2023 181 24 August

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

Deuterons are atomic nuclei composed of a neutron and a proton held together
by the strong interaction. Unbound ensembles composed of a deuteron and a
third nucleon have been investigated in the past using scattering experiments
and they constitute a fundamental reference in nuclear physics to constrain
nuclear interactions and the properties of nuclei. In this work K+–d and p–d
femtoscopic correlations measured by the ALICE Collaboration in proton–proton
(pp) collisions at $\sqrt{s}=13$ TeV at the Large Hadron Collider (LHC) are
presented. It is demonstrated that correlations in momentum space between
deuterons and kaons or protons allow us to study three-hadron systems at
distances comparable with the proton radius. The analysis of the K+–d
correlation shows that the relative distances at which deuterons and
proton/kaons are produced are around 2 fm. The analysis of the p–d correlation
shows that only a full three-body calculation that accounts for the internal
structure of the deuteron can explain the data. In particular, the sensitivity
of the observable to the short-range part of the interaction is demonstrated.
These results indicate that correlations involving light nuclei in pp
collisions at the LHC will also provide access to any three-body systems in
the strange and charm sectors.

The study of many-body systems is a key aspect of modern nuclear physics
because of its relevance for the structure of nuclear bound states [1, 2, 3]
and for the equation of state of dense nuclear matter [4, 5]. Effects that go
beyond the simple addition of the strong interaction between pairs of nucleons
emerge already in the description of the most basic properties of light
nuclei. Realistic potentials describing nucleon–nucleon interactions [6, 7]
have therefore been complemented with phenomenological models of three-nucleon
forces [8, 9]. In calculations using potentials derived from chiral effective
field theories (EFTs) [10, 2], the many-body forces appear naturally as
subleading terms in the chiral expansion. They find contributions of the order
of 10% to the ground-state energies of $A\leq 12$ nuclei from genuine three-
body nucleon forces [11, 12], and deliver predictions for heavier and neutron-
rich nuclear structures.

In this context, two-nucleon scattering data and properties of the $A=3$
systems are still the most important ingredients to constrain the parameters
of nuclear interactions derived from EFT [13, 14, 15]. In particular,
differential scattering observables for the p–d system have allowed for the
computation of a full-fledged three-body wave function that accounts for all
the relevant two- and three-body interactions at work in the p–(pn) system for
the short and the asymptotic range [16, 17, 18]. In this work, it is
demonstrated that such a standard candle of the three-body nuclear interaction
can also be investigated by means of p–d correlations in momentum space
measured at the LHC.

Momentum correlations of deuteron with other hadron species have already been
considered as a tool to study both the deuteron production mechanism [19] and
the final-state interactions for many-body systems. Different experimental
correlations such as p–d and d–d have been measured [20, 21, 22, 23] in O–Au
reactions at E/A $=$ 25, 35, and 60 MeV and in 40Ar–58Ni reactions at 77
MeV/u. The data showed a clear signature of the strong final-state interaction
among light nuclei and nucleons, but the specific description of the process
from a many-body perspective, as well as the tools to precisely measure the
relative distances between particles, were not available at the time of those
analyses.

Deuteron–hadron momentum correlations can also be investigated at the LHC,
since light (anti)nuclei can be abundantly produced and accurately measured in
ultra-relativistic nucleus-nucleus collisions [24, 25, 26, 27, 28, 29, 30, 31,
32]. Recent femtoscopy analyses carried out by ALICE in pp, p–Pb, and Pb–Pb
collisions have demonstrated that it is possible to study the strong
interaction among several hadron pairs [33, 34, 35, 36, 37, 38, 39] given the
short distances at which hadrons can be produced in such colliding systems
[40].

In this work, by means of a comprehensive study of the K+–d and p–d
correlation functions measured in pp collisions at center-of-mass energy
$\sqrt{s}=13$ TeV with the ALICE detector at the LHC, evidence is provided
that deuterons are formed at distances of the order of 2 fm from other
hadrons. The measurement of the p–d correlation at such short distances
constitutes an innovative method to study three-body systems at the LHC, with
the potential of extending such studies to the strangeness and charm sector.
Indeed, in the strangeness sector, a similar approach as the one adopted for
standard nuclear physics is envisaged for the future by improving the database
of hypernuclei [41, 42, 43], scattering experiments [44], and femtoscopy
measurements in hadron–hadron collisions [45, 46]. Direct measurements of the
hyperon–deuteron systems at short distances would provide complementary
information to these standard methods.

## Correlation function from scattering parameters

Final-state interactions involving light nuclei such as deuterons have been
studied in the past via scattering experiments [47, 48, 49, 50, 51]. In
scattering theory, the nuclear interaction in the asymptotic regime, can be
investigated by associating a plane wave to the incoming particle and building
the outgoing wave as a superposition of spherical waves with phase shifts
$\delta_{l}$, with $l$ denoting the relative angular momentum between the
projectile and the target. The interaction determines the values of
$\delta_{l}$, and for $l=0$, referred to as $s$-wave scattering, a scattering
length $a_{0}$, is commonly used to characterize the interaction at zero
energy and can be related to the differential cross section measured in
scattering experiments. These measurements enable also the determination of
the effective range of the interaction, $d_{0}$.

Scattering experiments have been already performed for the K+–d and p–d
systems allowing for the extraction of the corresponding scattering
parameters, as reported in Table 1. In the case of K+–d , such parameters are
spin averaged and they are calculated with two different methods: i) via an
effective range fit (ER) to the cross section predictions at threshold
anchored to the available scattering data [52]; ii) from the well-known K–N
interactions [53] using the fixed-center approximation (FCA) [54]. The
negative values of the K+–d scattering length ($a_{0}$) refer to a repulsive
strong interaction. In the case of the p–d system, the parameters for the spin
doublet ($S=1/2$) and quartet ($S=3/2$) channels were obtained by using
theoretical calculations [55, 56, 57, 58, 59] and a vast collection of
scattering data [47, 48, 49, 50, 51]. The positive sign of the p–d scattering
parameters reported in Table 1 corresponds to a repulsive interaction for the
quartet state ($S=3/2$), but for the doublet state ($S=1/2$), the 3He bound
state emerges, and the standard effective range expansion has to be modified
(see Eq. 2 in [58]).

Table 1: Scattering lengths $a_{0}$ and effective ranges $d_{0}$ for the p–d and K+–d $s$-wave states. For the p–d , the two spin states (doublet and quartet) are reported. For the meson–baryon system, negative values of scattering length refer to a repulsive interaction. For the baryon–baryon system, negative and positive values of $a_{0}$ refer to attractive and repulsive interactions (for cases where the potential does not support two-body bound states), respectively. System | Spin averaged | $S=1/2$ | $S=3/2$ | References |
---|---|---|---|---|---
$a_{0}$(fm) |  $d_{0}$(fm) |  $a_{0}$(fm) |  $d_{0}$(fm) |  $a_{0}$(fm) |  $d_{0}$(fm) |
K+–d | $-0.470$ | $1.75$ | — | — | — | — | ER [52] |
$-0.540$ | $0.0$ | — | — | — | — | FCA [53, 54] |
p–d |  |  | $2.73^{+0.10}_{-0.10}$ | 2.27${}^{+0.12}_{-0.12}$ | $11.88_{+0.40}^{-0.10}$ | 2.63${}^{+0.01}_{-0.02}$ | Arvieux [55] |
|  | $1.30^{+0.20}_{-0.20}$ | — | $11.40^{+1.80}_{-1.20}$ | 2.05${}^{+0.25}_{-0.25}$ | VanOers [56] |
|  | $4.0$ | — | $11.1$ | — | Huttel [57] |
|  | $0.024$ | — | $13.8$ | — | Kievsky [58] |
|  | $-0.13^{+0.04}_{-0.04}$ | — | $14.70_{-2.30}^{+2.30}$ | — | Black [59] |

An alternative method to test the accuracy of the relative wave function in a
two-hadron system is the measurement of the correlation function among the
pairs of interest produced in hadron–hadron collisions [36]. The theoretical
correlation function can be expressed [60, 61] as $C(k^{*})\,=\,\int
d^{3}r^{*}S(r^{*})|\psi(\vec{k^{*}},\vec{r^{*}})|^{2}$, where $S(r^{*})$ is
the distribution of the distance $r^{*}$ between the emitted particles in a
hadron–hadron collision, defining the particle source;
$\psi(\vec{k^{*}},\vec{r^{*}})$ represents the wave function of the relative
motion for the pair of interest and $k^{*}$ is the reduced relative momentum
of the pair ($k^{*}\,=\,|\vec{p^{*}_{2}}-\vec{p^{*}_{1}}|/2$). The asterisk
indicates that the quantities are evaluated in the pair rest frame, where
$p^{*}_{1}=-p^{*}_{2}$. The Lednický-Lyuboshitz (LL) formalism [62, 63]
provides a simplified analytical treatment of the wave function (see Methods
for details), that can relate the correlation function to its asymptotic
behavior where the core nuclear strong interaction is not considered. The
analytical formula for the correlation function is obtained assuming a
Gaussian source distribution in $r^{*}$, and a single set of scattering
parameters. The formula is averaged over spin and isospin and only considers
$s$-waves in the scattering process.

