2021 199 30 September General Balance Functions ALICE Collaboration††thanks:
See Appendix A for the list of collaboration members ALICE Collaboration

First measurements of balance functions (BFs) of all combinations of
identified charged hadron $(\pi,\rm K,\rm p)$ pairs in Pb–Pb collisions at
$\sqrt{s_{{}_{\rm NN}}}=2.76$ TeV recorded by the ALICE detector are
presented. The BF measurements are carried out as two-dimensional differential
correlators versus the relative rapidity ($\Delta y$) and azimuthal angle
($\Delta\varphi$) of hadron pairs, and studied as a function of collision
centrality. The $\Delta\varphi$ dependence of BFs is expected to be sensitive
to the light quark diffusivity in the quark–gluon plasma. While the BF
azimuthal widths of all pairs substantially decrease from peripheral to
central collisions, the longitudinal widths exhibit mixed behaviors: BFs of
$\pi\pi$ and cross-species pairs narrow significantly in more central
collisions, whereas those of $\rm KK$ and $\rm pp$ are found to be independent
of collision centrality. This dichotomy is qualitatively consistent with the
presence of strong radial flow effects and the existence of two stages of
quark production in relativistic heavy-ion collisions. Finally, the first
measurements of the collision centrality evolution of BF integrals are
presented, with the observation that charge balancing fractions are nearly
independent of collision centrality in Pb–Pb collisions. Overall, the results
presented provide new and challenging constraints for theoretical models of
hadron production and transport in relativistic heavy-ion collisions.

Convincing evidence for the production of strongly interacting quark–gluon
plasma (QGP) in heavy-ion (AA) collisions has been reported from a variety of
measurements at the Relativistic Heavy Ion Collider (RHIC) and the Large
Hadron Collider (LHC) [1, 2, 3, 4], including observations of strong elliptic
flow [5, 6, 7], suppression of high transverse momentum ($p_{\rm T}$) hadron
production [8, 9, 10, 11, 12, 13], suppression of quarkonium states[14, 15,
16, 17, 18, 19], as well as dihadron correlation functions [20, 21]. Many of
these findings are quantitatively explained by hydrodynamic calculations in
which the QGP matter undergoes radial and azimuthally anisotropic collective
motion. The existence of the latter is well established based on measurements
of flow coefficients with finite pseudorapidity ($\eta$) gap and multi-
particle cumulants, whereas the presence of the former is inferred in part
from the increase of average transverse momenta with the mass of hadrons [22],
the centrality dependence of event-by-event $p_{\rm T}$ fluctuations [23, 24],
as well as the observed narrowing of the near-side peak of BFs in central
collisions relative to that observed in peripheral collisions [25, 26, 27, 28,
29, 30]. Balance functions essentially amount to differences of correlation
functions of like-sign and unlike-sign charges. They are measured, typically,
as functions of particle pair separation in azimuth angle and rapidity. They
indicate the degree to which the production of a positive charge is
accompanied by the production of a negative charge somewhere in phase space.
As such, BFs probe the balancing of charge distributions in momentum space and
theoretical studies show they are sensitive to the details of the time (i.e.,
whether particles are produced early or late), production mechanisms, and
transport of balancing charges.

Measurements of BFs were originally proposed as a tool to investigate the
delayed hadronization and two stages of quark production in the QGP formed in
AA collisions [31]. These terms refer to the notion that quark production
occurs in two distinct stages, the first at the onset, and the second at the
very end (just before hadronization and freeze-out) of AA collisions. The two
stages are posited to be separated by a period of isentropic expansion whose
duration depends on the multiplicity of produced quarks and gluons and thus
the collision impact parameter. BFs could also provide a precise probe of
balancing particle production [32, 33, 34, 35], the hadrochemistry of particle
production [34, 36], as well as the collision dynamics [37, 38]. Recent
studies also indicate that the BF dependence on pair separation in azimuth are
sensitive to the diffusivity of light quarks, a measure of the diffusion and
scattering of quarks within the QGP, which has thus far received only limited
attention [39, 36]. Finally, BFs also provide a tool to calibrate measurements
of the Chiral Magnetic Effect [40, 41] and net charge/baryon fluctuations
deemed essential for the determination of QGP susceptibilities [42, 43].

Few measurements of BFs of identified hadrons have been reported to date. At
RHIC, these include BF measurements of charged hadrons, pion pairs, kaon
pairs, as well as proton/antiproton pairs [25, 26, 27], whereas at the LHC,
only charged hadron BFs have been reported [28, 29]. Of these, only the
results published by ALICE were fully corrected for detector acceptance and
particle losses (efficiency). Integrals of measured BFs have not been
considered and no cross-species BFs have been published. Theoretical analyses
of measured BFs have consequently focused mainly on the interpretation of the
narrowing with collision centrality of charged hadron BFs. The full potential
of BFs as a probe of the evolution dynamics and chemistry of the QGP has thus
so far been underexploited. In this paper, general balance functions of
identified charged hadron species $(\pi,\rm K,\rm p)$ are reported for the
first time. These general BFs are corrected for efficiency and non uniform
acceptance effects and it becomes possible to study the effects of two-stage
quark production, light quark diffusivity, and relative balancing fractions
using BFs of nine distinct identified pairs of charged hadron species.

The BF of a species of interest, $\alpha$, and an associated species, $\beta$,
was originally defined in terms of conditional densities [31] but it is
convenient to compute BFs in terms of normalized cumulants $R_{2}$ according
to

$\begin{aligned}
B^{\alpha\beta}(\vec{p}_{\alpha},\vec{p}_{\beta})=\frac{1}{2}&\left\\{\rho_{1}^{\beta^{-}}(\vec{p}_{\beta^{-}})\left[R_{2}^{\alpha^{+}\beta^{-}}(\vec{p}_{\alpha^{+}},\vec{p}_{\beta^{-}})-{R_{2}^{\alpha^{-}\beta^{-}}(\vec{p}_{\alpha^{-}},\vec{p}_{\beta^{-}})}\right]+\right.\\\
&\left.\;\;\;\rho_{1}^{\beta^{+}}(\vec{p}_{\beta^{+}})\left[R_{2}^{\alpha^{-}\beta^{+}}(\vec{p}_{\alpha^{-}},\vec{p}_{\beta^{+}})-{R_{2}^{\alpha^{+}\beta^{+}}(\vec{p}_{\alpha^{+}},\vec{p}_{\beta^{+}})}\right]\right\\}\end{aligned},$
(1)

with

$R_{2}^{\alpha\beta}(\vec{p}_{\alpha},\vec{p}_{\beta})\equiv\frac{\rho_{2}^{\alpha\beta}(\vec{p}_{\alpha},\vec{p}_{\beta})}{{\rho_{1}^{\alpha}(\vec{p}_{\alpha})}{\rho_{1}^{\beta}(\vec{p}_{\beta})}}-1$
(2)

