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2020 126 8 July

Pion–kaon femtoscopy in Pb$-$Pb collisions at $\mathbf{\sqrt{{\textit{s}}_{\rm
NN}}}=2.76$ TeV

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

In this paper, the first femtoscopic analysis of pion–kaon correlations at the
LHC is reported. The analysis was performed on the Pb–Pb collision data at
$\mathbf{\sqrt{{\textit{s}}_{\rm NN}}}=2.76$ TeV recorded with the ALICE
detector. The non-identical particle correlations probe the spatio-temporal
separation between sources of different particle species as well as the
average source size of the emitting system. The sizes of the pion and kaon
sources increase with centrality, and pions are emitted closer to the centre
of the system and/or later than kaons. This is naturally expected in a system
with strong radial flow and is qualitatively reproduced by hydrodynamic
models. ALICE data on pion–kaon emission asymmetry are consistent with
(3+1)-dimensional viscous hydrodynamics coupled to a statistical hadronisation
model, resonance propagation, and decay code THERMINATOR 2 calculation, with
an additional time delay between 1 and 2 fm$/c$ for kaons. The delay can be
interpreted as evidence for a significant hadronic rescattering phase in
heavy-ion collisions at the LHC.

##  1 Introduction

The main goal of the heavy-ion programme at the Large Hadron Collider (LHC) is
to study the deconfined state of strongly interacting matter. This state,
where the relevant degrees of freedom are quarks and gluons, is called the
quark-gluon plasma (QGP). Experimental results from RHIC suggest that the QGP
behaves as a fluid with small specific viscosity [1, 2, 3, 4]. The
characteristics in momentum space can be accessed from radial and elliptic
flow, transverse momentum spectra or from event-by-event fluctuations. The
space-time structure, relevant for the size and pressure gradients of the
system, can be accessed using two-particle correlations.

Non-identical particle correlations are sensitive to the relative space-time
emission shifts of different particle species [5, 6, 7]. The difference
between mean emission space-time coordinates of two particle species at
freeze-out is called emission asymmetry. It occurs as a consequence of the
collective expansion of the system, the presence of short-lived resonances
decaying into the considered particles, the radial flow of these resonances,
and the possibility of having additional rescattering between the chemical and
kinetic boundaries of the evolution of the system [7]. Measurements of
correlations of non-identical particles in low-energy heavy-ion collisions
allowed one to establish an emission time ordering of the nuclear fragments
[8, 9]. In relativistic heavy-ion collisions they provided independent
evidence of collective transverse expansion in Au–Au collisions at
$\sqrt{s_{\rm NN}}=130$ GeV at the Relativistic Heavy Ion Collider (RHIC)
[10].

The Hanbury Brown and Twiss (HBT) [11, 12, 13, 14, 15, 16] pion correlation
radii are a measure of the source size of pions of a given momentum. Together
with measurements of the elliptic flow and the transverse momentum spectra of
identified particles they have been fundamental in identifying the relevant
stages of ultra-relativistic heavy-ion collisions and their properties [17].
Furthermore, a recent measurement of the kaon femtoscopic radii in Pb–Pb
collisions [18] showed that (when compared for the same event centrality and
pair $m_{\rm T}$) they are systematically larger than the ones from pions and
those predicted by models based on a hydrodynamic evolution coupled to
statistical hadronisation. Only after including the hadronic rescattering
phase could the model [19] reproduce the data for pions and kaons
simultaneously. The mean emission time of kaons (11.6 fm$/c$) and of pions
(9.5 fm$/c$) were reported [18]. The difference is attributed to the
rescattering through the K∗ resonance.

Particle yields and spectra add further support to models which include the
formation of a dense hadronic phase in the final stages of the evolution of
the fireball created in heavy-ion collisions. The suppression or the
enhancement of the yield (with respect to pp collisions) of short-lived
resonances due to rescattering (suppression) or regeneration (enhancement) in
the hadronic phase has been proposed as an observable for the estimation of
the lifetime and properties of the hadronic phase [20, 21, 22]. The
measurements of several resonances, from the very short-lived $\uprho$ meson
($\tau=1.4$ fm$/c$), K∗ ($\tau=4$ fm$/c$), $\Lambda(1520)$ ($\tau=10$ fm$/c$)
to longer-lived $\upphi$ ($\tau=46$ fm$/c$), demonstrate strong suppression of
short-lived resonances in central collisions [23, 24, 25]. The observed
suppression can result from a long-lasting hadronic rescattering phase.

Recently, pion–kaon correlations were studied theoretically with a (3+1)
viscous hydrodynamic model [26], coupled to the statistical hadronisation,
resonance decay, and propagation code THERMINATOR 2 [28]. The model uses a
parameterisation of the equation of state interpolating between the lattice
results [27] for high temperatures and the hadron gas equation of state at low
temperatures. The hadronisation occurs via the Cooper-Frye formalism without
distinction between chemical and kinetic freeze-out. No further interactions
between the hadrons are considered, however, the emission time of each species
can be delayed by hand, mimicking the effect of rescattering. The femtoscopic
emission asymmetry was shown to be highly sensitive to this delay. Moreover,
it can be decoupled from other mechanisms like flow or resonance contributions
present at freeze-out, including the K∗ resonance [28]. This approach has been
explored for pion–kaon pairs. Detailed predictions for different emission
scenarios for the pion–kaon radii and their emission asymmetry as a function
of the source volume have been made for Pb–Pb collisions at $\sqrt{s_{\rm
NN}}$ = 2.76 TeV in [28].

In this work $\rm\uppi^{+}K^{+}$, $\rm\uppi^{-}K^{+}$, $\rm\uppi^{+}K^{-}$,
and $\rm\uppi^{-}K^{-}$ momentum correlations are analysed using the
femtoscopy technique. Two methods are used to evaluate the emission asymmetry
in order to strengthen the results. The first method decomposes the
correlations into terms of one dimensional spherical harmonic (SH)
coefficients [29] while the second one is based on the Cartesian
representation of the correlation function [5]. The source size parameter
$R_{\rm out}$ and the emission asymmetry $\mu_{\rm out}$ are measured as a
function of the cube root of the average charged-particle multiplicity density
$\langle\text{d}N_{\rm ch}/\text{d}\eta\rangle^{1/3}$. Finally, the obtained
results are compared with detailed model calculations [28] assuming the
previously found delayed kaon emission [18].

