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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-EP-2020-09929 May 2020

© 2020 CERN for the benefit of the ALICE Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

Elliptic and triangular flow of (anti)deuterons in Pb–Pb collisions at√sNN = 5.02 TeV

ALICE Collaboration*

Abstract

The measurements of the (anti)deuterons elliptic flow (v2) and the first measurements of triangu-lar flow (v3) in Pb–Pb collisions at a center-of-mass energy per nucleon–nucleon collisions

√sNN =

5.02 TeV are presented. A mass ordering at low transverse momentum (pT) is observed when com-paring these measurements with those of other identified hadrons, as expected from relativistic hydro-dynamics. The measured (anti)deuterons v2 lies between the predictions from the simple coalescenceand blast-wave models, which provide a good description of the data only for more peripheral andfor more central collisions, respectively. The mass number scaling, which is violated for v2 is ap-proximately valid for the (anti)deuterons v3. The measured v2 and v3 are also compared with thepredictions from a coalescence approach with phase-space distributions of nucleons generated byiEBE-VISHNU with AMPT initial conditions coupled with UrQMD, and from a dynamical modelbased on relativistic hydrodynamics coupled to the hadronic afterburner SMASH. The model predic-tions are consistent with the data within the uncertainties in mid-central collisions, while a deviationis observed in the most central collisions.

*See Appendix A for the list of collaboration members

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

1 Introduction

The production mechanism of light (anti)nuclei in high-energy hadronic collisions is still not fully clearand is under intense debate in the scientific community [1–5]. The understanding of the production ofloosely-bound multi-baryon states in heavy-ion collisions has additional complications due to the factthat the phase transition is followed by a hadrons gas phase with intense re-scattering of hadrons. At theLarge Hadron Collider (LHC) energies, the lifetime of the hadronic phase between chemical and kineticfreezeout is in the range 4–7 fm/c [6] and the kinetic freezeout temperature, when elastic interactionscease, is of the order of 100 MeV [7, 8]. The binding energy of multi-baryon systems such as light(anti)nuclei typically does not exceed a few MeV, which is almost two orders of magnitude smaller thanthe temperature of the system. Considering the high density of hadrons in the post-hadronization stageand the large dissociation cross sections of light (anti)nuclei, it is not clear how such loosely-boundsystems can survive under these extreme conditions.

Existing phenomenological models provide very different interpretations for this observation. In thestatistical hadronization model [1–3, 9, 10], light (anti)nuclei as well as all other hadron species areassumed to be emitted by a source in local thermal and hadrochemical equilibrium. Their abundances arefixed at the chemical freeze-out, occurring at a temperature of Tchem = 156 ± 4 MeV for Pb–Pb collisionsat the LHC [11]. This model provides a good description of the measured hadron yields in centralnucleus–nucleus collisions [1]. However, the mechanism of hadron production and the propagation ofloosely-bound states through the hadron gas phase are not addressed by this model. In the context of thestatistical hadronization model, it has been conjectured that such objects could be produced at the phasetransition as compact colorless quark clusters with the same quantum numbers of the final state hadrons.The survival of these states at high temperatures is interpreted as due to the low interaction cross sectionwith the surrounding medium [1].

In the coalescence approach, multi-baryon states are assumed to be formed by the coalescence of baryonsat the kinetic freeze-out. In the simplest versions of this model [12, 13], baryons are treated as point-likeparticles and the coalescence happens instantaneously if the momentum difference between nucleonsis smaller than a given threshold, which is typically of the order of 100 MeV/c, while spatial coor-dinates are ignored. In the state-of-the-art implementations of the coalescence approach [4, 14], thequantum-mechanical properties of baryons and their bound states are taken into account and the coales-cence probability is calculated from the overlap between the wave functions of baryons and the Wignerdensity of the final-state cluster. All light (anti)nuclei produced at the phase transition are assumed to bedestroyed by the interactions in the hadron gas phase and regenerated with the same amount only at thelatest stage of the system evolution.

To address the open question of the survival of loosely-bound multi-baryon states in the hadron gas phasewith intense re-scattering, models based on relativistic hydrodynamics coupled to a hadronic afterburnerhave been recently developed [4, 5]. In these models, nucleons and light nuclei are produced at the phasetransition using the Cooper-Frye formula [15], which describes the hadron production based on the localenergy density of the fireball, and their yields are fixed to the value predicted by the thermal modelat the chemical freeze-out temperature. Their propagation through the hadronic medium is simulatedbased on known interaction cross sections and resonant states using different transport codes. Existingcalculations are based on UrQMD [16, 17], with light nuclei being produced by nucleon coalescence, andSMASH [5], where (anti)deuterons are assumed to be destroyed and regenerated with equal rates in thehadronic stage. The model based on UrQMD with nucleon coalescence [4] provides a good descriptionof the elliptic flow of (anti)deuterons measured in Pb–Pb collisions at

√sNN = 2.76 TeV [18] and of

that of (anti)3He measured in Pb–Pb collisions at√

sNN = 5.02 TeV [19]. The model is able to describethe low-pT spectra of deuterons, but over-predicts the deuterons data above 2.5 GeV/c and the (anti)3Hespectra in the full momentum interval. The hybrid model based on SMASH successfully describes themeasured (anti)deuterons pT-spectra and coalescence parameter B2, defined as the ratio of the invariant

2

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

yield of deuterons and that of protons squared, measured in Pb–Pb collisions at√

sNN = 2.76 TeV [18].

A conceptually similar approach, based on the analogy between the evolution of the early universe afterthe Big Bang and the space–time evolution of the system created in heavy-ion collisions, has recentlybeen developed [20]. The production of light (anti)(hyper)nuclei in heavy-ion collisions at the LHC isconsidered in the framework of the Saha equation assuming that disintegration and regeneration reactionsinvolving light nuclei proceed in relative chemical equilibrium after the chemical freeze-out of hadrons.

The existing models depict radically different pictures of the post-hadronization stage for loosely-boundstates. Considering this scenario, the measurements of radial and anisotropic flow of light (anti)nuclei,i.e. the harmonics (vn) of the Fourier decomposition of their azimuthal production distribution withrespect to a symmetry plane of the collision, are relevant to study their propagation through the hadrongas phase and the dynamics of their interactions with other particles. Compared to the elliptic flow, thetriangular flow of light (anti)nuclei has a better sensitivity to the fluctuating initial conditions as well asthe properties of the created systems. Therefore, tighter constrains to on theoretical model that describethe production mechanism of light (anti)nuclei can be set.

The elliptic flow of (anti)deuterons was measured as a function of the transverse momentum (pT) for dif-ferent centrality classes in Pb–Pb collisions at

√sNN = 2.76 TeV [18]. A clear mass ordering is observed

at low pT (pT < 3 GeV/c) when this measurement is compared to that of other hadrons species [21],as expected from relativistic hydrodynamics. The simple coalescence model, based on the assumptionthat the (anti)deuterons invariant yield is proportional to the invariant yield of (anti)protons squared, isfound to overestimate the measured v2 in all centrality intervals. The data are better described by theblast-wave model, a simplified version of the relativistic hydrodynamic approach in which the collectiveexpansion is described using a parameterized hydrodynamic flow field. The elliptic flow of (anti)3Hewas measured in Pb–Pb collisions at

√sNN = 5.02 TeV [19]. Also in the case of (anti)3He, the mass

ordering is observed for pT < 3 GeV/c and the measured elliptic flow lies between the predictions of theblast-wave [22] and the simple coalescence model. A better description of the measurement is providedby a more sophisticated coalescence model where the phase-space distributions of protons and neutronsare generated by the iEBE-VISHNU hybrid model with AMPT initial conditions [4]. The picture that hasemerged so far, regarding the elliptic flow of (anti)nuclei measured at LHC energies, is that the simplecoalescence and blast-wave models represent the upper and lower edges of a region where the data aremostly located. Recent developments in the coalescence approach, which take into account momentum-space correlations of nucleons and their quantum-mechanical properties, provide a better description ofthe data [4, 5].

In this paper, a precision measurement of the (anti)deuterons elliptic flow and first ever measurementof (anti)deuterons triangular flow for different pT and centrality intervals in Pb–Pb collisions at

√sNN =

5.02 TeV are presented. Thanks to the large data sample collected at higher energy, the elliptic flowmeasurement is performed in wider pT and up to a higher centrality intervals compared to that in Pb–Pbcollisions at

√sNN = 2.76 TeV, allowing for a more differential comparison with the theoretical models.

2 The ALICE detector

A detailed description of the ALICE detector can be found in [23] and references therein. The main sub-detectors used for the present analysis are the V0 detector, the Inner Tracking System (ITS), the TimeProjection Chamber (TPC), and the Time-of-Flight detector (TOF), which are located inside a solenoidalmagnet that provides a uniform field of 0.5 T directed along the beam direction. The V0 detector [24]consists of two arrays of scintillation counters placed around the beam vacuum tube on either side ofthe interaction point: one covering the pseudorapidity interval 2.8 < η < 5.1 (V0A) and the other onecovering −3.7 < η <−1.7 (V0C). Each V0 array consists of four rings in the radial direction, with eachring comprising eight cells with the same azimuthal size. The scintillator arrays have an intrinsic time

3

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

resolution better than 0.5 ns, and their timing information is used in coincidence for offline rejection ofevents produced by the interaction of the beams with residual gas in the vacuum pipe. The V0 scintillatorsare used to determine the collision centrality from the measured charged-particle multiplicity [25–27] andto measure the orientation of the symmetry plane of the collision.

The ITS [28], designed to provide high-resolution track points in the vicinity of the nominal vertexposition, is composed of three subsystems of silicon detectors placed around the interaction region witha cylindrical symmetry. The Silicon Pixel Detector (SPD) is the subsystem closest to the beam vacuumtube and it is made of two layers of pixel detectors. The third and the fourth layers are formed by SiliconDrift Detectors (SDD), while the outermost two layers are equipped with double-sided Silicon StripDetectors (SSD). The ITS covers the pseudorapidity interval |η |< 0.9.

The same pseudorapidity interval is covered by the TPC, which is the main tracking detector, consistingof a hollow cylinder whose axis coincides with the nominal beam axis.

The active volume of 90 m3 is filled with a gas mixture containing 88% Ar and 12% CO2.

The trajectory of a charged particle is estimated using up to 159 space points. The charged-particle tracksare then built by combining the hits in the ITS and the reconstructed space points in the TPC. The TPC isalso used for particle identification (PID) by measuring the specific energy loss (dE/dx) in the TPC gas.

The TOF detector [29] covers the full azimuth in the pseudorapidity interval |η | < 0.9. The detector isbased on the Multi-gap Resistive Plate Chambers (MRPCs) technology and it is located, with a cylin-drical symmetry, at an average radial distance of 380 cm from the beam axis. The TOF allows forPID, based on the difference between the measured time-of-flight and its expected value, computed foreach mass hypothesis from the track momentum and length. The resolution on the measurement of thetime-of-flight is about 60 ps in heavy-ion collisions.

3 Data sample and analysis techniques

3.1 Event and track selections

The data sample used for the measurements presented in this paper was recorded by ALICE in 2015during the LHC Pb–Pb run at

√sNN = 5.02 TeV. A minimum bias trigger was used during the data

taking, which required coincident signals in both V0 detectors. An offline event selection is applied toremove beam-gas collisions using the timing information provided by the V0 detectors and the Zero-Degree Calorimeters [23]. Events with multiple primary vertices identified with the SPD are tagged aspileup and removed from the analysis. In addition, events with significantly different charged-particlemultiplicities measured by the V0 detector and by the tracking detectors at midrapidity, which havedifferent readout times, are rejected. After the offline event selection, the remaining contribution ofbeam-gas events is smaller than 0.02% [23] and the fraction of pileup events is found to be negligible.The primary vertex position is determined from tracks reconstructed in the ITS and TPC as describedin [23] and only events with a reconstructed primary vertex position along the beam axis within 10 cmfrom the from the nominal interaction point are selected. The total number of events selected for theanalysis for centrality 0–70% is about 73 million.