where $\rho_{1}^{\alpha}(\vec{p}_{\alpha})\equiv{\rm d}N/{\rm
d}\vec{p}_{\alpha}$ and
$\rho_{2}^{\alpha\beta}(\vec{p}_{\alpha},\vec{p}_{\beta})\equiv{\rm d}N/{\rm
d}\vec{p}_{\alpha}{\rm d}\vec{p}_{\beta}$ are single- and particle-pair
densities of species $\alpha$ and $\beta$ measured at momenta
$\vec{p}_{\alpha}$ and $\vec{p}_{\beta}$, respectively, while labels $+$ and
$-$ stand for positive and negative charges. Normalized cumulants $R_{2}$ are
robust observables, i.e., independent to first order of measurement
efficiencies. They are sensitive to the strength of correlation between
species $\alpha$ and $\beta$. Their properties were described in several
publications [44, 45, 46, 47]. The combination of $R_{2}$ correlation
functions, normalized by single particle densities, as per Eq. (1), is
strictly equivalent to the balance function introduced in Ref. [32, 31] and
measures the correlation between positive and negative particles of species
$\alpha$ and $\beta$ constrained by charge conservation. Integrals of
inclusive charge balance functions,
$I_{B}^{+-}(\Omega)\equiv\int_{\Omega}B^{+-}{\rm d}\Delta\eta$, are expected
to lie within the range $0<I_{B}^{+-}(\Omega)\leq 1$ for limited acceptances
$\Omega$. However, they converge to unity for full acceptance coverage.
Furthermore, fractions $I_{B}^{\alpha\beta}(\Omega)/I_{B}^{\alpha}(\Omega)$
are determined by the hadrochemistry of the QGP and transport properties of
the medium. In the full acceptance coverage limit, the denominator of this
fraction must satisfy
$I_{B}^{\alpha}(\Omega)\equiv\sum_{\beta}I_{B}^{\alpha\beta}(\Omega)\rightarrow
1$ [43].

In this paper, the identified particle BFs at the LHC for nine pairs of
charged hadrons ($\pi^{\pm}$, ${\rm K}^{\pm}$ and $\rm p/\overline{p}$)
$\otimes$ ($\pi^{\pm}$, ${\rm K}^{\pm}$, and $\rm p/\overline{p}$) as joint
functions of the relative rapidity ($\Delta y$) and azimuthal angle
($\Delta\varphi$) are reported. Measurements of
$R_{2}^{\alpha\beta}(\vec{p}_{\alpha},\vec{p}_{\beta})$ are carried out in
terms of the rapidity and azimuthal angle $y_{\alpha}$, $\varphi_{\alpha}$,
$y_{\beta}$, and $\varphi_{\beta}$ for fixed $p_{\rm T}$ ranges, and averaged
across the pair acceptance to yield correlation functions
$R_{2}^{\alpha\beta}(\Delta y,\Delta\varphi)$ with $\Delta
y=y_{\alpha}-y_{\beta}$ and $\Delta\varphi=\varphi_{\alpha}-\varphi_{\beta}$
following the procedure used in Ref. [44]. The densities of associated
particles, $\rho_{1}^{\beta}(\vec{p}_{\beta})$, used in Eq. (1), are drawn
from prior measurements [22]. BFs are corrected for particle losses,
acceptance, and efficiency, thereby enabling determination of their integrals
and collision centrality dependence. As such, these BFs are sensitive to the
timescales at which particles are produced during the system evolution and the
transport of conserved charges [31], but they also enable more sensitive
probes of the hadrochemistry of the collisions. Indeed, whereas contributions
to single-particle spectra from hadronic resonance decays must be inferred
from models, integrals of the BFs are directly sensitive to the magnitude of
these contributions. For instance, by comparing the integrals of
$\pi^{+}\pi^{-}$ and $\pi^{\pm}{\rm K}^{\mp}$ BFs, sensitivity to the relative
strengths of processes that lead to such correlated pairs of particles is
acquired. Indeed, it becomes possible to better probe the role of hadronic
resonance decay contributions and increased sensitivity to the hadrochemistry
of the QGP and its susceptibilities is gained [36].

The BFs presented are based on $1\times 10^{7}$ minimum bias (MB) Pb–Pb
collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV collected in 2010 by the ALICE
collaboration. Descriptions of the ALICE detector and its performance have
been reported elsewhere [48, 49]. The minimum bias trigger required a
combination of hits in the V0 detectors and layers of the SPD detector. The V0
detectors, which cover the full azimuth and the pseudorapidity ranges
$-3.7<\eta<-1.7$ and $2.8<\eta<5.1$, also provided a measurement of the
charged particle multiplicity used to classify collisions into centrality
classes corresponding to 0–5% (most central) to 80–90% (most peripheral) of
the Pb–Pb hadronic cross section [50]. Some centrality classes have been
combined to optimize the statistical accuracy of the BFs reported. Particle
momenta were determined based on Kalman fits of charged particle tracks
reconstructed in the Time Projection Chamber (TPC). The particle
identification (PID) of charged hadrons was performed based on specific energy
loss (${\rm d}E/{\rm d}x$) measured in the TPC and particle velocities
measured in the Time-of-Flight detector (TOF). Track quality criteria based on
the number of space points, the distance of closest approach to the collision
primary vertex, and the $\chi^{2}$ of the Kalman fits were used to restrict
the measurements to primary particles produced by the Pb–Pb collisions and
suppress contamination from tracks resulting from weak decays and interactions
of particles with the apparatus. Additionally, PID selection criteria based on
deviations of ${\rm d}E/{\rm d}x$ and TOF from their respective expectation
values, at a given momentum, and for each species of interest, were used to
optimize the species purity. These and other selection criteria are reported
in detail below in the context of a discussion of systematic uncertainties.
The analysis focused on the low $p_{\rm T}$ range, commonly known as the
“bulk" physics regime. Slightly different $p_{\rm T}$ ranges were used for
each species to optimize yields and species purity. Charged pions and kaons
were selected in the range $0.2\leq p_{\rm T}\leq 2.0$ GeV/$c$, whereas
(anti-)protons are within $0.5\leq p_{\rm T}\leq 2.5$ GeV/$c$. The selected
rapidity range, largely determined by the TOF coverage, was set to
$|y_{\pi}|\leq 0.8$ and $|y_{\rm p}|\leq 0.6$ for measurements of $B^{\pi\pi}$
and $B^{\rm pp}$, respectively, and set to $|y|\leq 0.7$ for all other BFs
reported.

