Evidence of Spin-Orbital Angular Momentum Interactions in Relativistic Heavy-Ion Collisions
S. Acharyaet al.* (The ALICE Collaboration)
(Received 21 November 2019; revised 25 February 2020; accepted 27 May 2020; published 30 June 2020) The first evidence of spin alignment of vector mesons (K0andϕ) in heavy-ion collisions at the Large Hadron Collider (LHC) is reported. The spin density matrix element ρ00 is measured at midrapidity (jyj<0.5) in Pb-Pb collisions at a center-of-mass energy ( ffiffiffiffiffiffiffiffi
sNN
p ) of 2.76 TeV with the ALICE detector.ρ00
values are found to be less than 1=3 (1=3 implies no spin alignment) at low transverse momentum (pT<2GeV=c) for K0 andϕ at a level of3σ and 2σ, respectively. No significant spin alignment is observed for theK0Smeson (spin¼0) in Pb-Pb collisions and for the vector mesons inppcollisions. The measured spin alignment is unexpectedly large but qualitatively consistent with the expectation from models which attribute it to a polarization of quarks in the presence of angular momentum in heavy-ion collisions and a subsequent hadronization by the process of recombination.
DOI:10.1103/PhysRevLett.125.012301
Ultrarelativistic heavy-ion collisions create a system of deconfined quarks and gluons, called the quark-gluon plasma (QGP)[1–3]and provide the opportunity to study its properties. In collisions with nonzero impact parameter, a large angular momentum ofOð107Þℏ[4] and magnetic field of Oð1014Þ T [5] are also expected. While the magnetic field is short lived (a few fm=c), the angular momentum is conserved and could affect the system throughout its evolution. Experimental observables like correlations in azimuthal angle[6,7]could be used to study the influence of these initial conditions on the properties and the dynamical evolution of the QGP and its subsequent hadronization.
Spin-orbit interactions have wide observable conse- quences in several branches of physics [8–10]. In the presence of a large angular momentum, the spin-orbit coupling of quantum chromodynamics (QCD) could lead to a polarization of quarks followed by a net-polarization of vector mesons (K0andϕ)[11–15]along the direction of the angular momentum.
The spin state of a vector meson is described by a3×3 Hermitian spin-density matrix [15]. Its trace is 1 and ρ11
and ρ−1−1 cannot be measured separately in two-body decays to pseudoscalar mesons. Consequently, there is only one independent diagonal element,ρ00. The elements of the spin-density matrix can be studied by measuring the
angular distributions of the decay products of vector mesons with respect to a quantization axis. Here two different quantization axes are used: (i) a vector perpendicular to the production plane (PP) of the vector meson and (ii) the normal to the reaction plane (RP) of the system. The PP is defined by the flight direction of the vector meson and the beam direction.
The spin-density matrix elementρ00 is determined from the distribution of the angle θ between the kaon decay daughter and the quantization axis in the decay rest frame [16,17],
dN
dcosθ∝½1−ρ00þcos2θð3ρ00−1Þ: ð1Þ ρ00is1=3in the absence of spin alignment and the angular distribution in Eq. (1) is uniform. The experimental signature of spin alignment is a nonuniform angular distribution (ρ00≠1=3).
The direction of the angular momentum in noncentral heavy-ion collisions is perpendicular to the reaction plane (subtended by the beam axis and impact parameter)[12].
The spin-orbit interaction is expected to lead to spin alignment with respect to the RP. The reaction plane orientation cannot be measured directly, but is estimated from the final state distributions of particles. This exper- imentally measured plane is called the event plane (EP) [18]. The deviation of the EP with respect to the RP is corrected using the EP resolution (R) and observed ρobs00 [19],
ρ00¼1 3þ
ρobs00 −1
3
4
1þ3R: ð2Þ
*Full author list given at the end of the article.
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Editors' Suggestion
There are specific qualitative predictions for the spin alignment effect [13]: (a) ρ00>1=3 if the hadronization of a polarized parton proceeds via fragmentation and less than 1=3 for hadronization via recombination, (b) ρ00 is expected to have a smaller deviation from 1=3 for both central (impact parameter ≲3fm) and peripheral (impact parameter≳11fm) heavy-ion collisions, and a maximum deviation for mid-central collisions, where the angular momentum is also maximal, (c) theρ00 value is expected to have maximum deviation from1=3at lowpT and reach the value of1=3at highpT in the recombination scenario, and (d) the effect is expected to be larger forK0compared toϕdue to their constituent quark composition. The initial large magnetic field might also affect theρ00 values[15].