Experimentally, the correlation function is defined as
$C(k^{*})\,=\,\xi(k^{*})\otimes\frac{N_{\mathrm{same}}(k^{*})}{N_{\mathrm{mixed}}(k^{*})}$,
where $\xi(k^{*})$ denotes the corrections for experimental effects (see
Methods for details), $N_{\mathrm{same}}(k^{*})$ is the number of detected
particle pairs in a given $k^{*}$ interval obtained by combining particles
produced in the same collision (event), which constitute a sample of
correlated pairs, and $N_{\mathrm{mixed}}(k^{*})$ is the number of
uncorrelated pairs in the same $k^{*}$ interval, obtained by combining
particles produced in different collisions (mixed events). In this work, the
interest resides in studying the final-state interaction for K+–d and p–d
pairs produced in pp collisions at $\sqrt{s}=13$ TeV. The analyzed data set
was collected using an online trigger to select high-multiplicity pp
collisions to enhance the pair sample size. Kaon ($\mbox{K}^{+}$), antikaon
($\mbox{K}^{-}$), proton (p), antiproton ($\overline{\mbox{p}}$), deuteron
(d), and antideuteron ($\overline{\mbox{d}}$) tracks are reconstructed with
the ALICE detector and their momentum in the laboratory frame $p$ is measured
in the range $p$ $\in$ $[0.2,4.1]$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. The particle
identification is carried out using measurements of the specific energy loss
in Time Projection Chamber (TPC) and time of flight (TOF detector), resulting
in samples of $\mbox{K}^{+}$($\mbox{K}^{-}$), p ($\overline{\mbox{p}}$), d
($\overline{\mbox{d}}$) with a purity of $99.8$ ($99.8$)%, $98.2$ ($97.9$)%,
and $100$ ($100$)% respectively, as estimated via Monte Carlo simulations.
Details on the experimental methods and the evaluation of the systematic
uncertainties are described in Methods. Once the kaons, protons, and deuterons
(and charge conjugates) are selected and their three-momenta measured, the
correlation functions can be built. Since it is assumed that the same
interaction governs hadron–hadron and antihadron–antihadron pairs [33], in the
following, the sum of particles and antiparticles is considered
($\mbox{K${}^{+}$--d}~{}\equiv\mbox{K${}^{+}$--d}~{}\oplus\mbox{$\mbox{K}^{-}$--$\overline{\mbox{d}}$}~{}$
and $\mbox{p--d}~{}\equiv\mbox{p--
d}~{}\oplus\mbox{$\overline{\mbox{p}}$--$\overline{\mbox{d}}$}~{}$).

r30ptt100pt

r20ptt14pt

Figure 1: Measured K+–d (left) and p–d (right) correlation functions. The data
are shown by the black symbols, the bars and the colored boxes represent the
statistical and systematic uncertainties, respectively. The square brackets
show the bin width of the measurement, while the horizontal black lines
represent the statistical uncertainty in the determination of the mean $k^{*}$
for each bin. Data are compared with theoretical correlation functions, shown
by colored bands, obtained using the LL approximation. The bandwidths
represent the uncertainties in the determination of the radius and the
residual contributions. See text for details.

Figure 1 shows the K+–d (left panel) and p–d (right panel) correlation
functions as a function of $k^{*}$ measured in pp collisions at $\sqrt{s}=13$
TeV with ALICE. Both correlation functions are below unity for values of
$k^{*}$ smaller than 200
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$, indicating an overall
repulsive interaction. The measured correlation functions are compared to
calculations performed using the LL approximation considering either only the
Coulomb interaction or, in addition, the strong interaction part determined by
the scattering parameters reported in Table 1 for the K+–d and p–d systems. In
order to compare the experimental data to the LL calculations, the source term
included in the formula of the correlation function and the feed-down
corrections due to particle decays and residual background contributions are
needed to match the experimental measurements.

The source term has been approximated as a Gaussian distribution, whose width,
defining the source size, need to be evaluated. The values of the p–d and K+–d
source sizes have been obtained from the results of independent analyses of
p–p correlations, which demonstrate the existence of a universal source for
any hadron–hadron pair in pp collisions at the LHC [40] and indicate that the
source size decreases with an increasing value of the pair transverse mass
$m_{\mathrm{T}}$ (see Methods). In addition, further modifications of the
source distribution due to strong decays of short-lived resonances decaying
into protons and kaons are taken into account. For p–d pairs an effective
source size of $r_{\text{eff}}^{\small{\mbox{p--d}~{}}}=$ $1.08\pm 0.06$ fm is
obtained. For the K+–d pairs the contribution of broad resonances with very
different decay times has been taken into account and the effective source
results in $r_{\text{eff}}^{\small{\mbox{K${}^{+}$--d}~{}}}=$
$1.35^{+0.04}_{-0.05}$ fm. Note that such small source sizes imply that the
most probable distance between particles is around 2 fm [64].

The calculated correlation functions using the LL method, shown by the colored
bands in Fig. 1 have been corrected for feed-down from weak and strong decays
and residual background contributions, using the data-driven methods described
in [33] and [65], respectively. The relative contributions from primarily
produced K+–d and p–d pairs to the corresponding inclusive sample are obtained
experimentally and are 0.92 and 0.82, respectively. The residual background
contribution is shown as the grey-colored band close to the unity. The width
of the theoretical bands stems from the uncertainty propagation of the
experimental determination of the source size, feed-down, and residual
background. Additional information on the source size and the different
contributions to the correlation function is provided in Methods.

The measured K+–d correlation function is lower than the Coulomb-only
prediction showing the presence of a repulsive strong interaction. The
calculations with the LL approximation using both sets of scattering
parameters (ER and FCA) provide an excellent description of the experimental
correlation function within uncertainties. Indeed, since both the Coulomb and
strong K+–d interactions are repulsive and there is no short-range structure
in this interaction, an asymptotic description is sufficient to describe the
data. Additionally, kaons are bosons and the proton and neutron that
constitute the deuteron are fermions, hence the LL approximation of point-like
and distinguishable particles is pertinent and the properties of the deuteron
are mapped in the K+–d scattering parameters. The agreement between the model
and the data, obtained for the small radius
($r_{\text{eff}}^{\small{\mbox{K${}^{+}$--d}~{}}}=$ $1.35^{+0.04}_{-0.05}$ fm)
that follows the same $m_{\mathrm{T}}$ scaling as all other hadron pairs,
shows that deuterons are produced at small distances with respect to other
hadrons in pp collisions at the LHC and this result provides an excellent
reference for the source term of correlations involving deuterons.

Instead, a huge discrepancy is observed when comparing the p–d data to
analogous calculations which consider protons and deuterons as distinguishable
point-like particles and employing the small source size obtained from the
$m_{\mathrm{T}}$ scaling. This can be seen by comparing the measured p–d
correlation in the right panel of Fig. 1 to the five different blue shaded
curves which are obtained using the five sets of scattering lengths reported
in Table 1.

The limitations of the LL approximation in describing in detail the p–d
interaction are several. The existence of the ${}^{3}{\rm He}$ bound state
introduces a particular short-range behavior in the doublet state due to
orthogonality requirements. Moreover, the spin structure of the quartet state
is completely symmetric implying as well a specific short-range behavior of
the corresponding spatial part to fulfill the requirements of the Pauli
principle. In addition, the correct antisymmetrization of the wave function is
not considered in the LL approximation, and such short-range features of the
interactions are not taken into account. On the other hand, the correlation
function obtained with the Coulomb-only assumption (green curve in the right
panel of Fig. 1) catches the correct amplitude of the experimental p–d
correlation function despite the sizable scattering parameters reported in
Table 1. This apparent mismatch is due to the fact that in this case, the
Coulomb repulsion between the proton and the deuteron reduces the impact of
the short-range part of the wave function in the correlation function, and the
three-fermion system is not correctly treated within the LL approximation even
if only the Coulomb interaction is considered.

