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Collective flow in ultra-relativistic heavy-ion collisions

Collective flow in ultra-relativistic heavy-ion collisions. Subrata Pal Tata Institute of Fundamental Research, Mumbai, India. Quantitative study of QCD phase diagram. Elastic scattering and kinetic freeze-out. Hadronic interaction and chemical freeze-out. parton evolution. detector.

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Collective flow in ultra-relativistic heavy-ion collisions

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  1. Collective flow in ultra-relativistic heavy-ion collisions Subrata Pal Tata Institute of Fundamental Research, Mumbai, India

  2. Quantitative study of QCD phase diagram Elastic scattering and kinetic freeze-out Hadronic interactionand chemical freeze-out parton evolution detector initial state pre-equilibrium Hadronization Conjectured Phase Diagram Courtesy: S. Bass Collective flow is one of the most promising observables Outline: • Prologue on Collective (Anisotropic) flow in HI collision • Models (Transport & Hydrodynamic) to study flow • Model predictions & comparisons with LHC flow data • Conclusions

  3. Flow in heavy-ion collision Origin of elliptic flow v2: spatial anisotropy and re-interaction Ollitrault PRD46 (1992) 229 vn are Fourier coeff in φ distrn of particles wrt reaction plane Entire Flow vector can be expressed in a complex plane: Origin of triangular flow v3: fluctuations in the position of participant nucleons vn(pT,) = magnitude (anisotropic flow) n(pT,)= phase (event-plane angle along minor axis) Alver & Roland, PRC81(2010) 054905 Odd harmonics = 0 Odd harmonics ≠ 0

  4. ε2 ε3 ε4 Initial spatial anisotopy  collective flow Harmonic flow vector relates to various moments of initial spatial anisotropy (eccentricities) of nucleons/partons … over (r,) of participants (nucleons/partons) n = magnitude (eccenticities) n = phase (participant-plane angle) In HI collision, Npart is finite and (r,) fluctuate randomly  EbyE distribution: p(n, m, …., n, m,…)  Collective/Hydro expansion (, EoS, /s, /s, …) Ideal Flow observable: Joint probability distribution of all vn and n Finite multiplicity only allows projections of full p(vn,..,n,..) on finite number of variables

  5. Flow observables All info on Vn can be obtained from multi-particle correlations (cumulants) 2-particle correlation: (short range: resonance decay, BE correlation, etc) nonflow Supress nonflow by placing -gaps between pairs Moments for m-particle azimuthal correlation: Azimuthal asymmetry implies n1+…+ nm = 0 Observables of flow and EbyE flow fluctuations: Cumulants&moments of p(vn), p(vn,vm) • Flowmagnitude involving vn: • p(vn)  p(vn,vm)  • Flow phases (event plane angles) involving n • Correlation involving mixed flow harmonics Large number of flow observables promise to constrain initial matter (QGP) properties

  6. “Eliminating” non-flow from EbyE flow fluctuations • Placing a  gap between pairs in v2{2} can “isolate” non-flow • v2{m} for m  4 are all equal •  non-flow is negligible and flow fluctuations are Gaussian

  7. ΔE AMultiPhase Transport model (AMPT) Inclusive hadron distribution – calculable in pQCD Energy loss Lin, Ko, Li, Zhang, SP, PRC72 (2005) 064901 • Initial particle distribution obtained from updated HIJING 2.0 model • Strings from HIJING converted to valence (anti)quarks – String Melting • Partons scatter in ZPC model with elastic scattering cross section: • Phase-space coalescence of freeze-out partons produce the hadrons • Hadrons evolve with (in)-elastic scatterings via ART transport model SP, Bleicher, PLB 709 (2012) 82 σ≈ 9s2/μ2

  8. Ideal and Dissipative Hydrodynamics Israel, Stewart, Ann. Phys. 118 (1979) 341. Muronga, PRC69 (2004) 034903. Romatschke, Int. J. Mod. Phys. E19 (2010) 1. Huovinen, Petreczky, NPA 837 (2010) 26 s95p-PCE EoS matching lattice data to hadron reson gas at TPCE 165 MeV Hadron spectra at freeze-out temp. Tdec120 MeV obtained by Cooper-Frye formula

  9. Non-equilibrium distribution function Grad, Comm. Pure App. Math 2 (1949) 2 Chapman-Enskog like derivation Bhalerao, Jaiswal, SP, Sreekanth, PRC89 (2014) 055903