This leads to ρ00> 1=3 for neutral and ρ00<1=3 for charged vector mesons. Hence magnetic field and angular momentum could have opposite effects on electrically neutral K0, ϕ. All of these features are probed for K0 andϕmesons in Pb-Pb collisions presented in this Letter.
As a cross check, a control measurement is carried out using pp collisions, which do not possess large initial angular momentum, and the same analysis is done in Pb-Pb collisions forK0S meson, which has zero spin. In addition, the measurements are carried out by randomizing the directions of the event (RNDEP) and production planes.
The analyses are carried out using 43 million minimum bias pp collisions at ffiffiffi
ps
¼13TeV, taken in 2015 and
14ffiffiffiffiffiffiffiffimillion minimum bias Pb-Pb collisions at
sNN
p ¼2.76TeV, collected in 2010. The minimum bias event selection in Pb-Pb collisions require at least one hit in any of V0A, V0C, and silicon pixel detectors while inpp collisions at least one hit in both V0A and V0C is required.
The events are further required to have a primary vertex position within 10cm of the detector center along the beam axis. The events were classified by collision central- ity classes based on the amplitude measured in the V0 counters [20]. The measurements are performed at mid- rapidity (jyj<0.5) as a function ofpT and are reported for ppcollisions as well as for different centrality classes in Pb-Pb collisions. TheK0Sanalysis is performed only for Pb- Pb collisions in the 20–40% centrality class which corre- sponds to the top 20–40% of V0 amplitude distribution.
The details of the ALICE detector, trigger conditions, centrality selection, and second order event plane estima- tion using the V0 detectors at forward rapidity, can be found in [20–23]. The K0 and ϕ candidates are recon- structed via their decays into charged Kπ and KK pairs, respectively, while theK0Sis reconstructed via its decay into two charged pions. The time projection chamber (TPC) [24] and time-of-flight (TOF) detector [25] are used to identify the decay products of these mesons via specific ionization energy loss and time-of-flight measurements, respectively. TheK0 andϕyields are determined via the invariant mass technique[26–28]. The background coming from combinatorial pairs and misidentified particles is
removed by constructing the invariant mass distribution from so-called mixed events for theK0andϕ[26,27]. The combinatorial background for theK0S candidates is signifi- cantly reduced by selecting the distinctiveV-shaped decay topology[28].
The invariant mass distributions are fitted with a Breit- Wigner and Voigtian (convolution of Breit-Wigner and Gaussian distributions) function for theK0andϕsignals, respectively, along with a second-order polynomial that describes the residual background [26,27]. Extracted yields are then corrected for the reconstruction efficiency and acceptance in each cosθ and pT bin [26,27]. The reconstruction efficiency is determined from Monte Carlo simulations of the ALICE detector response based on
GEANT3 simulation [26,27]. The signal extraction proce- dures for the vector mesons andK0S are identical to those used in earlier publications reporting thepTdistribution of the mesons[26–28]. The mass peak positions and widths of the resonances across all the cosθ bins for various pT
intervals inppcollisions and in different centrality classes of Pb-Pb collisions are consistent with those obtained from earlier analyses[26–28]and no significant dependence on cosθ is seen. The resulting efficiency and acceptance correcteddN=dcosθ distributions for selected pT inter- vals in minimum biasppcollisions and in 10–50% central Pb-Pb collisions are shown in Fig. 1. These distributions are fitted with the functional form given in Eq. (1) to determineρ00for eachpT bin inppand Pb-Pb collisions.