Deuteron (d) and antideuteron (d) candidates are selected from charged-particle tracks reconstructedin the ITS and TPC in the kinematic range |η | < 0.8 and 0.8 < pT < 6 GeV/c. Only tracks withat least 70 clusters out of a maximum of 159 and with a χ2 per degree-of-freedom for the track fitlower than 2 are accepted. In addition, in order to guarantee a track-momentum resolution of 2% inthe measured pT range and a dE/dx resolution of about 6%, each track is required to be reconstructedfrom at least 80% of the number of expected TPC clusters and to have at least one hit in either of thetwo innermost layers of the ITS. The distances of closest approach (DCA) to the primary vertex in the

4

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

plane perpendicular and parallel to the beam axis for the selected tracks are determined with a resolutionbetter than 300 µm [23]. To suppress the contribution of secondary particles, the reconstructed tracksare required to have a longitudinal DCA smaller than 2 cm and a transverse DCA smaller than 0.0105+0.0350/p1.1

T cm, with pT in units of GeV/c. The latter corresponds to approximately 7σDCA(pT), whereσDCA(pT) is the transverse DCA resolution in the corresponding pT interval.

3.2 (Anti)deuterons identification

The (anti)deuterons identification technique used in this analysis is similar to that used in the previousmeasurement in Pb–Pb collisions at

√sNN = 2.76 TeV [18]. For transverse momenta up to 1.4 GeV/c

(anti)deuterons are identified using the only the TPC information by requiring that the average dE/dx iswithin 3σ from the expected average value for the (anti)deuteron mass hypothesis. For pT > 1.4 GeV/cthe 3σ TPC identification is complemented by the signal provided by the TOF detector. The numberof (anti)deuterons in each pT interval is extracted from a fit of the ∆M = mTOF −mdpdg , where mTOF

is the particle mass calculated using the time-of-flight measured by the TOF and mdpdg is the nominalmass of deuterons taken from [30]. In the left panel of Fig. 1 the ∆M distribution for (anti)deuteronswith 2.2 ≤ pT < 2.4 GeV/c in the centrality interval 20–30%, is shown. The d+d signal is fitted using aGaussian with an exponential tail, while the background, originating from TOF hits incorrectly associatedto tracks extrapolated from the TPC, is modeled with an exponential function.

Deuterons and antideuterons are summed together (d+d) in all the centrality intervals and for pT largerthan 1.4 GeV/c. This is possible since the v2 and v3 measured for v2 and v3 for d and d are consistentwithin the statistical uncertainties. At lower pT, deuterons produced by spallation in interactions betweenparticles and the detector material or in the beam vacuum tube constitute a significant background. Forthis reason, for pT < 1.4 GeV/c only antideuterons, which are not affected by this background, are usedin the analysis. Since no difference is expected for the v2 and v3 of d and d, hereafter deuterons willdenote results for antideuteron for pT < 1.4 GeV/c and the sum of d and d elsewhere. The contributionof secondary deuterons produced in weak decays of hypertritons is negligible considering that the pro-duction rate of (hyper)nuclei with mass number A= 3 is suppressed compared to that of A = 2 by a factorof approximately 300 in Pb–Pb collisions at

√sNN = 2.76 TeV [31]. A similar suppression is expected in

Pb–Pb collisions at√

sNN = 5.02 TeV.

3.3 Flow analysis techniques

The particle azimuthal distribution of charged particles with respect to the n-th order flow symmetryplane Ψn [32–35] can be expressed as a Fourier series

Ed3N

dp3 =1

2π

d2N

pTdpTdy

(

1+∞

∑n=1

2vn cos (n(ϕ −Ψn))

)

, (1)

where E is the energy of the particle, p the momentum, ϕ the azimuthal angle, y the rapidity, and

vn = 〈cos (n(ϕ −Ψn))〉. (2)

The second coefficient of the Fourier series (v2) is called elliptic flow and is related to the initial geo-metrical anisotropy of the overlap region of the colliding nuclei. The third-order flow coefficient (v3),called triangular flow, is generated by fluctuations in the initial distribution of nucleons and gluons inthe overlap region [34, 36, 37]. The same fluctuations are responsible for the v2 measured in most cen-tral collisions (centrality < 5%) [38]. The vn coefficients are measured using the Scalar Product (SP)method [32, 39]. This is a two-particle correlation technique based on the scalar product of the unit flowvector of the particle of interest, k, and the Q-vector. The unit flow vector is denoted by un,k = exp(inϕk),where ϕk is the azimuthal angle of the particle k.

5

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

The Q-vector is computed from a set of reference flow particles and is defined as:

Qn = ∑wieinϕi (3)

where, in general, ϕi is the azimuthal angle for the i-th reference flow particle, n is the order of theharmonic, and wi is a weight applied to correct for reference flow.

The vn flow coefficients are calculated as

vn{SP}= 〈〈un,kQ∗n〉〉

√

〈QnQA∗n 〉〈QnQB∗

n 〉〈QA

n QB∗n 〉

. (4)

Single brackets 〈...〉 denote an average over all events, while double brackets 〈〈...〉〉 indicate an averageover all particles in all events, and ∗ denotes the complex conjugate. The denominator is a correctionfactor that is introduced to take into account the resolution of the Qn vector. In this analysis, the Qn

vector is calculated from the azimuthal distribution of the energy deposition measured in the V0A, whilethe QA

n and QBn vectors are determined from the azimuthal distribution of the energy deposited in the V0C

and the azimuthal distribution of tracks reconstructed in the TPC, respectively. Using these detectors, apseudorapidity gap |∆η |> 2 between the particle of interest and the reference flow particles is introduced.Such a pseudorapidity gap reduces non-flow effects, which are correlations not arising from the collectiveexpansion of the system (e.g. resonances decays and jets).

The purity of the sample of deuterons identified using the TPC in the 0.8 < pT < 1.4 GeV/c interval isaround 100%. In this transverse momentum interval the v2 and v3 coefficients were evaluated on a track-by-track basis and then averaged in each pT interval. For higher pT, the vn coefficients are calculated indifferent ranges of ∆M. The vn(∆M) contains contributions from the signal (vsig

n ) and from the background(vbkg

n )

vn(∆M) = vsign

Nsig

Ntot (∆M)+ vbkgn (∆M)

Nbkg

Ntot (∆M), (5)

where Nsig is the number of deuterons, Nbkg the number of background particles and Ntot is their sum.The signal vn is extracted from a fit to the observed vn as a function of ∆M, in which v

bkgn is described

using a first-order polynomial function, and vsign is a free fit parameter. Nsig and Nbkg are obtained from

the fit to the ∆M distribution using a Gaussian with an exponential tail for the signal and an exponentialfor the background. The signal extraction procedure is illustrated in Fig. 1 for 2.2 ≤ pT < 2.4 GeV/c(2.0 ≤ pT < 2.4 GeV/c for v3) in the centrality interval 20–30%.

The elliptic and triangular flow of deuterons are measured in centrality intervals of 5% width and thenthe results in wider centrality intervals are obtained as weighted averages of these measurements usingthe number of deuteron candidates, in the same centrality interval of 5% width as a weight, similarly towhat was performed in [19].

3.4 Systematic uncertainties

The sources of systematic uncertainties for the elliptic and triangular flow of deuterons are related toevent selection, tracking, (anti-)deuterons identification, and the technique used for the signal extraction.The contribution related to the event selection is estimated by taking into account the differences in thev2 and v3 measurements obtained using different event-selection criteria. In particular, the fiducial regionfor the vertex position along the beam axis is varied from the range [−10,10] cm to [−7,7] cm to probethe magnitude of potential edge effects. To investigate possible effects due to charge asymmetries duringtracking and geometrical asymmetries in the detector, the differences between the results obtained by

6

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

0.4− 0.2− 0 0.2 0.4)2c (GeV/M∆

0

5

10

15

310×)2 cC

ount

s/(2

0 M

eV/

c < 2.4 GeV/T

p ≤2.2 = 5.02 TeVNNsPb −ALICE Pb

30%−20

dd + Signal + BackgroundBackground

0.4− 0.2− 0 0.2 0.4)2c (GeV/M∆

0

0.1

0.2

0.3| > 2

}η∆

{SP

, |T

ot2

v

c < 2.4 GeV/T

p ≤2.2

= 5.02 TeVNNsPb −ALICE Pb

30%−20

dd + Fit

0.4− 0.2− 0 0.2 0.4)2c (GeV/M∆

0

0.05

0.1

0.15

| > 2

}η∆

{SP

, |T

ot3

v

c < 2.4 GeV/T

p ≤2.0

= 5.02 TeVNNsPb −ALICE Pb

30%−20

dd + Fit

Figure 1: (Color online) Raw yield (left), v2 (middle) and v3 (right) of d+d candidates as a function of ∆M for2.2 ≤ pT < 2.4 GeV/c (2.0 ≤ pT < 2.4 GeV/c for v3) and in the centrality interval 20–30%. The data pointsrepresent the measurements. The curve on the left panel is the total fit (signal plus background) as described inthe text. The curves in the middle and right panel are the fits performed using Eq. 5. Vertical bars represent thestatistical uncertainties.

using opposite magnetic field polarities are included. Analogously, the default centrality estimator ischanged to that based on the number of hits in the first or second layer of the ITS. Finally, the effectrelated to pileup rejection is tested by requiring a stronger correlation between the V0 and central barrelmultiplicities. These contributions are assumed to be independent and added in quadrature. The totalsystematic uncertainty due to event selection is found to be around 1.5% for both v2 and v3.

To estimate the systematic uncertainties due to reconstruction and identification of deuterons, the trackselection and the TPC PID criteria are varied with respect to the default choice and the vn measurementsare repeated for each of these different settings. The RMS of the distribution of vn measurements in eachpT interval is considered as systematic uncertainty. To minimize the effect of statistical fluctuations, all

variations smaller than 2√

∣

∣σ 20 −σ 2

i

∣

∣ are not included in the estimate of the systematic uncertainties [40],

where σ0 is the statistical uncertainty of the default value while σi is that corresponding to the ith selectioncriterion. The probability distribution for the variations of data points due to systematic effects related totracking and PID is assumed to be uniform in each pT interval and the difference between the maximumand minimum value divided by

√12 is assigned as systematic uncertainty. This contribution ranges from

1% and 3% depending on pT and centrality.

To estimate the contribution to the systematic uncertainties due to the signal extraction, the function usedto describe the v

bkgn is changed. In addition to a first-order polynomial, a constant function and a second-

order polynomial are also used, and the maximum difference with respect to the default measurement isconsidered as systematic uncertainty. A contribution up to 5% is observed for central collisions and forpT < 2 GeV/c. Moreover, different functions and fitting ranges are used to describe the signal and thebackground of Eq. 5. More specifically, besides a Gaussian function with an exponential tail, a Gaussianis also used for the signal, while single and double exponential, and linear functions are also used for thebackground. This contribution is relevant only for pT > 1.4 GeV/c, where the TOF is used to extract thesignal, and is found to vary from 1% to 6% depending on pT and centrality. Table 1 shows the summaryof the different contributions to the systematic uncertainties for the v2 and v3 of deuterons. The totaluncertainties are given by their sum in quadrature, assuming that all contributions are independent.