  10. Initial conditions/uncertainities in Hydro VISH2+1 viscous hydro Song, Heinz et al: PRC77, 064901; PRL 106, 192301; PRC84, 024911 Each parton (in AMPT) at swis represented by 2D Gaussian for transverse energy density Bhalerao, Jaiswal, SP, in prep. • Within sw = 0.3-0.8 fm/c, vn(pT) insensitive to switching time. • vn(pT) similar for Grad and Chapman-Enskog form of f in viscous corrections at freeze-out. • Minor “uncertainties” under control • Largest uncertainty comes from model initial conditions Ma, Wang, PRL 106 (2011) 162301 AMPT b=0

  11. vn{2} in models with different initial conditions IP-Glasma +3D visc Schenke, et al PRL106 (2011) 042301 AMPT&VISH2+1: Bhalerao, Jaiswal SP, in prep. CGC models (IP-Glasma ): Colliding nuclei at high energy treated as coherent condensate of gluons  Classical Yang-Mills equation for gluon fields. Additional color charge fluctuations at partonic scales. • For b0: v2 > v3 > v4 > v5 > v6 Flux tube or hot spots • Models with distinct initialconditions can explain data !! • Observables beyond vn{2} required Flux tube + Id. Hydro Gardim et al, PRL 109 (2012) 202302

  12. vn{2} in ultra-central collisions at LHC • CMS 0-0.2%: v2(pT) saturates and v3, v4, v5, v6 successively becomes larger than v2 with increasing pT • AMPT plus VISH2+1 gives correct trend but overpredicts flow data • As 2  3 one expects v2  v3(fluctuation dominated) • IC with NN correlation in 3D viscous hydro suppresses v2 more than v3 •  hierarchy of vn(pT) still not in complete agreement with CMS flow data Denicol et al, arXiv:1406.7792

  13. p(vn) distribution • P(vn) in AMPT+Hydro agrees with data Alternative: Estimate EbyE vn and n from initial eccentricity vector (n,n) Coeffs C contain all info of medium’s response on hydro evolution UrQMD + 3D ideal Hydro Estimated Event Plane angle Petersen et al, PRC 82 (2010) 041901 With vn = Cnn  p(n) = p(vn)/Cn Strong correlation between PP nand EP n for n=2,3 AMPT+Hydro suggests Cn increases faster at large n than vn  n

  14. Centrality dependence of p(vn) distribution • vn{2} well described by AMPT+Hydro and other models with different IC • IC conditions and/or hydro response do not agree with v2dataatall centralities

  15. Event-by-Event fluctuations in n & vn Fluctuations in EP n(pT,) could lead to spread in the correlation between EbyE n and EbyE vn • v2 shows stronger linear correlation than v3, as hydro more sensitive to large scale structures as for v2 • v4  C44 + C4222, the correlation is weak • Higher harmonics vn has stronger correlation with /s Niemi et al, PRC 87 (2013) 054901

  16. Event plane correlations p(n,m,...) EP correlators involve  3-particles  higher order correlations  Res n vn measured with single EP: Correlations from multi-particles: k1+2k2+…+nkn=0 {SP} {EP} Res(1)Res(22) … Res(knn) Experimental analysis: (i) each EP in different -window; (ii) windows pairwise separated by gaps  decrease statistics 2-subevent method for EP correlators Bhalerao, Ollitrault, SP, PRC88 (2013) 024909 Consider 2 subevents (A,B) separated by a -gap. Construct flow vector for each subevent: EP method: Resolution dependent Scalar product method: Well-defined flow observable

  17. 2-plane correlators Final state correlators – AMPT Initial state correlators – MC Glauber Final state correlators– VISH2+1 Bhalerao, Ollitrault, SP, PRC 88 (2013) 024909 Jia, Mohapatra, EPJC 73 (2013) 2510 Qui & Heinz, PLB 717 (2012) 261 EP EP • Strong corr. between 2 and 4 from fluctuation & almond shape 2 • Weak corr. between 2 and 3 • EP corr. in AMPT agree with data • Final-state corr. retain the initial info • Strong corr. between: • 2 & 4 as v4  (v2)2 • 2 & 6 as v6  (v2)3 MC-Glauber (/s=0.08) vs MC-KLN (/s=0.20)  Correlators are sensitive to IC

  18. 3-plane and 4-plane correlators Generalize to higher order correlations involving kn particle in harmonic n • AMPT results agree with 3-plane EP correlation data • 4-plane correlators more sensitive to EP & SP methods EP EP

  19. Flow fluctuations with moments for two subevents (A,B) about midrapidity Flow vector Bhalerao, Ollitrault, SP, arXiv:1411.5160 Stat. properties of flow Vncontained in moments Testing the hypothesis: Corr: (v2)2 v4 with (v2)2 fluctuations with (v2)4 Testing the hypothesis: Corr: v2v3v5 with (v2)2 AMPT supports conjectured nonlinear correlation at all centralities  Can be tested experimentally with (v3)2 Corr: (v2)2 v4 with (v2)2