##  2 Data selection

In this paper, pion–kaon correlation results obtained with Pb–Pb collisions at
$\sqrt{s_{\rm NN}}$ = 2.76 TeV are presented. This measurement used 40 million
events collected by ALICE in 2011. A detailed description of the ALICE
detector and its performance in the LHC Run 1 (2009–2013) is given in [30,
31].

Events were triggered and classified according to their centrality determined
using the measured signal amplitudes in the V0 detectors [32]. Three trigger
configurations were used: minimum bias, semi-central (10–50% collision
centrality), and central (0–10% collision centrality) [32]. The analyses were
performed in six centrality classes: (0–5%), (5–10%), (10–20%), (20–30%),
(30–40%), and (40–50%), separately for positive and negative magnetic field
polarity. The reconstructed primary vertex is required to lie within $\pm 7$
cm of the nominal interaction point along the beam axis in order to have
uniform tracking and particle identification performance.

Charged particle tracking is performed using the Time Projection Chamber (TPC)
[30, 33] and the Inner Tracking System (ITS) [30]. The ITS allows for high
spatial resolution in determining the primary collision vertex. In this
analysis, the determination of the track momenta was performed using tracks
reconstructed only from TPC signals and constrained to the primary vertex. A
TPC track segment is reconstructed from at least 70 space points (clusters)
out of a maximum of 159. The $\chi^{2}$ of the track fit, normalised to the
number of degrees of freedom, is required to be $\chi^{2}/\text{ndf}<2$. The
distances of closest approach (DCA) of a track to the primary vertex in the
transverse ($\rm DCA_{\text{xy}}$) and longitudinal ($\rm DCA_{z}$) directions
are required to be less than 2.4 cm and 3.2 cm, respectively. These selections
are imposed to reduce the contamination from secondary tracks originating from
weak decays and from interaction with the detector material. The transverse
momenta and pseudorapidities of pions and kaons were restricted to
$0.19<p_{\text{T}}<1.5$ GeV$/c$ and $|\eta|<0.8$. All selections are
summarised in Table 1.

The charged-particle tracks are identified as pions and kaons using the
combined information of their specific ionisation energy loss (d$E/\text{d}x$)
in the TPC and the time-of-flight information from the Time-Of-Flight (TOF)
detectors [34]. For each reconstructed particle, the signals from both the TPC
and the TOF (d$E/\text{d}x$ and time of flight, respectively) are compared
with the ones predicted for a pion or kaon. A value $N_{\sigma}$ is assigned
to each track denoting the number of standard deviations between the measured
track d$E$/d$x$ or time of flight and the expected one. For pions, the signal
(d$E/\text{d}x$ for $p_{\rm T}<500$ MeV$/c$, combined d$E/\text{d}x$ and time
of flight above this value) is allowed to differ from the calculation by
3$\sigma$. For kaons, five selections were used, as detailed in Table 1,
together with variations used for uncertainty estimation. The selection
criteria are optimised to obtain a high-purity sample while maximising
efficiency, especially in the regions where separating kaons from other
particle species is challenging. The purity was estimated from Monte Carlo
simulations using the HIJING [35] event generator coupled to the GEANT3 [36]
transport package and was found to be above 98% for both the pion and kaon
samples.

Table 1: Single particle selection criteria, together with particle
identification variations used for uncertainty estimation. Track selection
---
$p_{\rm T}$ |  $0.19<p_{\rm T}<1.5$ GeV/$c$
$|\eta|$ | $<0.8$
$\rm DCA_{\rm transverse}$ to primary vertex |  $<2.4$ cm
$\rm DCA_{\rm longitudinal}$ to primary vertex |  $<3.0$ cm
Kaon selection
| default | loose | strict
$N_{\sigma,\rm TPC}$ (for $p<0.4$ GeV/$c$) | $<2$ | $<2.5$ | $<2$
$N_{\sigma,\rm TPC}$ (for $0.4<p<0.45$ GeV/$c$) | $<1$ | $<2$ | $<1$
$N_{\sigma,\rm TPC}$ (for $p>0.45$ GeV/$c$) | $<3$ | $<3$ | $<2$
$N_{\sigma,\rm TOF}$ (for $0.5<p<0.8$ GeV/$c$) | $<2$ | $<3$ | $<2$
$N_{\sigma,\rm TOF}$ (for $0.8<p<1.0$ GeV/$c$) | $<1.5$ | $<2.5$ | $<1.5$
$N_{\sigma,\rm TOF}$ (for $1.0<p<1.5$ GeV/$c$) | $<1$ | $<2$ | $<1$
Pion selection
| default | loose | strict
$N_{\sigma,\rm TPC}$ (for $p<0.5$ GeV/$c$) | $<3$ | $<3$ | $<2.5$
$\sqrt{N_{\sigma,\rm TPC}^{2}+N_{\sigma,\rm TOF}^{2}}$ (for $p>0.5$ GeV/$c$) | $<3$ | $<3$ | $<2.5$

The identified tracks from each event are combined into pairs. Two-particle
detector acceptance effects, including track splitting, track merging, as well
as effects coming from $\rm\gamma\rightarrow e^{+}e^{-}$ conversion,
contribute to the measured distributions. The following selections are applied
to reduce these effects. For pairs of tracks within $|\Delta\eta|<0.1$ an
exclusion on the fraction of merged points is introduced. The merged fraction
is defined as the ratio of the number of steps of $1$ cm considered in the TPC
radius range for which the distance between the tracks is less than $3$ cm to
the total number of steps. Pairs with a merged fraction above 3% were removed.
The $\rm e^{+}e^{-}$ pairs originating from photon conversions can be
misidentified as a real pion–kaon pair and it is necessary to remove spurious
correlations arising from such pairs. These pairs are removed if their
invariant mass, assuming the electron mass for both particles, is less than
0.002 GeV$/c^{2}$, and the relative polar angle, $\Delta\theta$, between the
two tracks is less than 0.008 rad.