4 Results and discussion

The v2 and v3 of deuterons measured in Pb–Pb collisions at√

sNN = 5.02 TeV are shown in Fig. 2 as afunction of pT for different centrality intervals. In the measured pT interval, an increasing trend is ob-served with increasing pT and going from central to more peripheral Pb–Pb collisions, as expected basedon the relativistic hydrodynamic description of the collective expansion of a hot and dense medium [41].

7

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

Table 1: Summary of the systematic uncertainties for the deuterons v2 and v3. The maximum deviation of thesystematic uncertainty is reported.

Source Valuev2 v3

Event selections 1.5% 1.5%Tracking and particle identification 1–3% 1–2%Signal extraction 1–4% 2–6%Total 2–7% 3–7%

Initial state fluctuations of the energy density distribution of partons in the colliding nuclei imply a non-zero v3 [37].

The measurement presented in this paper shows that these initial state effects, already observed for otherhadron species at LHC energies [42, 43], are also visible for deuterons.

0 1 2 3 4 5 6)c (GeV/

Tp

0

0.2

0.4

0.6| > 2

}η∆

{S

P, |

2v

5%−0

10%−5

20%−10

30%−20

40%−30

50%−40

60%−50

70%−60

= 5.02 TeVNNsPb −ALICE Pb

dd +

0 1 2 3 4 5 6)c (GeV/

Tp

0

0.1

0.2

0.3

| > 2

}η∆

{S

P, |

3v

20%−0

40%−20

60%−40

= 5.02 TeVNNsPb −ALICE Pb

dd +

Figure 2: (Color online) Elliptic (v2, left) and triangular (v3, right) flow of deuterons as a function of pT fordifferent centrality intervals measured in Pb–Pb collisions at

√sNN = 5.02 TeV. The horizontal line at zero is to

guide the eye. Vertical bars and boxes represent the statistical and systematic uncertainties, respectively.

The measurement of the deuterons v2 in Pb–Pb collisions at√

sNN = 5.02 TeV is compared to that inPb–Pb collisions at

√sNN = 2.76 TeV [18] in Fig. 3 for two centrality intervals. The observed v2 and

their trend are similar at the two center-of-mass energies, but a decrease of the observed elliptic flow for agiven pT is observed with increasing center-of-mass energy. This effect is more pronounced in peripheralrather than in central collisions. A similar effect was observed for the proton v2 measurements [43] and isinterpreted as partially due to the increasing radial flow with increasing collision energy, which producesa shift of the v2 towards higher pT.

The effect due to radial flow is assessed quantitatively by comparing the ratio of the deuteron and protonv2 as a function of pT at the two energies. The ratio between the deuteron v2 in Pb–Pb collisions at√

sNN = 5.02 TeV to that measured at√

sNN = 2.76 TeV, with v2 and pT scaled by the mass numberA = 2, is shown in Fig. 4 for two centrality intervals in comparison with the same ratio for protons. Asindicated by these ratios, the radial flow effects are quantitatively very similar for protons and deuterons.It has to be noted that a mass scaling would lead to the same conclusion since the binding energy of

8

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

0 1 2 3 4 5 6)c (GeV/

Tp

0

0.1

0.2

0.3

0.4

0.52

vALICE Pb−Pb

20%−10

dd +

0 1 2 3 4 5 6)c (GeV/

Tp

0

0.1

0.2

0.3

0.4

0.5

50%−40

2.76 TeV

5.02 TeV

Figure 3: (Color online) Deuterons v2 measured in Pb–Pb collisions at√

sNN = 5.02 TeV (red square) comparedto that measured at

√sNN = 2.76 TeV [18] (light blue circles) for two centrality intervals (10–20% and 40–50%).

Both protons and deuteron elliptic flow were measured for pseudorapidity gap between the particle of interest andthe reference flow particle |∆η |> 0.9. Vertical bars and boxes represent the statistical and systematic uncertainties,respectively.

deuteron is of 2.2 MeV, i.e. the deuteron mass is approximately equal to 2mp, where mp is the protonmass.

0 1 2 3 4 5 6)c (GeV/A/

Tp

0.5

1

1.52.76

TeV

5.02

TeV

: A/ 2

v

ALICE Pb−Pb

20%−10

0 1 2 3 4 5 6)c (GeV/A/

Tp

0.5

1

1.5

50%−40

pp + dd +

Figure 4: (Color online) Ratio of the v2 of deuterons measured in Pb–Pb collisions at√

sNN = 5.02 TeV to thatmeasured at

√sNN = 2.76 TeV (red circles) compared with the same ratio obtained for protons (blue squares) for

two centrality intervals (10–20% on the left panel and 40–50% on the right panel). For a direct comparison ofprotons and deuterons, the measured v2 and pT have were divided by A. Vertical bars and boxes represent thestatistical and systematic uncertainties, respectively.

The elliptic flow of deuterons is compared to that of pions, kaons, protons and (anti)3He measured at thesame center-of-mass energy [19, 43] in Fig. 5. Since the (anti)3He elliptic flow is measured in centralityintervals of 20% width due to its rarer production compared to that of lighter hadrons, the v2 of pions,kaons, protons and deuterons are re-calculated to match the same centrality intervals. This is achieved

9

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

by averaging the v2 measurements of these particles in narrower centrality intervals weighted by thecorresponding pT spectra [8, 44]. A clear mass ordering of v2 is observed at low pT, as expected for asystem expansion driven by the pressure gradient as described by relativistic hydrodynamics [41, 45, 46].

0 1 2 3 4 5 6) c (GeV/

Tp

0

0.1

0.2

0.3

0.4

0.5

0.62v

d d + He3He + 3

±π ± K

p p +

ALICE

20%− = 5.02 TeV, 0NNsPb, −Pb

0 1 2 3 4 5 6) c (GeV/

Tp

40%−20

0 1 2 3 4 5 6) c (GeV/

Tp

60%−40

Figure 5: (Color online) Comparison of the elliptic flow of pions, kaons, protons, deuterons and (anti)3He indifferent centrality intervals for Pb–Pb collisions at

√sNN = 5.02 TeV. (Anti)3He v2 is measured using the Event

Plane method [19]. Vertical bars and boxes represent the statistical and systematic uncertainties, respectively.

In Fig. 6, the deuterons v3 is compared to that of pions, kaons, and protons at the same center-of-massenergy [43] for the centrality intervals 0–20% (left) and 20–40% (right). Also for the v3, a clear massordering is observed for pT . 2.5 GeV/c and pT . 3 GeV/c for the centrality intervals 0–20% and20–40%, respectively.

0 1 2 3 4 5 6)c (GeV/

Tp

0.05−

0

0.05

0.1

0.15

0.2

0.25| > 2

}η

∆{S

P, |

3v

20%−0

±π±K

pp + dd +

0 1 2 3 4 5 6)c (GeV/

Tp

0.05

0

0.05

0.1

0.15

0.2

0.25

40%−20

= 5.02 TeVNNsPb −ALICE Pb

Figure 6: (Color online) Triangular flow (v3) of deuterons, pions, kaons, and protons [43] as a function of pT

for the centrality intervals 0–20% and 20–40%. Vertical bars and boxes represent the statistical and systematicuncertainties, respectively.

4.1 Comparison with the blast-wave model predictions

The elliptic flow of deuterons is compared with the expectations of the blast-wave model [22, 47, 48],which is based on the assumption that the system produced in heavy-ion collisions is locally thermal-ized and expands collectively with a common velocity field. The system is assumed to undergo aninstantaneous kinetic freeze-out at the temperature Tkin and to be characterized by a common transverseradial flow velocity at the freeze-out surface. A simultaneous fit of the v2 and the pT spectra of pions,kaons, and protons [8, 43] with the blast-wave model is performed in the transverse-momentum ranges

10

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

0.5 ≤ pπT < 1 GeV/c, 0.7 ≤ pK

T < 2 GeV/c, and 0.7 ≤ ppT < 2.5 GeV/c. The four free parameters of the

blast-wave function are the kinetic freeze-out temperature (Tkin), the variation in the azimuthal density ofthe source (s2), the mean transverse expansion rapidity (ρ0), and the amplitude of its azimuthal variation(ρa), as described in [47]. The values of these parameters extracted from the fits are reported in Table 2for each centrality interval. These values are employed to predict the elliptic flow of deuterons under theassumption that the same kinetic freeze-out conditions apply for all particles produced in the collision.The deuteron mass is taken from [30].

Table 2: Blast-wave parameters extracted from the simultaneous fits of the pT spectra and v2 of pions, kaons, andprotons measured at

√sNN = 5.02 TeV. See text for details. The error assigned to each parameter is shown only

with one significant digit.

Centrality Fit parameters

Tkin (MeV) s2 (10−2) ρ0 (10−1) ρa (10−2)

0–5% 104 ± 1 2.63 ± 0.01 8.57 ± 0.01 0.83 ± 0.01

5–10% 106 ± 1 4.15 ± 0.01 8.85 ± 0.01 1.47 ± 0.01

10–20% 107 ± 1 6.09 ± 0.01 9.12 ± 0.01 2.17 ± 0.01

20–30% 109 ± 1 8.25 ± 0.01 9.02 ± 0.01 2.85 ± 0.01

30–40% 111 ± 1 10.1 ± 0.01 8.61 ± 0.01 3.25 ± 0.01

40–50% 116 ± 1 12.3 ± 0.01 7.73 ± 0.01 3.30 ± 0.01

50–60% 121 ± 1 14.5 ± 0.01 6.93 ± 0.01 2.85 ± 0.01

60–70% 129 ± 1 17.4 ± 0.01 5.95 ± 0.01 1.74 ± 0.01

The blast-wave fits to the v2 of pions, kaons, and protons and the predictions for the deuterons v2 arereported in Fig. 7 for the centrality intervals 10–20% and 40–50%. In the lower panels, the data-to-fitratios for pions, kaons, and protons and the ratios of the deuterons v2 to the model are shown. Becauseof the finite size of the pT intervals, the average of the blast-wave function within the interval, weightedby the pT spectrum of the corresponding particle species, is considered in the calculation of these ratios.

The predictions of the blast-wave model underestimate the deuterons elliptic flow experimental valuesin semi-peripheral collisions for pT > 1.4 GeV/c, while they are close to the measurements for centralevents in the measured pT interval. This is better observed in Fig. 8, which shows the centrality evolutionof the data-to-model ratios.

4.2 Test of the coalescence hypothesis

The deuterons v2 and v3 are compared to the expectations of a coalescence approach based on mass num-ber scaling and isospin symmetry, for which the proton and neutron v2 (v3) are identical. In particular,the v2 (v3) measured for protons [43] was used to predict the v2 (v3) of deuterons using the followingrelation [49]

v2(3),d(pT) =2v2(3),p(pT/2)

1+2v22(3),p(pT/2)

. (6)

The results of this calculation for different centrality intervals for v2 are shown in the left panel of Fig. 9.The measured elliptic flow in 10–20% and 40–50% centrality intervals of deuterons is compared withcoalescence model predictions from Eq. 6 using the measured vn of protons. Similarly, the right panel ofFig. 9 shows a comparison between the calculated and measured v3 in the 0–20% and 20–40% centralityintervals.

The coalescence model overestimates the deuteron v2 by about 20% to 30% in central collisions andis close to the data for semi-peripheral collisions, as illustrated in Fig. 10 which shows the centrality

11

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5| > 2

}η

∆{S

P, |

2v

ALICE

= 5.02 TeVNNsPb −Pb

20%−10

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1.0

1.5

Dat

a/M

odel

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5Data

±π±K

pp + dd +

blast-wave fitCombined

±π±K

pp +

Predicted

dd +

50%−40

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1.0

1.5

Figure 7: (Color online) Blast-wave fits to the v2 (pT) of pions, kaons, and protons [43] and predictions of thedeuterons v2 (pT) for the centrality intervals 10–20% (left) and 40–50% (right). In the lower panels, the data-to-fitratios are shown for pions, kaons, and protons as well as the ratio of the deuterons v2 to the blast-wave predictions.Vertical bars and boxes sent the statistical and systematic uncertainties, respectively. The dashed line at one is toguide the eye.

