1 / 29

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.

kberg
Télécharger la présentation

Collective flow in ultra-relativistic heavy-ion collisions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related