##  3 Correlation functions

The femtoscopic correlation function $C({\bm{k}}^{*})$, as a function of the
pion and kaon relative three-momenta
$\bm{k}^{*}=\frac{1}{2}(\bm{p}^{*}_{\uppi}-\bm{p}^{*}_{\text{K}})$ in the pair
rest frame (PRF) indicated with the asterisk, is constructed as

$C(\bm{k}^{*})=\mathcal{N}\frac{A({\bm{k}}^{*})}{B(\bm{k}^{*})},$ (1)

where $A(\bm{k}^{*})$ is the distribution constructed from the same event and
$B(\bm{k}^{*})$ is the reference distribution from particles belonging to
different events using the event mixing method [37]. The normalisation
constant $\mathcal{N}$ is used to ensure that the ratio reaches unity outside
the momentum range where the correlation function is affected by final state
interactions, i.e. $0.15<k^{*}<0.20$ GeV$/c$, where
$k^{*}=\left|{\bm{k}}^{*}\right|$. The average transverse momentum of pions
and kaons belonging to pairs with $k^{*}<40$ MeV/$c$ is $0.27$ GeV/$c$ (std.
dev. $0.07$ GeV/$c$) and $0.93$ GeV/$c$ (std. dev. $0.23$ GeV/$c$),
respectively, independent of centrality.

The first and second moments of the distribution of the spatio-temporal
separation of emission points in the PRF can be obtained from correlation
functions either in the three-dimensional Cartesian representation [5] or
using its decomposition into spherical harmonics (SH) [38, 29]. The three-
momentum and position differences can be projected onto the out-side-long
orthogonal axes, where the long axis is the beam axis, the out axis is in the
direction of the transverse pair velocity in the laboratory system, while the
side axis is perpendicular to the long and out axes [39, 40]. At midrapidity,
the emission asymmetry – displacement between pion and kaon sources – can
exist only in the out direction [28]. In this work, the emission asymmetry in
the out direction is obtained with two different methods and they are
explained hereafter.

The SH decomposition allows one to project the three-dimensional information
contained in the correlation function into a set of one-dimensional
distributions. The method applied here uses the direct decomposition of
$A(\bm{k}^{*})$ and $B(\bm{k}^{*})$ during the filling of the discrete
distributions [29]. The numerator can be written as

$A(\bm{k}^{*})=\sqrt{4\pi}\sum_{l=0}^{\infty}\sum_{m=0}^{l}A_{l}^{m}(k^{*})Y_{l}^{m}(\theta^{*},\varphi^{*}),$
(2)

where $Y_{l}^{m}(\theta^{*},\varphi^{*})$ are the spherical harmonics and
$A_{l}^{m}(k^{*})=\frac{1}{4\pi}\int_{4\pi}A(\bm{k}^{*}){Y_{l}^{m}}^{*}(\theta^{*},\varphi^{*})\text{d}\Omega^{*}$.
A similar definition is valid also for the denominator. The $l<3$ terms from
the infinite set of numerator and denominator distributions are filled for
each reconstructed pair using the corresponding
$Y_{l}^{m}(\theta^{*},\varphi^{*})$ weight for its $\theta^{*}$ and
$\varphi^{*}$ angles. From these one-dimensional distributions, the components
of the correlation function can be calculated following the method introduced
in [29].

Figure 1: The $C^{0}_{0}$ (top panel), $\Re C^{1}_{1}$ (middle panel), and
$\Im C^{1}_{1}$ (bottom panel) SH components of the charged pion–kaon
femtoscopic correlation functions for Pb–Pb collisions at $\sqrt{s_{\rm NN}}$
= 2.76 TeV in the 5–10% centrality class, positive field polarity. The
different charge combinations of pions and kaons are shown with different
colours and markers. The statistical and systematic uncertainties are shown as
vertical bars and boxes, respectively.

The femtoscopic information relevant for the emission asymmetry measurement is
contained in two one-dimensional correlation functions, $C^{0}_{0}$ and the
real part of $C^{1}_{1}$, where $C^{i}_{j}$ is defined as
$A^{i}_{j}/B^{i}_{j}$. The $C^{0}_{0}$ and $\Re C^{1}_{1}$ functions are
mostly sensitive to the source size and the emission asymmetry, respectively
[29]. Additionally, the values of $C^{0}_{1}$ (asymmetry in the long
direction) and $\Im C^{1}_{1}$ are checked for zero emission asymmetry. Their
deviations from zero may indicate track reconstruction problems in the
detector. Higher order components are small and irrelevant for this analysis.

The $C^{0}_{0}$, $\Re C^{1}_{1}$, and $\Im C^{1}_{1}$ components of the
correlation function in the SH representation are shown in Fig. 1 for the
different pairs. For like-sign pairs, the $C^{0}_{0}$ correlation goes below
unity at low $k^{*}$, reflecting the repulsive character of the mutual Coulomb
interaction. For unlike-sign pairs, the effect is opposite (see also Fig. 2).
For the $\Re C^{1}_{1}$ correlation function, the deviation from unity is
directly related to the emission asymmetry between the two particle species.
The $\Im C^{1}_{1}$ should be flat by symmetry and thus is a good check for
detector and analysis biases.

For the Cartesian representation analysis, the reconstructed pairs were
divided into two different correlation functions, namely $C_{+}({k^{*}})$ and
$C_{-}({k^{*}})$, where the sign reflects the sign of $k^{*}_{\rm out}$. These
correlation functions represent two different scenarios where the first
particle (by construction the pion) is faster or slower than the second one
(the kaon). The difference between them reflects the space-time emission
asymmetry.

