}}|<0.5$), for MB and HM pp collisions at $\sqrt{s}=13$
TeV. Distributions are shown for both data and PYTHIA 8 calculations. In both
data and simulations, the probability to observe a single jet is suppressed in
HM relative to MB events by 2–3%, while the probability to observe multiple
jets is significantly enhanced.

The effect of the HM selection bias shown in Figs. 4, 5 and 6 on the
acoplanarity distributions in Fig. 3 can be understood as follows. The HM
requirement preferentially selects events with a recoil jet in the V0C
acceptance. For the leading-order (LO) di-jet channel, in which the TT and
recoil jet are azimuthally back-to-back, this depletes both the per-trigger
rate for recoil jets observed in the central barrel
($|\eta_{\mathrm{jet}}|<0.9-R$) at $\Delta\varphi\sim\pi$ and the relative
rate of single recoil jets in the acceptance. The recoil jets observed in the
ALICE central barrel in HM events therefore arise at enhanced rate from
higher-order production processes, with multiple recoil jets in the final
state. These jets from higher-order processes have broader distribution in
$\Delta\varphi$ than jets from LO production. This picture is confirmed by
carrying out the PYTHIA 8 analysis for much larger recoil jet acceptance,
$|\eta_{\mathrm{jet}}|<5.6$. In that case, no back-to-back yield depletion is
observed.

The yield suppression and azimuthal broadening seen in Fig. 3 may therefore
arise from the effect of different phase space being used for EA
characterization (V0A and V0C) and recoil jet measurement (central barrel),
combined with the HM selection bias towards events with a jet in the V0C
acceptance. It therefore cannot be attributed uniquely to jet quenching in HM-
selected events.

This conclusion about interpretability in terms of jet quenching of the
effects seen in Fig. 3 is more general than this specific analysis, however.
The bias of the HM event selection identified here is generic, and must also
be taken into account for the interpretation in terms of QGP formation of
other phenomena observed in small systems.

##  9 Summary

This article reports a search for jet quenching effects in high multiplicity
pp collisions at $\sqrt{s}=13$ TeV, based on the semi-inclusive azimuthal
distribution of charged-particle jets recoiling from a high-$p_{\mathrm{T}}$
hadron trigger in the ALICE central barrel acceptance. Significant azimuthal
broadening is observed in events selected to have high multiplicity in forward
detectors, which may arise from jet quenching. However, similar broadening is
also observed in simulations with the PYTHIA 8 event generator, which does not
incoporate jet quenching.

Detailed analysis of the data and simulations reveals that the high-
multiplicity event selection, which is based on the V0 detectors at forward
and backward rapidities, preferentially selects events with an energetic jet
in the forward detector, consequently biasing the acoplanarity distribution
measured in the central region. We conclude that this observable is therefore
not uniquely sensitive to jet quenching effects in small collision systems.
This bias is generic, however, and it should likewise be taken into account in
the interpretation of other measurements which probe the formation of a quasi-
equilibrated quark–gluon plasma in small collision systems.

## 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; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; 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 (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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##  Appendix A The ALICE Collaboration

S. Acharya 126, D. Adamová 86, G. Aglieri Rinella 33, M. Agnello 30, N.
Agrawal 51, Z. Ahammed 134, S. Ahmad 16, S.U. Ahn 71, I. Ahuja 38, A.
Akindinov 142, M. Al-Turany 97, D. Aleksandrov 142, B. Alessandro 56, H.M.
Alfanda 6, R. Alfaro Molina 67, B. Ali 16, A. Alici 26, N. Alizadehvandchali
115, A. Alkin 33, J. Alme 21, G. Alocco 52, T. Alt 64, A.R. Altamura 50, I.
Altsybeev 95, M.N. Anaam 6, C. Andrei 46, N. Andreou 114, A. Andronic 137, V.
Anguelov 94, F. Antinori 54, P. Antonioli 51, N. Apadula 74, L. Aphecetche
103, H. Appelshäuser 64, C. Arata 73, S. Arcelli 26, M. Aresti 23, R. Arnaldi
56, J.G.M.C.A. Arneiro 110, I.C. Arsene 20, M. Arslandok 139, A. Augustinus
33, R. Averbeck 97, M.D. Azmi 16, H. Baba123, A. Badalà 53, J. Bae 104, Y.W.