## Correlation function of a three–body system

In order to correctly describe the three-body system p–(pn) the microscopic
p–d wave function must be employed in the calculation of the p–d correlation
function. The latter has been obtained by projecting the p–d wave functions on
the initial three-nucleon state created after the pp collisions. The relevant
source term in this calculation depends on an effective nucleon–nucleon source
radius $r_{\text{eff}}^{\text{NN}}$ [66, 67], since the single nucleons are
the relevant degrees of freedom. Details of the calculation are presented in
Methods and in [68].

r135ptt94pt

r135ptt84pt

Figure 2: Measured p–d correlation function plotted as a function of the p–d
relative momentum $k^{*}$ alongside theoretical calculations. The experimental
data are represented by circular symbols. The black vertical bars and orange
boxes correspond to the statistical and systematic uncertainties,
respectively. The square brackets indicate the measurement bin width and the
horizontal black lines represent the statistical uncertainty in the
determination of the mean $k^{*}$ for each bin.. The non-femtoscopic
background contributions are represented by the gray band of the cubic
baseline. Left panel: the orange and turquoise bands depict calculations
obtained using an optimized Born approximation and Coulomb +
antisymmetrization of the three-particle wave function, respectively. Right
panel: the dark red band represents a fit of the modeled correlation
calculated considering p–d as a three-body system with all relevant partial
waves. The blue-colored band corresponds to a calculation that includes only
the $s$-wave contribution. The light red band represents a calculation of the
correlation function using Pionless EFT at NLO (see text). All calculations
are multiplied by the cubic baseline, and the bandwidths of all calculations
account for uncertainties in the determination of the radius and residual
contributions. The lower panels present the difference between the measured
and calculated correlation function, expressed as the number of standard
deviations, $\text{n}_{\sigma}$, taking into account the statistical
uncertainties of the data and the model uncertainties.

Three different versions of the p–d wave function have been investigated to
study the microscopic behavior of the p–d system. First, a Born approximation
of the p–d wave function that contains the correct antisymmetrization for the
p–(pn) system but where the short-range contribution of the wave function has
been omitted. Hence, this calculation accounts only for the asymptotic part of
the wave function similar to the LL model but considers the microscopic
structure of the p–d system.

The left panel of Fig. 2 shows how the Born approximation compares to the
experimental data, including $\text{n}_{\sigma}$ values that quantify the
data-model deviation. It can be seen that this calculation is not sufficiently
accurate to reproduce the data, although the antisymmetrization is correctly
accounted for. For $k^{*}$ below 60
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$, this calculation
predicts non-physical values and therefore they are excluded from the figure.
In the same panel, the comparison to the full-fledged Coulomb-only calculation
considering the dynamics of three nucleons in the p–d system is shown as well,
indicating also a clear disagreement with the data.

The second wave function that has been tested has been obtained employing the
Hyperspherical Harmonics (HH) method [16]. It accounts for all the relevant
two- and three-body interactions at work in the p–(pn) system for the short
and the asymptotic range, it accurately describes the three-body dynamics, and
it is calculated using p–d scattering observables [16, 17, 18]. The nuclear
interaction includes the AV18 two-nucleon (NN) [6] plus the Urbana IX (UIX)
three-nucleon (NNN) [8] and the Coulomb potentials. The blue curve in the
right panel of Fig. 2 has been obtained by including the NN and NNN
interactions only in the $J^{\pi}=\frac{1}{2}^{+},\frac{3}{2}^{+}$ partial
waves relative to the p–d system, which are dominated by the $s$-wave
contributions [68]. The $\text{n}_{\sigma}$ distribution in the lower panel
shows that the calculation with even partial waves describes the data
moderately well but fails in the small relative momentum part. The agreement
improves when more partial waves up to $J^{\pi}=\frac{7}{2}^{-}$ are included
in the calculation, where the $p$-waves contribute predominantly, as it is
shown by the red curve of the right panel of Fig. 2. The full calculation has
been fitted to the experimental data allowing for a multiplicative baseline
(gray curve in Fig. 2) as a residual background. The same background has been
used for the comparison of the other calculations, and the curves’ widths
represent the propagated uncertainty of the source parameter and baseline. The
full calculation describes the experimental data very accurately, as indicated
by the $\text{n}_{\sigma}$ values for the red band remaining consistently
close to or below one across the entire range of $k^{*}$.

As an additional check, the light red band in the right panel of Fig. 2 shows
the p–d correlation function calculated in pionless effective field theory
[69] (Pionless EFT) calculation at next-to-leading order (NLO). The nuclear
interaction within this approach is much simpler than the AV18+UIX potential
[68]; the NN interaction is determined by only the $s$-wave NN scattering
lengths and effective ranges up to NLO, while the NNN interaction is fixed by
either the [3]H binding energy or the n–d $s$-wave scattering length. For the
Pionless EFT calculation, the additional uncertainty from truncating the EFT
expansion at NLO can be estimated as 10%. Taking this into account, in the
regime where the theory is applicable ($k^{*}$ below the pion mass $\sim$ 140
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$), the Pionless EFT
results are largely compatible with the HH calculation using the AV18+UIX
force.

Figure 3: Ratio of theoretical p–d correlation functions obtained with full
three-body calculations (AV18 for NN + UIX for NNN interaction) to those
obtained using an AV18 for NN interaction only for different values of the
two-nucleon effective source size $r_{\text{eff}}^{\text{NN}}$.

The fact that the experimental p–d correlation function can only be described
by a full-fledged calculation of a three-body system that considers the single
nucleons as active degrees of freedom and that the shape of the correlation
function is also sensitive to the inclusion of different partial waves in the
interaction demonstrates for the first time that deuteron–proton correlations
measured in pp collisions at the LHC access the three-nucleon system at short
distances. Indeed, past measurements of correlations involving deuterons [20,
21, 22, 23] have been interpreted by means of the LL calculation combined with
a value of the source radius larger than the one found for other hadron–hadron
pairs in the same colliding system. This misinterpretation of the data was
caused by the lack of correct microscopic calculations of the p–d system.

In order to test the sensitivity of the p–d correlation function to genuine
three-baryon interactions, the full-fledged p–d calculation has been carried
out excluding such interactions [68]. Figure 3 shows the ratio of the
calculated p–d correlation with the AV18+UIX interactions to the calculation
including only the AV18 NN interactions evaluated for different values of the
two-nucleon source size $r_{\text{eff}}^{\text{NN}}$. The current precision of
the data does not allow for testing such effects. However, this will be
possible on the larger data samples that will be collected during the LHC Run
3 (2022–2025) with the ALICE upgraded apparatus [70]. The integrated
luminosity will be increased by one order of magnitude with respect to the
dataset used in the current work [71], enabling the study of the interaction
at small distances by triggering on p–d pairs with large $m_{\text{T}}$
values. Such studies can also be extended to systems such $\Lambda/\Sigma$–d
or $\Lambda^{+}_{\textrm{c}}$–d to investigate three-baryon systems in the
strange and charm sectors which are otherwise inaccessible.

## Acknowledgements

The ALICE Collaboration is grateful to Prof. Johann Haidenbauer and Prof.
Tetsuo Hyodo for providing the derivation of the K+–d scattering parameters,
and to Stanisław Mrówczyński and Urs Wiedemann for fruitful discussions.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland; National Science Foundation, Grant No. PHY–2044632; U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under the FRIB Theory Alliance, award DE-SC0013617.

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## Methods

### Event selection

A data sample of inelastic pp collisions at $\sqrt{s}=13$ TeV was recorded
with ALICE [72, 73] at the LHC. General details on the event selection, pile-
up rejection, and the primary vertex reconstruction can be found in [74]. A
trigger that requires the total signal amplitude measured in the V0 detector
[75] to exceed a certain threshold was employed to select high-multiplicity
(HM) events. The V0 detector comprises two plastic scintillator arrays placed
on both sides of the interaction point at pseudorapidities $$2.8$<\eta<$5.1$$
and $$-3.7$<\eta<$-1.7$$. The pseudorapidity is defined as
$\eta=-\textrm{ln}\left[\textrm{tan}\left(\frac{\theta}{2}\right)\right]$,
where $\theta$ is the polar angle of the particle with respect to the proton
beam axis.

At $\sqrt{s}=13$ TeV, the average number of charged particles produced in HM
events in the range $|\eta|<$0.5$$ is 30. This $\eta$ range corresponds to the
region within $26$ degrees of the transverse plane perpendicular to the beam
axis. The HM events constitute only $0.17\text{\,}\mathrm{\char
37\relax}\text{/}$ of the pp collisions that produce at least one charged
particle in the pseudorapidity range $|\eta|<$1.0$$. A total of $1\times
10^{9}$ HM events were analyzed. Additional details on the HM event selection
can be found in [74].

### Particle Tracking and Identification

For the identification and momentum measurement of charged particles, the
Inner Tracking System (ITS) [76], Time Projection Chamber (TPC) [77], and
Time-Of-Flight (TOF) [78] detectors of ALICE are employed. All three detectors
are located inside a uniform magnetic field generated by the L3 solenoid
($0.5\text{\,}\mathrm{T}$), leading to a bending of the trajectories of
charged particles. The measurement of the curvature is used to reconstruct the
particle momenta. Typical transverse momentum ($p_{\rm{T}}$) resolutions for
kaons, protons, and deuterons vary from about $2\text{\,}\mathrm{\char
37\relax}\text{/}$ for tracks with $p_{\rm T}\,=$10\text{\,}\text{/}$$ GeV/$c$
to below $1\text{\,}\mathrm{\char 37\relax}\text{/}$ for $p_{\rm
T}\,<$1\text{\,}\text{/}$$ GeV/$c$. The particle identity is determined by the
energy lost per unit of track length inside the TPC detector and by the
particle velocity measured in the TOF detector. For additional experimental
details, see [73]. Basic details on the selection criteria of the proton,
kaon, and deuteron tracks used in this work can be found in [79].