It can be observed from Fig. 2 that the correlation function is not exactly
equal to unity at large values of $k^{*}$, but has some intrinsic slope mainly
due to the presence of elliptic flow, resonance decays, and due to global
conservation of energy and momentum. These background correlations have to be
subtracted before fitting the correlation functions in both the SH and
Cartesian representations. The procedure to estimate the non-femtoscopic
background is described in detail in [41], where it is shown that for
$\uppi^{\pm}K^{\pm}$ pairs the non-femtoscopic baseline can be parameterised
by a common $6^{\rm th}$ order polynomial function for all pair combinations.
The same approach is used to correct the effect of non-femtoscopic background
in the present analysis and the resulting background estimation is shown in
Fig. 2 as a solid black line for the $C_{0}^{0}$ and $\Re C_{1}^{1}$
components of pion–kaon pairs of different charge sign combinations.

Figure 2: The $C^{0}_{0}$ (top panel) and $\Re C^{1}_{1}$ (botton panel)
components of the pion–kaon correlation functions in the 5–10% centrality
class showing the non-femtoscopic background in the spherical-harmonic
representation, positive field polarity. The background fit corresponds to a
6${}^{\text{th}}$ order polynomial function common for all charge
combinations. The two structures visible in the correlation function at 0.11
GeV$/c$ and at 0.29 GeV$/c$ correspond to the remaining effect from track
merging and the K∗ resonance, respectively. The statistical and systematic
uncertainties are shown as vertical bars and boxes, respectively.

##  4 Fitting of the correlation functions

The experimental correlation functions in both representations are compared to
theoretical functions calculated with the software package CorrFit [42]. These
functions are calculated as

$C(\bm{k}^{*})=\frac{\int
S({r^{*}})|\Psi_{\uppi\text{K}}({r^{*}},\bm{k}^{*})|^{2}\text{d}^{4}{r^{*}}}{\int
S({r^{*}})\text{d}^{4}{r^{*}}},$ (3)

where the four-vector ${r^{*}}={x^{*}_{\uppi}}-{x^{*}_{\text{K}}}$ is the
space-time position difference of a pion and a kaon, $S({r^{*}})$ is the
source emission function which is the probability of emitting a pair of
particles at a given position difference. The possible dependence of the
source on $\bm{k}^{*}$ has been neglected. This approximation has been proven
for radii larger than 1–2 fm [15]. $\Psi_{\uppi\text{K}}$ is the pion–kaon
pair wave function. It accounts for the Coulomb and strong final-state
interactions (FSI), the former being dominant for the correlation effect [28].

In order to be able to compare the resulting radii to those obtained from
identical-particle femtoscopy, we parameterise the source in the
longitudinally comoving coordinate system (LCMS), defined for each pair such
that the longitudinal pair momentum vanishes. The relative two-particle source
can be expressed as

$S(\bm{r})\propto\exp\left(-\frac{[r_{\text{out}}-\mu_{\text{out}}]^{2}}{2R_{\text{out}}^{2}}-\frac{r_{\text{side}}^{2}}{2R_{\text{side}}^{2}}-\frac{r_{\text{long}}^{2}}{2R_{\text{long}}^{2}}\right),$
(4)

where $R_{\text{out}}$, $R_{\text{side}}$, and $R_{\text{long}}$ are the
femtoscopic radii in the three directions and $\mu_{\text{out}}$ is the
emission asymmetry. In order to avoid a large set of fitting parameters, the
relations $R_{\text{side}}=R_{\text{out}}$ and
$R_{\text{long}}=1.3R_{\text{out}}$ are used, which are based on measured
radii from identical pion femtoscopy from the same experimental data [16]. In
this approach only two independent parameters are needed to characterise the
correlation function for the whole system: $\mu_{\text{out}}$ and
$R_{\text{out}}$. In order to (numerically) compute the fit function
corresponding to Eq. 3, the relative positions between pions and kaons are
sampled from Eq. 4, while their momenta are sampled from the respective
experimental distributions from the same data set. The positions and momenta
are then boosted from the LCMS to the PRF. The fit value is the mean wave
function squared in the PRF.

The fitting procedure also accounts for the purity of the sample, defined as
the percentage of the properly identified primary particle pairs originating
from the 3D Gaussian profile, referred to as the “Gaussian core”. Products of
decays of long lived resonances are considered as not correlated. Following
the method proposed in [7], the values for the purity parameter depend on the
misidentification, on the secondary contamination from weak decays, and on the
percentage of pions and kaons that come from strongly decaying resonances
constituting the long-range tails in the source distribution, outside the
Gaussian core. These three purity factors are denoted as $p$, $f$, and $g$,
respectively. The pair purity (also referred to as the primary fraction) is
evaluated independently for each centrality class and magnetic field polarity
and is defined as:

$P_{\uppi^{\pm}K^{\pm}}=p_{\uppi^{\pm}}\cdot p_{{\rm K}^{\pm}}\cdot
f_{\uppi^{\pm}}\cdot f_{{\rm K}^{\pm}}\cdot g.$ (5)

All parameters except $g$ are obtained from a detailed simulation of the
detector response calculated using the HIJING Monte Carlo model with particle
transport performed by GEANT3. The $g$ values are taken from a calculation in
[7] following the methodology used in [28]. The total value of the pair purity
is 0.73 for the 0–5% centrality class and decreases smoothly to 0.61 for the
40–50% centrality class.

The experimental finite momentum resolution has been incorporated in the
fitting procedure. The ideal three-momenta of 20 000 randomly selected pairs
from analysed data per $k^{*}$ bin used in the fitting routine were smeared by
the momentum-dependent experimental momentum and angular resolutions. These
were obtained from Monte Carlo simulations using a detailed description of the
experimental set-up.

Each of the correlation functions obtained for the six event centralities,
four charge combinations, and two polarities of the electric field have been
fitted independently. The values of the radii and emission asymmetry are
obtained using a $\chi^{2}$ minimisation in the
$R_{\text{out}}-\mu_{\text{out}}$ plane. The fitting is done in the range
$0<k^{*}<0.1$ GeV$/c$ using the CorrFit package [42]. A fit example of the
$C_{0}^{0}(k^{*})$ and $\Re C_{1}^{1}(k^{*})$ parts of the correlation
function for $\uppi^{-}\text{K}^{-}$ and $\uppi^{-}\text{K}^{+}$ is shown in
Fig. 3. Note that the poor $\chi^{2}$ values reflect the residual deviations
from a Gaussian distribution, rather than an improperly performed fit. The
non-Gaussianity comes mainly from combining different pair transverse momenta,
representing three spatial dimensions in a one-dimensional correlation
function, and the presence of daughters of short-lived (up to $\omega$)
resonance decays.