Baek 41, X. Bai 119, R. Bailhache 64, Y. Bailung 48, A. Balbino 30, A.
Baldisseri 129, B. Balis 2, D. Banerjee 4, Z. Banoo 91, R. Barbera 27, F.
Barile 32, L. Barioglio 95, M. Barlou78, B. Barman42, G.G. Barnaföldi 138,
L.S. Barnby 85, V. Barret 126, L. Barreto 110, C. Bartels 118, K. Barth 33, E.
Bartsch 64, N. Bastid 126, S. Basu 75, G. Batigne 103, D. Battistini 95, B.
Batyunya 143, D. Bauri47, J.L. Bazo Alba 101, I.G. Bearden 83, C. Beattie 139,
P. Becht 97, D. Behera 48, I. Belikov 128, A.D.C. Bell Hechavarria 137, F.
Bellini 26, R. Bellwied 115, S. Belokurova 142, Y.A.V. Beltran 45, G. Bencedi
138, S. Beole 25, Y. Berdnikov 142, A. Berdnikova 94, L. Bergmann 94, M.G.
Besoiu 63, L. Betev 33, P.P. Bhaduri 134, A. Bhasin 91, M.A. Bhat 4, B.
Bhattacharjee 42, L. Bianchi 25, N. Bianchi 49, J. Bielčík 36, J. Bielčíková
86, J. Biernat 107, A.P. Bigot 128, A. Bilandzic 95, G. Biro 138, S. Biswas 4,
N. Bize 103, J.T. Blair 108, D. Blau 142, M.B. Blidaru 97, N. Bluhme39, C.
Blume 64, G. Boca 22,55, F. Bock 87, T. Bodova 21, A. Bogdanov142, S. Boi 23,
J. Bok 58, L. Boldizsár 138, M. Bombara 38, P.M. Bond 33, G. Bonomi 133,55, H.
Borel 129, A. Borissov 142, A.G. Borquez Carcamo 94, H. Bossi 139, E. Botta
25, Y.E.M. Bouziani 64, L. Bratrud 64, P. Braun-Munzinger 97, M. Bregant 110,
M. Broz 36, G.E. Bruno 96,32, M.D. Buckland 24, D. Budnikov 142, H. Buesching
64, S. Bufalino 30, P. Buhler 102, N. Burmasov 142, Z. Buthelezi 68,122, A.
Bylinkin 21, S.A. Bysiak107, M. Cai 6, H. Caines 139, A. Caliva 29, E. Calvo
Villar 101, J.M.M. Camacho 109, P. Camerini 24, F.D.M. Canedo 110, M. Carabas
125, A.A. Carballo 33, F. Carnesecchi 33, R. Caron 127, L.A.D. Carvalho 110,
J. Castillo Castellanos 129, F. Catalano 33,25, C. Ceballos Sanchez 143, I.
Chakaberia 74, P. Chakraborty 47, S. Chandra 134, S. Chapeland 33, M. Chartier
118, S. Chattopadhyay 134, S. Chattopadhyay 99, T.G. Chavez 45, T. Cheng 97,6,
C. Cheshkov 127, B. Cheynis 127, V. Chibante Barroso 33, D.D. Chinellato 111,
E.S. Chizzali I,95, J. Cho 58, S. Cho 58, P. Chochula 33, D. Choudhury42, P.
Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T. Chujo 124, M.
Ciacco 30, C. Cicalo 52, F. Cindolo 51, M.R. Ciupek97, G. ClaiII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 96,32, M. Colocci 26, M. Concas
III,33, G. Conesa Balbastre 73, Z. Conesa del Valle 130, G. Contin 24, J.G.
Contreras 36, M.L. Coquet 129, P. Cortese 132,56, M.R. Cosentino 112, F. Costa
33, S. Costanza 22,55, C. Cot 130, J. Crkovská 94, P. Crochet 126, R. Cruz-
Torres 74, P. Cui 6, A. Dainese 54, M.C. Danisch 94, A. Danu 63, P. Das 80, P.
Das 4, S. Das 4, A.R. Dash 137, S. Dash 47, R.M.H. David45, A. De Caro 29, G.
de Cataldo 50, J. de Cuveland39, A. De Falco 23, D. De Gruttola 29, N. De
Marco 56, C. De Martin 24, S. De Pasquale 29, R. Deb 133, R. Del Grande 95, L.