Kaons are identified via the measurement of the specific energy loss in TPC
within a momentum range
$p\in[0.2,2.0]~{}\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. This
information is combined with the time of flight measurement for momentum
$p>0.4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. In the kaon
sample, the contamination from electrons produced via photon conversion in the
detector material is removed by excluding kaon candidates in the momentum
range $0.5<p<0.65$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$.
The selected candidates that simultaneously fulfill the selection criteria of
the pion (using TPC and TOF information) or proton (using TPC information) are
also excluded from the sample.

Protons are selected within a transverse momentum range of $0.5<p_{\rm
T}\,<4.05$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. They are
identified by requiring TPC information for candidate tracks with momentum
$p<$0.75\text{\,}\text{/}$$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$, while TPC and TOF
information are both required for candidates with $p>$0.75\text{\,}\text{/}$$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. The identification of
deuterons is performed with the TPC in the momentum range $0.4<p<1.4$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. For the analysis of
K+–d pairs, the deuteron acceptance is extended by using TOF identification in
the region
$1.4<p<2.3~{}\mathrm{GeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$.

The selection of kaons, protons and deuterons constitute the main source of
systematic uncertainties associated to the measured correlation function. All
particle selection criteria are varied with respect to their default values.
In order to account for the effect of possible correlations, the analysis of
K+–d (p–d ) pairs is repeated 40 (44) times using random combinations of such
selection criteria. The associated systematic uncertainty of the measured
correlation function for each $k^{*}$ point is given by the root mean square
of all 40 (44) resulting correlation functions. The total systematic
uncertainties are maximal at low $k^{*}$, reaching a value of
$3\text{\,}\mathrm{\char 37\relax}\text{/}$ and $7\text{\,}\mathrm{\char
37\relax}\text{/}$ for K+–d and p–d , correspondingly.

### Characterization of the source of particles

The distribution $S(r^{*})$ of the distance $r^{*}$ at which particles are
emitted, is described by a Gaussian function whose width characterizes the
source size. In [40], the baryon–baryon source sizes are determined as a
function of the transverse mass of the baryon–baryon pair, $\smash{m_{\rm
T}\,=\left(k_{\rm T}\,^{2}+m^{2}\right)^{1/2}}$, where $m$ is the average mass
and $\smash[b]{k_{\rm
T}\,=\,\,\mid\bm{p}\bf{{}_{\textrm{T},~{}\textrm{1}}}+\bm{p}\bf{{}_{\textrm{T},~{}\textrm{2}}}\mid}$/2
is the transverse momentum of the pair. For p–d and K+–d pairs, it is assumed
that the common source for all baryons still holds for any hadron–hadron pair
[40] . The measured $\langle m_{\mathrm{T}}\rangle$ for p–d and K+–d pairs are
$1.64\text{\,}\mathrm{GeV}\text{/}\mathrm{\text{$c$}}$ and
$1.50\text{\,}\mathrm{GeV}\text{/}\mathrm{\text{$c$}}$, respectively, implying
source sizes of $r_{\text{core}}^{\small\mbox{K${}^{+}$--d}~{}}=~{}$$1.04\pm
0.04$ fm and $r_{\text{core}}^{\small\mbox{p--d}~{}}=$ $0.99\pm 0.05$ fm,
where $r_{\textrm{core}}$ denotes the width of the Gaussian distribution
defining the source before taking into account the effect produced by short-
lived resonances.

In pp collisions at $\sqrt{s}~{}=~{}13$ TeV, about $2/3$ of the protons and
$1/3$ of the kaons originate from the decay of short-lived resonances with a
lifetime $(c\tau)$ of a few fm. Table 2 shows the major relative contributions
to the proton and kaon samples by several resonances, according to statistical
hadronization [80]. The effect of such resonances on the source size is
evaluated by folding the Gaussian source with an exponential distribution
containing the resonance decay constant, following [40]. The resulting source
distribution for p–d can be parameterized with an effective Gaussian source
radius equal to $r_{\text{eff}}^{\small{\mbox{p--d}~{}}}=$ $1.08\pm 0.06$
$\mathrm{fm}\text{/}$. For K+–d pairs, the resulting source distribution is
described using a sum of two Gaussian functions with radii $1.10\pm 0.04$
$\mathrm{fm}\text{/}$ and $2.14^{+0.03}_{-0.07}$ $\mathrm{fm}\text{/}$ with
weights of $0.76$ and $0.24$, respectively. The effective source size quoted
in the text $r_{\text{eff}}^{\small{\mbox{K${}^{+}$--d}~{}}}=$
$1.35^{+0.04}_{-0.05}$ $\mathrm{fm}\text{/}$ results from the weighted sum of
the two Gaussians. Note that a description with a single Gaussian (1G) for the
K+–d source distribution, including the effects of resonances is not
satisfactory, but it is nevertheless illustrative to compare the resulting
radius of $r_{\text{eff1G}}^{\small{\mbox{K${}^{+}$--d}~{}}}=$ $1.22\pm 0.04$
$\mathrm{fm}\text{/}$ with the p–d radius $r_{\text{eff}}^{\small{\mbox{p--
d}~{}}}=$ $1.08\pm 0.06$ $\mathrm{fm}\text{/}$.

In the case of the three-body calculation for the p–d system, the formalism
requires as input the two-particle source size for each pairwise source of the
p–(pn) system. For nucleon pairs an average core source size of
$r_{\text{core}}^{\text{NN}}=$ $1.35\pm 0.14$ fm has been estimated using the
measured $\langle m_{\mathrm{T}}\rangle$ for p–d and the measured $\langle
p_{\mathrm{T}}\rangle$ of deuteron and protons below $k^{*}<400$
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. The source size
$r_{\text{core}}^{\text{NN}}$ is enhanced by the strongly decaying resonances
that feed to protons and neutrons. Similar to the case of p–d and K+–d pairs
this effect in the source size is taken into account by folding the Gaussian
source with an exponential distribution. The resulting source distribution for
NN pairs can be characterized by an effective Gaussian source radius equal to
$r_{\text{eff}}^{\text{NN}}=$ $1.43^{+0.16}_{-0.16}$ $\mathrm{fm}\text{/}$.
This source size is an average of distances between the p–p and p–n pairs that
form the p–d system.

Table 2: Fractions of protons and kaons feeding from the strongly-decaying short-lived decays of resonances. The contribution of kaons from the $\phi(1020)$ decays are considered as feed-down to the correlation functions. protons | kaons
---|---
resonances | $c\tau(\mathrm{fm})$ | fractions(%) | resonances | $c\tau(\mathrm{fm})$ | fractions(%)
$\Delta^{++}$ | 1.64 | $21.87$ | $\mathrm{K^{*}(892)^{0}}$ | 3.89 | $21$
$\Delta^{+}$ | 1.64 | $14.60$ | $\mathrm{K^{*}(892)^{+}}$ | 3.88 | $11$
$\Delta^{0}$ | 1.64 | $7.20$ | $\mathrm{a_{0}(980)^{+}}$ | 2.63 | $1$
N$(1440)^{0}$ | 0.56 | $0.91$ | $\mathrm{K_{2}^{*}(1430)^{0}}$ | 1.81 | $1$
N$(1520)^{0}$ | 1.64 | $1.75$ | $\mathrm{K_{1}^{*}(1270)^{0}}$ | 2.19 | $1$
N$(1680)^{0}$ | 1.52 | $1.15$ | $\phi(1020)$ | 46.32 | $(6)$
N$(1535)^{+}$ | 1.31 | $1.02$ | $-$ | $-$ | $-$
N$(1440)^{+}$ | 0.56 | $0.91$ | $-$ | $-$ | $-$

### Corrections of the Correlation Function

The experimental correlation function, defined as
$C(k^{*})=\xi(k^{*})\otimes\frac{N_{\mathrm{same}}(k^{*})}{N_{\mathrm{mixed}}(k^{*})}$,
is corrected, via $\xi(k^{*})$, for normalization and the unfolding of
momentum resolution effects. A normalization factor $\mathcal{N}$ is used to
correct for the different yields in same- and mixed-event distributions. The
value of the normalization factor is chosen such that the mean value of the
correlation function is equal to unity. It is obtained by dividing the
integral of the $N_{\mathrm{same}}(k^{*})$ and $N_{\mathrm{mixed}}(k^{*})$ in
a region where the effect of final-state interactions is negligible (for p–d :
200 $<$ $k^{*}$ $<$ 500
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$and in the case of K+–d
: 300 $<$ $k^{*}$ $<$ 600
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$).