  20. New method to study e-by-e flow fluctuations Single particle distribution: Fourier coeff. Vn(p)  Vn(pT,) Pair distrbn as EbyE single distrbn: Statistics of Vn(p) embedded in Fourier Coeff: Construct bins in p(pT,). Estimate Vn(p) in a event with: Covariance matrix  Eigenvalues   0 Pair correln: self-corr. >0 (flow) <0 (non-flow) Principal Component Analysis (PCA): Diagonalize PC: with eigenvalues: =1 (no flow fluctuations) and >1 give statistics and momentum dependence of flow fluctuations Bhalerao, Ollitrault, SP, Teaney: arXiv:1410.7739

  21. Principal components versus  Bhalerao, Ollitrault, SP, Teaney: arXiv:1410.7739 Within AMPT: Construct a pair distrb in -3    3 with  = 0.5 Diagonalize the 1212 matrix: Vn(1, 2). To compare with usual per particle anisotropy: n=0: Relative multiplicity fluctuations n=2: Elliptic flow, n=3:Triangular flow • v0(1) () gives global 12 relative fluctuation indep. of  • v0(2) () is odd parity with (2)  (1)/60 • v0(3) () has alternating parities as A-A and analysis is symmetric =0 • Higher modes fall within statistical fluctuations

  22. Principal components versus pT Within AMPT: Construct a pair distrb inpT bins Diagonalize the matrix: Vn(pT1, pT2) . ALICE data forVn(pT1, pT2) used in PCA PLB:708 (2012) 249. n=0: Relative multiplicity fluctuations n=2: Elliptic flow, n=3:Triangular flow • v0(1) (pT) gives 12 fluctuation in total multip. • v0(2) (pT) increases with pT  radial flow fuct. • LO: v2(1) & v3(1) identical to measured v2 & v3 • NLO: vn(1) have smaller magnitudes and increase with pT PCA use all info (momenta) in 2-particle azimuthal correlations

  23. Summary & Conclusions • Ultimate goal: First principal calculation of non-equilibrium QCD for initial stages of HIC  not yet possible • Pragmatic approach: Use “state-of-art” models to constrain the required initial state structures from experimental data • Observable: Anisotropic flow and flow fluctuations provide large number independent info. • Open issues: vn{2} hierarchy in ultra-central collisions; p(vn) distribution, multiparticle correlation analysis  further constrain the initial condition

  24. ΔE AMultiPhase Transport model (AMPT) Inclusive hadron distribution – calculable in pQCD Energy loss Lin, Ko, Li, Zhang, SP, PRC72 (2005) 064901 Karsch, NPA698 (2002) LHC RHIC SPS σ ~ 1/(t-μ2)2 TC ~ 170 MeV εC ~ 700 MeV/fm3

  25. Hard jets & its energy loss in AMPT Momentum distribution of hard partons from LO pQCD in p+p collision Gaussian GRV94 NLO Total energy loss by a jet of energy E via gluon radiation L = 3 fm, αS = 0.48 Parton density # of gluons emitted from energy loss ΔE is related to entropy increase ΔS T = ε(r,τ)/3ρ(r,τ) From parton cascade Radiated gluons scatter in medium withσ ~ 1/(t-μ2)2 Parton hadron duality: Ng → Nπ

  26. AMPT with updated HIJING 2.0 Deng,Wang,Xu, PLB 701 (2011) 133 • GRV parametrization of parton distribution function • c.m. energy dependence in 2-component HIJING 2.0 PDF in nucleus: Impact parameter dependent shadowing sq = 0.1 (fixed) from deep-inelastic-scattering data off nuclear targets. sgfitted to centrality dependence of measured dNch/dy in A+A collision.

  27. dNch/dy in HIC at RHIC & LHC SP, Bleicher, PLB 709 (2012) 82 Parameters in AMPT In string fragmentation function, Default HIJING: a=0.9, b=0.5 GeV-2. s=0.33, =3.226 fm-1   = 1.5 mb HIJING: dNch/dη||η|0.5 = 705 (RHIC) = 1775 (LHC) • Parton scattering leads to 15% reductions in particle multiplicity. • Hadron scattering insensitive to dN/dη. AMPT hadron yield ratios at LHC

  28. Centrality dependence of dNch/dη Au+Au collisions at RHIC: Measured charged hadron multiplicity density per participant pair constrains the gluon shadowing parameter sg= 0.10 - 0.17 [5] Pb+Pb collisions at LHC: Stronger centrality dependence in ALICE due to large minijet production (at small x) gives a stringent constraint on gluon shadowing of sg≈0.17

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