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5

Dat

a/B

last

-wav

e

40%−30

dd +

0 1 2 3 4 5 6

0.5

1

1.5

Dat

a/B

last

-wav

e

5%−0

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5 50%−40

0 1 2 3 4 5 6

0.5

1

1.5 10%−5

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5 60%−50

0 1 2 3 4 5 6

0.5

1

1.5 20%−10

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5 70%−60

ALICE = 5.02 TeVNNsPb −Pb

0 1 2 3 4 5 6

0.5

1

1.5 30%−20

Figure 8: (Color online) Data-to-model ratios of the deuterons v2 to the blast-wave predictions as a function ofpT for different centrality intervals as indicated in each pad. Vertical bars and boxes represent the statistical andsystematic uncertainties, respectively.

evolution of the data-to-model ratio. The coalescence approach seems to have a slightly better agreement

12

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5| > 2

}η

∆{S

P, |

2v

ALICE

= 5.02 TeVNNsPb −Pb

20%−10

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1.0

)co

al2

v)/

(d 2

v(

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5 Coalescencedd +

50%−40

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1.00 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4| > 2

}η

∆{S

P, |

3v

ALICE

= 5.02 TeVNNsPb −Pb

20%−0

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1.0

)co

al3

v)/

(d 3

v(

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4 Coalescencedd +

40%−20

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1.0

Figure 9: (Color online) Measured deuterons v2 and v3 (red circles) compared with the expectations from simplecoalescence (Eq. 6) (blue shaded bands) for two centrality intervals. In the left panel, the v2 measurements in the10–20% and 40–50% centrality intervals is shown. The right panel displays the results of v3 in the 0–20% and 20–40% centrality intervals. The bottom panels show the ratio between the measured v2 (v3) and the expectations fromthe coalescence model. In each panel, vertical bars and boxes represent the statistical and systematic uncertainties,respectively. The line at one is to guide the eye.

with deuterons v3; however, the large statistical uncertainties on the v3 measurements do not allow forconclusive statements.

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5)co

al2

v)/

(d 2

v(

40%−30Coalescence

dd + 0 1 2 3 4 5 6

0.5

1

1.5)co

al2

v)/

(d 2

v(

5%−0

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5 50%−400 1 2 3 4 5 6

0.5

1

1.5 10%−5

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5 60%−500 1 2 3 4 5 6

0.5

1

1.5 20%−10

0 1 2 3 4 5 6)c (GeV/

Tp

0.5

1

1.5 70%−60

ALICE = 5.02 TeVNNsPb −Pb

0 1 2 3 4 5 6

0.5

1

1.5 30%−20

Figure 10: (Color online) Centrality evolution of the deuterons v2 compared with the expectations from simplecoalescence model (Eq. 6). Vertical bars and boxes represent the statistical and systematic uncertainties, respec-tively.

4.3 Comparison with iEBE-VISHNU and coalescence calculations

In Fig. 11, the deuterons v2 and v3 are compared to a model [4] implementing light nuclei formationvia coalescence of nucleons originating from a hydrodynamical evolution of the fireball coupled to anUrQMD simulation of the hadronic cascade [16, 17]. In this model, the coalescence probability is cal-culated as the superposition of the wave functions of protons and neutrons and the Wigner function of

13

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

the deuterons. The coalescence happens in a flowing medium introducing position-momentum correla-tions, which are absent in the simple coalescence approach. The phase-space distributions of protons andneutrons are generated from the iEBE-VISHNU hybrid model with AMPT [50] initial conditions. Thismodel provides a good description of the protons spectra up to 3 GeV/c and of the deuterons v2 measuredin Pb–Pb collisions at

√sNN = 2.76 TeV [4]. The predictions are consistent with the measured deuterons

v2 for events with centrality larger than 20% and for measured v3 within the statistical and systematicaluncertainties, while some discrepancy at the level of 2σ (taking into account statistical and systematicaluncertainties in quadrature) are observed for for the centrality interval 10–20% as shown in Fig. 11.

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5| > 2

}η∆

{SP

, |2

v

dd + 20%− Data 1030%− Data 2040%− Data 30

iEBE-VISHNU + Coalescence

20%−10

30%−20

40%−30

ALICE = 5.02 TeVNNsPb −Pb

0 1 2 3 4 5 6)c (GeV/

Tp

0.04−0.02−0.000.020.04

Mod

el−

Dat

a

0 1 2 3 4 5 6

0

0.05

0.1

0.15

0.2

0.25| > 2

}η∆

{SP

, |3

v

dd +

20%− Data 0

40%− Data 20

iEBE-VISHNU + Coalescence

20%−0

40%−20

ALICE = 5.02 TeVNNsPb −Pb

0 1 2 3 4 5 6)c (GeV/

Tp

0.04−0.02−0.00

0.02

0.04

Mod

el−

Dat

a

Figure 11: Elliptic (left) and triangular (right) flow of deuterons compared to the predictions iEBE-VISHNUhybrid model with AMPT initial conditions [4]. The predictions are shown as bands whose widths represent thestatistical uncertainties associated with the model. The data-to-model differences are shown in the lower panels.Vertical bars and boxes represent the statistical and systematic uncertainties, respectively.

4.4 Comparison with a hybrid (hydrodynamics + transport) approach expectations

The deuterons v2 measured in the centrality intervals 10–20%, 20–30%, and 30–40% is compared inFig. 12 with the predictions from a hybrid model based on relativistic viscous hydrodynamics, with fluc-tuating initial conditions generated by TRENTo [51], coupled to the hadronic afterburner SMASH [5].The simulations are obtained by using the JETSCAPE 1.0 event generator [52]. The parameters ofthis model, including the shear and bulk viscosities, are tuned to the measurements of pT spectra and az-imuthal flow of pions, kaons, and protons obtained by ALICE in Pb–Pb collisions at

√sNN = 2.76 TeV [7,

21] and by PHENIX and STAR in Au–Au collisions at√

sNN = 200 GeV [53–55]. The interactions ofdeuterons with other hadrons in the hadron gas phase are simulated using SMASH in which all knownresonances and the experimentally known cross sections, most importantly πd → πnp and its inversereaction, are included.

In this model, the number of deuterons at the kinetic freezeout is independent from their primordialabundance at the Cooper-Frye hypersurface. It was found that even when their initial number is setto zero, the number of deuterons regenerated in the hadronic phase converges towards the equilibriumvalue, which is the same as that predicted by the statistical hadronization model. Considering that in this

14

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

model only ∼ 1% of the primordial deuterons survive the hadronic stage, the elliptic flow of deuteronsobserved after the kinetic freezeout is almost identical to that of the regenerated ones. For this reason,deuterons are not sampled at the Cooper-Frye hypersurface for these predictions.

The model predictions are consistent with the measured v2 within the uncertainties in the centralityintervals 20–30% and 30–40% for 0.8< pT < 4 GeV/c, while the data are overestimated by up to 30%in the centrality interval 10–20% for pT > 2 GeV/c.

0 1 2 3 4 5 6

0

0.1

0.2

0.3

0.4

0.5| > 2

}η∆

{SP

, |2

v dd +

20%− Data 1030%− Data 2040%− Data 30

JETSCAPE 1.0 sims

20%−10

30%−20

40%−30

ALICE

= 5.02 TeVNNsPb −Pb

0 1 2 3 4 5 6)c (GeV/

Tp

0.04−0.02−0.00

0.02

0.04

Mod

el−

Dat

a

Figure 12: Measured deuterons v2 compared to the predictions from a microscopic model [5] based on theJETSCAPE generator [52]. The model predictions, based on SMASH afterburner and which used TRENTo [51]initial conditions, are shown as bands. The width of the band represents the statistical uncertainty associated withthe model. In the lower panel the data-to-model differences are shown. Vertical bars and boxes represent thestatistical and systematic uncertainties, respectively.

5 Summary

The measurements of the deuterons v2 and the first measurement of v3 in Pb–Pb collisions at√

sNN =5.02 TeV are presented. The observed centrality and pT dependence are consistent with the expectationsfrom relativistic hydrodynamics. A mass ordering is observed for pT < 3 GeV/c when comparing theseresults with the measured v2 and v3 of pions, kaons, and protons. The shift of the deuterons v2 towardshigher pT with respect to the measurement in Pb–Pb collisions at

√sNN = 2.76 TeV, mainly due to a

stronger radial flow at higher center-of-mass energy, is consistent with that observed for the proton v2

measurement.

The results of this measurement are compared with the expectations from the simple coalescence ap-proach, in which the deuterons v2 is obtained from that of protons assuming that the deuterons invariantyield is proportional to that of protons squared, and with the predictions of the blast-wave model. Thedeuterons v2 is overestimated by a simple coalescence approach, which describes the data only in periph-

15

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

eral (centrality > 50%) collisions. On the other hand, the blast-wave model underestimates the peripheralmeasurements and it is close to the data in central collisions. These results are consistent with the sce-nario previously seen for deuterons and 3He elliptic flow: these simplified models bracket a region wherethe light nuclei v2 is located and describe reasonably the data in different multiplicity regimes, indicatingthat none of these two models is able to describe the deuterons production measurement from low to highmultiplicity environments.

Similar considerations are valid for the deuterons v3 with some limitations due to the rather large statisti-cal uncertainties. This specific aspect will be addressed with the larger data sample that will be collectedin Run 3 following the ALICE upgrade, where a significant improvement of the statistical precision isexpected. This measurement will be crucial to better constrain models that describe the production oflight nuclei in heavy-ion collisions.

A more advanced coalescence model coupled to hydrodynamics and the hadronic afterburner UrQMD,which takes into account the quantum-mechanical properties of nucleons and nuclei and space-momentumcorrelations of nucleons, provides a good description of the deuterons v2 and v3 for pT > 2.5 GeV/c.The model predictions deviate from the data at lower pT, in particular for the centrality interval 10–20%. The same model provides a good description of the deuterons v2 measured in Pb–Pb collisionsat

√sNN = 2.76 TeV and that of 3He at

√sNN = 5.02 TeV. The deuterons v2 is also compared to the

predictions from a hybrid model based on relativistic hydrodynamics coupled to the hadronic afterburnerSMASH. The model predictions are consistent with the data within the uncertainties in the centralityintervals 20–30% and 30–40%, while a deviation of up to 30% is observed in the centrality interval10–20% for 2 < pT < 3 GeV/c.

In general, the state-of-the-art implementations of coalescence and the hybrid approach based on hy-drodynamics coupled to hadronic afterburners provide better descriptions of the data compared to thesimple coalescence and blast-wave models. Further efforts, both on experimental and theoretical side,are needed to have a more comprehensive understanding of dynamics and production of light nuclei.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable con-tributions to the construction of the experiment and the CERN accelerator teams for the outstandingperformance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources andsupport 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 buildingand running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics In-stitute) 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 National-stiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and HighTechnologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo àPesquisa 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 Educationand Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear(CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, CzechRepublic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN andDanish 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 Physiquedes Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesmin-

16

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

isterium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für SchwerionenforschungGmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Researchand Religions, Greece; National Research, Development and Innovation Office, Hungary; Departmentof Atomic Energy Government of India (DAE), Department of Science and Technology, Governmentof India (DST), University Grants Commission, Government of India (UGC) and Council of Scientificand Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi - MuseoStorico 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 So-ciety 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) andDirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatievoor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway;Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pak-istan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, NationalScience Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information andNational Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and ScientificResearch, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of AtomicPhysics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science ofthe Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation andRussian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport ofthe Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; SwedishResearch Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organi-zation for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Scienceand Technology Development Agency (NSDTA) and Office of the Higher Education Commission underNRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academyof 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 ofEnergy, Office of Nuclear Physics (DOE NP), United States of America.