The shape of the measured correlation function is affected by the finite
resolution in the determination of the momentum of particles. The measured
same- and mixed-event distributions are unfolded for the momentum smearing
using MC simulations. The correction for the measured correlation function due
to the momentum resolution effect with the MC event generator is found to be
at most 3% for p–d and 9% for K+–d at low $k^{*}$. Moreover, the resolution
effects due to the merging of trajectories which cross the detector at a
distance comparable with the spatial resolution of the detector (ITS or TPC)
were evaluated and found to be negligible.

While the measured p–d and K+–d correlation functions are dominated by the
interaction between p–d and K+–d pairs consisting of primary particles
produced in the collision, they are also influenced by the effects caused by
the misidentification of particles and by the contribution of secondary
particles produced in weak decays. Due to the large decay times of weakly
decaying particles, the final-state interaction between their decay products
and the primary particle of interest is absent, thus leading to either a flat
contribution or a residual signature of the interaction with the parent
hadron. The contributions to $C(k^{*})$ from the genuine correlation of
primary particles, the misidentified hadrons, and the secondary particles are
quantified by the so-called $\lambda$ parameters, which are computed from the
purity and the primary fraction of each particle species as described in [33].
The $\lambda$ parameters for the genuine correlation function of p–d and K+–d
are listed in Table 3. All the residual correlations not stemming from genuine
primary pairs in the p–d and K+–d correlation functions are assumed to be
equal to unity regardless of the values of $k^{*}$ and the theoretical
correlation functions shown in Figs. 1 and 2 are corrected using the
corresponding $\lambda$ parameters.

Table 3: $\lambda$ parameters of the genuine particle pairs for p–d and K+–d. $\lambda$ parameter | value
---|---
$\lambda_{\mathrm{pd}}$ | 79.7%
$\lambda_{\mathrm{\bar{p}\bar{d}}}$ | 84.1%
$\lambda_{\mathrm{K^{+}d}}$ | 90.1%
$\lambda_{\mathrm{K^{-}\bar{d}}}$ | 94.1%

The uncertainties on the determination of the residual contributions and the
source size are propagated to the theoretical correlation functions and
contribute, together with the intrinsic theoretical uncertainties of each
model, to the width of the bands shown in Fig. 1 and Fig. 2.

In addition to the residual correlation, the theoretical correlation function
is also corrected for the rising tail effect of the experimental correlation
in the region where the final-state interaction is negligible and that can be
originated from effects such as energy conservation. A multiplicative cubic
baseline $BL(k^{*})=a+b{k^{*}}^{2}+c{k^{*}}^{3}$ is used to describe the data
at large $k^{*}$. For K+–d correlations, the baseline is pre-fitted in the
region of 300 $<$ $k^{*}$ $<$ 1800
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$. In the case of the
p–d correlation function, the parameters $a$, $b$ and $c$ are obtained from a
fit to the data in the region 0 $<$ $k^{*}$ $<$ 700
$\mathrm{MeV}\kern-0.50003pt/\kern-0.20004pt\textit{c}$ including the
theoretical correlation function and the multiplicative baseline. The baseline
is represented by the gray bands in Figs. 1 and 2.

### The Lednický-Lyuboshitz Model

The final-state interaction for two charged point-like particles has been
modeled in [63]. The definition of the relative $s$-wave function for a system
of two charged point-like distinguishable particles is given as

$\psi(\vec{k}^{*},\vec{r}^{*})=e^{i\delta_{c}}\sqrt{A_{c}(\eta)}\left[e^{-i\vec{k}^{*}\cdot\vec{r}^{*}}F(-i\eta,1,i\xi)+f_{C}(k^{*})\frac{\tilde{G}(\rho,\eta)}{r*}\right]\,,$
(1)

where $\eta=(k^{*}a_{C})^{-1}$, $a_{C}$ is the Bohr radius including the sign
of the interaction between the pair of particles,
$\xi=\rho(1+\cos(\theta^{*}))$, and $\rho=k^{*}r^{*}$. Where $\theta^{*}$ is
the angle between $\vec{k}^{*}$ and $\vec{r}^{*}$. The term
$A_{C}(\eta)=2\pi\eta\left[\exp(2\pi\eta)-1\right]^{-1}$ is a Coulomb-barrier
penetration factor, also known as Gamow factor. The Coulomb interaction
(asymptotic form) in the wave function is described by the term
$e^{-\iota\vec{k}^{*}\vec{\cdot}r^{*}}F(\alpha,\,1,\,z)$ together with
$\widetilde{G}(\rho,\eta)$, where
$F(\alpha,\,1,\,z)=1+\frac{\alpha\,z}{!2}++\frac{\alpha(\alpha+1)\,z^{2}}{!2^{2}}+\cdots$
is a confluent hypergeometric function and
$\widetilde{G}(\rho,\eta)=\sqrt{Ac}(G_{0}+iF_{0})$ is a combination of the
regular $(F_{0})$ and singular $(G_{0})$ $s$-wave Coulomb functions. The
strong nuclear interaction is computed using the Coulomb-corrected scattering
amplitude $f_{\mathrm{C}}$ defined as

$f_{C}(k^{*})=\left[\frac{1}{-a_{0}}+\frac{d_{0}{k^{*}}^{2}}{2}-ik^{*}A_{C}(k^{*})-\frac{2}{a_{C}}h((k^{*})\right]^{-1}.$
(2)

The function $h(k^{*})$ is written as
$h(k^{*})=\frac{1}{(k^{*}a_{C})^{2}}\sum^{\infty}_{n=1}\left[n\left(n^{2}+(k^{*}a_{C})^{-2}\right)\right]^{-1}-\gamma+\ln|k^{*}a_{C}|$,
where the constant $\gamma=0.5772$ is the Euler constant.

### Three-body formalism for the p–d correlation function

In order to account for the internal structure of the deuteron, a calculation
of the proton–deuteron correlation function that includes a microscopic p–d
wave function $\Psi_{m_{2},m_{1}}({\bm{x}},{\bm{y}})$ has been carried out.
This wave function accounts for all the relevant two- and three-body
interactions at work in the p–(pn) system for the short and asymptotic ranges.
It accurately describes the three-body dynamics [16, 17, 18] since it is tuned
on p–d scattering observables. The variables ${\bm{x}}$ and ${\bm{y}}$ are the
Jacobi vectors of the system, and they asymptotically denote the distance of
the p–n system within the deuteron and the p–d distance, respectively. The
indices $m_{2}$ and $m_{1}$ are quantum numbers of the spin operators for the
deuteron and the proton when they are very well apart. The three-body
correlation is calculated using the formalism discussed in [66, 67]. More
details about the employed wave functions and the computation of the p–d
correlation function can be found in [68]. In general, the formalism is based
on the following expressions

$\displaystyle C_{pd}(k)$ $\displaystyle=$
$\displaystyle\frac{1}{A_{\mathrm{d}}}{\frac{1}{6}}\sum_{m_{2},m_{1}}\int
d^{3}r_{1}d^{3}r_{2}d^{3}r_{3}\;S_{1}(r_{1})S_{1}(r_{2})S_{1}(r_{3})|\Psi_{m_{2},m_{1}}|^{2}\
,$ (3) $\displaystyle A_{\mathrm{d}}$ $\displaystyle=$
$\displaystyle{\frac{1}{3}}\sum_{m_{2}}\int
d^{3}r_{1}d^{3}r_{2}\;S_{1}(r_{1})S_{1}(r_{2})|\phi_{m_{2}}|^{2}\ ,$ (4)
$\displaystyle S_{1}(r)$ $\displaystyle=$ $\displaystyle\frac{1}{(2\pi
R_{\text{M}}^{2})^{\frac{3}{2}}}e^{-r^{2}/2R_{\text{M}}^{2}}\ ,$ (5)

where $\phi_{m_{2}}$ is the deuteron wave function and $S_{1}(r)$ represents
the single particle source term of radius $R_{\text{M}}$, while the factor 6
in the denominator of Eq. 3 takes into account the possible spin
configurations. The quantity $A_{\mathrm{d}}$ can be related to the
probability of deuteron formation in the reaction. Note that in this
calculation, the accurate p–d wave function is different from the approximated
form employed in [66, 67]. By considering a suitable choice of coordinates,
one can demonstrate [19] that the parameter $R_{M}$ corresponds to the
effective radius for the two-nucleon system. For the p–d system, $R_{M}$ has
been estimated considering the measured $\langle m_{\mathrm{T}}\rangle$ of the
p–d pairs and the average transverse momentum $\langle p_{\mathrm{T}}\rangle$
of the deuterons and protons used for the correlation. The value
$R_{M}=\,r_{\text{eff}}^{\text{NN}}=$$1.43^{+0.16}_{-0.16}$
$\mathrm{fm}\text{/}$ has been obtained and used in the calculation.