Dello Stritto 29, W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B.
Diab 129, R.A. Diaz 143,7, T. Dietel 113, Y. Ding 6, J. Ditzel 64, R. Divià
33, D.U. Dixit 19, Ø. Djuvsland21, U. Dmitrieva 142, A. Dobrin 63, B. Dönigus
64, J.M. Dubinski 135, A. Dubla 97, S. Dudi 90, P. Dupieux 126, M. Durkac106,
N. Dzalaiova13, T.M. Eder 137, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D.
Elia 50, B. Erazmus 103, F. Ercolessi 26, B. Espagnon 130, G. Eulisse 33, D.
Evans 100, S. Evdokimov 142, L. Fabbietti 95, M. Faggin 28, J. Faivre 73, F.
Fan 6, W. Fan 74, A. Fantoni 49, M. Fasel 87, P. Fecchio30, A. Feliciello 56,
G. Feofilov 142, A. Fernández Téllez 45, L. Ferrandi 110, M.B. Ferrer 33, A.
Ferrero 129, C. Ferrero 56, A. Ferretti 25, V.J.G. Feuillard 94, V. Filova 36,
D. Finogeev 142, F.M. Fionda 52, E. Flatland33, F. Flor 115, A.N. Flores 108,
S. Foertsch 68, I. Fokin 94, S. Fokin 142, E. Fragiacomo 57, E. Frajna 138, U.
Fuchs 33, N. Funicello 29, C. Furget 73, A. Furs 142, T. Fusayasu 98, J.J.
Gaardhøje 83, M. Gagliardi 25, A.M. Gago 101, T. Gahlaut47, C.D. Galvan 109,
D.R. Gangadharan 115, P. Ganoti 78, C. Garabatos 97, A.T. Garcia 130, J.R.A.
Garcia 45, E. Garcia-Solis 9, C. Gargiulo 33, P. Gasik 97, A. Gautam 117, M.B.
Gay Ducati 66, M. Germain 103, A. Ghimouz124, C. Ghosh134, M. Giacalone 51, G.
Gioachin 30, P. Giubellino 97,56, P. Giubilato 28, A.M.C. Glaenzer 129, P.
Glässel 94, E. Glimos 121, D.J.Q. Goh76, V. Gonzalez 136, M. Gorgon 2, K.
Goswami 48, S. Gotovac34, V. Grabski 67, L.K. Graczykowski 135, E. Grecka 86,
A. Grelli 59, C. Grigoras 33, V. Grigoriev 142, S. Grigoryan 143,1, F. Grosa
33, J.F. Grosse-Oetringhaus 33, R. Grosso 97, D. Grund 36, N.A. Grunwald94,
G.G. Guardiano 111, R. Guernane 73, M. Guilbaud 103, K. Gulbrandsen 83, T.
Gündem 64, T. Gunji 123, W. Guo 6, A. Gupta 91, R. Gupta 91, R. Gupta 48, S.P.
Guzman 45, K. Gwizdziel 135, L. Gyulai 138, C. Hadjidakis 130, F.U. Haider 91,
S. Haidlova 36, H. Hamagaki 76, A. Hamdi 74, Y. Han 140, B.G. Hanley 136, R.
Hannigan 108, J. Hansen 75, M.R. Haque 135, J.W. Harris 139, A. Harton 9, H.
Hassan 116, D. Hatzifotiadou 51, P. Hauer 43, L.B. Havener 139, S.T. Heckel
95, E. Hellbär 97, H. Helstrup 35, M. Hemmer 64, T. Herman 36, G. Herrera
Corral 8, F. Herrmann137, S. Herrmann 127, K.F. Hetland 35, B. Heybeck 64, H.
Hillemanns 33, B. Hippolyte 128, F.W. Hoffmann 70, B. Hofman 59, G.H. Hong
140, M. Horst 95, A. Horzyk2, Y. Hou 6, P. Hristov 33, C. Hughes 121, P.
Huhn64, L.M. Huhta 116, T.J. Humanic 88, A. Hutson 115, D. Hutter 39, R.
Ilkaev142, H. Ilyas 14, M. Inaba 124, G.M. Innocenti 33, M. Ippolitov 142, A.