References

[1] A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, “Decoding the phase structure ofQCD via particle production at high energy”, Nature 561 (2018) 321–330,arXiv:1710.09425 [nucl-th].

[2] V. Vovchenko and H. Stocker, “Examination of the sensitivity of the thermal fits to heavy-ionhadron yield data to the modeling of the eigenvolume interactions”,Phys. Rev. C95 (2017) 044904, arXiv:1606.06218 [hep-ph].

[3] A. Andronic, P. Braun-Munzinger, J. Stachel, and H. Stocker, “Production of light nuclei,hypernuclei and their antiparticles in relativistic nuclear collisions”,Phys. Lett. B697 (2011) 203–207, arXiv:1010.2995 [nucl-th].

[4] W. Zhao, L. Zhu, H. Zheng, C. M. Ko, and H. Song, “Spectra and flow of light nuclei in relativisticheavy ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and at theCERN Large Hadron Collider”, Phys. Rev. C98 (2018) 054905, arXiv:1807.02813 [nucl-th].

[5] D. Oliinychenko, L.-G. Pang, H. Elfner, and V. Koch, “Microscopic study of deuteron productionin Pb–Pb collisions at

√sNN = 2.76 TeV via hydrodynamics and a hadronic afterburner”,

Phys. Rev. C99 no. 4, (2019) 044907, arXiv:1809.03071 [hep-ph].

17

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

[6] ALICE Collaboration, S. Acharya et al., “Evidence of rescattering effect in Pb–Pb collisions atthe LHC through production of K∗(892)0 and φ(1020) mesons”, Phys. Lett. B802 (2020) 135225,arXiv:1910.14419 [nucl-ex].

[7] ALICE Collaboration, B. Abelev et al., “Production of charged pions, kaons and protons at largetransverse momenta in pp and Pb–Pb collisions at

√sNN =2.76 TeV”,

Phys. Lett. B736 (2014) 196–207, arXiv:1401.1250 [nucl-ex].

[8] ALICE Collaboration, S. Acharya et al., “Production of charged pions, kaons, and (anti-)protonsin Pb-Pb and inelastic pp collisions at

√sNN = 5.02 TeV”, Phys. Rev. C 101 no. 4, (2020) 044907,

arXiv:1910.07678 [nucl-ex].

[9] N. Sharma, J. Cleymans, B. Hippolyte, and M. Paradza, “A Comparison of p-p, p-Pb, Pb–PbCollisions in the Thermal Model: Multiplicity Dependence of Thermal Parameters”,Phys. Rev. C99 (2019) 044914, arXiv:1811.00399 [hep-ph].

[10] F. Becattini, E. Grossi, M. Bleicher, J. Steinheimer, and R. Stock, “Centrality dependence ofhadronization and chemical freeze-out conditions in heavy ion collisions at

√sNN = 2.76 TeV”,

Phys. Rev. C90 (2014) 054907, arXiv:1405.0710 [nucl-th].

[11] ALICE Collaboration, S. Acharya et al., “Production of 4He and 4He in Pb–Pb collisions at√sNN = 2.76 TeV at the LHC”, Nucl. Phys. A971 (2018) 1–20, arXiv:1710.07531 [nucl-ex].

[12] S. T. Butler and C. A. Pearson, “Deuterons from High-Energy Proton Bombardment of Matter”,Phys. Rev. 129 (1963) 836–842.

[13] J. I. Kapusta, “Mechanisms for deuteron production in relativistic nuclear collisions”,Phys. Rev. C21 (1980) 1301–1310.https://link.aps.org/doi/10.1103/PhysRevC.21.1301.

[14] R. Scheibl and U. W. Heinz, “Coalescence and flow in ultrarelativistic heavy ion collisions”,Phys. Rev. C59 (1999) 1585–1602, arXiv:nucl-th/9809092 [nucl-th].

[15] F. Cooper and G. Frye, “Single-particle distribution in the hydrodynamic and statisticalthermodynamic models of multiparticle production”, Phys. Rev. D 10 (Jul, 1974) 186–189.https://link.aps.org/doi/10.1103/PhysRevD.10.186.

[16] S. A. Bass et al., “Microscopic models for ultrarelativistic heavy ion collisions”,Prog. Part. Nucl. Phys. 41 (1998) 255–369, arXiv:nucl-th/9803035 [nucl-th].

[17] M. Bleicher et al., “Relativistic hadron hadron collisions in the ultrarelativistic quantum moleculardynamics model”, J. Phys. G25 (1999) 1859–1896, arXiv:hep-ph/9909407 [hep-ph].

[18] ALICE Collaboration, S. Acharya et al., “Measurement of deuteron spectra and elliptic flow inPb–Pb collisions at

√sNN = 2.76 TeV at the LHC”, Eur. Phys. J. C77 (2017) 658,

arXiv:1707.07304 [nucl-ex].

[19] ALICE Collaboration, S. Acharya et al., “Measurement of the (anti-)3He elliptic flow in Pb-Pbcollisions at

√sNN = 5.02 TeV”, Phys. Lett. B 805 (2020) 135414,

arXiv:1910.09718 [nucl-ex].

[20] V. Vovchenko, K. Gallmeister, J. Schaffner-Bielich, and C. Greiner, “Nucleosynthesis in heavy-ioncollisions at the LHC via the Saha equation”, Physics Letters B 800 (2020) 135131,arXiv:1903.10024 [hep-ph].

18

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

[21] ALICE Collaboration, B. Abelev et al., “Elliptic flow of identified hadrons in Pb–Pb collisions at√sNN = 2.76 TeV”, JHEP 06 (2015) 190, arXiv:1405.4632 [nucl-ex].

[22] E. Schnedermann, J. Sollfrank, and U. W. Heinz, “Thermal phenomenology of hadrons from200-A/GeV S+S collisions”, Phys. Rev. C48 (1993) 2462–2475,arXiv:nucl-th/9307020 [nucl-th].

[23] ALICE Collaboration, B. Abelev et al., “Performance of the ALICE Experiment at the CERNLHC”, Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].

[24] ALICE Collaboration, E. Abbas et al., “Performance of the ALICE VZERO system”,JINST 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].

[25] ALICE Collaboration, K. Aamodt et al., “Centrality dependence of the charged-particlemultiplicity density at mid-rapidity in Pb–Pb collisions at

√sNN = 2.76 TeV”,

Phys. Rev. Lett. 106 (2011) 032301, arXiv:1012.1657 [nucl-ex].

[26] ALICE Collaboration, B. Abelev et al., “Centrality determination of Pb–Pb collisions at√s = 2.76 TeV with ALICE”, Phys. Rev. C88 (2013) 044909, arXiv:1301.4361 [nucl-ex].

[27] ALICE Collaboration, S. Acharya et al., “Centrality determination in heavy ion collisions”,.https://cds.cern.ch/record/2636623.

[28] ALICE Collaboration, K. Aamodt et al., “Alignment of the ALICE Inner Tracking System withcosmic-ray tracks”, JINST 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det].

[29] A. Akindinov et al., “Performance of the ALICE Time-Of-Flight detector at the LHC”,Eur. Phys. J. Plus 128 (2013) 44.

[30] Particle Data Group Collaboration, M. Tanabashi et al., “Review of particle physics”,Phys. Rev. D 98 (Aug, 2018) 030001.https://link.aps.org/doi/10.1103/PhysRevD.98.030001.

[31] ALICE Collaboration, J. Adam et al., “Production of light nuclei and anti-nuclei in pp and Pb–Pbcollisions at energies available at the CERN Large Hadron Collider”,Phys. Rev. C93 no. 2, (2016) 024917, arXiv:1506.08951 [nucl-ex].

[32] S. A. Voloshin, A. M. Poskanzer, and R. Snellings, “Collective phenomena in non-central nuclearcollisions”, Landolt-Bornstein 23 (2010) 293–333, arXiv:0809.2949 [nucl-ex].

[33] J.-Y. Ollitrault, A. M. Poskanzer, and S. A. Voloshin, “Effect of flow fluctuations and nonflow onelliptic flow methods”, Phys. Rev. C80 (2009) 014904, arXiv:0904.2315 [nucl-ex].

[34] B. Alver and G. Roland, “Collision geometry fluctuations and triangular flow in heavy-ioncollisions”, Phys. Rev. C81 (2010) 054905, arXiv:1003.0194 [nucl-th]. [Erratum: Phys.Rev.C82,039903(2010)].

[35] Z. Qiu and U. W. Heinz, “Event-by-event shape and flow fluctuations of relativistic heavy-ioncollision fireballs”, Phys. Rev. C84 (2011) 024911, arXiv:1104.0650 [nucl-th].

[36] R. S. Bhalerao and J.-Y. Ollitrault, “Eccentricity fluctuations and elliptic flow at RHIC”,Phys. Lett. B641 (2006) 260–264, arXiv:nucl-th/0607009 [nucl-th].

[37] B. H. Alver, C. Gombeaud, M. Luzum, and J.-Y. Ollitrault, “Triangular flow in hydrodynamicsand transport theory”, Phys. Rev. C82 (2010) 034913, arXiv:1007.5469 [nucl-th].

19

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

[38] ALICE Collaboration, K. Aamodt et al., “Higher harmonic anisotropic flow measurements ofcharged particles in Pb-Pb collisions at

√sNN=2.76 TeV”, Phys. Rev. Lett. 107 (2011) 032301,

arXiv:1105.3865 [nucl-ex].

[39] STAR Collaboration, C. Adler et al., “Elliptic flow from two and four particle correlations inAu+Au collisions at s(NN)**(1/2) = 130-GeV”, Phys. Rev. C66 (2002) 034904,arXiv:nucl-ex/0206001 [nucl-ex].

[40] R. Barlow, “Systematic errors: Facts and fictions”, in Advanced Statistical Techniques in Particle

Physics. Proceedings, Conference, Durham, UK, March 18-22, 2002, pp. 134–144. 2002.arXiv:hep-ex/0207026 [hep-ex].http://www.ippp.dur.ac.uk/Workshops/02/statistics/proceedings//barlow.pdf.

[41] S. Jeon and U. Heinz, “Introduction to Hydrodynamics”, Int. J. Mod. Phys. E24 (2015) 1530010,arXiv:1503.03931 [hep-ph].

[42] ALICE Collaboration, J. Adam et al., “Higher harmonic flow coefficients of identified hadrons inPb-Pb collisions at

√sNN = 2.76 TeV”, JHEP 09 (2016) 164, arXiv:1606.06057 [nucl-ex].

[43] ALICE Collaboration, S. Acharya et al., “Anisotropic flow of identified particles in Pb–Pbcollisions at

√sNN = 5.02 TeV”, JHEP 09 (2018) 006, arXiv:1805.04390 [nucl-ex].

[44] ALICE Collaboration, J. Adam et al., “Preliminary Physics Summary: Deuteron andanti-deuteron production in pp collisions at

√s = 13 TeV and in Pb–Pb collisions at

√sNN = 5.02

TeV ”,. https://cds.cern.ch/record/2272148.

[45] P. Huovinen, P. F. Kolb, U. W. Heinz, P. V. Ruuskanen, and S. A. Voloshin, “Radial and ellipticflow at RHIC: Further predictions”, Phys. Lett. B503 (2001) 58–64,arXiv:hep-ph/0101136 [hep-ph].