For the EP results, the resolution valuesR are 0.71, 0.53, 0.72, 0.66, and 0.40 for 10–50%, 0–10%, 10–30%,
θ* cos
0 0.2 0.4 0.6 0.8 1
)*θ/dcosN) (devtN(1/
0 0.05 0.1
(c)
c < 0.6 GeV/
pT
≤ , 0.0 K*0
× 7) ( c < 0.8 GeV/
pT
≤ , 0.5 φ
Production plane pp
)*θ/dcosN) (devtN(1/ 0
2 4
(a)
c < 1.2 GeV/
pT
≤ , 0.8 K*0
× 5) ( c < 0.7 GeV/
pT
≤ , 0.5 φ
Event plane
−50%) Pb (10
− Pb
Bar: Stat. uncertainty on yield Box: Syst. uncertainty on yield
θ *]
- 1)cos2
ρ00 ) + (3 ρ00 [(1 - N0
Variation of fit function due
ρ00 to syst. uncertainty on
θ* cos
0 0.2 0.4 0.6 0.8 1
)*θ/dcosN) (devtN(1/
0 5 (b) 10
c < 1.2 GeV/
pT
≤ , 0.4 K*0
× 8) ( c < 0.8 GeV/
pT
≤ , 0.5 φ
Production plane
−50%) Pb (10
− Pb
ALICE
FIG. 1. Angular distribution of the decay daughter in the rest frame of the meson with respect to the quantization axis atjyj<
0.5 for pp collisions at ffiffiffi ps
¼13TeV and Pb-Pb collisions at ffiffiffiffiffiffiffiffi
sNN
p ¼2.76TeV. Panels (a) and (b) show results forK0andϕ with respect to EP and PP. Panel (c) is the results for vector mesons inppcollisions with respect to PP.
30–50%, and 50–80% collision centralities, respec- tively[29].
There are three main sources of systematic uncertainties in the measurements of the angular distribution of vector meson decays. (i) Meson yield extraction: this contribution is estimated by varying the fit ranges for the yield extraction, the normalization range for the signalþ background and background invariant mass distributions, the procedure to integrate the signal function to get the yields, and by leaving the width of the resonance peak free or keeping it fixed to the PDG value as discussed in Refs. [26,27]. The uncertainties for ρ00 is at a level of 12(8)% at the lowestpT and decrease withpT to 4(3)% at the highestpT studied for theK0ðϕÞ. (ii) Track selection:
this contribution includes variations of the selection on the distance of closest approach to the collision vertex, the number of crossed pad rows in the TPC [24], the ratio of found clusters to the expected clusters, and the quality of the track fit. The systematic uncertainties for ρ00 are 14(6)% at the lowest pT and about 11(5)% at the highest pT forK0ðϕÞ. (iii) Particle identification: this is evaluated by varying the particle identification criteria related to the TPC and TOF detectors. The corresponding uncertainty is 5(3)% at the lowestpTand about 4(4.5)% at the highestpT studied forK0ðϕÞ. Systematic uncertainties due to differ- ent variations are considered as uncorrelated and the total systematic uncertainty onρ00 is obtained by adding all the contributions in quadrature. Several consistency checks are carried out and details can be found in the Supplemental Material [17]. The final measurement is reported for the average yield of particles (K0) and antiparticles (K¯0) as results for K0 andK¯0 were consistent.
Figure2shows the measuredρ00as a function ofpT for K0 andϕmesons in ppcollisions and Pb-Pb collisions, along with the measurements forK0Sin Pb-Pb collisions. In mid-central (10–50%) Pb-Pb collisions,ρ00is below1=3at the lowest measured pT and increases to 1=3 within uncertainties for pT >2GeV=c. At low pT, the central value of ρ00 is smaller for K0 than for ϕ, although the results are compatible within uncertainties. In pp colli- sions, ρ00 is independent of pT and equal to 1=3 within uncertainties. For the spin zero hadronK0S,ρ00is consistent with 1=3 within uncertainties in Pb-Pb collisions. The results with random event plane directions are also com- patible with no spin alignment for the studied pT range, except for the smallestpT bin, whereρ00less than1=3but still larger than for EP and PP measurements. The results for the random production plane (the momentum vector direction of each vector meson is randomized) are similar to RNDEP measurements. These results indicate that a spin alignment is present at lower pT, which is a qualitatively consistent with predictions [13].
Figure3showsρ00forK0andϕmesons as a function of average number of participating nucleons (hNparti)[20,22]
for Pb-Pb collisions at ffiffiffiffiffiffiffiffi sNN
p ¼2.76TeV. Large hNparti
correspond to central collisions and small hNparti corre- spond to peripheral collisions (see Table I of the Supplemental Material[17]). In the lowest pT range,ρ00 shows maximum deviation from 1=3 for intermediate centrality and approaches1=3for both central and periph- eral collisions. This centrality dependence is qualitatively consistent with the dependence of the initial angular momentum on impact parameter in heavy-ion collisions [4]. At higher pT, ρ00 is consistent with 1=3 for all centrality classes. For the low-pT measurements in 10– 30% (20–40% forϕmeson with respect to PP) mid-central Pb-Pb collisions, the maximum deviations ofρ00from1=3 with respect to the PP (EP) are 3.2 (2.6)σand 2.1 (1.9)σfor K0 and ϕ mesons, respectively. The errors (σ) are calculated by adding statistical and systematic uncertainties in quadrature.