Track reconstruction efficiencies and PID purity were studied with Monte Carlo
simulations of Pb–Pb collisions produced with the HIJING generator [51] and
propagated through a model of the ALICE detector with GEANT3 [52]. Selected
track quality and PID criteria yield purities of 97%, 95%, and 94% for
$\pi^{\pm}$, ${\rm K}^{\pm}$, and ${\rm p/\overline{p}}$, respectively,
thereby minimizing species contamination and its impact on correlation
functions. Corrections for track losses were carried out using a weighting
technique [46]. Weights are calculated independently for positive and negative
tracks of each species considered, for each centrality range, both magnetic
field polarities used in the measurements, versus $y$, $\varphi$, $p_{\rm T}$,
as well as the longitudinal position of the primary vertex (PV) of each event,
$z_{\text{vtx}}$. Various selection criteria were applied to minimize residual
instrumental effects while optimizing particle yields. The PV is required to
be in the range $|z_{\rm vtx}|\leq 6$ cm of the nominal interaction point.
Tracks are required to have a minimum of 70 reconstructed TPC space points
(hits), out of a maximum of 159, and a track fit with $\chi^{2}$ value per
degree of freedom smaller than $2.0$ to ensure good track quality.
Contamination of BFs by secondary particles (i.e., weak decays or particles
scattered within the detector) is suppressed by requiring distances of closest
approach (DCA) to PV chosen as DCA${}_{z}\leq 2.0$ cm in the longitudinal
direction and DCA${}_{xy}\leq 0.04,0.04,2.0$ cm in the transverse plane for
$\pi^{\pm}$, ${\rm p/\overline{p}}$, and ${\rm K}^{\pm}$, respectively.
Contamination by $\rm e^{+}e^{-}$ pairs from photon conversions are suppressed
by removing tracks closer than $1\sigma_{{\rm d}E/{\rm d}x}$ to the TPC Bethe-
Bloch median, at a given momentum, for electrons.

Systematic uncertainties on the amplitudes of $B^{\alpha,\beta}$ and their
integrals were calculated as quadratic sums of systematic uncertainties of the
correlation function $R_{2}^{\alpha,\beta}$ and the systematic uncertainties
on the published single particle densities [22] used in the computation of the
BFs. Uncertainties on $R_{2}^{\alpha,\beta}$ were assessed based on variations
of conditions and selection parameters employed in the analysis and a
statistical test [53] was used to identify potential biases introduced by
those variations and determine their statistical significance. Systematic
uncertainties, corresponding to a relative deviation at the maximum of
$B^{\alpha,\beta}$ associated with operation with two solenoidal magnetic
field polarities, are smaller than 4%. Potential biases associated with track
selection criteria are up to 3%, whereas the presence of misidentified and
secondary particles contribute up to 4%, while kinematic dependencies of the
detection efficiency are estimated to be 1%. Systematic uncertainties on the
single particle densities [22] are species and collision centrality dependent
and typically range from 5 to 10%.

In order to obtain BF for all nine combinations of $\pi^{\pm}$, ${\rm
K}^{\pm}$, and ${\rm p/\overline{p}}$ species pairs,
$R_{2}^{\alpha\beta}(\Delta y,\Delta\varphi)$ correlators were first measured,
in each centrality class, for all 36 $\alpha\beta$ permutations of positive
and negative $\pi$, ${\rm K}$, and ${\rm p}$. These were then combined
according to Eq. (1) and multiplied by the single particle densities
$\rho_{1}^{\beta}$ in the $|y|\leq 0.5$ rapidity range [22]. Figure 1
presents, for illustrative purposes, $B^{\alpha\beta}(\Delta y,\Delta\varphi)$
of $\pi\pi$, ${\rm KK}$, and ${\rm pp}$ pairs in semicentral collisions.

Figure 1: Balance functions $B^{\alpha\beta}(\Delta y,\Delta\varphi)$ of pairs
$\alpha\beta=\pi\pi$ (left), ${\rm KK}$ (center), and ${\rm pp}$ (right)
measured in semicentral Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=2.76\;\text{TeV}$.

The nine measured BFs exhibit common features, including prominent near-side
peaks centered at $(\Delta y,\Delta\varphi)=(0,0)$ and relatively flat and
featureless away-sides. The flat away-side arises from the fact that positive
and negative particles of a given species feature essentially equal azimuthal
anisotropy relative to the collision symmetry plane. It is also an indicator
of the fast radial flow profile of the emitting sources [37], although the
various species pairs demonstrate different centrality-dependent near-side
peak shapes, widths, and magnitudes that indicate that they are subject to
different charge balancing pair production and transport mechanisms, as well
as final state effects. For instance, $B^{\pi\pi}$ exhibits a deep and narrow
dip at $(\Delta y,\Delta\varphi)=(0,0)$, within the near-side correlation
peak, resulting in part from the Hanbury Brown–Twiss (HBT) effect, with a
depth and width that vary with the source size and thus the centrality [32].
$B^{{\rm KK}}$ exhibits much weaker HBT effects, whereas $B^{{\rm pp}}$ also
features a narrow dip centered at $(\Delta y,\Delta\varphi)=(0,0)$ within a
somewhat elongated near-side peak may reflect annihilation of ${\rm
p\overline{p}}$ pairs.

Figure 2: Balance function of species pairs $(\pi,{\rm K},{\rm
p})\otimes(\pi,{\rm K},{\rm p})$ projected onto the $\Delta y$ axis for
particle pairs within the full range $|\Delta\varphi|\leq\pi$. Vertical bars
and open boxes represent statistical and systematic uncertainties,
respectively. Figure 3: Balance function projections of species pairs
$(\pi,{\rm K},{\rm p})\otimes(\pi,{\rm K},{\rm p})$ onto the $\Delta\varphi$
axis for the different particle pairs. Vertical bars and open boxes represent
statistical and systematic uncertainties, respectively.

The evolution with collision centrality of $B^{\alpha\beta}$, for all nine
combinations $\alpha,\beta=\pi,{\rm K},{\rm p}$, is examined by considering
their projections onto the $\Delta y$ and $\Delta\varphi$ axes in Figs. 2 and
3, respectively. The shape and amplitude of $B^{\pi\pi}$ projections onto
$\Delta y$ exhibit the strongest centrality dependence, whereas those of
$B^{\pi{\rm K}}$, $B^{\pi{\rm p}}$, $B^{{\rm K}\pi}$ and $B^{{\rm p}\pi}$
display significantly smaller dependence on centrality. Uncertainties on the
rest of the $\Delta y$ projections do not make it possible to claim any
centrality dependence albeit some hints are visible in the cases of $B^{{\rm
KK}}$ and $B^{{\rm pp}}$.

Figure 4: Longitudinal ($\Delta y$) $\sigma$ widths (left), azimuthal
($\Delta\varphi$) $\sigma$ widths (center), and integrals (right) of balance
functions of the full species matrix of $\pi^{\pm}$, ${\rm K}^{\pm}$, and
${\rm p/\overline{p}}$ with centrality. For $\Delta y$ and $\Delta\varphi$
widths, ${\rm K}\pi$, ${\rm p}\pi$, and ${\rm pK}$ have the same values with
$\pi{\rm K}$, $\pi{\rm p}$, and ${\rm Kp}$, respectively. For the longitudinal
widths, the relative azimuthal angle range for all the species pairs is the
full azimuth range $|\Delta\varphi|\leq\pi$. For the azimuthal widths, the
relative rapidity range used for all species pairs is $|\Delta y|\leq 1.2$,
with the exception of $|\Delta y|\leq 1.4$ for $\pi\pi$ and $|\Delta y|\leq
1.0$ for $\rm pp$. Vertical bars represent statistical uncertainties while
systematic uncertainties are displayed as dash line bands.