Isakov 84,86, T. Isidori 117, M.S. Islam 99, M. Ivanov 97, M. Ivanov13, V.
Ivanov 142, K.E. Iversen 75, M. Jablonski 2, B. Jacak 74, N. Jacazio 26, P.M.
Jacobs 74, S. Jadlovska106, J. Jadlovsky106, S. Jaelani 82, C. Jahnke 110,
M.J. Jakubowska 135, M.A. Janik 135, T. Janson70, S. Ji 17, S. Jia 10, A.A.P.
Jimenez 65, F. Jonas 87, D.M. Jones 118, J.M. Jowett 33,97, J. Jung 64, M.
Jung 64, A. Junique 33, A. Jusko 100, M.J. Kabus 33,135, J. Kaewjai105, P.
Kalinak 60, A.S. Kalteyer 97, A. Kalweit 33, V. Kaplin 142, A. Karasu Uysal
72, D. Karatovic 89, O. Karavichev 142, T. Karavicheva 142, P. Karczmarczyk
135, E. Karpechev 142, U. Kebschull 70, R. Keidel 141, D.L.D. Keijdener59, M.
Keil 33, B. Ketzer 43, S.S. Khade 48, A.M. Khan 119, S. Khan 16, A. Khanzadeev
142, Y. Kharlov 142, A. Khatun 117, A. Khuntia 36, B. Kileng 35, B. Kim 104,
C. Kim 17, D.J. Kim 116, E.J. Kim 69, J. Kim 140, J.S. Kim 41, J. Kim 58, J.
Kim 69, M. Kim 19, S. Kim 18, T. Kim 140, K. Kimura 92, S. Kirsch 64, I. Kisel
39, S. Kiselev 142, A. Kisiel 135, J.P. Kitowski 2, J.L. Klay 5, J. Klein 33,
S. Klein 74, C. Klein-Bösing 137, M. Kleiner 64, T. Klemenz 95, A. Kluge 33,
A.G. Knospe 115, C. Kobdaj 105, T. Kollegger97, A. Kondratyev 143, N.
Kondratyeva 142, E. Kondratyuk 142, J. Konig 64, S.A. Konigstorfer 95, P.J.
Konopka 33, G. Kornakov 135, S.D. Koryciak 2, A. Kotliarov 86,36, V. Kovalenko
142, M. Kowalski 107, V. Kozhuharov 37, I. Králik 60, A. Kravčáková 38, L.
Krcal 33,39, M. Krivda 100,60, F. Krizek 86, K. Krizkova Gajdosova 33, M.
Kroesen 94, M. Krüger 64, D.M. Krupova 36, E. Kryshen 142, V. Kučera 58, C.
Kuhn 128, P.G. Kuijer 84, T. Kumaoka124, D. Kumar134, L. Kumar 90, N. Kumar90,
S. Kumar 32, S. Kundu 33, P. Kurashvili 79, A. Kurepin 142, A.B. Kurepin 142,
A. Kuryakin 142, S. Kushpil 86, M.J. Kweon 58, Y. Kwon 140, S.L. La Pointe 39,
P. La Rocca 27, A. Lakrathok105, M. Lamanna 33, R. Langoy 120, P. Larionov 33,
E. Laudi 33, L. Lautner 33,95, R. Lavicka 102, R. Lea 133,55, H. Lee 104, I.
Legrand 46, G. Legras 137, J. Lehrbach 39, T.M. Lelek2, R.C. Lemmon 85, I.
León Monzón 109, M.M. Lesch 95, E.D. Lesser 19, P. Lévai 138, X. Li10, J. Lien
120, R. Lietava 100, I. Likmeta 115, B. Lim 25, S.H. Lim 17, V. Lindenstruth
39, A. Lindner46, C. Lippmann 97, D.H. Liu 6, J. Liu 118, G.S.S. Liveraro 111,
I.M. Lofnes 21, C. Loizides 87, S. Lokos 107, J. Lomker 59, P. Loncar34, X.
Lopez 126, E. López Torres 7, P. Lu 97,119, F.V. Lugo 67, J.R. Luhder 137, M.
Lunardon 28, G. Luparello 57, Y.G. Ma 40, M. Mager 33, A. Maire 128, M.V.
Makariev 37, M. Malaev 142, G. Malfattore 26, N.M. Malik 91, Q.W. Malik20,
S.K. Malik 91, L. Malinina VI,143, D. Mallick 130,80, N. Mallick 48, G.