Figure 3: The $C_{0}^{0}(k^{*})$ and $\Re C_{1}^{1}(k^{*})$ parts of the
correlation function for (left) $\rm\uppi^{-}K^{-}$ and (right)
$\rm\uppi^{-}K^{+}$ pairs, shown as markers for the 5–10% centrality, with the
corresponding fits calculated using the CorrFit package shown as dashed lines.
Only half of the statistics is used, corresponding to one magnetic field
(positive field polarity). The statistical and systematic uncertainties are
shown as vertical lines and boxes, respectively. Figure 4: Pion–kaon
correlation functions in the Cartesian representation for all charge
combinations. The $C_{-}$ is on the negative side of the $k^{*}$ axes while
$C_{+}$ is on the positive. The femtoscopic fits are shown as a solid black
line and were computed using the CorrFit package. The statistical and
systematic uncertainties are smaller than the markers.

The systematic uncertainties are estimated by varying the particle
identification and selection criteria, the normalisation range of the
correlation functions, the background fit range of the polynomial that is used
for estimation of non-femtoscopic contributions, the fit range, and the
momentum resolution parameters used for smearing. Values of these variations
and their individual contributions to the systematic uncertainty are
summarised in Table 2. All the systematic uncertainties are evaluated
independently for each centrality class and the maximum value is reported in
the table. The primary pair fractions are treated separately. They introduce a
significant and correlated systematic error for all centralities.

The final uncertainty is obtained combining the systematic and statistical
uncertainties using the covariance ellipses method. For each of the eight fit
results (pair combinations and magnetic field polarities) as well as for each
systematic variation, 104 points are generated following a two-dimensional
Gaussian distribution in the $R_{\text{out}}$–$\mu_{\text{out}}$ space, where
the mean and covariance are taken from the fit. The covariance ellipses are
calculated from the sample of generated points in each centrality bin. The
systematic uncertainties used for the final result are obtained using
1$\sigma$ covariance ellipses. Negligible correlation between
$R_{\text{out}}$–$\mu_{\text{out}}$ parameters is observed.

Additionally, the analysis was done in the Cartesian representation [5] using
the projected $C_{+}$ and $C_{-}$ correlation functions shown in Fig. 4. The
results of this analysis are fully compatible with those from SH within
uncertainties. However, these results are not incorporated as another source
of systematic uncertainty since the Cartesian method yields three times larger
statistical uncertainties of $\mu_{\rm out}$.

Table 2: Input parameters to CorrFit used to fit the correlation functions and variation of relevant parameters and ranges used for the evaluation of the systematic uncertainties of $R_{\text{out}}$ and $\mu_{\rm out}$. The first three uncertainty sources affect the correlation functions and are visualised in Figs. 1 and 2. The uncertainties were estimated for all the centrality ranges independently and maximum value is reported. The variation of primary pair fractions was not included in the covariance ellipse calculation and is shown separately as a correlated model-dependent systematic uncertainty indicated with a $\dagger$ symbol. Uncertainties from fits using only Coulomb interaction, indicated with symbol $\ddagger$, are not included in the final systematic uncertainty. The ranges indicated with § symbol include exclusion of 0.1–0.125 GeV/$c$ and 0.265–0.315 GeV/$c$, to account for splitting effects and $\rm K^{*}$ resonance.  Uncertainty source |  Default value |  Variations |  max $R_{\rm out}$ (%) |  max $\mu_{\rm out}$ (%)
---|---|---|---|---
PID |  Default in Table 1 |  Loose and strict in Table 1 |  3.0 |  12.0
Background fit range ($k^{*}$ in GeV/$c$) |  0.0–0.5§ |  0.0–0.265§, 0.125–0.5§ |  2.6 |  17.3
Normalisation range ($k^{*}$ in GeV/$c$) |  0.15–0.2 |  0.1–0.12, 0.18–0.21 |  3.3 |  18.0
Fit range ($k^{*}$ in GeV/$c$) |  0–0.1 |  0–0.08/0.12, 0.005–0.1 |  3.7 |  13.4
Momentum resolution |  Procedure from [30, 31] |  $+$12% |  3.6 |  10.3
Primary fraction$\dagger$ |  In Sec. 4 |  $\pm$10% |  15.0$\dagger$ |  20.0$\dagger$
Analysis type |  SH |  Cartesian coordinates |  1.6 |  3.1
$\Psi_{\uppi\text{K}}\ddagger$ |  Strong and Coulomb |  Coulomb only |  33.0$\ddagger$ |  8.7$\ddagger$
|  |  |  |

Fits to correlation functions considering only Coulomb interaction show a
systematic and centrality-dependent decrease for $R_{\text{out}}$ of the order
of 33% with a significantly increased $\chi^{2}$ of the fit. For this reason
these are not included in the evaluation of the uncertainties. However, the
effect on the asymmetry parameter, supporting the prediction made in [28], is
about 9%, in line with other variations and demonstrating the prevalence of
the Coulomb interaction for the emission asymmetry measurement.