The relation between the ρ00 values with respect to different quantization axes can be expressed using Eq.(2)
) c (GeV/
pT
1 2 3 4 5
0.1 0.2 0.3 0.4
0.5 Random plane K*0
(e)
ALICE
|< 0.5
|y 0.1
0.2 0.3 0.4
0.5 Production plane K*0
(c) 0.1
0.2 0.3 0.4
0.5 Event plane K*0
(a)
) c (GeV/
pT
1 2 3 4 5
0.1 0.2 0.3 0.4 0.5 Random plane
φ
−50%) Pb (10
− Pb pp
−40%) Pb (20
−
S, Pb K0
(f) 0.1 0.2 0.3 0.4 0.5 Production plane
φ
(d) 0.1 0.2 0.3 0.4 0.5 Event plane
φ
(b)
= 1/3 ρ00
00ρ 00ρ
00ρ 00ρ
00ρ 00ρ
FIG. 2. Transverse momentum dependence ofρ00for K0,ϕ, and K0S mesons at jyj<0.5 in Pb-Pb collisions at ffiffiffiffiffiffiffiffi
sNN
p ¼
2.76TeV and minimum bias pp collisions at ffiffiffi ps
¼13TeV.
Results are shown for spin alignment with respect to the event plane [panels (a),(b)], production plane [(c),(d)], and random event plane [(e),(f)] forK0(left column) andϕ(right column).
The statistical and systematic uncertainties are shown as bars and boxes, respectively.
and calculating the corresponding factor R. This gives Δρ00ðRNDEPÞ ¼Δρ00ðEPÞ×14(R¼0for random plane) andΔρ00ðPPÞ ¼Δρ00ðEPÞ×ð1þ3v2Þ=4(R¼v2for pro- duction plane, wherev2is the second Fourier coefficient of the azimuthal distribution of produced particles relative to the event plane angle). Here Δρ00¼ρ00-1=3. This is further confirmed using a toy model simulation with the PYTHIA 8.2 event generator[30]by incorporatingv2and spin alignment (see the Supplemental Material [17] for further details).
In the past, spin alignment measurements in eþe− [31–33], hadron-proton [34] and nucleon-nucleus colli- sions[35]were carried out to understand the role of spin in the dynamics of particle production, findingρ00>1=3and off-diagonal elements close to zero with respect to the PP.
For pp collisions at ffiffiffi ps
¼13TeV, we find ρ00∼1=3 within the studiedpT range (see Fig.2). New preliminary results from RHIC have found deviations ofρ00from1=3 indicating spin alignment for vector mesons at lower ffiffiffiffiffiffiffiffi sNN
p [36,37]. The ρ00 for ϕ mesons in mid-central Pb-Pb collisions at ffiffiffiffiffiffiffiffi
sNN
p ¼2.76TeV is less than 1=3 while the preliminary finding for mid-central Au-Au collisions atffiffiffiffiffiffiffiffi
sNN
p ¼200GeV isρ00 greater than 1=3. The ρ00>1=3 for ϕ mesons has been interpreted as evidence for a coherent ϕ meson field [38]. Similar conclusions cannot be easily applied toK0as it consists of valence quarks of unequal mass (s and d¯), which makes it impossible to separate the effects of vorticity and due to electromangetic and mesonic fields. Significant polarization of Λbaryons (spin¼1=2) was reported at low RHIC energies. The polarization is found to decrease with increasing ffiffiffiffiffiffiffiffi sNN
p
[39,40]. At the LHC, the global polarization forΛbaryon is compatible with zero within uncertainties [PΛð%Þ ¼ 0.010.060.03] [41]. The spin alignment for vector mesons in heavy ion collisions could have contributions from angular momentum [12,13], electromagnetic fields [15] and mesonic fields [38]. While no quantitative theoretical calculation for vector meson polarization at LHC energies exists, the expected order of magnitude can be estimated and the measurements for vector mesons and hyperons can be related in a model dependent way.