Mandaglio 31,53, S.K. Mandal 79, V. Manko 142, F. Manso 126, V. Manzari 50, Y.
Mao 6, R.W. Marcjan 2, G.V. Margagliotti 24, A. Margotti 51, A. Marín 97, C.
Markert 108, P. Martinengo 33, M.I. Martínez 45, G. Martínez García 103,
M.P.P. Martins 110, S. Masciocchi 97, M. Masera 25, A. Masoni 52, L.
Massacrier 130, O. Massen 59, A. Mastroserio 131,50, O. Matonoha 75, S.
Mattiazzo 28, A. Matyja 107, C. Mayer 107, A.L. Mazuecos 33, F. Mazzaschi 25,
M. Mazzilli 33, J.E. Mdhluli 122, Y. Melikyan 44, A. Menchaca-Rocha 67, J.E.M.
Mendez 65, E. Meninno 102,29, A.S. Menon 115, M. Meres 13, S. Mhlanga113,68,
Y. Miake124, L. Micheletti 33, D.L. Mihaylov 95, K. Mikhaylov 143,142, A.N.
Mishra 138, D. Miśkowiec 97, A. Modak 4, B. Mohanty80, M. Mohisin Khan IV,16,
M.A. Molander 44, S. Monira 135, C. Mordasini 116, D.A. Moreira De Godoy 137,
I. Morozov 142, A. Morsch 33, T. Mrnjavac 33, V. Muccifora 49, S. Muhuri 134,
J.D. Mulligan 74, A. Mulliri23, M.G. Munhoz 110, R.H. Munzer 64, H. Murakami
123, S. Murray 113, L. Musa 33, J. Musinsky 60, J.W. Myrcha 135, B. Naik 122,
A.I. Nambrath 19, B.K. Nandi 47, R. Nania 51, E. Nappi 50, A.F. Nassirpour 18,
A. Nath 94, C. Nattrass 121, M.N. Naydenov 37, A. Neagu20, A. Negru125, L.
Nellen 65, R. Nepeivoda 75, S. Nese 20, G. Neskovic 39, N. Nicassio 50, B.S.
Nielsen 83, E.G. Nielsen 83, S. Nikolaev 142, S. Nikulin 142, V. Nikulin 142,
F. Noferini 51, S. Noh 12, P. Nomokonov 143, J. Norman 118, N. Novitzky 87, P.
Nowakowski 135, A. Nyanin 142, J. Nystrand 21, M. Ogino 76, S. Oh 18, A.
Ohlson 75, V.A. Okorokov 142, J. Oleniacz 135, A.C. Oliveira Da Silva 121, A.
Onnerstad 116, C. Oppedisano 56, A. Ortiz Velasquez 65, J. Otwinowski 107, M.
Oya92, K. Oyama 76, Y. Pachmayer 94, S. Padhan 47, D. Pagano 133,55, G. Paić
65, A. Palasciano 50, S. Panebianco 129, H. Park 124, H. Park 104, J. Park 58,
J.E. Parkkila 33, Y. Patley 47, R.N. Patra91, B. Paul 23, H. Pei 6, T.
Peitzmann 59, X. Peng 11, M. Pennisi 25, S. Perciballi 25, D. Peresunko 142,
G.M. Perez 7, Y. Pestov142, V. Petrov 142, M. Petrovici 46, R.P. Pezzi 103,66,
S. Piano 57, M. Pikna 13, P. Pillot 103, O. Pinazza 51,33, L. Pinsky115, C.
Pinto 95, S. Pisano 49, M. Płoskoń 74, M. Planinic89, F. Pliquett64, M.G.
Poghosyan 87, B. Polichtchouk 142, S. Politano 30, N. Poljak 89, A. Pop 46, S.
Porteboeuf-Houssais 126, V. Pozdniakov 143, I.Y. Pozos 45, K.K. Pradhan 48,
S.K. Prasad 4, S. Prasad 48, R. Preghenella 51, F. Prino 56, C.A. Pruneau 136,
I. Pshenichnov 142, M. Puccio 33, S. Pucillo 25, Z. Pugelova106, S. Qiu 84, L.
Quaglia 25, S. Ragoni 15, A. Rai 139, A. Rakotozafindrabe 129, L. Ramello
132,56, F. Rami 128, S.A.R. Ramirez 45, T.A. Rancien73, M. Rasa 27, S.S.
