The comparison of methods for elliptic flow measurements

The comparison of methods for elliptic flow measurements with the MPD Experiment at NICA Dim Idrisov 1, Vinh Ba Luong 1, Nikolay Geraksiev 2, 3, Arkadiy Taranenko 1, Alexander Demanov 1, Anton Truttse 1, Petr Parfenov 1 1 National Research Nuclear University MEPh. I 2 VBLHEP JINR 3 FPT, Plovdiv University “Paisii Hilendarski” For the MPD Collaboration This work is supported by the RFBR according to the research project No. 18 -02 -40086 The Conference "RFBR Grants for NICA", 20 -23 October 2020, Dubna, Russia

Outline • Elliptic flow (v 2) at NICA energies • Description of direct cumulant, event plane and scalar product methods • Sensitivity of different methods to flow fluctuations and nonflow • Feasibility study of elliptic flow (v 2) of identified hadrons and V 0 particles in MPD (NICA): ‒ Acceptance corrections ‒ Elliptic flow of identified charged particles ‒ Elliptic flow of V 0 particles ‒ Comparison of v 2 results for Bi+Bi and Au+Au collisions at √s. NN = 7. 7 Ge. V • Summary and outlook 2

Elliptic flow at NICA energies - direct flow - elliptic flow Taranenko et. al. Phys. Part. Nuclei 51, 309– 313 (2020) • • • v 2 is sensitive to the properties of strongly interacting matter: – At √s. NN=4. 5 Ge. V pure string/hadronic cascade models (Ur. QMD, SMASH, …) give similar v 2 signal compared to STAR data – At √s. NN≥ 7. 7 Ge. V pure string/hadronic cascade models underestimate v 2 – need hybrid models with QGP phase (v. HLLE+Ur. QMD, AMPT with string melting, …) Strong energy dependence of v 2 at √s. NN=3 -11 Ge. V – v 2≈0 at √s. NN=3. 3 Ge. V and negative below Lack of differential measurements of v 2 at NICA energies (p. T, centrality, PID, …) 3

MPD Experiment at NICA Multi-Purpose Detector (MPD) Stage 1 Event plane, centrality: FHCal (2<|η|<5) or TPC (|η|<1. 5) Time Projection Chamber (TPC) Tracking of charged particles within (|η| < 1. 5, 2π in φ ) PID at low momenta Time of Flight (TOF) PID at high momenta -5<η<-2 FHCal -1. 5<η<1. 5 TPC 0. 2<p. T<3 Ge. V/c 2<η<5 FHCal 4

Setup, event and track selection Ur. QMD Au+Au: Nevents= 10 M at √s. NN = 4. 5, 11. 5 Ge. V Nevents= 25 M at √s. NN = 11 Ge. V (for K 0, Λ) Nevents= 20 M at √s. NN = 7. 7 Ge. V Bi+Bi: Nevents= 17 M at √s. NN = 7. 7 Ge. V Reconstruction GEANT 4 TPC FHCal TOF. . . Flow analysis Event classification: Track multiplicity FHCal energy Track selection: NTPC hits > 16 0. 2 < p. T< 3 Ge. V/c |η| < 1. 5 PID based on TPC+TOF (Mpd. Pid) MPDRoot, August 2020 5

Description of event plane and scalar product methods using TPC Using v 2 of produced particles in TPC to determine Qn (1)) (2)) Left Right (3)) Event Plane: (4)) -1. 5 < η < -0. 05 < η < 1. 5 Left half (η<-0. 05) → η(5)) Right half (η>0. 05) → η+ Scalar Product: (6)) Similar to methods used in L. Adamczyk, et al. , Phys. Rev. C 86 (2012) 054908 6

Description of event plane method using FHCal Using v 1 of particles in FHCal to determine Qn (3)) (1)) (4)) (2)) E – energy deposition in FHCal modules (2<|η|<5) Energy distribution in FHCal 7