The evolution with collision centrality of the measured BFs is further
characterized in terms of their longitudinal and azimuthal standard deviation
($\sigma$) widths, noted $\sigma_{\Delta y}$ and $\sigma_{\Delta\varphi}$,
respectively, as well as their integral, $I_{\rm B}^{\alpha\beta}$, as shown
in Fig. 4. In the longitudinal direction, the widths $\sigma_{\Delta y}$ of
all species pairs, except those of ${\rm KK}$ and ${\rm pp}$ pairs, exhibit a
significant narrowing from peripheral to central collisions. In contrast,
$B^{{\rm KK}}$ is essentially independent in both shape and width
$\sigma_{\Delta y}$ with changing collision centrality, whereas the overall
width $\sigma_{\Delta y}$ of $B^{\rm pp}$ features little centrality
dependence even though this balance function exhibits some shape dependence on
centrality, as observed in Fig. 2.

Differences in the evolution of the longitudinal $\sigma$ of pions and kaons
BFs were already observed in Au–Au collisions at RHIC [26] and were then
interpreted as resulting in part from strong radial flow profiles and two-
stage emission [54, 32]. The independence of the width $\sigma_{\Delta y}$ of
the $B^{{\rm KK}}$ relative to the narrowing BFs of all other pairs observed
in this work suggests two-stage quark production might also be at play at the
TeV collision scale. Indeed, pions might be predominantly formed from the
light u, $\rm\bar{u}$, d, and $\rm\bar{d}$ quarks most abundantly produced in
the second quark production stage, whereas kaon production would largely
result from $\rm s\rm\bar{s}$ pairs predominantly created during the early
stages of collisions [54, 32].

Several distinct models have had success in describing the yield of produced
hadrons, and more specifically baryons. Such models invoke a range of
production mechanisms including parton fragmentation, effective mostly at
high-$p_{\rm T}$, as well as parton coalescence and recombination, playing a
predominant role at low and intermediate $p_{\rm T}$ [55, 56, 57]. Statistical
thermal models and production models involving color transparency [58] and
baryon junctions [59] have also had a good measure of success. Single particle
spectra of baryons thus do not provide sufficiently discriminating constraints
to fully identify baryon production mechanisms. The added information provided
by cross-species BFs shall thus contribute by adding new constraints for
models of particle production and transport. In particular, given that
neutrons, protons, and their excited states are composed of light u and d
quarks, believed to be copiously produced in late stage emission (within the
context of the two-stage quark production model), it is conceivable that these
baryons are predominantly produced by coalescence (recombination) of light
quarks in the late stage of the collisions. However, baryons (B) and
antibaryons ($\overline{\rm B}$) have a relatively large mass and carry a
conserved baryonic charge. The question then arises as to whether $\rm
B\overline{B}$ correlated pairs might originate before the formation of
thermalized QGP, during the early stages of AA collisions. Late $\rm
B\overline{B}$ production is expected to be characterized by narrow
longitudinal BFs while early stage emissions would produce pairs with a much
wider $\Delta y$ range [54, 32]. It is clear from Fig. 2 that $B^{\rm pp}$
must extend beyond the acceptance of the measurement reported in this paper.
This suggests that pp pairs have rather wide balance functions that might
result from early $\rm B\overline{B}$ pair separation. Detailed models of $\rm
B\overline{B}$ production and transport that account for (strong) decays from
resonant states are required, evidently, to firmly establish this conclusion.

Figure 4 shows that the $\sigma_{\Delta\varphi}$ widths of the nine BFs
exhibit narrowing trends from peripheral to central collisions. The widths
$\sigma_{\Delta\varphi}$ feature a wide spread of values at a given collision
centrality, with those of ${\rm KK}$ pairs being the largest and those of
${\rm\pi K}$ the smallest. The widths also exhibit similar reductions with
increasing collision centrality. These observations are in agreement with
azimuthal BFs already reported from observations at RHIC for unidentified
charged particle and identified $\pi\pi$, $\rm KK$ pairs [25, 26], as well as
unidentified charged particle BFs in collisions at the LHC [28, 29]. This
narrowing is qualitatively understood as resulting from the larger estimated
transverse expansion velocity present in more central AA collisions [60]. It
competes with an opposing trend associated with light quark diffusivity,
expected to broaden and smear out the long range tails of the $\Delta\varphi$
BFs for systems featuring increasingly large lifespans [39]. Given the radial
boost profile and contributions from resonance decays can be largely
calibrated based on the shape of single particle $p_{\rm T}$ spectra, the BF
projections presented in Fig. 2, 3 and the evolution of their widths
$\sigma_{\Delta y}$ and $\sigma_{\Delta\varphi}$, shown in Fig. 4, then
provide the first comprehensive set of azimuthal BFs to estimate the
diffusivity of light quarks at the LHC [39, 36].

Contributions of $\phi\rightarrow{\rm K}^{+}+{\rm K}^{-}$ decays to $B^{\rm
KK}$ were studied using simulated events from the HIJING generator [51]. The
amplitude of the near-side peak of $B^{\rm KK}$ is reduced by about 30% when
contributions from $\phi$-meson decays are explicitly excluded, while the
correlator $\Delta y$ and $\Delta\varphi$ widths increase by about 7–8%.
Effects associated with radial flow, not present in HIJING, could reduce this
broadening effect and possibly induce a narrowing of the $\Delta y$ width of
$B^{\rm KK}$ in more central collisions. However, no such narrowing is
observed thereby signaling a more intricate production and transport evolution
with competing contributions from $\phi$ produced at hadronization of the QGP
and by coalescence of kaons within a hadron phase.