##  5 Results

The final extracted radii, $R_{\text{out}}$, and emission asymmetry,
$\mu_{\text{out}}$, are calculated as a weighted averages between the values
obtained from the analysis of correlation functions corresponding to two
magnetic field polarities and four possible charge combinations of charged
pion–kaon pairs, using the SH representation. The obtained values are shown as
a function of $\langle$d$N_{\rm ch}/$d$\eta\rangle^{1/3}$ in Fig. 5. The
radius increases smoothly from 4 fm to 9 fm when going from the 40–50%
centrality interval to 0–5%. At the same time, the emission asymmetry evolves
from a starting value of $\mu_{\rm out}=-2.5$ fm and reaches $\mu_{\rm
out}=-4$ fm for the most central events. In the same figure, the predictions
published in [28] are shown as lines for different hypotheses of the extra
delay for kaons, starting from the default setting with no delay to a maximum
of 3.2 fm$/c$ extra emission time. This delay reduces the asymmetry produced
naturally which originates from the collective behaviour of the expanding
system created in the collisions modelled with THERMINATOR 2 [43]. The
agreement between the measured and predicted radii is good for peripheral
events but measurements are larger by 1.5 fm for the most central events. On
the other hand, the emission asymmetry measurement follows the predicted
trends for all centralities. The data points lie between the curves
corresponding to time delays of 1.0 and 2.1 fm$/c$.

Figure 5: Pion–kaon source size (upper panel) and emission asymmetry (lower
panel) for Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV as a function of
$\langle$d$N_{\rm ch}/$d$\eta\rangle^{1/3}$. The solid lines show predictions
from calculation of source size and emission asymmetry using the THERMINATOR 2
model with default and selected values of additional delay with a mean time of
$\Delta\uptau$ and width $\upsigma_{\text{t}}$ for kaons [28]. The statistical
and systematic uncertainties are combined and shown as square brackets. The
uncertainty related to the fraction of primary pairs is reported separately as
a correlated model-dependent systematic uncertainty of $\pm$15% (20%).

The model-dependent systematic errors of 15% and 20% for the radii and
asymmetry, respectively, are present also in the theoretical prediction, as
the same values for the fraction of particles within the Gaussian core are
used to obtain the radii and emission asymmetry [7]. Therefore, this
additional systematic uncertainty would synchronously move the results up and
down and the prediction lines without changing their interpretation.

##  6 Discussion

In this work the first femtoscopy analysis of pion–kaon pairs at the LHC is
presented. The collective behaviour of the matter created in Pb–Pb collisions
generates a natural asymmetry in the emission of pions and kaons due to their
different masses. This is related to the kaon emission distribution, which is
more strongly influenced by flow than pions [7]. The analysis was implemented
using the spherical harmonics and the Cartesian representation of the
femtoscopic correlation function. The non-femtoscopic background present in
the raw ratios was subtracted using a combined fit to the four possible charge
combinations. The final results are compared to state-of-the-art
hydrodynamical calculations where an additional delay for kaons was introduced
to mimic the behaviour during the hadron rescattering phase.

The radii values predicted by the theoretical calculation [28] have several
assumptions included in the particle distributions which are different from
the experiment. One of them is that the presence of the strong interaction
does not modify the emission asymmetry visible in the correlation functions.
Our analysis confirms this statement; removal of strong interaction from the
fit has significant influence on the radii (33%) but moderate influence on the
emission asymmetry (9%). Even though pions and kaons have been selected
according to ALICE acceptance and momentum ranges, the optimisation of the
purity of the data sample modified the transverse momentum distribution. This
experimental effect biases the distributions towards lower momentum values,
hence it increases the source radii.

The obtained width of the relative pion–kaon source, $R_{\text{out}}$, can be
compared to the pion and kaon source radii extracted from identical-particle
correlation analyses added in quadrature. The pion–kaon pairs used in the
current analysis are predominantly composed of soft pions ($0.2\leq
m_{\text{T}}\leq 0.3$ GeV/$c$) and hard kaons ($1.0\leq m_{\text{T}}\leq 1.3$
GeV/$c$). The pion and kaon source radii measured for these ranges of
transverse mass ($m_{\rm T}$) in 0–10% central collisions were 7–8.5 fm and
4–5 fm, respectively [18]. Added in quadrature, this yields 8–10 fm, well in
agreement with the most central pion–kaon point in Fig. 5. Similarly, for
30–50% centrality class, the pion and kaon sources are 4–4.5 fm and 2–3 fm,
respectively, and their combination yields 4.5–5.5 fm, again in reasonable
agreement with the average of two most peripheral intervals in Fig. 5.

The emission asymmetry presented here coincides with the predictions
calculated including a delay of the kaon emission of 1.0–2.1 fm$/c$. The
difference between the $\mu_{\rm out}$ values predicted in Ref. [28] and the
measured value, averaged over centrality and normalised to the total
uncertainty of our measurement, is shown in Table 3.

Table 3: Centrality-averaged difference between the $\mu_{\rm out}$ predicted using THERMINATOR with different values of the added kaon delay $\Delta\tau$ [28] and the one measured in this analysis, divided by the total uncertainty of the measurement $\sigma^{\rm exp}$. $\Delta\tau$ | $(\mu_{\rm out}^{\rm THERM}-\mu_{\rm out}^{\rm exp})/\sigma^{\rm exp}$
---|---
no delay |  $-$3.62
1.0 fm/$c$ |  $-$1.02
2.1 fm/$c$ | 2.15
3.2 fm/$c$ | 5.26
|

The values obtained for the emission asymmetry are in line with those
predicted by the hydrokinetic model [19], the broken $m_{\text{T}}$ scaling of
the radii of kaons with respect to pions observed in [18], and from the short-
lived resonances measured by ALICE [23, 24, 25]. This measurement is another
confirmation of the hadron rescattering phase.

In order to better understand the relevant effects influencing the emission
asymmetry, it would be natural to continue the studies measuring other
systems. It would be especially interesting to measure the $\uppi$p and Kp
systems and probe the validity of the relation
$\mu_{\text{out}}^{\uppi\text{p}}=\mu_{\text{out}}^{\uppi\text{K}}+\mu_{\text{out}}^{\text{Kp}}$
[7]. Final-state interactions such as the ones taking place in a long-lasting
rescattering phase might modify or distort this picture.