Description of direct cumulant method for flow measurements 2 and 4 particle azimuthal correlations (1)) where (2)) (3)) Elliptic flow estimate with direct cumulant method (4)) (5)) δ – nonflow contribution (Bose-Einstein correlations, resonance decays, …) This method was introduced by Ante Bilandzic in Phys. Rev. C 83: 044913, 2011 26. 08. 20 8

v 2 of V 0 particles: invariant mass fit method Data set: 25 million events, Ur. QMD 3. 4 non-hydro, 11. 0 Ge. V, minbias Geant 4 simulation, full reconstruction with: TPCv 7, TOFv 7, FHCal Centrality by TPC multiplicity, Event-plane method with FHCal Particle decays reconstructed with Mpd. Particle realistic cuts Differential flow signal extraction by bins in transverse momentum (or rapidity) with a simultaneous fit 9

Non-uniform acceptance FHCal L, R FHCal L FHCal R Area 15°< φ < 45° is off How robust the future measurements against non-uniform acceptance? 10

Acceptance correction The applied acceptance corrections eliminated the influence of non-uniform acceptance 11

Sensitivity of different methods to flow fluctuations Elliptic flow fluctuations: The difference between v 2{2} and v 2{4}: The difference between v 2 EP{Ψ 1, FHCal} and v 2 EP{Ψ 2, TPC}: J. Adam et al. The ALICE Collaboration Phys. Rev. Lett. 116 (2016) 132302 12

Comparison of v 2 measurements using different method 13

Performance study of v 2 of charged hadrons in MPD Reconstructed (reco) and generated (true) v 2 values are in a good agreement for all methods 14

Performance study of v 2 of pions and protons in MPD Reconstructed and generated v 2 of pions and protons have a good agreement for all methods 15

Performance study for v 2 of V 0 particles Reasonable agreement between reconstructed and generated v 2 signals for both K 0 and Λ 16

Au+Au vs. Bi+Bi collisions for reconstructed data in MPD TPC event plane The results show a little difference for resolution and elliptic flow between two colliding systems 17

Au+Au vs. Bi+Bi collisions for reconstructed data in MPD FHCal event plane Expected small difference between colliding systems 18

Summary and outlook v 2 at NICA energies shows strong energy dependence: At √s. NN=4. 5 Ge. V v 2 from Ur. QMD, SMASH are in a good agreement with the experimental data At √s. NN≥ 7. 7 Ge. V Ur. QMD, SMASH underestimate v 2 – need hybrid models with QGP phase Lack of existing differential measurements of v 2 (p. T, centrality, PID, …) Comparison of methods for elliptic flow measurements using Ur. QMD model: The differences between methods are well understood and could be attributed to non-flow and fluctuations Feasibility study for elliptic flow in MPD: Acceptance corrections allows one to perform v 2 measurements with non-uniform acceptance in MPD v 2 of identified charged hadrons: results from reconstructed and generated data are in a good agreement for all methods v 2 of K 0 and Λ particles: results from reconstructed (using invariant mass fits) and generated data are in a good agreement Small differences in v 2 for 2 colliding systems (Au+Au, Bi+Bi) were observed as expected Outlook: v 1, v 2 and v 3 measurements for the hybrid models (production of 60 M events for v. HLLE+Ur. QMD at √s. NN= 11 Ge. V is ongoing) 19

Thank you for you attention 20

Backup 21

Setup, event and track selection Ur. QMD Reconstruction GEANT 4 Au+Au: Nevents= 10 M at √s. NN = 4. 5, 11. 5 Ge. V Nevents= 20 M at √s. NN = 7. 7 Ge. V Bi+Bi: Nevents= 7 M at √s. NN = 7. 7 Ge. V TPC FHCal TOF. . . Flow analysis Event classification: Track multiplicity FHCal energy Track selection: Primary tracks (2σ DCA cut) N > 16 TPC hits 0. 2 < p < 3 Ge. V/c T |η| < 1. 5 PID based on TPC+TOF (Mpd. Pid) MPDRoot, August 2020 22

