Collective flow in ultrarelativistic heavyion collisions Subrata Pal

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Collective flow in ultra-relativistic heavyion collisions Subrata Pal Tata Institute of Fundamental Research, Mumbai,

Collective flow in ultra-relativistic heavyion collisions Subrata Pal Tata Institute of Fundamental Research, Mumbai, India

Quantitative study of QCD phase diagram initial state Hadronic interaction and chemical freeze-out parton

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

Flow in heavy-ion collision Origin of elliptic flow v 2: spatial anisotropy and re-interaction

Flow in heavy-ion collision Origin of elliptic flow v 2: spatial anisotropy and re-interaction Ollitrault PRD 46 (1992) 229 vn are Fourier coeff in φ distrn of particles wrt reaction plane Entire Flow vector can be expressed in a complex plane: vn(p. T, ) = magnitude (anisotropic flow) n(p. T, ) = phase (event-plane angle along minor axis) Odd harmonics = 0 Odd harmonics ≠ 0 Origin of triangular flow v 3: fluctuations in the position of participant nucleons Alver & Roland, PRC 81(2010) 054905 3

Initial spatial anisotopy collective flow Harmonic flow vector relates to various moments of initial

Initial spatial anisotopy collective flow Harmonic flow vector relates to various moments of initial spatial anisotropy (eccentricities) of nucleons/partons ε 2 ε 3 … over (r, ) of participants (nucleons/partons) n = magnitude (eccenticities) n = phase (participant-plane angle) ε 4 In HI collision, Npart is finite and (r, ) fluctuate randomly Eby. E distribution: p( n, m, …. , n, m, …) Collective/Hydro expansion ( , Eo. 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 4

Flow observables All info on Vn can be obtained from multi-particle correlations (cumulants) 2

Flow observables All info on Vn can be obtained from multi-particle correlations (cumulants) 2 -particle correlation: nonflow (short range: resonance decay, BE correlation, etc) Supress nonflow by placing -gaps between pairs Moments for m-particle azimuthal correlation: Azimuthal asymmetry implies n 1+…+ nm = 0 Observables of flow and Eby. E flow fluctuations: v. Flow magnitude involving vn: Cumulants & moments of p(vn), p(vn, vm) p(vn) p(vn, vm) v. Flow phases (event plane angles) involving n v. Correlation involving mixed flow harmonics Large number of flow observables promise to constrain initial matter (QGP) properties 5

“Eliminating” non-flow from Eby. E flow fluctuations Ø Placing a gap between pairs in

“Eliminating” non-flow from Eby. E flow fluctuations Ø Placing a gap between pairs in v 2{2} can “isolate” non-flow Ø v 2{m} for m 4 are all equal non-flow is negligible and flow fluctuations are Gaussian 6

A Multi. Phase Transport model (AMPT) Inclusive hadron distribution – calculable in p. QCD

A Multi. Phase Transport model (AMPT) Inclusive hadron distribution – calculable in p. QCD ΔE Energy loss Lin, Ko, Li, Zhang, SP, PRC 72 (2005) 064901 SP, Bleicher, PLB 709 (2012) 82 7

Ideal and Dissipative Hydrodynamics Israel, Stewart, Ann. Phys. 118 (1979) 341. Muronga, PRC 69

Ideal and Dissipative Hydrodynamics Israel, Stewart, Ann. Phys. 118 (1979) 341. Muronga, PRC 69 (2004) 034903. Romatschke, Int. J. Mod. Phys. E 19 (2010) 1. Huovinen, Petreczky, NPA 837 (2010) 26 s 95 p-PCE Eo. S matching lattice data to hadron reson gas at TPCE 165 Me. V Hadron spectra at freeze-out temp. Tdec 120 Me. V obtained by Cooper-Frye formula 8

Non-equilibrium distribution function Grad, Comm. Pure App. Math 2 (1949) 2 Chapman-Enskog like derivation

Non-equilibrium distribution function Grad, Comm. Pure App. Math 2 (1949) 2 Chapman-Enskog like derivation Bhalerao, Jaiswal, SP, Sreekanth, PRC 89 (2014) 055903 9

Initial conditions/uncertainities in Hydro Ma, Wang, PRL 106 (2011) 162301 AMPT b=0 VISH 2+1

Initial conditions/uncertainities in Hydro Ma, Wang, PRL 106 (2011) 162301 AMPT b=0 VISH 2+1 viscous hydro Song, Heinz et al: PRC 77, 064901; PRL 106, 192301; PRC 84, 024911 Each parton (in AMPT) at sw is represented by 2 D Gaussian for transverse energy density Bhalerao, Jaiswal, SP, in prep. Ø Within sw = 0. 3 -0. 8 fm/c, vn(p. T) insensitive to switching time. Ø vn(p. T) 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 10

vn{2} in models with different initial conditions AMPT&VISH 2+1: Bhalerao, Jaiswal SP, in prep.