The evolution of the collision centrality of the integrals
$I_{B}^{\alpha\beta}$ of the nine species-pairs $B^{\alpha\beta}(\Delta
y,\Delta\varphi)$ shown in the right panel of Fig. 4 is also of considerable
interest. By definition, a balance function $B^{\alpha\beta}(\Delta
y,\Delta\varphi,\Delta p_{\rm T})$ measures the “likelihood" of finding a
charge balancing particle of a type $\beta$, e.g., $\pi^{+}$, with a pair
separation $\Delta y$, $\Delta\varphi$, $\Delta p_{\rm T}$ away from a
reference particle of type $\alpha$, e.g., $\pi^{-}$. But charge balancing can
be accomplished, on average, by distinct species, e.g., $\rm p$, $\rm K^{+}$,
and more rarely produced heavier particles, in additions to $\pi^{+}$. The
integral, $I^{\alpha\beta}_{B}(4\pi)$, of $B^{\alpha\beta}(\Delta
y,\Delta\varphi,\Delta p_{\rm T})$ over the full phase space is thus
proportional to the average fraction (and probability in the full phase space
limit) of balancing partners of species $\beta$. Indeed, neglecting
contributions from species other than pions, kaons, and protons, one expects
the sum, $I^{\alpha}_{B}(4\pi)\equiv I^{\alpha\pi}_{B}(4\pi)+I^{\alpha\rm
K}_{B}(4\pi)+I^{\alpha\rm p}_{B}(4\pi)$ to converge to unity,
$I^{\alpha}_{B}(4\pi)\approx 1$, in the full acceptance limit [43]. Integrals
$I^{\alpha\beta}_{B}(4\pi)$ thus amount to probabilities
$I^{\alpha\beta}_{B}(4\pi)/I^{\alpha\pi}_{B}(4\pi)$ of having charge balancing
of a species $\alpha$ by a species of type $\beta$ and are indicators of the
hadronization chemistry of the QGP, that is, what fraction of species $\alpha$
are accompanied (balanced), on average, by a species $\beta$ [43]. However,
when measured in a limited acceptance, integrals
$I^{\alpha\beta}_{B}(\Omega<4\pi)$ cannot, strictly speaking, be considered
charge balancing probabilities. They nonetheless provide useful indicators of
the hadrochemistry as well as the flavour and baryon number transport in AA
collisions. As such, integrals $I^{\alpha\beta}_{B}$ shown in Fig. 4 as a
function of collision centrality are surprising on two accounts. First, they
show that the balance fractions are all, but one, approximately independent of
collision centrality. The notable exception is the $\pi\pi$ integral which
increases by about 20% from peripheral to central collisions. Second, close
examination of these pairing fractions show they are rather different than
inclusive probabilities of observing $\pi$, ${\rm K}$, and ${\rm
p/\overline{p}}$ in Pb–Pb collisions. For instance, $I_{\rm B}^{{\rm K}\pi}$
is not larger than $I_{\rm B}^{\rm KK}$ by the $\pi/{\rm K}\sim 6.7$ ratio of
inclusive single particle yields and $I_{\rm B}^{\rm pp}$ is larger than
$I_{\rm B}^{\rm pK}$ also in contrast to observed ${\rm K/p}\sim 3$ yield
ratios [22]. Hadron species charge balancing pairing fractions are thus indeed
very different than the relative probabilities of single hadrons, and as such,
provide new and useful information to further probe the hadronization of the
QGP. This difference should not be too much of a surprise given the set of
processes $\mathcal{P}_{2}$ that lead to a specific balancing pair
$\alpha\beta$ (e.g., $\mathcal{P}_{2}:\rightarrow\alpha^{\pm}+\beta^{\mp}+X$)
is, by construction, far smaller than the set of processes $\mathcal{P}_{1}$
leading to a given particle species $\alpha$ or $\beta$ (e.g.,
$\mathcal{P}_{1}:\rightarrow\alpha^{\pm}+X$ or
$\mathcal{P}_{1}:\rightarrow\beta^{\mp}+Y$). It is remarkable, nonetheless,
that the pairing fractions $I_{\rm B}^{\alpha\beta}$ exhibit essentially no
collision centrality dependence while single particle yield ratios are known
to exhibit a weak dependence on collision centrality [61, 9]. Note that the
observed rise of $I_{\rm B}^{\pi\pi}$ in more central collisions may
artificially result from increased kinematic focusing of pions with centrality
in the $p_{\rm T}$ and $\Delta y$ acceptance of this measurement. The higher
velocity flow fields encountered in more central Pb–Pb collisions could indeed
shift and focus the yield of associated pions. Why such a shift is not as
important for other charge balancing pairs remains to be elucidated with a
comprehensive model accounting for the flow velocity profile and appropriate
sets of charge conserving processes yielding balancing charges in the final
state of collisions. Recent deployments of hydrodynamic models feature the
former but lack the latter [62, 63, 64]. Further theoretical work is thus
required to interpret the observed collision centrality dependence of the
pairing probabilities displayed in Fig. 4. As such calculations become
available, the data reported in this work, and specifically the integral
$I^{\alpha\beta}_{B}$ shown in Fig. 4, shall provide increased sensitivity to
the hadrochemistry of the QGP and its susceptibilities.

In summary, this paper presents the first measurements of the collision
centrality evolution of same and cross-species balance functions of identified
$\pi^{\pm}$, ${\rm K}^{\pm}$ and $\rm p/\overline{p}$ at the LHC. Measured as
functions of particle pair separation in rapidity ($\Delta y$) and azimuth
($\Delta\varphi$), the BFs exhibit prominent near-side peaks centered at
$(\Delta y,\Delta\varphi)=(0,0)$ which feature different shapes, amplitudes,
and widths, and varied dependencies on collision centrality. The BFs of
species-pairs measured in this work feature narrowing $\Delta\varphi$ widths
in more central collisions, owing to the strong radial flow field present in
central Pb–Pb collisions. Theoretical studies beyond the scope of this work
shall use this data to put upper limits on the diffusivity coefficients of
light quarks. In the longitudinal direction, the $\sigma$ widths of BFs of all
species pairs decrease with centrality except for those of ${\rm KK}$ and
${\rm pp}$ pairs. The shape and width of ${\rm KK}$ BFs are independent of
collision centrality, while the ${\rm pp}$ BFs peak shapes depend only
minimally on centrality. The observed centrality independence of the ${\rm
KK}$ and narrowing $\sigma$ of other species in the longitudinal direction are
qualitatively consistent with effects associated with radial flow and the two-
stage quark production scenario, which posits that quark production occurs
predominantly in early and late stages separated by a period of isentropic
expansion. Integrals $I^{\alpha\beta}_{B}$ constitute an important finding of
this study as they indicate that pairing fractions $I^{\alpha\beta}_{B}$ are
nearly independent of collision centrality, and provide a valuable
quantitative characterization of the hadronization of the QGP.