Räsänen 44, R. Rath 51, M.P. Rauch 21, I. Ravasenga 84, K.F. Read 87,121, C.
Reckziegel 112, A.R. Redelbach 39, K. Redlich V,79, C.A. Reetz 97, A.
Rehman21, F. Reidt 33, H.A. Reme-Ness 35, Z. Rescakova38, K. Reygers 94, A.
Riabov 142, V. Riabov 142, R. Ricci 29, M. Richter 20, A.A. Riedel 95, W.
Riegler 33, A.G. Riffero 25, C. Ristea 63, M.V. Rodriguez 33, M. Rodríguez
Cahuantzi 45, K. Røed 20, R. Rogalev 142, E. Rogochaya 143, T.S. Rogoschinski
64, D. Rohr 33, D. Röhrich 21, P.F. Rojas45, S. Rojas Torres 36, P.S. Rokita
135, G. Romanenko 26, F. Ronchetti 49, A. Rosano 31,53, E.D. Rosas65, K.
Roslon 135, A. Rossi 54, A. Roy 48, S. Roy 47, N. Rubini 26, D. Ruggiano 135,
R. Rui 24, P.G. Russek 2, R. Russo 84, A. Rustamov 81, E. Ryabinkin 142, Y.
Ryabov 142, A. Rybicki 107, H. Rytkonen 116, J. Ryu 17, W. Rzesa 135, O.A.M.
Saarimaki 44, S. Sadhu 32, S. Sadovsky 142, J. Saetre 21, K. Šafařík 36, P.
Saha42, S.K. Saha 4, S. Saha 80, B. Sahoo 47, B. Sahoo 48, R. Sahoo 48, S.
Sahoo61, D. Sahu 48, P.K. Sahu 61, J. Saini 134, K. Sajdakova38, S. Sakai 124,
M.P. Salvan 97, S. Sambyal 91, D. Samitz 102, I. Sanna 33,95, T.B.
Saramela110, P. Sarma 42, V. Sarritzu 23, V.M. Sarti 95, M.H.P. Sas 33, S.
Sawan80, J. Schambach 87, H.S. Scheid 64, C. Schiaua 46, R. Schicker 94, F.
Schlepper 94, A. Schmah97, C. Schmidt 97, H.R. Schmidt93, M.O. Schmidt 33, M.
Schmidt93, N.V. Schmidt 87, A.R. Schmier 121, R. Schotter 128, A. Schröter 39,
J. Schukraft 33, K. Schweda 97, G. Scioli 26, E. Scomparin 56, J.E. Seger 15,
Y. Sekiguchi123, D. Sekihata 123, M. Selina 84, I. Selyuzhenkov 97, S.
Senyukov 128, J.J. Seo 94,58, D. Serebryakov 142, L. Šerkšnytė 95, A. Sevcenco
63, T.J. Shaba 68, A. Shabetai 103, R. Shahoyan33, A. Shangaraev 142, A.
Sharma90, B. Sharma 91, D. Sharma 47, H. Sharma 54,107, M. Sharma 91, S.
Sharma 76, S. Sharma 91, U. Sharma 91, A. Shatat 130, O. Sheibani115, K.
Shigaki 92, M. Shimomura77, J. Shin12, S. Shirinkin 142, Q. Shou 40, Y.
Sibiriak 142, S. Siddhanta 52, T. Siemiarczuk 79, T.F. Silva 110, D. Silvermyr
75, T. Simantathammakul105, R. Simeonov 37, B. Singh91, B. Singh 95, K. Singh
48, R. Singh 80, R. Singh 91, R. Singh 48, S. Singh 16, V.K. Singh 134, V.
Singhal 134, T. Sinha 99, B. Sitar 13, M. Sitta 132,56, T.B. Skaali20, G.
Skorodumovs 94, M. Slupecki 44, N. Smirnov 139, R.J.M. Snellings 59, E.H.
Solheim 20, J. Song 17, C. Sonnabend 33,97, F. Soramel 28, A.B. Soto-hernandez
88, R. Spijkers 84, I. Sputowska 107, J. Staa 75, J. Stachel 94, I. Stan 63,
P.J. Steffanic 121, S.F. Stiefelmaier 94, D. Stocco 103, I. Storehaug 20, P.