[46] C. Shen, U. Heinz, P. Huovinen, and H. Song, “Radial and elliptic flow in Pb+Pb collisions at theLarge Hadron Collider from viscous hydrodynamic”, Phys. Rev. C84 (2011) 044903,arXiv:1105.3226 [nucl-th].

[47] STAR Collaboration, C. Adler et al., “Identified particle elliptic flow in Au + Au collisions at√sNN = 130 GeV”, Phys. Rev. Lett. 87 (2001) 182301, arXiv:nucl-ex/0107003 [nucl-ex].

[48] P. J. Siemens and J. O. Rasmussen, “Evidence for a blast wave from compressed nuclear matter”,Phys. Rev. Lett. 42 (1979) 880–883.https://link.aps.org/doi/10.1103/PhysRevLett.42.880.

[49] D. Molnar and S. A. Voloshin, “Elliptic flow at large transverse momenta from quarkcoalescence”, Phys. Rev. Lett. 91 (2003) 092301, arXiv:nucl-th/0302014 [nucl-th].

[50] Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, “A Multi-phase transport model forrelativistic heavy ion collisions”, Phys. Rev. C72 (2005) 064901,arXiv:nucl-th/0411110 [nucl-th].

[51] J. S. Moreland, J. E. Bernhard, and S. A. Bass, “Alternative ansatz to wounded nucleon and binarycollision scaling in high-energy nuclear collisions”, Phys. Rev. C92 no. 1, (2015) 011901,arXiv:1412.4708 [nucl-th].

[52] JETSCAPE Collaboration, K. Kauder, “JETSCAPE v1.0 Quickstart Guide”,Nucl. Phys. A982 (2019) 615–618, arXiv:1807.09615 [hep-ph].

20

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

[53] PHENIX Collaboration, S. S. Adler et al., “Identified charged particle spectra and yields in au+aucollisions at

√sNN = 200 gev”, Phys. Rev. C 69 (Mar, 2004) 034909.

https://link.aps.org/doi/10.1103/PhysRevC.69.034909.

[54] STAR Collaboration, J. Adams et al., “Identified particle distributions in pp and Au+Au collisionsat√

sNN = 200 GeV”, Phys. Rev. Lett. 92 (2004) 112301, arXiv:nucl-ex/0310004 [nucl-ex].

[55] STAR Collaboration, J. Adams et al., “Azimuthal anisotropy in Au+Au collisions at√sNN = 200 GeV”, Phys. Rev. C72 (2005) 014904, arXiv:nucl-ex/0409033 [nucl-ex].

21

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

A The ALICE Collaboration

S. Acharya141 , D. Adamová95 , A. Adler74 , J. Adolfsson81 , M.M. Aggarwal100 , G. Aglieri Rinella34 ,M. Agnello30 , N. Agrawal10 ,54 , Z. Ahammed141 , S. Ahmad16 , S.U. Ahn76 , Z. Akbar51 , A. Akindinov92 ,M. Al-Turany107 , S.N. Alam40 ,141 , D.S.D. Albuquerque122 , D. Aleksandrov88 , B. Alessandro59 ,H.M. Alfanda6 , R. Alfaro Molina71 , B. Ali16 , Y. Ali14 , A. Alici10 ,26 ,54 , N. Alizadehvandchali125 ,A. Alkin2 ,34 , J. Alme21 , T. Alt68 , L. Altenkamper21 , I. Altsybeev113 , M.N. Anaam6 , C. Andrei48 ,D. Andreou34 , A. Andronic144 , M. Angeletti34 , V. Anguelov104 , C. Anson15 , T. Anticic108 , F. Antinori57 ,P. Antonioli54 , N. Apadula80 , L. Aphecetche115 , H. Appelshäuser68 , S. Arcelli26 , R. Arnaldi59 , M. Arratia80 ,I.C. Arsene20 , M. Arslandok104 , A. Augustinus34 , R. Averbeck107 , S. Aziz78 , M.D. Azmi16 , A. Badalà56 ,Y.W. Baek41 , S. Bagnasco59 , X. Bai107 , R. Bailhache68 , R. Bala101 , A. Balbino30 , A. Baldisseri137 , M. Ball43 ,S. Balouza105 , D. Banerjee3 , R. Barbera27 , L. Barioglio25 , G.G. Barnaföldi145 , L.S. Barnby94 , V. Barret134 ,P. Bartalini6 , C. Bartels127 , K. Barth34 , E. Bartsch68 , F. Baruffaldi28 , N. Bastid134 , S. Basu143 , G. Batigne115 ,B. Batyunya75 , D. Bauri49 , J.L. Bazo Alba112 , I.G. Bearden89 , C. Beattie146 , C. Bedda63 , I. Belikov136 ,A.D.C. Bell Hechavarria144 , F. Bellini34 , R. Bellwied125 , V. Belyaev93 , G. Bencedi145 , S. Beole25 ,A. Bercuci48 , Y. Berdnikov98 , D. Berenyi145 , R.A. Bertens130 , D. Berzano59 , M.G. Besoiu67 , L. Betev34 ,A. Bhasin101 , I.R. Bhat101 , M.A. Bhat3 , H. Bhatt49 , B. Bhattacharjee42 , A. Bianchi25 , L. Bianchi25 ,N. Bianchi52 , J. Bielcík37 , J. Bielcíková95 , A. Bilandzic105 , G. Biro145 , R. Biswas3 , S. Biswas3 , J.T. Blair119 ,D. Blau88 , C. Blume68 , G. Boca139 , F. Bock96 , A. Bogdanov93 , S. Boi23 , J. Bok61 , L. Boldizsár145 ,A. Bolozdynya93 , M. Bombara38 , G. Bonomi140 , H. Borel137 , A. Borissov93 , H. Bossi146 , E. Botta25 ,L. Bratrud68 , P. Braun-Munzinger107 , M. Bregant121 , M. Broz37 , E. Bruna59 , G.E. Bruno33 ,106 ,M.D. Buckland127 , D. Budnikov109 , H. Buesching68 , S. Bufalino30 , O. Bugnon115 , P. Buhler114 , P. Buncic34 ,Z. Buthelezi72 ,131 , J.B. Butt14 , S.A. Bysiak118 , D. Caffarri90 , A. Caliva107 , E. Calvo Villar112 ,J.M.M. Camacho120 , R.S. Camacho45 , P. Camerini24 , F.D.M. Canedo121 , A.A. Capon114 , F. Carnesecchi26 ,R. Caron137 , J. Castillo Castellanos137 , A.J. Castro130 , E.A.R. Casula55 , F. Catalano30 , C. Ceballos Sanchez75 ,P. Chakraborty49 , S. Chandra141 , W. Chang6 , S. Chapeland34 , M. Chartier127 , S. Chattopadhyay141 ,S. Chattopadhyay110 , A. Chauvin23 , C. Cheshkov135 , B. Cheynis135 , V. Chibante Barroso34 ,D.D. Chinellato122 , S. Cho61 , P. Chochula34 , T. Chowdhury134 , P. Christakoglou90 , C.H. Christensen89 ,P. Christiansen81 , T. Chujo133 , C. Cicalo55 , L. Cifarelli10 ,26 , L.D. Cilladi25 , F. Cindolo54 , M.R. Ciupek107 ,G. Clai54 ,ii, J. Cleymans124 , F. Colamaria53 , D. Colella53 , A. Collu80 , M. Colocci26 , M. Concas59 ,iii, G. ConesaBalbastre79 , Z. Conesa del Valle78 , G. Contin24 ,60 , J.G. Contreras37 , T.M. Cormier96 , Y. Corrales Morales25 ,P. Cortese31 , M.R. Cosentino123 , F. Costa34 , S. Costanza139 , P. Crochet134 , E. Cuautle69 , P. Cui6 ,L. Cunqueiro96 , D. Dabrowski142 , T. Dahms105 , A. Dainese57 , F.P.A. Damas115 ,137 , M.C. Danisch104 ,A. Danu67 , D. Das110 , I. Das110 , P. Das86 , P. Das3 , S. Das3 , A. Dash86 , S. Dash49 , S. De86 , A. De Caro29 ,G. de Cataldo53 , J. de Cuveland39 , A. De Falco23 , D. De Gruttola10 , N. De Marco59 , S. De Pasquale29 ,S. Deb50 , H.F. Degenhardt121 , K.R. Deja142 , A. Deloff85 , S. Delsanto25 ,131 , W. Deng6 , P. Dhankher49 , D. DiBari33 , A. Di Mauro34 , R.A. Diaz8 , T. Dietel124 , P. Dillenseger68 , Y. Ding6 , R. Divià34 , D.U. Dixit19 ,Ø. Djuvsland21 , U. Dmitrieva62 , A. Dobrin67 , B. Dönigus68 , O. Dordic20 , A.K. Dubey141 , A. Dubla90 ,107 ,S. Dudi100 , M. Dukhishyam86 , P. Dupieux134 , R.J. Ehlers96 , V.N. Eikeland21 , D. Elia53 , B. Erazmus115 ,F. Erhardt99 , A. Erokhin113 , M.R. Ersdal21 , B. Espagnon78 , G. Eulisse34 , D. Evans111 , S. Evdokimov91 ,L. Fabbietti105 , M. Faggin28 , J. Faivre79 , F. Fan6 , A. Fantoni52 , M. Fasel96 , P. Fecchio30 , A. Feliciello59 ,G. Feofilov113 , A. Fernández Téllez45 , A. Ferrero137 , A. Ferretti25 , A. Festanti34 , V.J.G. Feuillard104 ,J. Figiel118 , S. Filchagin109 , D. Finogeev62 , F.M. Fionda21 , G. Fiorenza53 , F. Flor125 , A.N. Flores119 ,S. Foertsch72 , P. Foka107 , S. Fokin88 , E. Fragiacomo60 , U. Frankenfeld107 , U. Fuchs34 , C. Furget79 , A. Furs62 ,M. Fusco Girard29 , J.J. Gaardhøje89 , M. Gagliardi25 , A.M. Gago112 , A. Gal136 , C.D. Galvan120 , P. Ganoti84 ,C. Garabatos107 , J.R.A. Garcia45 , E. Garcia-Solis11 , K. Garg115 , C. Gargiulo34 , A. Garibli87 , K. Garner144 ,P. Gasik105 ,107 , E.F. Gauger119 , M.B. Gay Ducati70 , M. Germain115 , J. Ghosh110 , P. Ghosh141 , S.K. Ghosh3 ,M. Giacalone26 , P. Gianotti52 , P. Giubellino59 ,107 , P. Giubilato28 , A.M.C. Glaenzer137 , P. Glässel104 , A. GomezRamirez74 , V. Gonzalez107 ,143 , L.H. González-Trueba71 , S. Gorbunov39 , L. Görlich118 , A. Goswami49 ,S. Gotovac35 , V. Grabski71 , L.K. Graczykowski142 , K.L. Graham111 , L. Greiner80 , A. Grelli63 , C. Grigoras34 ,V. Grigoriev93 , A. Grigoryan1 , S. Grigoryan75 , O.S. Groettvik21 , F. Grosa30 ,59 , J.F. Grosse-Oetringhaus34 ,R. Grosso107 , R. Guernane79 , M. Guittiere115 , K. Gulbrandsen89 , T. Gunji132 , A. Gupta101 , R. Gupta101 ,I.B. Guzman45 , R. Haake146 , M.K. Habib107 , C. Hadjidakis78 , H. Hamagaki82 , G. Hamar145 , M. Hamid6 ,R. Hannigan119 , M.R. Haque63 ,86 , A. Harlenderova107 , J.W. Harris146 , A. Harton11 , J.A. Hasenbichler34 ,H. Hassan96 , Q.U. Hassan14 , D. Hatzifotiadou10 ,54 , P. Hauer43 , L.B. Havener146 , S. Hayashi132 ,S.T. Heckel105 , E. Hellbär68 , H. Helstrup36 , A. Herghelegiu48 , T. Herman37 , E.G. Hernandez45 , G. HerreraCorral9 , F. Herrmann144 , K.F. Hetland36 , H. Hillemanns34 , C. Hills127 , B. Hippolyte136 , B. Hohlweger105 ,