##  Appendix A The ALICE Collaboration

S. Acharya 129, D. Adamová 89, G. Aglieri Rinella 35, M. Agnello 32, N.
Agrawal 53, Z. Ahammed 137, S. Ahmad 16, S.U. Ahn 74, I. Ahuja 40, A.
Akindinov 146, M. Al-Turany 100, D. Aleksandrov 146, B. Alessandro 59, H.M.
Alfanda 6, R. Alfaro Molina 70, B. Ali 16, A. Alici 28, N. Alizadehvandchali
118, A. Alkin 35, J. Alme 22, G. Alocco 54, T. Alt 67, A.R. Altamura 52, I.
Altsybeev 98, M.N. Anaam 6, C. Andrei 48, N. Andreou 117, A. Andronic 140, V.
Anguelov 97, F. Antinori 56, P. Antonioli 53, N. Apadula 77, L. Aphecetche
106, H. Appelshäuser 67, C. Arata 76, S. Arcelli 28, M. Aresti 24, R. Arnaldi
59, J.G.M.C.A. Arneiro 113, I.C. Arsene 21, M. Arslandok 142, A. Augustinus
35, R. Averbeck 100, M.D. Azmi 16, H. Baba126, A. Badalà 55, J. Bae 107, Y.W.
Baek 43, X. Bai 122, R. Bailhache 67, Y. Bailung 50, A. Balbino 32, A.
Baldisseri 132, B. Balis 2, D. Banerjee 4, Z. Banoo 94, R. Barbera 29, F.
Barile 34, L. Barioglio 98, M. Barlou81, B. Barman44, G.G. Barnaföldi 141,
L.S. Barnby 88, V. Barret 129, L. Barreto 113, C. Bartels 121, K. Barth 35, E.
Bartsch 67, N. Bastid 129, S. Basu 78, G. Batigne 106, D. Battistini 98, B.
Batyunya 147, D. Bauri49, J.L. Bazo Alba 104, I.G. Bearden 86, C. Beattie 142,
P. Becht 100, D. Behera 50, I. Belikov 131, A.D.C. Bell Hechavarria 140, F.
Bellini 28, R. Bellwied 118, S. Belokurova 146, Y.A.V. Beltran 47, G. Bencedi
141, S. Beole 27, Y. Berdnikov 146, A. Berdnikova 97, L. Bergmann 97, M.G.
Besoiu 66, L. Betev 35, P.P. Bhaduri 137, A. Bhasin 94, M.A. Bhat 4, B.
Bhattacharjee 44, L. Bianchi 27, N. Bianchi 51, J. Bielčík 38, J. Bielčíková
89, J. Biernat 110, A.P. Bigot 131, A. Bilandzic 98, G. Biro 141, S. Biswas 4,
N. Bize 106, J.T. Blair 111, D. Blau 146, M.B. Blidaru 100, N. Bluhme41, C.
Blume 67, G. Boca 23,57, F. Bock 90, T. Bodova 22, A. Bogdanov146, S. Boi 24,
J. Bok 61, L. Boldizsár 141, M. Bombara 40, P.M. Bond 35, G. Bonomi 136,57, H.
Borel 132, A. Borissov 146, A.G. Borquez Carcamo 97, H. Bossi 142, E. Botta
27, Y.E.M. Bouziani 67, L. Bratrud 67, P. Braun-Munzinger 100, M. Bregant 113,
M. Broz 38, G.E. Bruno 99,34, M.D. Buckland 26, D. Budnikov 146, H. Buesching
67, S. Bufalino 32, P. Buhler 105, N. Burmasov 146, Z. Buthelezi 71,125, A.
Bylinkin 22, S.A. Bysiak110, M. Cai 6, H. Caines 142, A. Caliva 31, E. Calvo
Villar 104, J.M.M. Camacho 112, P. Camerini 26, F.D.M. Canedo 113, M. Carabas
128, A.A. Carballo 35, F. Carnesecchi 35, R. Caron 130, L.A.D. Carvalho 113,
J. Castillo Castellanos 132, F. Catalano 35,27, C. Ceballos Sanchez 147, I.
Chakaberia 77, P. Chakraborty 49, S. Chandra 137, S. Chapeland 35, M. Chartier
121, S. Chattopadhyay 137, S. Chattopadhyay 102, T.G. Chavez 47, T. Cheng
100,6, C. Cheshkov 130, B. Cheynis 130, V. Chibante Barroso 35, D.D.
Chinellato 114, E.S. Chizzali I,98, J. Cho 61, S. Cho 61, P. Chochula 35, D.
Choudhury44, P. Christakoglou 87, C.H. Christensen 86, P. Christiansen 78, T.
Chujo 127, M. Ciacco 32, C. Cicalo 54, F. Cindolo 53, M.R. Ciupek100, G.
ClaiII,53, F. Colamaria 52, J.S. Colburn103, D. Colella 99,34, M. Colocci 28,
M. Concas III,35, G. Conesa Balbastre 76, Z. Conesa del Valle 133, G. Contin
26, J.G. Contreras 38, M.L. Coquet 132, P. Cortese 135,59, M.R. Cosentino 115,
F. Costa 35, S. Costanza 23,57, C. Cot 133, J. Crkovská 97, P. Crochet 129, R.
Cruz-Torres 77, P. Cui 6, A. Dainese 56, M.C. Danisch 97, A. Danu 66, P. Das
83, P. Das 4, S. Das 4, A.R. Dash 140, S. Dash 49, R.M.H. David47, A. De Caro
31, G. de Cataldo 52, J. de Cuveland41, A. De Falco 24, D. De Gruttola 31, N.
De Marco 59, C. De Martin 26, S. De Pasquale 31, R. Deb 136, R. Del Grande 98,
L. Dello Stritto 31, W. Deng 6, P. Dhankher 19, D. Di Bari 34, A. Di Mauro 35,
B. Diab 132, R.A. Diaz 147,7, T. Dietel 116, Y. Ding 6, J. Ditzel 67, R. Divià
35, D.U. Dixit 19, Ø. Djuvsland22, U. Dmitrieva 146, A. Dobrin 66, B. Dönigus
67, J.M. Dubinski 138, A. Dubla 100, S. Dudi 93, P. Dupieux 129, M. Durkac109,
N. Dzalaiova13, T.M. Eder 140, R.J. Ehlers 77, F. Eisenhut 67, R. Ejima95, D.
Elia 52, B. Erazmus 106, F. Ercolessi 28, B. Espagnon 133, G. Eulisse 35, D.
Evans 103, S. Evdokimov 146, L. Fabbietti 98, M. Faggin 30, J. Faivre 76, F.
Fan 6, W. Fan 77, A. Fantoni 51, M. Fasel 90, P. Fecchio32, A. Feliciello 59,
G. Feofilov 146, A. Fernández Téllez 47, L. Ferrandi 113, M.B. Ferrer 35, A.
Ferrero 132, C. Ferrero 59, A. Ferretti 27, V.J.G. Feuillard 97, V. Filova 38,
D. Finogeev 146, F.M. Fionda 54, F. Flor 118, A.N. Flores 111, S. Foertsch 71,
I. Fokin 97, S. Fokin 146, E. Fragiacomo 60, E. Frajna 141, U. Fuchs 35, N.
Funicello 31, C. Furget 76, A. Furs 146, T. Fusayasu 101, J.J. Gaardhøje 86,
M. Gagliardi 27, A.M. Gago 104, T. Gahlaut49, C.D. Galvan 112, D.R.
Gangadharan 118, P. Ganoti 81, C. Garabatos 100, A.T. Garcia 133, J.R.A.
Garcia 47, E. Garcia-Solis 9, C. Gargiulo 35, P. Gasik 100, A. Gautam 120,
M.B. Gay Ducati 69, M. Germain 106, A. Ghimouz127, C. Ghosh137, M. Giacalone
53, G. Gioachin 32, P. Giubellino 100,59, P. Giubilato 30, A.M.C. Glaenzer
132, P. Glässel 97, E. Glimos 124, D.J.Q. Goh79, V. Gonzalez 139, M. Gorgon 2,
K. Goswami 50, S. Gotovac36, V. Grabski 70, L.K. Graczykowski 138, E. Grecka
89, A. Grelli 62, C. Grigoras 35, V. Grigoriev 146, S. Grigoryan 147,1, F.
Grosa 35, J.F. Grosse-Oetringhaus 35, R. Grosso 100, D. Grund 38, N.A.
Grunwald97, G.G. Guardiano 114, R. Guernane 76, M. Guilbaud 106, K.
Gulbrandsen 86, T. Gündem 67, T. Gunji 126, W. Guo 6, A. Gupta 94, R. Gupta
94, R. Gupta 50, S.P. Guzman 47, K. Gwizdziel 138, L. Gyulai 141, C.
Hadjidakis 133, F.U. Haider 94, S. Haidlova 38, H. Hamagaki 79, A. Hamdi 77,