Stratmann 137, S. Strazzi 26, A. Sturniolo 31,53, C.P. Stylianidis84, A.A.P.
Suaide 110, C. Suire 130, M. Sukhanov 142, M. Suljic 33, R. Sultanov 142, V.
Sumberia 91, S. Sumowidagdo 82, S. Swain61, I. Szarka 13, M. Szymkowski 135,
S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 111, G.J. Tambave 80, S. Tang
6, Z. Tang 119, J.D. Tapia Takaki 117, N. Tapus125, L.A. Tarasovicova 137,
M.G. Tarzila 46, G.F. Tassielli 32, A. Tauro 33, G. Tejeda Muñoz 45, A.
Telesca 33, L. Terlizzi 25, C. Terrevoli 115, S. Thakur 4, D. Thomas 108, A.
Tikhonov 142, N. Tiltmann 33,137, A.R. Timmins 115, M. Tkacik106, T. Tkacik
106, A. Toia 64, R. Tokumoto92, K. Tomohiro92, N. Topilskaya 142, M. Toppi 49,
T. Tork 130, P.V. Torres65, V.V. Torres 103, A.G. Torres Ramos 32, A. Trifiró
31,53, A.S. Triolo 33,31,53, S. Tripathy 51, T. Tripathy 47, S. Trogolo 33, V.
Trubnikov 3, W.H. Trzaska 116, T.P. Trzcinski 135, A. Tumkin 142, R. Turrisi
54, T.S. Tveter 20, K. Ullaland 21, B. Ulukutlu 95, A. Uras 127, G.L. Usai 23,
M. Vala38, N. Valle 22, L.V.R. van Doremalen59, M. van Leeuwen 84, C.A. van
Veen 94, R.J.G. van Weelden 84, P. Vande Vyvre 33, D. Varga 138, Z. Varga 138,
M. Vasileiou 78, A. Vasiliev 142, O. Vázquez Doce 49, O. Vazquez Rueda 115, V.
Vechernin 142, E. Vercellin 25, S. Vergara Limón45, R. Verma47, L. Vermunt 97,
R. Vértesi 138, M. Verweij 59, L. Vickovic34, Z. Vilakazi122, O. Villalobos
Baillie 100, A. Villani 24, A. Vinogradov 142, T. Virgili 29, M.M.O. Virta
116, V. Vislavicius75, A. Vodopyanov 143, B. Volkel 33, M.A. Völkl 94, K.
Voloshin142, S.A. Voloshin 136, G. Volpe 32, B. von Haller 33, I. Vorobyev 95,
N. Vozniuk 142, J. Vrláková 38, J. Wan40, C. Wang 40, D. Wang40, Y. Wang 40,
Y. Wang 6, A. Wegrzynek 33, F.T. Weiglhofer39, S.C. Wenzel 33, J.P. Wessels
137, S.L. Weyhmiller 139, J. Wiechula 64, J. Wikne 20, G. Wilk 79, J.
Wilkinson 97, G.A. Willems 137, B. Windelband 94, M. Winn 129, J.R. Wright
108, W. Wu40, Y. Wu 119, R. Xu 6, A. Yadav 43, A.K. Yadav 134, S. Yalcin 72,
Y. Yamaguchi 92, S. Yang21, S. Yano 92, Z. Yin 6, I.-K. Yoo 17, J.H. Yoon 58,
H. Yu12, S. Yuan21, A. Yuncu 94, V. Zaccolo 24, C. Zampolli 33, F. Zanone 94,
N. Zardoshti 33, A. Zarochentsev 142, P. Závada 62, N. Zaviyalov142, M. Zhalov
142, B. Zhang 6, C. Zhang 129, L. Zhang 40, S. Zhang 40, X. Zhang 6, Y.