Considering only the angular momentum contribution and recombination as the process of hadronization [13], theρ00of vector mesons are related to quark polarization as ρ00 ¼ ð1−PqPq¯Þ=ð3þPqPq¯ÞwherePqandPq¯are quark and antiquark polarization, respectively. Assuming Pu¼ Pu¯ ¼Pd¼Pd¯ andPs¼Ps¯, the measured pT integrated ρ00 values forK0andϕmesons in 10–50% Pb-Pb colli- sions could translate to light quark polarization of∼0.8and strange quark polarization of ∼0.2. Using a thermal and nonrelativistic approach as discussed in[42], vorticity (ω) and temperature (T) are related to ρ00 and vector meson polarization (PV) as ρ00≃13f1−½ðω=TÞ2=3g and PV≃ð2ω=3TÞ, respectively. Also in this approach, the measuredρ00forK0would correspond toK0polarization of ∼0.6 and the ρ00 for ϕ mesons would give ϕ meson polarization of∼0.3.
In the recombination model, Λ polarization depends linearly on quark polarization whereas vector meson polarization depends quadratically on it. One would there- fore expect the polarization forK0to be of the same order or smaller than the one measured for theΛat LHC[41], i.e., vanishing small [Oð0.01%Þ] rather than order 1. The large effect observed for theρ00in mid-central Pb-Pb collisions at lowpTis therefore puzzling. This result should stimulate further theoretical work in order to study which effects could make such a huge difference between Λ and K0 polarization. Possible reasons may include the transfer of the quark polarization to the hadrons (baryon vs meson), details of the hadronization mechanism (recombination vs fragmentation), rescattering, regeneration, and possibly the lifetime and mass of the relevant hadron. Moreover, the vector mesons are predominantly directly produced whereas the hyperons have large contributions from res- onance decays.
In conclusion, for the first time, evidence has been found for a significant spin alignment of vector mesons in heavy- ion collisions. The effect is strongest at lowpTwith respect to a vector perpendicular to the reaction plane and for mid- central (10–50%) collisions. These observations are quali- tatively consistent with expectations from the effect of large initial angular momentum in noncentral heavy-ion colli- sions, which leads to quark polarization via spin-orbit coupling, subsequently transferred to hadronic degrees of freedom by hadronization via recombination. However, the measured spin alignment is surprisingly large compared to
part〉
〈N
0 100 200 300
0.1 0.2 0.3 0.4
0.5 < 1.2 (GeV/c) pT
≤ 0.8
) c < 5.0 (GeV/
pT
≤ 3.0 Event plane K*0
part〉
〈N
0 100 200 300
0.1 0.2 0.3 0.4 Event plane 0.5
φ
) c < 0.7 (GeV/
pT
≤ 0.5
) c < 5.0 (GeV/
pT
≤ 3.0
ALICE y| < 0.5
| 0.1
0.2 0.3 0.4 0.5
) c < 1.2 (GeV/
pT
≤ 0.4
) c < 5.0 (GeV/
pT
≤ 3.0
Production plane K*0
0.1 0.2 0.3 0.4 0.5
= 2.76 TeV sNN
−Pb, Pb
) c < 0.8 (GeV/
pT
≤ 0.5
) c < 5.0 (GeV/
pT
≤ 3.0
Production plane
φ = 1/3
ρ00
00ρ 00ρ
00ρ 00ρ
FIG. 3. Measurements ofρ00as a function ofhNpartiforK0and ϕmesons at low and highpTin Pb-Pb collisions. The statistical and systematic uncertainties are shown as bars and boxes, respectively. Some data points are shifted horizontally for better visibility.
the polarization measured for Λ hyperons where, in addition, a strong decrease in polarization with ffiffiffiffiffiffiffiffi
sNN
p is observed. In future measurements, the difference in the polarization of K and Ko, due to their difference in magnetic moment, would be directly sensitive to the effect of the large initial magnetic field produced in heavy-ion collisions.
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 `a 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 `a l’Energie Atomique (CEA), Institut National de Physique Nucl´eaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS) and R´egion des Pays de la Loire, France; Bundesministerium für Bildung und Forschung
(BMBF) and GSI Helmholtzzentrum für
Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary;
Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India;
Indonesian Institute of Science, Indonesia; Centro Fermi
—Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico;
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia;
National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut &
Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.
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