In summary, the first measurement of the emission asymmetry of pions and kaons
for different centralities at the LHC has been performed. $R_{\text{out}}$ was
measured to be 9 fm for central collisions and decreases as a function of
centrality to 4.5 fm for more peripheral collisions. At the same time, the
magnitude of the emission asymmetry changed from $\mu_{\rm out}=-4.5$ fm to
$\mu_{\rm out}=-2$ fm. This confirms the importance of the collective
expansion of the system with the pions emitted closer to the centre of the
collision and/or later than kaons. However, the collective motion is not
enough to reproduce the trend of the emission asymmetry which according to
state-of-the-art models based on 3+1 viscous hydrodynamics demands an
additional time delay of 1–2 fm$/c$ for kaons in order to reproduce the
measured trend. This observation is in agreement with a hydrodynamic evolution
of the expanding system and favors a stronger radial flow in central
collisions together with a dense and long-lasting hadronic rescattering phase
at the end of the evolution of the fireball at LHC energies.

## 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; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, 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 Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg95&A. Adlerorg74&J. Adolfssonorg81&M.M.
Aggarwalorg100&S. Aghaorg14&G. Aglieri Rinellaorg34&M. Agnelloorg30&N.
Agrawalorg10,org54&Z. Ahammedorg141&S. Ahmadorg16&S.U. Ahnorg76&Z.
Akbarorg51&A. Akindinovorg92&M. Al-Turanyorg107&S.N. Alamorg40&D.S.D.
Albuquerqueorg122&D. Aleksandrovorg88&B. Alessandroorg59&H.M. Alfandaorg6&R.
Alfaro Molinaorg71&B. Aliorg16&Y. Aliorg14&A. Aliciorg10,org26,org54&N.
Alizadehvandchaliorg125&A. Alkinorg2,org34&J. Almeorg21&T. Altorg68&L.
Altenkamperorg21&I. Altsybeevorg113&M.N. Anaamorg6&C. Andreiorg48&D.
Andreouorg34&A. Andronicorg144&M. Angelettiorg34&V. Anguelovorg104&T.
Antičićorg108&F. Antinoriorg57&P. Antonioliorg54&N. Apadulaorg80&L.
Aphecetcheorg115&H. Appelshäuserorg68&S. Arcelliorg26&R. Arnaldiorg59&M.
Arratiaorg80&I.C. Arseneorg20&M. Arslandokorg104&A. Augustinusorg34&R.
Averbeckorg107&S. Azizorg78&M.D. Azmiorg16&A. Badalàorg56&Y.W. Baekorg41&S.
Bagnascoorg59&X. Baiorg107&R. Bailhacheorg68&R. Balaorg101&A. Balbinoorg30&A.
Baldisseriorg137&M. Ballorg43&S. Balouzaorg105&D. Banerjeeorg3&R.
Barberaorg27&L. Barioglioorg25&G.G. Barnaföldiorg145&L.S. Barnbyorg94&V.
Barretorg134&P. Bartaliniorg6&C. Bartelsorg127&K. Barthorg34&E.
Bartschorg68&F. Baruffaldiorg28&N. Bastidorg134&S. Basuorg143&G.
Batigneorg115&B. Batyunyaorg75&D. Bauriorg49&J.L. Bazo Albaorg112&I.G.
Beardenorg89&C. Beattieorg146&C. Beddaorg63&I. Belikovorg136&A.D.C. Bell
Hechavarriaorg144&F. Belliniorg34&R. Bellwiedorg125&V. Belyaevorg93&G.
Bencediorg145&S. Beoleorg25&A. Bercuciorg48&Y. Berdnikovorg98&D.
Berenyiorg145&R.A. Bertensorg130&D. Berzanoorg59&M.G. Besoiuorg67&L.
Betevorg34&A. Bhasinorg101&I.R. Bhatorg101&M.A. Bhatorg3&H. Bhattorg49&B.
Bhattacharjeeorg42&A. Bianchiorg25&L. Bianchiorg25&N. Bianchiorg52&J.
Bielčíkorg37&J. Bielčíkováorg95&A. Bilandzicorg105&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg88&C. Blumeorg68&G.
Bocaorg139&F. Bockorg96&A. Bogdanovorg93&S. Boiorg23&J. Bokorg61&L.
Boldizsárorg145&A. Bolozdynyaorg93&M. Bombaraorg38&G. Bonomiorg140&H.
Borelorg137&A. Borissovorg93&H. Bossiorg146&E. Bottaorg25&L. Bratrudorg68&P.
Braun-Munzingerorg107&M. Bregantorg121&M. Brozorg37&E. Brunaorg59&G.E.
Brunoorg33,org106&M.D. Bucklandorg127&D. Budnikovorg109&H. Bueschingorg68&S.
Bufalinoorg30&O. Bugnonorg115&P. Buhlerorg114&P. Buncicorg34&Z.
Butheleziorg72,org131&J.B. Buttorg14&S.A. Bysiakorg118&D. Caffarriorg90&A.
Calivaorg107&E. Calvo Villarorg112&J.M.M. Camachoorg120&R.S. Camachoorg45&P.
Cameriniorg24&F.D.M. Canedoorg121&A.A. Caponorg114&F. Carnesecchiorg26&R.
Caronorg137&J. Castillo Castellanosorg137&A.J. Castroorg130&E.A.R.
Casulaorg55&F. Catalanoorg30&C. Ceballos Sanchezorg75&P. Chakrabortyorg49&S.
Chandraorg141&W. Changorg6&S. Chapelandorg34&M. Chartierorg127&S.
Chattopadhyayorg141&S. Chattopadhyayorg110&A. Chauvinorg23&C.
Cheshkovorg135&B. Cheynisorg135&V. Chibante Barrosoorg34&D.D.
Chinellatoorg122&S. Choorg61&P. Chochulaorg34&T. Chowdhuryorg134&P.
Christakoglouorg90&C.H. Christensenorg89&P. Christiansenorg81&T.
Chujoorg133&C. Cicaloorg55&L. Cifarelliorg10,org26&F. Cindoloorg54&M.R.
Ciupekorg107&G. Claiorg54orgI&J. Cleymansorg124&F. Colamariaorg53&J.S.
Colburnorg111&D. Colellaorg53&A. Colluorg80&M. Colocciorg26&M.
Concasorg59orgII&G. Conesa Balbastreorg79&Z. Conesa del Valleorg78&G.
Continorg24,org60&J.G. Contrerasorg37&T.M. Cormierorg96&Y. Corrales
Moralesorg25&P. Corteseorg31&M.R. Cosentinoorg123&F. Costaorg34&S.
Costanzaorg139&P. Crochetorg134&E. Cuautleorg69&P. Cuiorg6&L.
Cunqueiroorg96&D. Dabrowskiorg142&T. Dahmsorg105&A. Daineseorg57&F.P.A.
Damasorg115,org137&M.C. Danischorg104&A. Danuorg67&D. Dasorg110&I.
Dasorg110&P. Dasorg86&P. Dasorg3&S. Dasorg3&A. Dashorg86&S. Dashorg49&S.
Deorg86&A. De Caroorg29&G. de Cataldoorg53&L. De Cilladiorg25&J. de
Cuvelandorg39&A. De Falcoorg23&D. De Gruttolaorg10&N. De Marcoorg59&C. De
Martinorg24&S. De Pasqualeorg29&S. Deborg50&H.F. Degenhardtorg121&K.R.
Dejaorg142&A. Delofforg85&S. Delsantoorg25,org131&W. Dengorg6&P.
Dhankherorg49&D. Di Bariorg33&A. Di Mauroorg34&R.A. Diazorg8&T.
Dietelorg124&P. Dillensegerorg68&Y. Dingorg6&R. Diviàorg34&D.U. Dixitorg19&Ø.
Djuvslandorg21&U. Dmitrievaorg62&A. Dobrinorg67&B. Dönigusorg68&O.
Dordicorg20&A.K. Dubeyorg141&A. Dublaorg90,org107&S. Dudiorg100&M.
Dukhishyamorg86&P. Dupieuxorg134&R.J. Ehlersorg96&V.N. Eikelandorg21&D.
Eliaorg53&B. Erazmusorg115&F. Erhardtorg99&A. Erokhinorg113&M.R.
Ersdalorg21&B. Espagnonorg78&G. Eulisseorg34&D. Evansorg111&S.
Evdokimovorg91&L. Fabbiettiorg105&M. Fagginorg28&J. Faivreorg79&F. Fanorg6&A.
Fantoniorg52&M. Faselorg96&P. Fecchioorg30&A. Felicielloorg59&G.
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Jansonorg74&M. Jercicorg99&O. Jevonsorg111&M. Jinorg125&F.
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Martinorg104&P. Martinengoorg34&J.L. Martinezorg125&M.I. Martínezorg45&G.
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Zurloorg140&