Zhang119, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii 142, Y. Zhi10, D. Zhou 6,
Y. Zhou 83, J. Zhu 97,6, Y. Zhu6, S.C. Zugravel 56, N. Zurlo 133,55

## Affiliation Notes

I Also at: Max-Planck-Institut für Physik, Munich, Germany
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: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VI Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Krakow, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 California Polytechnic State University, San Luis Obispo, California, United
States
6 Central China Normal University, Wuhan, China
7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
9 Chicago State University, Chicago, Illinois, United States
10 China Institute of Atomic Energy, Beijing, China
11 China University of Geosciences, Wuhan, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovak Republic
14 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica, Università di Pavia, Pavia, 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.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
31 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
33 European Organization for Nuclear Research (CERN), Geneva, Switzerland
34 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
35 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
36 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
37 Faculty of Physics, Sofia University, Sofia, Bulgaria
38 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
40 Fudan University, Shanghai, China
41 Gangneung-Wonju National University, Gangneung, Republic of Korea
42 Gauhati University, Department of Physics, Guwahati, India
43 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
44 Helsinki Institute of Physics (HIP), Helsinki, Finland
45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
46 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
47 Indian Institute of Technology Bombay (IIT), Mumbai, India
48 Indian Institute of Technology Indore, Indore, India
49 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
50 INFN, Sezione di Bari, Bari, Italy
51 INFN, Sezione di Bologna, Bologna, Italy
52 INFN, Sezione di Cagliari, Cagliari, Italy
53 INFN, Sezione di Catania, Catania, Italy
54 INFN, Sezione di Padova, Padova, Italy
55 INFN, Sezione di Pavia, Pavia, Italy
56 INFN, Sezione di Torino, Turin, Italy
57 INFN, Sezione di Trieste, Trieste, Italy
58 Inha University, Incheon, Republic of Korea
59 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
60 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovak Republic
61 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
62 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
63 Institute of Space Science (ISS), Bucharest, Romania
64 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
65 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
66 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
67 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
68 iThemba LABS, National Research Foundation, Somerset West, South Africa
69 Jeonbuk National University, Jeonju, Republic of Korea
70 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
71 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
72 KTO Karatay University, Konya, Turkey
73 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 Nara Women’s University (NWU), Nara, Japan
78 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
79 National Centre for Nuclear Research, Warsaw, Poland
80 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
81 National Nuclear Research Center, Baku, Azerbaijan
82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia
83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež,
Czech Republic
87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States
89 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
90 Physics Department, Panjab University, Chandigarh, India
91 Physics Department, University of Jammu, Jammu, India
92 Physics Program and International Institute for Sustainability with Knotted
Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan
93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Physik Department, Technische Universität München, Munich, Germany
96 Politecnico di Bari and Sezione INFN, Bari, Italy
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
98 Saga University, Saga, Japan
99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata,
India
100 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France
104 Sungkyunkwan University, Suwon City, Republic of Korea
105 Suranaree University of Technology, Nakhon Ratchasima, Thailand
106 Technical University of Košice, Košice, Slovak Republic
107 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
108 The University of Texas at Austin, Austin, Texas, United States
109 Universidad Autónoma de Sinaloa, Culiacán, Mexico
110 Universidade de São Paulo (USP), São Paulo, Brazil
111 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
112 Universidade Federal do ABC, Santo Andre, Brazil
113 University of Cape Town, Cape Town, South Africa
114 University of Derby, Derby, United Kingdom
115 University of Houston, Houston, Texas, United States
116 University of Jyväskylä, Jyväskylä, Finland
117 University of Kansas, Lawrence, Kansas, United States
118 University of Liverpool, Liverpool, United Kingdom
119 University of Science and Technology of China, Hefei, China
120 University of South-Eastern Norway, Kongsberg, Norway
121 University of Tennessee, Knoxville, Tennessee, United States
122 University of the Witwatersrand, Johannesburg, South Africa
123 University of Tokyo, Tokyo, Japan
124 University of Tsukuba, Tsukuba, Japan
125 University Politehnica of Bucharest, Bucharest, Romania
126 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
127 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
128 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
129 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
130 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
131 Università degli Studi di Foggia, Foggia, Italy
132 Università del Piemonte Orientale, Vercelli, Italy
133 Università di Brescia, Brescia, Italy
134 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
135 Warsaw University of Technology, Warsaw, Poland
136 Wayne State University, Detroit, Michigan, United States
137 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
138 Wigner Research Centre for Physics, Budapest, Hungary
139 Yale University, New Haven, Connecticut, United States
140 Yonsei University, Seoul, Republic of Korea
141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
142 Affiliated with an institute covered by a cooperation agreement with CERN
143 Affiliated with an international laboratory covered by a cooperation
agreement with CERN.