Y. Han 143, B.G. Hanley 139, R. Hannigan 111, J. Hansen 78, M.R. Haque 138,
J.W. Harris 142, A. Harton 9, H. Hassan 119, D. Hatzifotiadou 53, P. Hauer 45,
L.B. Havener 142, S.T. Heckel 98, E. Hellbär 100, H. Helstrup 37, M. Hemmer
67, T. Herman 38, G. Herrera Corral 8, F. Herrmann140, S. Herrmann 130, K.F.
Hetland 37, B. Heybeck 67, H. Hillemanns 35, B. Hippolyte 131, F.W. Hoffmann
73, B. Hofman 62, G.H. Hong 143, M. Horst 98, A. Horzyk2, Y. Hou 6, P. Hristov
35, C. Hughes 124, P. Huhn67, L.M. Huhta 119, T.J. Humanic 91, A. Hutson 118,
D. Hutter 41, R. Ilkaev146, H. Ilyas 14, M. Inaba 127, G.M. Innocenti 35, M.
Ippolitov 146, A. Isakov 87,89, T. Isidori 120, M.S. Islam 102, M. Ivanov 100,
M. Ivanov13, V. Ivanov 146, K.E. Iversen 78, M. Jablonski 2, B. Jacak 77, N.
Jacazio 28, P.M. Jacobs 77, S. Jadlovska109, J. Jadlovsky109, S. Jaelani 85,
C. Jahnke 114, M.J. Jakubowska 138, M.A. Janik 138, T. Janson73, S. Ji 17, S.
Jia 10, A.A.P. Jimenez 68, F. Jonas 90, D.M. Jones 121, J.M. Jowett 35,100, J.
Jung 67, M. Jung 67, A. Junique 35, A. Jusko 103, M.J. Kabus 35,138, J.
Kaewjai108, P. Kalinak 63, A.S. Kalteyer 100, A. Kalweit 35, V. Kaplin 146, A.
Karasu Uysal 75, D. Karatovic 92, O. Karavichev 146, T. Karavicheva 146, P.
Karczmarczyk 138, E. Karpechev 146, U. Kebschull 73, R. Keidel 145, D.L.D.
Keijdener62, M. Keil 35, B. Ketzer 45, S.S. Khade 50, A.M. Khan 122,6, S. Khan
16, A. Khanzadeev 146, Y. Kharlov 146, A. Khatun 120, A. Khuntia 38, A.
Kievsky 58, B. Kileng 37, B. Kim 107, C. Kim 17, D.J. Kim 119, E.J. Kim 72, J.
Kim 143, J.S. Kim 43, J. Kim 61, J. Kim 72, M. Kim 19, S. Kim 18, T. Kim 143,
K. Kimura 95, S. Kirsch 67, I. Kisel 41, S. Kiselev 146, A. Kisiel 138, J.P.
Kitowski 2, J.L. Klay 5, J. Klein 35, S. Klein 77, C. Klein-Bösing 140, M.
Kleiner 67, T. Klemenz 98, A. Kluge 35, A.G. Knospe 118, C. Kobdaj 108, T.
Kollegger100, A. Kondratyev 147, N. Kondratyeva 146, E. Kondratyuk 146, J.
Konig 67, S. König 20, S.A. Konigstorfer 98, P.J. Konopka 35, G. Kornakov 138,
S.D. Koryciak 2, A. Kotliarov 89, V. Kovalenko 146, M. Kowalski 110, V.
Kozhuharov 39, I. Králik 63, A. Kravčáková 40, L. Krcal 35,41, M. Krivda
103,63, F. Krizek 89, K. Krizkova Gajdosova 35, M. Kroesen 97, M. Krüger 67,
D.M. Krupova 38, E. Kryshen 146, V. Kučera 61, C. Kuhn 131, P.G. Kuijer 87, T.
Kumaoka127, D. Kumar137, L. Kumar 93, N. Kumar93, S. Kumar 34, S. Kundu 35, P.
Kurashvili 82, A. Kurepin 146, A.B. Kurepin 146, A. Kuryakin 146, S. Kushpil
89, M.J. Kweon 61, Y. Kwon 143, S.L. La Pointe 41, P. La Rocca 29, A.
Lakrathok108, M. Lamanna 35, R. Langoy 123, P. Larionov 35, E. Laudi 35, L.
Lautner 35,98, R. Lavicka 105, R. Lea 136,57, H. Lee 107, I. Legrand 48, G.
Legras 140, J. Lehrbach 41, T.M. Lelek2, R.C. Lemmon 88, I. León Monzón 112,
M.M. Lesch 98, E.D. Lesser 19, P. Lévai 141, X. Li10, J. Lien 123, R. Lietava
103, I. Likmeta 118, B. Lim 27, S.H. Lim 17, V. Lindenstruth 41, A. Lindner48,
C. Lippmann 100, D.H. Liu 6, J. Liu 121, G.S.S. Liveraro 114, I.M. Lofnes 22,
C. Loizides 90, S. Lokos 110, J. Lomker 62, P. Loncar36, X. Lopez 129, E.
López Torres 7, P. Lu 100,122, F.V. Lugo 70, J.R. Luhder 140, M. Lunardon 30,
G. Luparello 60, Y.G. Ma 42, M. Mager 35, A. Maire 131, M.V. Makariev 39, M.
Malaev 146, G. Malfattore 28, N.M. Malik 94, Q.W. Malik21, S.K. Malik 94, L.
Malinina VI,147, D. Mallick 133,83, N. Mallick 50, G. Mandaglio 33,55, S.K.
Mandal 82, V. Manko 146, F. Manso 129, V. Manzari 52, Y. Mao 6, R.W. Marcjan
2, L.E. Marcucci 25, G.V. Margagliotti 26, A. Margotti 53, A. Marín 100, C.
Markert 111, P. Martinengo 35, M.I. Martínez 47, G. Martínez García 106,
M.P.P. Martins 113, S. Masciocchi 100, M. Masera 27, A. Masoni 54, L.
Massacrier 133, O. Massen 62, A. Mastroserio 134,52, O. Matonoha 78, S.
Mattiazzo 30, A. Matyja 110, C. Mayer 110, A.L. Mazuecos 35, F. Mazzaschi 27,
M. Mazzilli 35, J.E. Mdhluli 125, Y. Melikyan 46, A. Menchaca-Rocha 70, J.E.M.
Mendez 68, E. Meninno 105,31, A.S. Menon 118, M. Meres 13, S. Mhlanga116,71,
Y. Miake127, L. Micheletti 35, D.L. Mihaylov 98, K. Mikhaylov 147,146, A.N.
Mishra 141, D. Miśkowiec 100, A. Modak 4, B. Mohanty83, M. Mohisin Khan IV,16,
M.A. Molander 46, S. Monira 138, C. Mordasini 119, D.A. Moreira De Godoy 140,
I. Morozov 146, A. Morsch 35, T. Mrnjavac 35, V. Muccifora 51, S. Muhuri 137,
J.D. Mulligan 77, A. Mulliri24, M.G. Munhoz 113, R.H. Munzer 67, H. Murakami
126, S. Murray 116, L. Musa 35, J. Musinsky 63, J.W. Myrcha 138, B. Naik 125,
A.I. Nambrath 19, B.K. Nandi 49, R. Nania 53, E. Nappi 52, A.F. Nassirpour 18,
A. Nath 97, C. Nattrass 124, M.N. Naydenov 39, A. Neagu21, A. Negru128, L.
Nellen 68, R. Nepeivoda 78, S. Nese 21, G. Neskovic 41, N. Nicassio 52, B.S.
Nielsen 86, E.G. Nielsen 86, S. Nikolaev 146, S. Nikulin 146, V. Nikulin 146,
F. Noferini 53, S. Noh 12, P. Nomokonov 147, J. Norman 121, N. Novitzky 90, P.
Nowakowski 138, A. Nyanin 146, J. Nystrand 22, M. Ogino 79, S. Oh 18, A.
Ohlson 78, A. Ohnishi 144, V.A. Okorokov 146, J. Oleniacz 138, A.C. Oliveira
Da Silva 124, A. Onnerstad 119, C. Oppedisano 59, A. Ortiz Velasquez 68, J.
Otwinowski 110, M. Oya95, K. Oyama 79, Y. Pachmayer 97, S. Padhan 49, D.
Pagano 136,57, G. Paić 68, A. Palasciano 52, S. Panebianco 132, H. Park 127,
H. Park 107, J. Park 61, J.E. Parkkila 35, Y. Patley 49, R.N. Patra94, B. Paul
24, H. Pei 6, T. Peitzmann 62, X. Peng 11, M. Pennisi 27, S. Perciballi 27, D.
Peresunko 146, G.M. Perez 7, Y. Pestov146, V. Petrov 146, M. Petrovici 48,
R.P. Pezzi 106,69, S. Piano 60, M. Pikna 13, P. Pillot 106, O. Pinazza 53,35,
L. Pinsky118, C. Pinto 98, S. Pisano 51, M. Płoskoń 77, M. Planinic92, F.
Pliquett67, M.G. Poghosyan 90, B. Polichtchouk 146, S. Politano 32, N. Poljak