22

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

J. Honermann144 , D. Horak37 , A. Hornung68 , S. Hornung107 , R. Hosokawa15 ,133 , P. Hristov34 , C. Huang78 ,C. Hughes130 , P. Huhn68 , T.J. Humanic97 , H. Hushnud110 , L.A. Husova144 , N. Hussain42 , S.A. Hussain14 ,D. Hutter39 , J.P. Iddon34 ,127 , R. Ilkaev109 , H. Ilyas14 , M. Inaba133 , G.M. Innocenti34 , M. Ippolitov88 ,A. Isakov95 , M.S. Islam110 , M. Ivanov107 , V. Ivanov98 , V. Izucheev91 , B. Jacak80 , N. Jacazio34 ,54 ,P.M. Jacobs80 , S. Jadlovska117 , J. Jadlovsky117 , S. Jaelani63 , C. Jahnke121 , M.J. Jakubowska142 ,M.A. Janik142 , T. Janson74 , M. Jercic99 , O. Jevons111 , M. Jin125 , F. Jonas96 ,144 , P.G. Jones111 , J. Jung68 ,M. Jung68 , A. Jusko111 , P. Kalinak64 , A. Kalweit34 , V. Kaplin93 , S. Kar6 , A. Karasu Uysal77 , D. Karatovic99 ,O. Karavichev62 , T. Karavicheva62 , P. Karczmarczyk142 , E. Karpechev62 , A. Kazantsev88 , U. Kebschull74 ,R. Keidel47 , M. Keil34 , B. Ketzer43 , Z. Khabanova90 , A.M. Khan6 , S. Khan16 , A. Khanzadeev98 ,Y. Kharlov91 , A. Khatun16 , A. Khuntia118 , B. Kileng36 , B. Kim61 , B. Kim133 , D. Kim147 , D.J. Kim126 ,E.J. Kim73 , H. Kim17 , J. Kim147 , J.S. Kim41 , J. Kim104 , J. Kim147 , J. Kim73 , M. Kim104 , S. Kim18 ,T. Kim147 , T. Kim147 , S. Kirsch68 , I. Kisel39 , S. Kiselev92 , A. Kisiel142 , J.L. Klay5 , C. Klein68 , J. Klein34 ,59 ,S. Klein80 , C. Klein-Bösing144 , M. Kleiner68 , T. Klemenz105 , A. Kluge34 , M.L. Knichel34 , A.G. Knospe125 ,C. Kobdaj116 , M.K. Köhler104 , T. Kollegger107 , A. Kondratyev75 , N. Kondratyeva93 , E. Kondratyuk91 ,J. Konig68 , S.A. Konigstorfer105 , P.J. Konopka34 , G. Kornakov142 , L. Koska117 , O. Kovalenko85 ,V. Kovalenko113 , M. Kowalski118 , I. Králik64 , A. Kravcáková38 , L. Kreis107 , M. Krivda64 ,111 , F. Krizek95 ,K. Krizkova Gajdosova37 , M. Krüger68 , E. Kryshen98 , M. Krzewicki39 , A.M. Kubera97 , V. Kucera34 ,61 ,C. Kuhn136 , P.G. Kuijer90 , L. Kumar100 , S. Kundu86 , P. Kurashvili85 , A. Kurepin62 , A.B. Kurepin62 ,A. Kuryakin109 , S. Kushpil95 , J. Kvapil111 , M.J. Kweon61 , J.Y. Kwon61 , Y. Kwon147 , S.L. La Pointe39 , P. LaRocca27 , Y.S. Lai80 , M. Lamanna34 , R. Langoy129 , K. Lapidus34 , A. Lardeux20 , P. Larionov52 , E. Laudi34 ,R. Lavicka37 , T. Lazareva113 , R. Lea24 , L. Leardini104 , J. Lee133 , S. Lee147 , S. Lehner114 , J. Lehrbach39 ,R.C. Lemmon94 , I. León Monzón120 , E.D. Lesser19 , M. Lettrich34 , P. Lévai145 , X. Li12 , X.L. Li6 , J. Lien129 ,R. Lietava111 , B. Lim17 , V. Lindenstruth39 , A. Lindner48 , C. Lippmann107 , M.A. Lisa97 , A. Liu19 , J. Liu127 ,S. Liu97 , W.J. Llope143 , I.M. Lofnes21 , V. Loginov93 , C. Loizides96 , P. Loncar35 , J.A. Lopez104 , X. Lopez134 ,E. López Torres8 , J.R. Luhder144 , M. Lunardon28 , G. Luparello60 , Y.G. Ma40 , A. Maevskaya62 , M. Mager34 ,S.M. Mahmood20 , T. Mahmoud43 , A. Maire136 , R.D. Majka146 ,i, M. Malaev98 , Q.W. Malik20 , L. Malinina75 ,iv,D. Mal’Kevich92 , P. Malzacher107 , G. Mandaglio32 ,56 , V. Manko88 , F. Manso134 , V. Manzari53 , Y. Mao6 ,M. Marchisone135 , J. Mareš66 , G.V. Margagliotti24 , A. Margotti54 , A. Marín107 , C. Markert119 ,M. Marquard68 , C.D. Martin24 , N.A. Martin104 , P. Martinengo34 , J.L. Martinez125 , M.I. Martínez45 ,G. Martínez García115 , S. Masciocchi107 , M. Masera25 , A. Masoni55 , L. Massacrier78 , E. Masson115 ,A. Mastroserio53 ,138 , A.M. Mathis105 , O. Matonoha81 , P.F.T. Matuoka121 , A. Matyja118 , C. Mayer118 ,F. Mazzaschi25 , M. Mazzilli53 , M.A. Mazzoni58 , A.F. Mechler68 , F. Meddi22 , Y. Melikyan62 ,93 ,A. Menchaca-Rocha71 , C. Mengke6 , E. Meninno29 ,114 , A.S. Menon125 , M. Meres13 , S. Mhlanga124 ,Y. Miake133 , L. Micheletti25 , L.C. Migliorin135 , D.L. Mihaylov105 , K. Mikhaylov75 ,92 , A.N. Mishra69 ,D. Miskowiec107 , A. Modak3 , N. Mohammadi34 , A.P. Mohanty63 , B. Mohanty86 , M. Mohisin Khan16 ,v,Z. Moravcova89 , C. Mordasini105 , D.A. Moreira De Godoy144 , L.A.P. Moreno45 , I. Morozov62 , A. Morsch34 ,T. Mrnjavac34 , V. Muccifora52 , E. Mudnic35 , D. Mühlheim144 , S. Muhuri141 , J.D. Mulligan80 , A. Mulliri23 ,55 ,M.G. Munhoz121 , R.H. Munzer68 , H. Murakami132 , S. Murray124 , L. Musa34 , J. Musinsky64 , C.J. Myers125 ,J.W. Myrcha142 , B. Naik49 , R. Nair85 , B.K. Nandi49 , R. Nania10 ,54 , E. Nappi53 , M.U. Naru14 ,A.F. Nassirpour81 , C. Nattrass130 , R. Nayak49 , T.K. Nayak86 , S. Nazarenko109 , A. Neagu20 , R.A. Negrao DeOliveira68 , L. Nellen69 , S.V. Nesbo36 , G. Neskovic39 , D. Nesterov113 , L.T. Neumann142 , B.S. Nielsen89 ,S. Nikolaev88 , S. Nikulin88 , V. Nikulin98 , F. Noferini10 ,54 , P. Nomokonov75 , J. Norman79 ,127 , N. Novitzky133 ,P. Nowakowski142 , A. Nyanin88 , J. Nystrand21 , M. Ogino82 , A. Ohlson81 , J. Oleniacz142 , A.C. Oliveira DaSilva130 , M.H. Oliver146 , C. Oppedisano59 , A. Ortiz Velasquez69 , T. Osako46 , A. Oskarsson81 ,J. Otwinowski118 , K. Oyama82 , Y. Pachmayer104 , V. Pacik89 , S. Padhan49 , D. Pagano140 , G. Paic69 , J. Pan143 ,S. Panebianco137 , P. Pareek50 ,141 , J. Park61 , J.E. Parkkila126 , S. Parmar100 , S.P. Pathak125 , B. Paul23 ,J. Pazzini140 , H. Pei6 , T. Peitzmann63 , X. Peng6 , L.G. Pereira70 , H. Pereira Da Costa137 , D. Peresunko88 ,G.M. Perez8 , S. Perrin137 , Y. Pestov4 , V. Petrácek37 , M. Petrovici48 , R.P. Pezzi70 , S. Piano60 , M. Pikna13 ,P. Pillot115 , O. Pinazza34 ,54 , L. Pinsky125 , C. Pinto27 , S. Pisano10 ,52 , D. Pistone56 , M. Płoskon80 ,M. Planinic99 , F. Pliquett68 , M.G. Poghosyan96 , B. Polichtchouk91 , N. Poljak99 , A. Pop48 ,S. Porteboeuf-Houssais134 , V. Pozdniakov75 , S.K. Prasad3 , R. Preghenella54 , F. Prino59 , C.A. Pruneau143 ,I. Pshenichnov62 , M. Puccio34 , J. Putschke143 , S. Qiu90 , L. Quaglia25 , R.E. Quishpe125 , S. Ragoni111 ,S. Raha3 , S. Rajput101 , J. Rak126 , A. Rakotozafindrabe137 , L. Ramello31 , F. Rami136 , S.A.R. Ramirez45 ,R. Raniwala102 , S. Raniwala102 , S.S. Räsänen44 , R. Rath50 , V. Ratza43 , I. Ravasenga90 , K.F. Read96 ,130 ,A.R. Redelbach39 , K. Redlich85 ,vi, A. Rehman21 , P. Reichelt68 , F. Reidt34 , X. Ren6 , R. Renfordt68 ,Z. Rescakova38 , K. Reygers104 , A. Riabov98 , V. Riabov98 , T. Richert81 ,89 , M. Richter20 , P. Riedler34 ,