## 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) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT)of Applied Science (IIST), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharya142, D. Adamová97, A. Adler75, J. Adolfsson82, G. Aglieri Rinella34,
M. Agnello30, N. Agrawal54, Z. Ahammed142, S. Ahmad16, S.U. Ahn77, I. Ahuja38,
Z. Akbar51, A. Akindinov94, M. Al-Turany109, S.N. Alam16, D. Aleksandrov90, B.
Alessandro60, H.M. Alfanda7, R. Alfaro Molina72, B. Ali16, Y. Ali14, A.
Alici25, N. Alizadehvandchali126, A. Alkin34, J. Alme21, T. Alt69, I.
Altsybeev114, M.N. Anaam7, C. Andrei48, D. Andreou92, A. Andronic145, M.
Angeletti34, V. Anguelov106, F. Antinori57, P. Antonioli54, C. Anuj16, N.
Apadula81, L. Aphecetche116, H. Appelshäuser69, S. Arcelli25, R. Arnaldi60,
I.C. Arsene20, M. Arslandok147, A. Augustinus34, R. Averbeck109, S. Aziz79,
M.D. Azmi16, A. Badalà56, Y.W. Baek41, X. Bai130,109, R. Bailhache69, Y.
Bailung50, R. Bala103, A. Balbino30, A. Baldisseri139, B. Balis2, D.
Banerjee4, R. Barbera26, L. Barioglio107, M. Barlou86, G.G. Barnaföldi146,
L.S. Barnby96, V. Barret136, C. Bartels129, K. Barth34, E. Bartsch69, F.
Baruffaldi27, N. Bastid136, S. Basu82, G. Batigne116, B. Batyunya76, D.
Bauri49, J.L. Bazo Alba113, I.G. Bearden91, C. Beattie147, I. Belikov138,
A.D.C. Bell Hechavarria145, F. Bellini25, R. Bellwied126, S. Belokurova114, V.
Belyaev95, G. Bencedi146,70, S. Beole24, A. Bercuci48, Y. Berdnikov100, A.
Berdnikova106, L. Bergmann106, M.G. Besoiu68, L. Betev34, P.P. Bhaduri142, A.
Bhasin103, I.R. Bhat103, M.A. Bhat4, B. Bhattacharjee42, P. Bhattacharya22, L.
Bianchi24, N. Bianchi52, J. Bielčík37, J. Bielčíková97, J. Biernat119, A.
Bilandzic107, G. Biro146, S. Biswas4, J.T. Blair120, D. Blau90,83, M.B.
Blidaru109, C. Blume69, G. Boca28,58, F. Bock98, A. Bogdanov95, S. Boi22, J.
Bok62, L. Boldizsár146, A. Bolozdynya95, M. Bombara38, P.M. Bond34, G.
Bonomi141,58, H. Borel139, A. Borissov83, H. Bossi147, E. Botta24, L.
Bratrud69, P. Braun-Munzinger109, M. Bregant122, M. Broz37, G.E. Bruno108,33,
M.D. Buckland129, D. Budnikov110, H. Buesching69, S. Bufalino30, O. Bugnon116,
P. Buhler115, Z. Buthelezi73,133, J.B. Butt14, A. Bylinkin128, S.A. Bysiak119,
M. Cai27,7, H. Caines147, A. Caliva109, E. Calvo Villar113, J.M.M. Camacho121,
R.S. Camacho45, P. Camerini23, F.D.M. Canedo122, F. Carnesecchi34,25, R.
Caron139, J. Castillo Castellanos139, E.A.R. Casula22, F. Catalano30, C.
Ceballos Sanchez76, P. Chakraborty49, S. Chandra142, S. Chapeland34, M.
Chartier129, S. Chattopadhyay142, S. Chattopadhyay111, A. Chauvin22, T.G.
Chavez45, T. Cheng7, C. Cheshkov137, B. Cheynis137, V. Chibante Barroso34,
D.D. Chinellato123, S. Cho62, P. Chochula34, P. Christakoglou92, C.H.
Christensen91, P. Christiansen82, T. Chujo135, C. Cicalo55, L. Cifarelli25, F.
Cindolo54, M.R. Ciupek109, G. ClaiII,54, J. CleymansI,125, F. Colamaria53,
J.S. Colburn112, D. Colella53,108,33, A. Collu81, M. Colocci34, M.
ConcasIII,60, G. Conesa Balbastre80, Z. Conesa del Valle79, G. Contin23, J.G.
Contreras37, M.L. Coquet139, T.M. Cormier98, P. Cortese31, M.R. Cosentino124,
F. Costa34, S. Costanza28,58, P. Crochet136, R. Cruz-Torres81, E. Cuautle70,
P. Cui7, L. Cunqueiro98, A. Dainese57, M.C. Danisch106, A. Danu68, P. Das88,
P. Das4, S. Das4, S. Dash49, A. De Caro29, G. de Cataldo53, L. De Cilladi24,
J. de Cuveland39, A. De Falco22, D. De Gruttola29, N. De Marco60, C. De
Martin23, S. De Pasquale29, S. Deb50, H.F. Degenhardt122, K.R. Deja143, L.
Dello Stritto29, W. Deng7, P. Dhankher19, D. Di Bari33, A. Di Mauro34, R.A.
Diaz8, T. Dietel125, Y. Ding137,7, R. Divià34, D.U. Dixit19, Ø. Djuvsland21,
U. Dmitrieva64, J. Do62, A. Dobrin68, B. Dönigus69, A.K. Dubey142, A.
Dubla109,92, S. Dudi102, M. Dukhishyam88, P. Dupieux136, N. Dzalaiova13, T.M.
Eder145, R.J. Ehlers98, V.N. Eikeland21, F. Eisenhut69, D. Elia53, B.
Erazmus116, F. Ercolessi25, F. Erhardt101, A. Erokhin114, M.R. Ersdal21, B.
Espagnon79, G. Eulisse34, D. Evans112, S. Evdokimov93, L. Fabbietti107, M.
Faggin27, J. Faivre80, F. Fan7, A. Fantoni52, M. Fasel98, P. Fecchio30, A.
Feliciello60, G. Feofilov114, A. Fernández Téllez45, A. Ferrero139, A.
Ferretti24, V.J.G. Feuillard106, J. Figiel119, S. Filchagin110, D. Finogeev64,
F.M. Fionda55,21, G. Fiorenza34,108, F. Flor126, A.N. Flores120, S.
Foertsch73, S. Fokin90, E. Fragiacomo61, E. Frajna146, U. Fuchs34, N.
Funicello29, C. Furget80, A. Furs64, J.J. Gaardhøje91, M. Gagliardi24, A.M.
Gago113, A. Gal138, C.D. Galvan121, P. Ganoti86, C. Garabatos109, J.R.A.
Garcia45, E. Garcia-Solis10, K. Garg116, C. Gargiulo34, A. Garibli89, K.
Garner145, P. Gasik109, E.F. Gauger120, A. Gautam128, M.B. Gay Ducati71, M.
Germain116, P. Ghosh142, S.K. Ghosh4, M. Giacalone25, P. Gianotti52, P.
Giubellino109,60, P. Giubilato27, A.M.C. Glaenzer139, P. Glässel106, D.J.Q.
Goh84, V. Gonzalez144, L.H. González-Trueba72, S. Gorbunov39, M. Gorgon2, L.
Görlich119, S. Gotovac35, V. Grabski72, L.K. Graczykowski143, L. Greiner81, A.