92, A. Pop 48, S. Porteboeuf-Houssais 129, V. Pozdniakov 147, I.Y. Pozos 47,
K.K. Pradhan 50, S.K. Prasad 4, S. Prasad 50, R. Preghenella 53, F. Prino 59,
C.A. Pruneau 139, I. Pshenichnov 146, M. Puccio 35, S. Pucillo 27, Z.
Pugelova109, S. Qiu 87, L. Quaglia 27, S. Ragoni 15, A. Rai 142, A.
Rakotozafindrabe 132, L. Ramello 135,59, F. Rami 131, S.A.R. Ramirez 47, T.A.
Rancien76, M. Rasa 29, S.S. Räsänen 46, R. Rath 53, M.P. Rauch 22, I.
Ravasenga 87, K.F. Read 90,124, C. Reckziegel 115, A.R. Redelbach 41, K.
Redlich V,82, C.A. Reetz 100, A. Rehman22, F. Reidt 35, H.A. Reme-Ness 37, Z.
Rescakova40, K. Reygers 97, A. Riabov 146, V. Riabov 146, R. Ricci 31, M.
Richter 21, A.A. Riedel 98, W. Riegler 35, A.G. Riffero 27, C. Ristea 66, M.V.
Rodriguez 35, M. Rodríguez Cahuantzi 47, K. Røed 21, R. Rogalev 146, E.
Rogochaya 147, T.S. Rogoschinski 67, D. Rohr 35, D. Röhrich 22, P.F. Rojas47,
S. Rojas Torres 38, P.S. Rokita 138, G. Romanenko 28, F. Ronchetti 51, A.
Rosano 33,55, E.D. Rosas68, K. Roslon 138, A. Rossi 56, A. Roy 50, S. Roy 49,
N. Rubini 28, D. Ruggiano 138, R. Rui 26, P.G. Russek 2, R. Russo 87, A.
Rustamov 84, E. Ryabinkin 146, Y. Ryabov 146, A. Rybicki 110, H. Rytkonen 119,
J. Ryu 17, W. Rzesa 138, O.A.M. Saarimaki 46, S. Sadhu 34, S. Sadovsky 146, J.
Saetre 22, K. Šafařík 38, P. Saha44, S.K. Saha 4, S. Saha 83, B. Sahoo 49, B.
Sahoo 50, R. Sahoo 50, S. Sahoo64, D. Sahu 50, P.K. Sahu 64, J. Saini 137, K.
Sajdakova40, S. Sakai 127, M.P. Salvan 100, S. Sambyal 94, D. Samitz 105, I.
Sanna 35,98, T.B. Saramela113, P. Sarma 44, V. Sarritzu 24, V.M. Sarti 98,
M.H.P. Sas 142, S. Sawan83, J. Schambach 90, H.S. Scheid 67, C. Schiaua 48, R.
Schicker 97, A. Schmah100, C. Schmidt 100, H.R. Schmidt96, M.O. Schmidt 35, M.
Schmidt96, N.V. Schmidt 90, A.R. Schmier 124, R. Schotter 131, A. Schröter 41,
J. Schukraft 35, K. Schweda 100, G. Scioli 28, E. Scomparin 59, J.E. Seger 15,
Y. Sekiguchi126, D. Sekihata 126, M. Selina 87, I. Selyuzhenkov 100, S.
Senyukov 131, J.J. Seo 97,61, D. Serebryakov 146, L. Šerkšnytė 98, A. Sevcenco
66, T.J. Shaba 71, A. Shabetai 106, R. Shahoyan35, A. Shangaraev 146, A.
Sharma93, B. Sharma 94, D. Sharma 49, H. Sharma 56,110, M. Sharma 94, S.
Sharma 79, S. Sharma 94, U. Sharma 94, A. Shatat 133, O. Sheibani118, K.
Shigaki 95, M. Shimomura80, J. Shin12, S. Shirinkin 146, Q. Shou 42, Y.
Sibiriak 146, S. Siddhanta 54, T. Siemiarczuk 82, T.F. Silva 113, D. Silvermyr
78, T. Simantathammakul108, R. Simeonov 39, B. Singh94, B. Singh 98, K. Singh
50, R. Singh 83, R. Singh 94, R. Singh 50, S. Singh 16, V.K. Singh 137, V.
Singhal 137, T. Sinha 102, B. Sitar 13, M. Sitta 135,59, T.B. Skaali21, G.
Skorodumovs 97, M. Slupecki 46, N. Smirnov 142, R.J.M. Snellings 62, E.H.
Solheim 21, J. Song 17, C. Sonnabend 35,100, F. Soramel 30, A.B. Soto-
hernandez 91, R. Spijkers 87, I. Sputowska 110, J. Staa 78, J. Stachel 97, I.
Stan 66, P.J. Steffanic 124, S.F. Stiefelmaier 97, D. Stocco 106, I. Storehaug
21, P. Stratmann 140, S. Strazzi 28, A. Sturniolo 33,55, C.P. Stylianidis87,
A.A.P. Suaide 113, C. Suire 133, M. Sukhanov 146, M. Suljic 35, R. Sultanov
146, V. Sumberia 94, S. Sumowidagdo 85, S. Swain64, I. Szarka 13, M.
Szymkowski 138, S.F. Taghavi 98, G. Taillepied 100, J. Takahashi 114, G.J.
Tambave 83, S. Tang 6, Z. Tang 122, J.D. Tapia Takaki 120, N. Tapus128, L.A.
Tarasovicova 140, M.G. Tarzila 48, G.F. Tassielli 34, A. Tauro 35, G. Tejeda
Muñoz 47, A. Telesca 35, L. Terlizzi 27, C. Terrevoli 118, S. Thakur 4, D.
Thomas 111, A. Tikhonov 146, A.R. Timmins 118, M. Tkacik109, T. Tkacik 109, A.
Toia 67, R. Tokumoto95, K. Tomohiro95, N. Topilskaya 146, M. Toppi 51, T. Tork
133, V.V. Torres 106, A.G. Torres Ramos 34, A. Trifiró 33,55, A.S. Triolo
35,33,55, S. Tripathy 53, T. Tripathy 49, S. Trogolo 35, V. Trubnikov 3, W.H.
Trzaska 119, T.P. Trzcinski 138, A. Tumkin 146, R. Turrisi 56, T.S. Tveter 21,
K. Ullaland 22, B. Ulukutlu 98, A. Uras 130, G.L. Usai 24, M. Vala40, N. Valle
23, L.V.R. van Doremalen62, M. van Leeuwen 87, C.A. van Veen 97, R.J.G. van
Weelden 87, P. Vande Vyvre 35, D. Varga 141, Z. Varga 141, M. Vasileiou 81, A.
Vasiliev 146, O. Vázquez Doce 51, O. Vazquez Rueda 118, V. Vechernin 146, E.
Vercellin 27, S. Vergara Limón47, R. Verma49, L. Vermunt 100, R. Vértesi 141,
M. Verweij 62, L. Vickovic36, Z. Vilakazi125, O. Villalobos Baillie 103, A.
Villani 26, A. Vinogradov 146, T. Virgili 31, M.M.O. Virta 119, V.
Vislavicius78, M. Viviani 58, A. Vodopyanov 147, B. Volkel 35, M.A. Völkl 97,
K. Voloshin146, S.A. Voloshin 139, G. Volpe 34, B. von Haller 35, I. Vorobyev
98, N. Vozniuk 146, J. Vrláková 40, J. Wan42, C. Wang 42, D. Wang42, Y. Wang
42, Y. Wang 6, A. Wegrzynek 35, F.T. Weiglhofer41, S.C. Wenzel 35, J.P.
Wessels 140, S.L. Weyhmiller 142, J. Wiechula 67, J. Wikne 21, G. Wilk 82, J.
Wilkinson 100, G.A. Willems 140, B. Windelband 97, M. Winn 132, J.R. Wright
111, W. Wu42, Y. Wu 122, R. Xu 6, A. Yadav 45, A.K. Yadav 137, S. Yalcin 75,
Y. Yamaguchi 95, S. Yang22, S. Yano 95, Z. Yin 6, I.-K. Yoo 17, J.H. Yoon 61,
H. Yu12, S. Yuan22, A. Yuncu 97, V. Zaccolo 26, C. Zampolli 35, F. Zanone 97,
N. Zardoshti 35, A. Zarochentsev 146, P. Závada 65, N. Zaviyalov146, M. Zhalov
146, B. Zhang 6, C. Zhang 132, L. Zhang 42, S. Zhang 42, X. Zhang 6, Y.
Zhang122, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii 146, Y. Zhi10, D. Zhou 6,
Y. Zhou 86, J. Zhu 100,6, Y. Zhu6, S.C. Zugravel 59, N. Zurlo 136,57

## Affiliation Notes

I Also at: Max-Planck-Institut für Physik, Munich, Germany
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VI Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

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