Relative elliptic flow fluctuations at 11. 5 Ge. V and 7. 7 Ge. V Star data: L. Adamczyk et al. (STAR Collaboration). Phys. Rev. C 86, 054908 (2012)) • Relative v 2 fluctuations (v 2{4}/v 2{2}) observed by STAR experiment can be reproduced both in the string/cascade models (Ur. QMD, SMASH) and hybrid model (AMPT with string melting) • Dominant source of v 2 fluctuations: participant eccentricity fluctuations in the initial geometry 23

Results for v 2 from Ur. QMD model of Au+Au collisions at √s. NN = 7. 7 Ge. V • v 2{4} is smaller than v 2{2} due to fluctuations and nonflow 24

Description of event plane method Left Right (1)) -1. 5 < η < -0. 05 < η < 1. 5 Left half (η<-0. 05) → ηRight half (η>0. 05) → η+ (2)) v 2{η-sub, EP} (3)) • η-sub EP method: resolution of the reaction plane Ψ 2 obtained from 2 sub-events STAR Collaboration: B. I. Abelev, et al. , Phys. Rev. C 77: 054901, 2008 25

Description of scalar product method (1)) Left Right (2)) • – particle unit vector • – event flow vector(Q-vector) -1. 5 < η < -0. 05 < η < 1. 5 Left half (η<-0. 05) → ηRight half (η>0. 05) → η+ • Elliptic flow measured using correlation between and (3)) 26

Results for v 2 for reconstructed events of MPD v 2{2} and v 2{4} are in good agreement with v 2{η-sub, EP} at 10 -40% centrality 27

Eccintricity: Bi+Bi vs Au+Au Ur. QMD model predicts small difference between εn of Au+Au and Bi+Bi 28

Sensitivity of different orders cumulants to elliptic flow fluctuations • How fluctuations affect the measured values of . The effect of the fluctuations on estimates can be obtained from • The difference between and vdc is sensitive to not only nonflow but also to the event-by-event fluctuations. The difference between with and without Δη gap is driven by the contribution from nonflow Ilya Selyuzhenkov for the ALICE collaboration, Prog. Theor. Phys. Suppl. 193 (2012) 153 -158 29

Cumulant results from Beam Energy Scans Niseem Magdy, Nucl. Phys. A 982 (2019) 255 -258 L. Adamczyk et al. (STAR Collaboration). Phys. Rev. C 86, 054908 (2012) Au+Au • The magnitude and trend of the fluctuations, have weak beam energy dependence • Methods of flow measurements have different sensitivity to flow fluctuations 30

Cumulant results from Beam Energy Scans Au+Au Comprasssion of (a) v 2{2} vs. ‹Nch›, (b) v 2{4} vs. ‹Nch› and (c) thir ratio for Au+Au collisions Niseem Magdy, Nucl. Phys. A 982 (2019) 255 -258 ar. Xiv: 1807. 07638 Ru+Ru, 1. 69 A Ge. V v 2 versus transverse momentum for protons measured in semi-central events and around mid-rapidity. N. Bastid, et al. , Phys. Rev. C 72 (2005) 011901 ar. Xiv: nucl-ex/0504002 31

Results for v 2 from Ur. QMD model of Au+Au collisions at √s. NN = 7. 7 Ge. V • Total number of generated minimum bias events - 88 M Left Right • Particle selection: charged hadrons, 0. 2<p. T<3 Ge. V/c • Configuration of cumulant method: 1. RFP and POI: charged hadrons; -1. 5 < η < -0. 05 < η < 1. 5 Left half (η<-0. 05) → ηRight half (η>0. 05) → η+ 2. calculations were performed taking into account the effect of autocorrelation • All 3 methods have the same kinematical cuts 32

Results for v 2 for reconstructed events of MPD v 2{2} and v 2{4} are in good agreement with v 2{η-sub, EP} at 10 -40% centrality 33

34