## Affiliation notes

org*Deceased

orgIItalian National Agency for New Technologies, Energy and Sustainable
Economic Development (ENEA), Bologna, Italy

orgIIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org14COMSATS University Islamabad, Islamabad, Pakistan

org15Creighton University, Omaha, Nebraska, United States

org16Department of Physics, Aligarh Muslim University, Aligarh, India

org17Department of Physics, Pusan National University, Pusan, Republic of
Korea

org18Department of Physics, Sejong University, Seoul, Republic of Korea

org19Department of Physics, University of California, Berkeley, California,
United States

org20Department of Physics, University of Oslo, Oslo, Norway

org21Department of Physics and Technology, University of Bergen, Bergen,
Norway

org22Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org23Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

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

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

org26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

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

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

org29Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org31Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org32Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

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

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

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

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

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

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

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

org40Fudan University, Shanghai, China

org41Gangneung-Wonju National University, Gangneung, Republic of Korea

org42Gauhati University, Department of Physics, Guwahati, India

org43Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org44Helsinki Institute of Physics (HIP), Helsinki, Finland

org45High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org46Hiroshima University, Hiroshima, Japan

org47Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org48Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org49Indian Institute of Technology Bombay (IIT), Mumbai, India

org50Indian Institute of Technology Indore, Indore, India

org51Indonesian Institute of Sciences, Jakarta, Indonesia

org52INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org53INFN, Sezione di Bari, Bari, Italy

org54INFN, Sezione di Bologna, Bologna, Italy

org55INFN, Sezione di Cagliari, Cagliari, Italy

org56INFN, Sezione di Catania, Catania, Italy

org57INFN, Sezione di Padova, Padova, Italy

org58INFN, Sezione di Roma, Rome, Italy

org59INFN, Sezione di Torino, Turin, Italy

org60INFN, Sezione di Trieste, Trieste, Italy

org61Inha University, Incheon, Republic of Korea

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

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

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

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

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

org67Institute of Space Science (ISS), Bucharest, Romania

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

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

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

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

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

org73Jeonbuk National University, Jeonju, Republic of Korea

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

org79Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org80Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org81Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org82Nagasaki Institute of Applied Science, Nagasaki, Japan

org83Nara Women’s University (NWU), Nara, Japan

org84National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org85National Centre for Nuclear Research, Warsaw, Poland

org86National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org87National Nuclear Research Center, Baku, Azerbaijan

org88National Research Centre Kurchatov Institute, Moscow, Russia

org89Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org90Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org91NRC Kurchatov Institute IHEP, Protvino, Russia

org92NRC «Kurchatov»Institute - ITEP, Moscow, Russia

org93NRNU Moscow Engineering Physics Institute, Moscow, Russia

org94Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org95Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org96Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org97Ohio State University, Columbus, Ohio, United States

org98Petersburg Nuclear Physics Institute, Gatchina, Russia

org99Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org100Physics Department, Panjab University, Chandigarh, India

org101Physics Department, University of Jammu, Jammu, India

org102Physics Department, University of Rajasthan, Jaipur, India

org103Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org104Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org105Physik Department, Technische Universität München, Munich, Germany

org106Politecnico di Bari, Bari, Italy

org107Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org108Rudjer Bošković Institute, Zagreb, Croatia

org109Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org110Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org111School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org112Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org113St. Petersburg State University, St. Petersburg, Russia

org114Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org115SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org116Suranaree University of Technology, Nakhon Ratchasima, Thailand

org117Technical University of Košice, Košice, Slovakia

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Technology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

org145Wigner Research Centre for Physics, Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea