Anisotropic flow of charged particles in Pb-Pb collisions at \(\sqrt{s_{\rm NN}}\) = 5.02 TeV

Anisotropic Flow of Charged Particles in Pb-Pb Collisions at p ffiffiffiffiffiffiffiffi s

¼ 5.02 TeV

J. Adamet al.^* (The ALICE Collaboration)

(Received 4 February 2016; published 1 April 2016)

We report the first results of elliptic (v2), triangular (v3), and quadrangular (v4) flow of charged particles in Pb-Pb collisions at a center-of-mass energy per nucleon pair of ffiffiffiffiffiffiffiffi

sNN

p ¼5.02TeV with the ALICE detector at the CERN Large Hadron Collider. The measurements are performed in the central pseudorapidity region jηj<0.8 and for the transverse momentum range 0.2< pT<5GeV=c. The anisotropic flow is measured using two-particle correlations with a pseudorapidity gap greater than one unit and with the multiparticle cumulant method. Compared to results from Pb-Pb collisions at

ffiffiffiffiffiffiffiffi sNN

p ¼2.76TeV, the anisotropic flow coefficientsv2,v3, andv4are found to increase byð3.00.6Þ%, ð4.31.4Þ%, and ð10.23.8Þ%, respectively, in the centrality range 0%–50%. This increase can be attributed mostly to an increase of the average transverse momentum between the two energies. The measurements are found to be compatible with hydrodynamic model calculations. This comparison provides a unique opportunity to test the validity of the hydrodynamic picture and the power to further discriminate between various possibilities for the temperature dependence of shear viscosity to entropy density ratio of the produced matter in heavy-ion collisions at the highest energies.

DOI:10.1103/PhysRevLett.116.132302

The goal of studies with relativistic heavy-ion collisions is to investigate the quark-gluon plasma (QGP), a state of matter where quarks and gluons move freely over distances that are large in comparison to the typical size of a hadron. The transition from normal nuclear matter to the QGP state is expected to occur at extreme values of energy density (0.2–0.5 GeV=fm³, according to lattice quantum chromody- namics calculations[1,2]), which are accessible in ultrarela- tivistic heavy-ion collisions at the Large Hadron Collider (LHC)[3,4]. The study of such collisions provides a unique opportunity to probe the properties of the QGP in a region of the QCD phase diagram where a crossover between the deconfined phase and normal nuclear matter is expected[5–9].

Studies of the azimuthal anisotropy of particle produc- tion have contributed significantly to the characterization of the system created in heavy-ion collisions [10,11].

Anisotropic flow, which measures the momentum anisotropy of the final-state particles, is sensitive both to the initial geometry of the overlap region and to the transport properties and equation of state of the system.

By using a general Fourier series decomposition of the azimuthal distribution of produced particles,

dN

dφ ∝1þ2X^∞

n¼1

v_ncos½nðφ−Ψ_nÞ; ð1Þ

anisotropic flow is quantified with coefficients vn and corresponding symmetry planes Ψn [12]. Because of the approximately ellipsoidal shape of the overlap region in noncentral heavy-ion collisions (i.e., collisions that corre- spond to a large impact parameter), the dominant flow coefficient isv2, referred to as elliptic flow. In the transition from highest RHIC to LHC energies, elliptic flow increases by 30% [13], as predicted by hydrodynamic models that include viscous corrections[14–18]. Nonvanishing values of higher anisotropic flow harmonicsv₃–v₆at the LHC are ascribed primarily to the response of the produced QGP to fluctuations of the initial energy density profile of the colliding nucleons [19–22]. Moreover, because of such fluctuations, each flow harmonic vn has a distinct sym- metry plane Ψn and recent measurements of their inter- correlations provide independent constraints on the QGP properties [23]. The combination of all such results demonstrates that the shear viscosity to entropy density ratio (η=s) of the QGP produced in ultrarelativistic heavy- ion collisions at RHIC and LHC has a value close to1=4π, a lower bound obtained in strong-coupling calculations based on the AdS=CFT conjecture[24].

Recently, predictions from Niemi et al. on anisotropic flow coefficients for Pb–Pb ffiffiffiffiffiffiffiffi

s_NN

p ¼5.02TeV collisions using the Eskola-Kajantie-Ruuskanen-Tuominen model were reported in Ref.[25]. These predictions have a special emphasis on the discriminating power between various parametrizations of the temperature dependence ofη=s. It was argued that in the transition from 2.76 to 5.02 TeV, the elliptic flow estimated from two-particle correlations (denoted further in the text asv₂f2g, where the number in the curly brackets indicates the number of particles that

*Full author list given at the end of the article.

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- bution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

are used in correlation[26]) can increase, at most,∼5%for all centrality classes. Details of the increase depend on the parametrization ofη=sðTÞ. On the other hand, higher flow harmonic observables, likev₃f2gandv₄f2g, are predicted to increase more rapidly, 10%–30%. With a different approach, where previously measured values of flow harmonics at lower LHC energies are taken as a baseline, Noronha-Hostler et al. [27] predict a larger increase for both elliptic and triangular flow in peripheral compared to central collisions in transition from 2.76 to 5.02 TeV. They conclude that the anisotropic flow already reaches satu- ration and its maximum value in central collisions at 2.76 TeV.

A necessary condition for the development of aniso- tropic flow is the initial anisotropy in the interaction region of the two colliding ions. These coordinate space anisot- ropies are described in terms of eccentricities, which are not directly accessible experimentally. Nonetheless, the theo- retical modeling of such eccentricities is actively being studied. For instance, hydrodynamic calculations based on a MC-Glauber model and MC–Kharzeev-Levin-Nardi ini- tial conditions do not agree on the details of the saturation of elliptic flow at LHC energies[28]. However, with these two initial state models, it was shown that the final spatial eccentricity decreases monotonically as the collision energy increases[28], and is expected to become negative only at the very large collision energies available at the LHC (see Fig. 9 in Ref.[28]).

In addition to the initial conditions, various other stages of evolution of the system in a heavy-ion collision may contribute to the development of anisotropic flow. At lower energies, the state of the system will primarily resemble a hadronic gas, and hadron rescattering is the dominant contribution to the anisotropic flow. At higher energies, anisotropic flow mostly develops in the thermalized color- deconfined QGP phase. However, even at these higher energies, the contribution from the hadronic phase can be significant. The relative amount of time the system spends in different phases varies with collision energy [28,29].

Radial flow, a measure for the average velocity of the system’s collective radial expansion, also increases as a function of collision energy, which translates into more particles being transferred to a higher transverse momen- tum (pT) region, thus leading to an increase in average anisotropic flow values. On the other hand, the opposite dependence of differentialv₂ðp_TÞis expected for light (an increase at lowpT) and heavy particles (a decrease at low pT) as a function of collision energy, which might yield to the saturation of the elliptic flow signal[28]. Finally, the relative importance of various stages in the system evolu- tion as a function of collision energy can also vary for each flow coefficient [29].

The data used in this Letter were recorded with the ALICE detector[30,31]in November 2015 in run 2 at the LHC with Pb-Pb collisions at ffiffiffiffiffiffiffiffi

s_NN

p ¼5.02TeV. Minimum

bias Pb–Pb events were triggered by the coincidence of signals from the V0 detector. The V0 detector is composed of two arrays of scintillator counters, V0-A and V0-C, which cover the pseudorapidity ranges2.8<η<5.1and

−3.7<η<−1.7, respectively [30]. Centrality quantifies the fraction of a geometrical cross section of the colliding nuclei. It is determined using the sum of the amplitudes of the V0-A and -C signals, which provides a resolution better than 0.5% and up to 20% for central Pb-Pb collisions, and better than 2% for peripheral collisions[32]. The off-line event selection employs the information from two zero degree calorimeters (ZDCs)[30]positioned 112.5 m from the interaction point on either side. Beam background events are removed using timing information from the V0 and the ZDCs, respectively. To ensure a uniform acceptance and reconstruction efficiency in the pseudorapidity region jηj<0.8, only events with a reconstructed vertex within 10 cm from the center of the detector along the beam direction were used. A sample of 140 k Pb-Pb collision events passed the selection criteria. Only one low lumi- nosity run (with a trigger rate of 27 Hz) was used, being least affected by pileup and distortions from space charge in the main tracking detector, the time projection cham- ber (TPC).

Charged tracks are reconstructed using the ALICE inner tracking system (ITS) and the TPC[30]. This combination ensures a high detection efficiency, optimum momentum resolution, and a minimum contribution from photon conversions and secondary charged particles produced either from the detector material or from weak decays.

In order to reduce the contamination from secondary particles, only tracks with a distance of closest approach to the interaction point of less than 3 cm, both in the longitudinal and transverse directions, are accepted. The tracking efficiency is calculated from a Monte Carlo simulation that uses HIJING [33] to simulate particle production. GEANT3 [34] is then used for transporting simulated particles, followed by a full calculation of the detector response (including the production of secondary particles) and track reconstruction performed with the ALICE reconstruction framework. The tracking efficiency is ∼70% at pT∼0.2GeV=c and increases to an approx- imately constant value of∼80%for pT >1GeV=c. The p_T resolution is better than 5% for the region presented in this Letter. The systematic uncertainty related to the nonuniform reconstruction efficiency was found to be at the level of 1%. The flow coefficients from tracks that are reconstructed from TPC space points alone were compared to coefficients extracted from particles that used both TPC clusters and ITS hits, which were found to agree within ∼2%. This difference was taken into account in the estimation of the systematic uncertainty. Altering the selection criteria for the tracks reconstructed with the TPC resulted in a variation of the results of 0.5%, at most. Other selection criteria that have been scrutinized are the

centrality determination, e.g., using the silicon pixel detec- tor (SPD), which contributed by less than 1%, the polarity of the magnetic field of the ALICE detector and the position of the reconstructed primary vertex, whose con- tributions were found to be negligible. The systematic uncertainties evaluated for each of the sources mentioned above were added in quadrature to obtain the total systematic uncertainty of the measurements.

In this Letter, we report the anisotropic flow measure- ments obtained from two- and multiparticle cumulants, using the approach proposed in Refs.[35–37]. These two measurements have different sensitivities to flow fluctua- tions and nonflow effects. Nonflow effects are azimuthal correlations not associated with the symmetry planes and usually arise from resonance decays and jets. Their con- tributions are expected to be suppressed when using a large pseudorapidity gap between particle pairs. Thus, in this study, we require a pseudorapidity gap of jΔηj>1. This observable is denoted as vnf2;jΔηj>1g. On the other hand, nonflow contributions to multiparticle cumulants vnf4g,vnf6g, vnf8g are found to be negligible in events with large multiplicities characteristic of heavy-ion collisions[38].

Figure1(a)presents the centrality dependence ofv2,v3, andv4 from two- and multiparticle cumulants, integrated over the pT range 0.2< pT <5.0 GeV=c, for 2.76 and 5.02 TeV Pb-Pb collisions. To elucidate the energy evo- lution of v₂, v₃, and v₄, the ratios of anisotropic flow measured at 5.02 to 2.76 TeV are presented in Figs.1(b)and 1(c). Assuming that nonflow effects are suppressed by the pseudorapidity gap, the remaining differences between two- and multiparticle cumulants of v₂ can be related to the strength of elliptic flow fluctuations, which are expected to give a positive and a negative contribution to the two- and multiparticle cumulant estimates, respec- tively [11]. Moreover, the multiparticle cumulants v₂f4g, v₂f6g, and v₂f8g are all observed to agree within 1%, which indicates that nonflow effects are largely suppressed.

It is seen that v2f2;jΔηj>1g increases from central to peripheral collisions and reaches a maximum value of 0.1040.001ðstatÞ 0.002ðsystÞ in the 40%–50% cen- trality class. For the higher harmonics, i.e.,v3 andv4, the values are smaller and the centrality dependence is much weaker.

Furthermore, the predictions of anisotropic flow coef- ficients v_n from the previously mentioned hydrodynamic model[27]are compared to the measurements in Fig.1(a).

These predictions combine the changes in initial spatial anisotropy and the hydrodynamic response (treated as systematic uncertainty and shown by the width of the bands). The predictions are compatible with the measured anisotropic flow vn coefficients. At the same time, a different hydrodynamic calculation [25], which employs both constant η=s¼0.20 and temperature dependent η=s, can also describe the increase in anisotropic flow

measurements of v2 [shown in Fig. 1(b)], v3 and v4

[see Fig.1(c)]. In particular, among the different scenarios proposed in Ref.[25], the measurements seem to favor a constantη=sgoing from ffiffiffiffiffiffiffiffi

sNN

p ¼2.76to 5.02 TeV Pb-Pb collisions.

The increase ofv₂andv₃from the two energies is rather moderate, while forv₄it is more pronounced. In addition, none of the ratios of flow harmonics exhibit a significant centrality dependence in the centrality range 0%–50%, and thus the results of a fit with a constant value over these ratios are reported. An increase of ð3.00.6Þ%, ð4.31.4Þ%, and ð10.23.8Þ% is obtained for elliptic, triangular, and quadrangular flow, respectively, over the centrality range 0%–50% in Pb-Pb collisions when going from 2.76 to 5.02 TeV. This increase of anisotropic flow is compatible with theoretical predictions described in Refs. [25,27]. Overall, these measurements support a low value ofη=sfor the system created in Pb-Pb collisions at ffiffiffiffiffiffiffiffi

s_NN

p ¼5.02TeV and seem to indicate that it does not

0.05 0.1

0.15 ^{5.02 TeV}

|>1}

η Δ {2, | v2

|>1}

η Δ {2, | v3

|>1}

η Δ {2, | v4

2{4}

v

2{6}

v

2{8}

v

2.76 TeV

|>1}

η Δ {2, | v2

|>1}

η Δ {2, | v3

|>1}

η Δ {2, | v4

2{4}

v

5.02 TeV, Ref. [27]

|>1}

η Δ {2, | v2

|>1}

η Δ {2, | v3

ALICE Pb-Pb Hydrodynamics

(a)

1 1.1

1.2 η/s(T), param1

/s = 0.20 η

(b)

Hydrodynamics, Ref. [25]

v2 v₃ v₄

0 10 20 30 40 50 60 70 80

1 1.1 1.2

(c)

Ratio

Centrality percentile

nv Ratio

FIG. 1. (a) Anisotropic flow vn integrated over thepT range 0.2< pT<5.0GeV=c, as a function of event centrality, for the two-particle (withjΔηj>1) and multiparticle cumulant methods.

Measurements for Pb-Pb collisions at ffiffiffiffiffiffiffiffi sNN

p ¼5.02(2.76) TeV are shown by solid (open) markers [20]. The ratios of v2f2;jΔηj>1g(red),v2f4g(gray) andv3f2;jΔηj>1g(blue), v₄f2;jΔηj>1g (green) between Pb-Pb collisions at 5.02 and 2.76 TeV are presented in Figs. 1(b) and 1(c). Various hydro- dynamic calculations are also presented[25,27]. The statistical and systematical uncertainties are summed in quadrature (the systematic uncertainty is smaller than the statistical uncertainty, which is typically within 5%). Data points are shifted for visibility.

increase significantly with respect to Pb-Pb collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼2.76TeV.

The anisotropic flow coefficients v2f2;jΔηj>1g, v₃f2;jΔηj>1g, and v₄f2;jΔηj>1g as a function of transverse momentum (p_T) are presented in Fig. 2 for the 0%–5% and 30%–40% centrality classes. For the 0%–5% centrality class, atpT>2GeV=c v3f2gis observed to become larger than v2f2g, while v4f2g is compatible withv2f2g, within uncertainties. For the 30%–40% central- ity class, we see thatv₂f2gis higher thanv₃f2gandv₄f2g for the entirep_T range measured, with no crossing of the different order flow coefficients observed. Figure 2(c) presents the pT differential v2f4g for the 10%–20%, 20%–30% and 30%–40% centrality classes. The v2f4g decreases from midcentral to central collisions over thepT

range measured. The comparison with the corresponding measurements from Pb-Pb collisions at ffiffiffiffiffiffiffiffi

s_NN

p ¼2.76TeV exhibits comparable values, as illustrated by the ratio of v₂f4g for the two energies in Fig. 2(d). This indicates that the increase observed in thep_T integrated flow results seen in Fig. 1 can be attributed to an increase of mean transverse momentum hp_Ti. The measurements of pT- differential flow are more sensitive to initial conditions and η=s, and they are expected to provide important informa- tion to constrain further details of the theoretical calcu- lations, e.g., determination of radial flow and freeze-out conditions.

Figure 3 presents the comparison of the fully pT

integrated v2 measured in the 20%–30% centrality in Pb-Pb collisions at the LHC with results at lower energies.

This integrated value in the full pT range is determined using two methods. The first uses fits to the efficiency-

corrected charged-particle spectra and the p_T differential v2f4g presented in Fig. 2, extrapolated to pT ¼0.

The error on the integratedv2 is estimated both from the uncertainty on thepT-differential measurements and from different parametrizations that provide a good fit of the data. The second calculatesv2f4gusing tracklets formed from SPD hits in the ITS, which have an acceptance of pT ≳50MeV=c. As each method uses different ALICE subdetectors, they can provide independent measurements of v₂ coefficients. For this centrality range, they agree within 1% for both energies. The values presented in the

0 0.1 0.2

5.02 TeV

|>1}

η Δ {2, | v2

|>1}

η Δ {2, | v3

|>1}

η Δ {2, | v4

2.76 TeV

|>1}

η Δ {2, | v2

|>1}

η Δ {2, | v3

|>1}

η Δ {2, | v4

ALICE Pb-Pb 0%-5% (a)

0 1 2 3 4 5

0 0.1 0.2

30%-40% (b)

0.1 0.2 0.3

0.4 (c)

2.76 TeV 10%-20%

20%-30%

30%-40%

5.02 TeV 10%-20%

20%-30%

30%-40%

ALICE Pb-Pb

) c (GeV/

pT

0 1 2 3 4 5

Ratio

0.9 1 1.1

(2.76 TeV) (d)

2{4}

v (5.02 TeV) /

2{4}

v 20%-30%

| > 1.0}ηΔ{2, |nv| > 1.0}ηΔ{2, |nv

) c (GeV/

pT

{4}2v

FIG. 2. vnðpTÞusing the two-particle cumulant method withjΔηj>1for (a) 0%–5% and (b) 30%–40% centrality classes; (c)v2ðpTÞ using four-particle cumulant method for the centrality 10%ffiffiffiffiffiffiffiffi –20%, 20%–30%, and 30%–40%. Measurements for Pb-Pb collisions at

sNN

p ¼2.76TeV are also presented as shading. (d) The ratio ofv2f4gin 20%–30% from two collision energies is also shown here.

The statistical and systematical uncertainties are summed in quadrature (the systematic uncertainty is smaller than the statistical uncertainty, which is typically within 5%).

(GeV) sNN

1 10 10² 10³ 10⁴

2v

−0.08

−0.06

−0.04

−0.02 0 0.02 0.04 0.06 0.08

ALICE STAR PHOBOS PHENIX NA49 CERES E877 EOS E895 FOPI

FIG. 3. Integrated elliptic flow (v2f4g) for the 20%–30% most central Pb-Pb collisions at ffiffiffiffiffiffiffiffi

sNN

p ¼5.02TeV compared withv2

measurements at lower energies with similar centralities (see Ref.[13] for references to all data points).

figure are weighted averages of these two measurements, using the inverse of the variance of each of them as weights.

A continuous increase of anisotropic flow for this centrality has been observed from SPS and RHIC to LHC energies.