Grelli63, C. Grigoras34, V. Grigoriev95, S. Grigoryan76,1, F. Grosa34,60, J.F.
Grosse-Oetringhaus34, R. Grosso109, G.G. Guardiano123, R. Guernane80, M.
Guilbaud116, K. Gulbrandsen91, T. Gunji134, W. Guo7, A. Gupta103, R. Gupta103,
S.P. Guzman45, L. Gyulai146, M.K. Habib109, C. Hadjidakis79, H. Hamagaki84, M.
Hamid7, R. Hannigan120, M.R. Haque143, A. Harlenderova109, J.W. Harris147, A.
Harton10, J.A. Hasenbichler34, H. Hassan98, D. Hatzifotiadou54, P. Hauer43,
L.B. Havener147, S.T. Heckel107, E. Hellbär109, H. Helstrup36, T. Herman37,
E.G. Hernandez45, G. Herrera Corral9, F. Herrmann145, K.F. Hetland36, H.
Hillemanns34, C. Hills129, B. Hippolyte138, B. Hofman63, B. Hohlweger92, J.
Honermann145, G.H. Hong148, D. Horak37, S. Hornung109, A. Horzyk2, R.
Hosokawa15, Y. Hou7, P. Hristov34, C. Hughes132, P. Huhn69, L.M. Huhta127,
C.V. Hulse79, T.J. Humanic99, H. Hushnud111, L.A. Husova145, A. Hutson126, D.
Hutter39, J.P. Iddon34,129, R. Ilkaev110, H. Ilyas14, M. Inaba135, G.M.
Innocenti34, M. Ippolitov90, A. Isakov97, T. Isidori128, M.S. Islam111, M.
Ivanov109, V. Ivanov100, V. Izucheev93, M. Jablonski2, B. Jacak81, N.
Jacazio34, P.M. Jacobs81, S. Jadlovska118, J. Jadlovsky118, S. Jaelani63, C.
Jahnke123,122, M.J. Jakubowska143, A. Jalotra103, M.A. Janik143, T. Janson75,
M. Jercic101, O. Jevons112, A.A.P. Jimenez70, F. Jonas98,145, P.G. Jones112,
J.M. Jowett 34,109, J. Jung69, M. Jung69, A. Junique34, A. Jusko112, J.
Kaewjai117, P. Kalinak65, A.S. Kalteyer109, A. Kalweit34, V. Kaplin95, A.
Karasu Uysal78, D. Karatovic101, O. Karavichev64, T. Karavicheva64, P.
Karczmarczyk143, E. Karpechev64, V. Kashyap88, A. Kazantsev90, U. Kebschull75,
R. Keidel47, D.L.D. Keijdener63, M. Keil34, B. Ketzer43, Z. Khabanova92, A.M.
Khan7, S. Khan16, A. Khanzadeev100, Y. Kharlov93,83, A. Khatun16, A.
Khuntia119, B. Kileng36, B. Kim17,62, C. Kim17, D.J. Kim127, E.J. Kim74, J.
Kim148, J.S. Kim41, J. Kim106, J. Kim74, M. Kim106, S. Kim18, T. Kim148, S.
Kirsch69, I. Kisel39, S. Kiselev94, A. Kisiel143, J.P. Kitowski2, J.L. Klay6,
J. Klein34, S. Klein81, C. Klein-Bösing145, M. Kleiner69, T. Klemenz107, A.
Kluge34, A.G. Knospe126, C. Kobdaj117, M.K. Köhler106, T. Kollegger109, A.
Kondratyev76, N. Kondratyeva95, E. Kondratyuk93, J. Konig69, S.A.
Konigstorfer107, P.J. Konopka34, G. Kornakov143, S.D. Koryciak2, A.
Kotliarov97, O. Kovalenko87, V. Kovalenko114, M. Kowalski119, I. Králik65, A.
Kravčáková38, L. Kreis109, M. Krivda112,65, F. Krizek97, K. Krizkova
Gajdosova37, M. Kroesen106, M. Krüger69, E. Kryshen100, M. Krzewicki39, V.
Kučera34, C. Kuhn138, P.G. Kuijer92, T. Kumaoka135, D. Kumar142, L. Kumar102,
N. Kumar102, S. Kundu34, P. Kurashvili87, A. Kurepin64, A.B. Kurepin64, A.
Kuryakin110, S. Kushpil97, J. Kvapil112, M.J. Kweon62, J.Y. Kwon62, Y.
Kwon148, S.L. La Pointe39, P. La Rocca26, Y.S. Lai81, A. Lakrathok117, M.
Lamanna34, R. Langoy131, K. Lapidus34, P. Larionov34,52, E. Laudi34, L.
Lautner34,107, R. Lavicka115,37, T. Lazareva114, R. Lea141,23,58, J.
Lehrbach39, R.C. Lemmon96, I. León Monzón121, E.D. Lesser19, M.
Lettrich34,107, P. Lévai146, X. Li11, X.L. Li7, J. Lien131, R. Lietava112, B.
Lim17, S.H. Lim17, V. Lindenstruth39, A. Lindner48, C. Lippmann109, A. Liu19,
D.H. Liu7, J. Liu129, I.M. Lofnes21, V. Loginov95, C. Loizides98, P. Loncar35,
J.A. Lopez106, X. Lopez136, E. López Torres8, J.R. Luhder145, M. Lunardon27,
G. Luparello61, Y.G. Ma40, A. Maevskaya64, M. Mager34, T. Mahmoud43, A.
Maire138, M. Malaev100, N.M. Malik103, Q.W. Malik20, S.K. Malik103, L.
MalininaIV,76, D. Mal’Kevich94, N. Mallick50, G. Mandaglio32,56, V. Manko90,
F. Manso136, V. Manzari53, Y. Mao7, G.V. Margagliotti23, A. Margotti54, A.
Marín109, C. Markert120, M. Marquard69, N.A. Martin106, P. Martinengo34, J.L.
Martinez126, M.I. Martínez45, G. Martínez García116, S. Masciocchi109, M.
Masera24, A. Masoni55, L. Massacrier79, A. Mastroserio140,53, A.M. Mathis107,
O. Matonoha82, P.F.T. Matuoka122, A. Matyja119, C. Mayer119, A.L. Mazuecos34,
F. Mazzaschi24, M. Mazzilli34, M.A. MazzoniI,59, J.E. Mdhluli133, A.F.
Mechler69, Y. Melikyan64, A. Menchaca-Rocha72, E. Meninno115,29, A.S.
Menon126, M. Meres13, S. Mhlanga125,73, Y. Miake135, L. Micheletti60, L.C.
Migliorin137, D.L. Mihaylov107, K. Mikhaylov76,94, A.N. Mishra146, D.
Miśkowiec109, A. Modak4, A.P. Mohanty63, B. Mohanty88, M. Mohisin KhanV,16,
M.A. Molander44, Z. Moravcova91, C. Mordasini107, D.A. Moreira De Godoy145, I.
Morozov64, A. Morsch34, T. Mrnjavac34, V. Muccifora52, E. Mudnic35, D.
Mühlheim145, S. Muhuri142, J.D. Mulligan81, A. Mulliri22, M.G. Munhoz122, R.H.
Munzer69, H. Murakami134, S. Murray125, L. Musa34, J. Musinsky65, J.W.
Myrcha143, B. Naik133,49, R. Nair87, B.K. Nandi49, R. Nania54, E. Nappi53,
A.F. Nassirpour82, A. Nath106, C. Nattrass132, T.K. Nayak88, A. Neagu20, L.
Nellen70, S.V. Nesbo36, G. Neskovic39, D. Nesterov114, B.S. Nielsen91, S.
Nikolaev90, S. Nikulin90, V. Nikulin100, F. Noferini54, S. Noh12, P.
Nomokonov76, J. Norman129, N. Novitzky135, P. Nowakowski143, A. Nyanin90, J.