23

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

W. Riegler34 , F. Riggi27 , C. Ristea67 , S.P. Rode50 , M. Rodríguez Cahuantzi45 , K. Røed20 , R. Rogalev91 ,E. Rogochaya75 , D. Rohr34 , D. Röhrich21 , P.F. Rojas45 , P.S. Rokita142 , F. Ronchetti52 , A. Rosano56 ,E.D. Rosas69 , K. Roslon142 , A. Rossi28 ,57 , A. Rotondi139 , A. Roy50 , P. Roy110 , O.V. Rueda81 , R. Rui24 ,B. Rumyantsev75 , A. Rustamov87 , E. Ryabinkin88 , Y. Ryabov98 , A. Rybicki118 , H. Rytkonen126 ,O.A.M. Saarimaki44 , R. Sadek115 , S. Sadhu141 , S. Sadovsky91 , K. Šafarík37 , S.K. Saha141 , B. Sahoo49 ,P. Sahoo49 , R. Sahoo50 , S. Sahoo65 , P.K. Sahu65 , J. Saini141 , S. Sakai133 , S. Sambyal101 , V. Samsonov93 ,98 ,D. Sarkar143 , N. Sarkar141 , P. Sarma42 , V.M. Sarti105 , M.H.P. Sas63 , E. Scapparone54 , J. Schambach119 ,H.S. Scheid68 , C. Schiaua48 , R. Schicker104 , A. Schmah104 , C. Schmidt107 , H.R. Schmidt103 ,M.O. Schmidt104 , M. Schmidt103 , N.V. Schmidt68 ,96 , A.R. Schmier130 , J. Schukraft89 , Y. Schutz136 ,K. Schwarz107 , K. Schweda107 , G. Scioli26 , E. Scomparin59 , J.E. Seger15 , Y. Sekiguchi132 , D. Sekihata132 ,I. Selyuzhenkov93 ,107 , S. Senyukov136 , D. Serebryakov62 , A. Sevcenco67 , A. Shabanov62 , A. Shabetai115 ,R. Shahoyan34 , W. Shaikh110 , A. Shangaraev91 , A. Sharma100 , A. Sharma101 , H. Sharma118 , M. Sharma101 ,N. Sharma100 , S. Sharma101 , O. Sheibani125 , K. Shigaki46 , M. Shimomura83 , S. Shirinkin92 , Q. Shou40 ,Y. Sibiriak88 , S. Siddhanta55 , T. Siemiarczuk85 , D. Silvermyr81 , G. Simatovic90 , G. Simonetti34 , B. Singh105 ,R. Singh86 , R. Singh101 , R. Singh50 , V.K. Singh141 , V. Singhal141 , T. Sinha110 , B. Sitar13 , M. Sitta31 ,T.B. Skaali20 , M. Slupecki44 , N. Smirnov146 , R.J.M. Snellings63 , C. Soncco112 , J. Song125 ,A. Songmoolnak116 , F. Soramel28 , S. Sorensen130 , I. Sputowska118 , J. Stachel104 , I. Stan67 , P.J. Steffanic130 ,E. Stenlund81 , S.F. Stiefelmaier104 , D. Stocco115 , M.M. Storetvedt36 , L.D. Stritto29 , A.A.P. Suaide121 ,T. Sugitate46 , C. Suire78 , M. Suleymanov14 , M. Suljic34 , R. Sultanov92 , M. Šumbera95 , V. Sumberia101 ,S. Sumowidagdo51 , S. Swain65 , A. Szabo13 , I. Szarka13 , U. Tabassam14 , S.F. Taghavi105 , G. Taillepied134 ,J. Takahashi122 , G.J. Tambave21 , S. Tang6 ,134 , M. Tarhini115 , M.G. Tarzila48 , A. Tauro34 , G. Tejeda Muñoz45 ,A. Telesca34 , L. Terlizzi25 , C. Terrevoli125 , D. Thakur50 , S. Thakur141 , D. Thomas119 , F. Thoresen89 ,R. Tieulent135 , A. Tikhonov62 , A.R. Timmins125 , A. Toia68 , N. Topilskaya62 , M. Toppi52 , F. Torales-Acosta19 ,S.R. Torres37 , A. Trifiró32 ,56 , S. Tripathy50 ,69 , T. Tripathy49 , S. Trogolo28 , G. Trombetta33 , L. Tropp38 ,V. Trubnikov2 , W.H. Trzaska126 , T.P. Trzcinski142 , B.A. Trzeciak37 ,63 , A. Tumkin109 , R. Turrisi57 ,T.S. Tveter20 , K. Ullaland21 , E.N. Umaka125 , A. Uras135 , G.L. Usai23 , M. Vala38 , N. Valle139 , S. Vallero59 ,N. van der Kolk63 , L.V.R. van Doremalen63 , M. van Leeuwen63 , P. Vande Vyvre34 , D. Varga145 , Z. Varga145 ,M. Varga-Kofarago145 , A. Vargas45 , M. Vasileiou84 , A. Vasiliev88 , O. Vázquez Doce105 , V. Vechernin113 ,E. Vercellin25 , S. Vergara Limón45 , L. Vermunt63 , R. Vernet7 , R. Vértesi145 , L. Vickovic35 , Z. Vilakazi131 ,O. Villalobos Baillie111 , G. Vino53 , A. Vinogradov88 , T. Virgili29 , V. Vislavicius89 , A. Vodopyanov75 ,B. Volkel34 , M.A. Völkl103 , K. Voloshin92 , S.A. Voloshin143 , G. Volpe33 , B. von Haller34 , I. Vorobyev105 ,D. Voscek117 , J. Vrláková38 , B. Wagner21 , M. Weber114 , S.G. Weber144 , A. Wegrzynek34 , S.C. Wenzel34 ,J.P. Wessels144 , J. Wiechula68 , J. Wikne20 , G. Wilk85 , J. Wilkinson10 , G.A. Willems144 , E. Willsher111 ,B. Windelband104 , M. Winn137 , W.E. Witt130 , J.R. Wright119 , Y. Wu128 , R. Xu6 , S. Yalcin77 , Y. Yamaguchi46 ,K. Yamakawa46 , S. Yang21 , S. Yano137 , Z. Yin6 , H. Yokoyama63 , I.-K. Yoo17 , J.H. Yoon61 , S. Yuan21 ,A. Yuncu104 , V. Yurchenko2 , V. Zaccolo24 , A. Zaman14 , C. Zampolli34 , H.J.C. Zanoli63 , N. Zardoshti34 ,A. Zarochentsev113 , P. Závada66 , N. Zaviyalov109 , H. Zbroszczyk142 , M. Zhalov98 , S. Zhang40 , X. Zhang6 ,Z. Zhang6 , V. Zherebchevskii113 , Y. Zhi12 , D. Zhou6 , Y. Zhou89 , Z. Zhou21 , J. Zhu6 ,107 , Y. Zhu6 ,A. Zichichi10 ,26 , G. Zinovjev2 , N. Zurlo140 ,

Affiliation notesi Deceased

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

iii Dipartimento DET del Politecnico di Torino, Turin, Italyiv M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russiav Department of Applied Physics, Aligarh Muslim University, Aligarh, India

vi Institute of Theoretical Physics, University of Wroclaw, Poland

Collaboration Institutes1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia2 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine3 Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS),

Kolkata, India4 Budker Institute for Nuclear Physics, Novosibirsk, Russia

24

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

5 California Polytechnic State University, San Luis Obispo, California, United States6 Central China Normal University, Wuhan, China7 Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France8 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba9 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico

10 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi’, Rome, Italy11 Chicago State University, Chicago, Illinois, United States12 China Institute of Atomic Energy, Beijing, China13 Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia14 COMSATS University Islamabad, Islamabad, Pakistan15 Creighton University, Omaha, Nebraska, United States16 Department of Physics, Aligarh Muslim University, Aligarh, India17 Department of Physics, Pusan National University, Pusan, Republic of Korea18 Department of Physics, Sejong University, Seoul, Republic of Korea19 Department of Physics, University of California, Berkeley, California, United States20 Department of Physics, University of Oslo, Oslo, Norway21 Department of Physics and Technology, University of Bergen, Bergen, Norway22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy31 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN

Sezione di Torino, Alessandria, Italy32 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy34 European Organization for Nuclear Research (CERN), Geneva, Switzerland35 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split,

Split, Croatia36 Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway37 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague,

Czech Republic38 Faculty of Science, P.J. Šafárik University, Košice, Slovakia39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt,

Germany40 Fudan University, Shanghai, China41 Gangneung-Wonju National University, Gangneung, Republic of Korea42 Gauhati University, Department of Physics, Guwahati, India43 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn,

Germany44 Helsinki Institute of Physics (HIP), Helsinki, Finland45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico46 Hiroshima University, Hiroshima, Japan47 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany48 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania49 Indian Institute of Technology Bombay (IIT), Mumbai, India50 Indian Institute of Technology Indore, Indore, India51 Indonesian Institute of Sciences, Jakarta, Indonesia52 INFN, Laboratori Nazionali di Frascati, Frascati, Italy53 INFN, Sezione di Bari, Bari, Italy54 INFN, Sezione di Bologna, Bologna, Italy55 INFN, Sezione di Cagliari, Cagliari, Italy

25

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

56 INFN, Sezione di Catania, Catania, Italy57 INFN, Sezione di Padova, Padova, Italy58 INFN, Sezione di Roma, Rome, Italy59 INFN, Sezione di Torino, Turin, Italy60 INFN, Sezione di Trieste, Trieste, Italy61 Inha University, Incheon, Republic of Korea62 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia63 Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands64 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia65 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India66 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic67 Institute of Space Science (ISS), Bucharest, Romania68 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany69 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico70 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil71 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico72 iThemba LABS, National Research Foundation, Somerset West, South Africa73 Jeonbuk National University, Jeonju, Republic of Korea74 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und

Mathematik, Frankfurt, Germany75 Joint Institute for Nuclear Research (JINR), Dubna, Russia76 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea77 KTO Karatay University, Konya, Turkey78 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France79 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3,

Grenoble, France80 Lawrence Berkeley National Laboratory, Berkeley, California, United States81 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden82 Nagasaki Institute of Applied Science, Nagasaki, Japan83 Nara Women’s University (NWU), Nara, Japan84 National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens,

Greece85 National Centre for Nuclear Research, Warsaw, Poland86 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India87 National Nuclear Research Center, Baku, Azerbaijan88 National Research Centre Kurchatov Institute, Moscow, Russia89 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark90 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands91 NRC Kurchatov Institute IHEP, Protvino, Russia92 NRC «Kurchatov» Institute - ITEP, Moscow, Russia93 NRNU Moscow Engineering Physics Institute, Moscow, Russia94 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom95 Nuclear Physics Institute of the Czech Academy of Sciences, Rež u Prahy, Czech Republic96 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States97 Ohio State University, Columbus, Ohio, United States98 Petersburg Nuclear Physics Institute, Gatchina, Russia99 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia

100 Physics Department, Panjab University, Chandigarh, India101 Physics Department, University of Jammu, Jammu, India102 Physics Department, University of Rajasthan, Jaipur, India103 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany104 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany105 Physik Department, Technische Universität München, Munich, Germany106 Politecnico di Bari, Bari, Italy107 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für

Schwerionenforschung GmbH, Darmstadt, Germany

26

Elliptic and triangular flow of (anti)deuterons ALICE Collaboration

108 Rudjer Boškovic Institute, Zagreb, Croatia109 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia110 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India111 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom112 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru113 St. Petersburg State University, St. Petersburg, Russia114 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria115 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France116 Suranaree University of Technology, Nakhon Ratchasima, Thailand117 Technical University of Košice, Košice, Slovakia118 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland119 The University of Texas at Austin, Austin, Texas, United States120 Universidad Autónoma de Sinaloa, Culiacán, Mexico121 Universidade de São Paulo (USP), São Paulo, Brazil122 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil123 Universidade Federal do ABC, Santo Andre, Brazil124 University of Cape Town, Cape Town, South Africa125 University of Houston, Houston, Texas, United States126 University of Jyväskylä, Jyväskylä, Finland127 University of Liverpool, Liverpool, United Kingdom128 University of Science and Technology of China, Hefei, China129 University of South-Eastern Norway, Tonsberg, Norway130 University of Tennessee, Knoxville, Tennessee, United States131 University of the Witwatersrand, Johannesburg, South Africa132 University of Tokyo, Tokyo, Japan133 University of Tsukuba, Tsukuba, Japan134 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France135 Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France136 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France137 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire

(DPhN), Saclay, France138 Università degli Studi di Foggia, Foggia, Italy139 Università degli Studi di Pavia, Pavia, Italy140 Università di Brescia, Brescia, Italy141 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India142 Warsaw University of Technology, Warsaw, Poland143 Wayne State University, Detroit, Michigan, United States144 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany145 Wigner Research Centre for Physics, Budapest, Hungary146 Yale University, New Haven, Connecticut, United States147 Yonsei University, Seoul, Republic of Korea

27