For these fully pT integrated coefficients, an increase of ð4.91.9Þ% is observed going from ffiffiffiffiffiffiffiffi

sNN

p ¼2.76 to 5.02 TeV, which is close to the values of the previously mentioned hydrodynamic calculations [25,27].

In summary, we have presented the first anisotropic flow measurements of charged particles in Pb-Pb collisions at ffiffiffiffiffiffiffiffi

s_NN

p ¼5.02TeV at the LHC. An average increase of ð3.00.6Þ%, ð4.31.4Þ%, and ð10.23.8Þ% is observed for the transverse momentum integrated elliptic, triangular, and quadrangular flow, respectively, over the centrality range 0%–50%, going from 2.76 to 5.02 TeV.

The transverse momentum dependence of anisotropic flow has also been investigated, and it does not change appreci- ably between the two LHC energies. Therefore, the increase in integrated flow coefficients can be attributed mostly to an increase in average transverse momentum. The measurements are found to be compatible with predictions from hydrodynamic models[25,27]. Further comparisons of pT-differential flow measurements and theoretical cal- culations, which are not available at this time, will provide extra constraints on the initial conditions and the transport properties of the QGP.

The ALICE Collaboration would like to thank all of 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 centers 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: the State Committee of Science, the World Federation of Scientists (WFS), and Swiss Fonds Kidagan, Armenia;

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de Amparo à Pesquisa do Estado de Sáo Paulo (FAPESP); the National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE), and the Ministry of Science and Technology of China (MSTC); the Ministry of Education and Youth of the Czech Republic; the Danish Natural Science Research Council, the Carlsberg Foundation, and the Danish National Research Foundation; the European Research Council under the European Community’s Seventh Framework Programme; the Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the

“Region Pays de Loire,”the“Region Alsace,”the“Region Auvergne,”and CEA, France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie (BMBF), and the Helmholtz Association; the General

Secretariat for Research and Technology, Ministry of Development, Greece; the National Research, Development and Innovation Office (NKFIH), Hungary;

the Department of Atomic Energy and Department of Science and Technology of the Government of India;

Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi—Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi,”Italy; the Japan Society for the Promotion of Science (JSPS) KAKENHI and MEXT, Japan;

the Joint Institute for Nuclear Research, Dubna; the National Research Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT), Direccion General de Asuntos del Personal Academico(DGAPA), México, Amerique Latine Formation academique–European Commission (ALFA-EC), and the EPLANET Program (European Particle Physics Latin American Network);

Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands;

Research Council of Norway (NFR); National Science Centre, Poland; Ministry of National Education and Institute for Atomic Physics and National Council of Scientific Research in Higher Education (CNCSI- UEFISCDI), Romania; the Ministry of Education and Science of Russian Federation, the Russian Academy of Sciences, the Russian Federal Agency of Atomic Energy, the Russian Federal Agency for Science and Innovations, and the Russian Foundation for Basic Research; the Ministry of Education of Slovakia; the Department of Science and Technology, South Africa; Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA), Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia (Consellería de Educación), Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency); the Swedish Research Council (VR) and the Knut and Alice Wallenberg Foundation (KAW); the Ukraine Ministry of Education and Science;

the United Kingdom Science and Technology Facilities Council (STFC); the United States Department of Energy, the United States National Science Foundation; Ministry of Science, Education and Sports of Croatia and Unity through Knowledge Fund, Croatia; Council of Scientific and Industrial Research (CSIR), New Delhi, India; and Pontificia Universidad Católica del Perú.

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F. Ronchetti,^72,35 L. Ronflette,¹¹³ P. Rosnet,⁷⁰A. Rossi,^35,29 F. Roukoutakis,⁸⁹ A. Roy,⁴⁸C. Roy,⁵⁵P. Roy,¹⁰⁰ A. J. Rubio Montero,¹⁰R. Rui,²⁵R. Russo,²⁶E. Ryabinkin,⁸⁰Y. Ryabov,⁸⁶A. Rybicki,¹¹⁷S. Saarinen,⁴⁵S. Sadhu,¹³²