Nystrand21, M. Ogino84, A. Ohlson82, V.A. Okorokov95, J. Oleniacz143, A.C.
Oliveira Da Silva132, M.H. Oliver147, A. Onnerstad127, C. Oppedisano60, A.
Ortiz Velasquez70, T. Osako46, A. Oskarsson82, J. Otwinowski119, M. Oya46, K.
Oyama84, Y. Pachmayer106, S. Padhan49, D. Pagano141,58, G. Paić70, A.
Palasciano53, J. Pan144, S. Panebianco139, J. Park62, J.E. Parkkila127, S.P.
Pathak126, R.N. Patra103,34, B. Paul22, H. Pei7, T. Peitzmann63, X. Peng7,
L.G. Pereira71, H. Pereira Da Costa139, D. Peresunko90,83, G.M. Perez8, S.
Perrin139, Y. Pestov5, V. Petráček37, M. Petrovici48, R.P. Pezzi116,71, S.
Piano61, M. Pikna13, P. Pillot116, O. Pinazza54,34, L. Pinsky126, C. Pinto26,
S. Pisano52, M. Płoskoń81, M. Planinic101, F. Pliquett69, M.G. Poghosyan98, B.
Polichtchouk93, S. Politano30, N. Poljak101, A. Pop48, S. Porteboeuf-
Houssais136, J. Porter81, V. Pozdniakov76, S.K. Prasad4, R. Preghenella54, F.
Prino60, C.A. Pruneau144, I. Pshenichnov64, M. Puccio34, S. Qiu92, L.
Quaglia24, R.E. Quishpe126, S. Ragoni112, A. Rakotozafindrabe139, L.
Ramello31, F. Rami138, S.A.R. Ramirez45, A.G.T. Ramos33, T.A. Rancien80, R.
Raniwala104, S. Raniwala104, S.S. Räsänen44, R. Rath50, I. Ravasenga92, K.F.
Read98,132, A.R. Redelbach39, K. RedlichVI,87, A. Rehman21, P. Reichelt69, F.
Reidt34, H.A. Reme-ness36, Z. Rescakova38, K. Reygers106, A. Riabov100, V.
Riabov100, T. Richert82, M. Richter20, W. Riegler34, F. Riggi26, C. Ristea68,
M. Rodríguez Cahuantzi45, K. Røed20, R. Rogalev93, E. Rogochaya76, T.S.
Rogoschinski69, D. Rohr34, D. Röhrich21, P.F. Rojas45, S. Rojas Torres37, P.S.
Rokita143, F. Ronchetti52, A. Rosano32,56, E.D. Rosas70, A. Rossi57, A. Roy50,
P. Roy111, S. Roy49, N. Rubini25, O.V. Rueda82, D. Ruggiano143, R. Rui23, B.
Rumyantsev76, P.G. Russek2, R. Russo92, A. Rustamov89, E. Ryabinkin90, Y.
Ryabov100, A. Rybicki119, H. Rytkonen127, W. Rzesa143, O.A.M. Saarimaki44, R.
Sadek116, S. Sadovsky93, J. Saetre21, K. Šafařík37, S.K. Saha142, S. Saha88,
B. Sahoo49, P. Sahoo49, R. Sahoo50, S. Sahoo66, D. Sahu50, P.K. Sahu66, J.
Saini142, S. Sakai135, M.P. Salvan109, S. Sambyal103, V. SamsonovI,100,95, D.
Sarkar144, N. Sarkar142, P. Sarma42, V.M. Sarti107, M.H.P. Sas147, J.
Schambach98, H.S. Scheid69, C. Schiaua48, R. Schicker106, A. Schmah106, C.
Schmidt109, H.R. Schmidt105, M.O. Schmidt34,106, M. Schmidt105, N.V.
Schmidt98,69, A.R. Schmier132, R. Schotter138, J. Schukraft34, K. Schwarz109,
K. Schweda109, G. Scioli25, E. Scomparin60, J.E. Seger15, Y. Sekiguchi134, D.
Sekihata134, I. Selyuzhenkov109,95, S. Senyukov138, J.J. Seo62, D.
Serebryakov64, L. Šerkšnytė107, A. Sevcenco68, T.J. Shaba73, A. Shabanov64, A.
Shabetai116, R. Shahoyan34, W. Shaikh111, A. Shangaraev93, A. Sharma102, H.
Sharma119, M. Sharma103, N. Sharma102, S. Sharma103, U. Sharma103, O.
Sheibani126, K. Shigaki46, M. Shimomura85, S. Shirinkin94, Q. Shou40, Y.
Sibiriak90, S. Siddhanta55, T. Siemiarczuk87, T.F. Silva122, D. Silvermyr82,
T. Simantathammakul117, G. Simonetti34, B. Singh107, R. Singh88, R. Singh103,
R. Singh50, V.K. Singh142, V. Singhal142, T. Sinha111, B. Sitar13, M. Sitta31,
T.B. Skaali20, G. Skorodumovs106, M. Slupecki44, N. Smirnov147, R.J.M.
Snellings63, C. Soncco113, J. Song126, A. Songmoolnak117, F. Soramel27, S.
Sorensen132, I. Sputowska119, J. Stachel106, I. Stan68, P.J. Steffanic132,
S.F. Stiefelmaier106, D. Stocco116, I. Storehaug20, M.M. Storetvedt36, P.
Stratmann145, C.P. Stylianidis92, A.A.P. Suaide122, C. Suire79, M. Sukhanov64,
M. Suljic34, R. Sultanov94, V. Sumberia103, S. Sumowidagdo51, S. Swain66, A.
Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi107, G. Taillepied136, J.
Takahashi123, G.J. Tambave21, S. Tang136,7, Z. Tang130, J.D. Tapia
TakakiVII,128, M. Tarhini116, M.G. Tarzila48, A. Tauro34, G. Tejeda Muñoz45,
A. Telesca34, L. Terlizzi24, C. Terrevoli126, G. Tersimonov3, S. Thakur142, D.
Thomas120, R. Tieulent137, A. Tikhonov64, A.R. Timmins126, M. Tkacik118, A.
Toia69, N. Topilskaya64, M. Toppi52, F. Torales-Acosta19, T. Tork79, A.
Trifiró32,56, S. Tripathy54,70, T. Tripathy49, S. Trogolo34,27, V. Trubnikov3,
W.H. Trzaska127, T.P. Trzcinski143, A. Tumkin110, R. Turrisi57, T.S. Tveter20,
K. Ullaland21, A. Uras137, M. Urioni58,141, G.L. Usai22, M. Vala38, N.
Valle28,58, S. Vallero60, L.V.R. van Doremalen63, M. van Leeuwen92, P. Vande
Vyvre34, D. Varga146, Z. Varga146, M. Varga-Kofarago146, M. Vasileiou86, A.
Vasiliev90, O. Vázquez Doce52,107, V. Vechernin114, E. Vercellin24, S. Vergara
Limón45, L. Vermunt63, R. Vértesi146, M. Verweij63, L. Vickovic35, Z.
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Zardoshti34, A. Zarochentsev114, P. Závada67, N. Zaviyalov110, M. Zhalov100,
B. Zhang7, S. Zhang40, X. Zhang7, Y. Zhang130, V. Zherebchevskii114, Y. Zhi11,
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Zurlo141,58

## Affiliation notes

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

## Collaboration Institutes

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