vn{2} in models with different initial conditions AMPT&VISH 2+1: Bhalerao, Jaiswal SP, in prep. IP-Glasma +3 D visc Schenke, et al PRL 106 (2011) 042301 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. Ø For b 0: v 2 > v 3 > v 4 > v 5 > v 6 Ø Models with distinct initial conditions can explain data !! Ø Observables beyond vn{2} required Flux tube or hot spots Flux tube + Id. Hydro Gardim et al, PRL 109 (2012) 202302 11

vn{2} in ultra-central collisions at LHC Ø CMS 0 -0. 2%: v 2(p. T)

vn{2} in ultra-central collisions at LHC Ø CMS 0 -0. 2%: v 2(p. T) saturates and v 3, v 4, v 5, v 6 successively becomes larger than v 2 with increasing p. T Ø AMPT plus VISH 2+1 gives correct trend but overpredicts flow data Ø As 2 3 one expects v 2 v 3 (fluctuation dominated) Ø IC with NN correlation in 3 D viscous hydro suppresses v 2 more than v 3 hierarchy of vn(p. T) still not in complete agreement with CMS flow data Denicol et al, ar. Xiv: 1406. 7792 12

p(vn) distribution Ø P(vn) in AMPT+Hydro agrees with data Alternative: Estimate Eby. E vn

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

Centrality dependence of p(vn) distribution § vn{2} well described by AMPT+Hydro and other models

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 v data at all centralities 2 14

Event-by-Event fluctuations in n & vn Fluctuations in EP n(p. T, ) could lead

Event-by-Event fluctuations in n & vn Fluctuations in EP n(p. T, ) could lead to spread in the correlation between Eby. E n and Eby. E vn § v 2 shows stronger linear correlation than v 3, as hydro more sensitive to large scale structures as for v 2 § v 4 C 4 4 + C 42 22, the correlation is weak § Higher harmonics vn has stronger correlation with /s Niemi et al, PRC 87 (2013) 054901 15

Event plane correlations p( n, m, . . . ) EP correlators involve 3

Event plane correlations p( n, m, . . . ) EP correlators involve 3 -particles higher order correlations vn measured with single EP: Res n Correlations from multi-particles: {EP} {SP} Res( 1) Res(2 2) … Res(kn n) k 1+2 k 2+…+nkn=0 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, PRC 88 (2013) 024909 Consider 2 subevents (A, B) separated by a -gap. Construct flow vector for each subevent: EP method: Scalar product method: Resolution dependent Well-defined flow observable 16

2 -plane correlators Initial state correlators – MC Glauber Jia, Mohapatra, EPJC 73 (2013)

2 -plane correlators Initial state correlators – MC Glauber Jia, Mohapatra, EPJC 73 (2013) 2510 Final state correlators – AMPT Final state correlators – VISH 2+1 Qui & Heinz, PLB (2012) 261 024909 Bhalerao, Ollitrault, SP, 717 PRC 88 (2013) 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 MC-Glauber ( /s=0. 08) vs MC-KLN ( /s=0. 20) Correlators are sensitive to IC § Strong corr. between: 2 & 4 as v 4 (v 2)2 2 & 6 as v 6 (v 2)3 17

3 -plane and 4 -plane correlators Generalize to higher order correlations involving kn particle

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

Flow fluctuations with moments Flow vector for two subevents (A, B) about midrapidity Stat.

Flow fluctuations with moments Flow vector for two subevents (A, B) about midrapidity Stat. properties of flow Vn contained in moments Bhalerao, Ollitrault, SP, ar. Xiv: 1411. 5160 Testing the hypothesis: Corr: (v 2)2 v 4 with (v 2)2 fluctuations with (v 2)4 Testing the hypothesis: Corr: v 2 v 3 v 5 with (v 2)2 with (v 3)2 AMPT supports conjectured nonlinear correlation at all centralities Can be tested experimentally 19

New method to study e-by-e flow fluctuations Single particle distribution: Pair distrbn as Eby.

New method to study e-by-e flow fluctuations Single particle distribution: Pair distrbn as Eby. E single distrbn: Fourier coeff. Vn(p) Vn(p. T, ) Statistics of Vn(p) embedded in Fourier Coeff: Construct bins in p (p. T, ). Estimate Vn(p) in a event with: Covariance matrix Eigenvalues 0 Pair correln: Principal Component Analysis (PCA): Diagonalize PC: self-corr. >0 (flow) <0 (non-flow) with eigenvalues: =1 (no flow fluctuations) and >1 give statistics and momentum dependence of flow fluctuations Bhalerao, Ollitrault, SP, Teaney: ar. Xiv: 1410. 7739 20

Principal components versus Within AMPT: Construct a pair distrb in -3 3 with =

Principal components versus Within AMPT: Construct a pair distrb in -3 3 with = 0. 5 Diagonalize the 12 12 matrix: Vn ( 1, 2). Bhalerao, Ollitrault, SP, Teaney: ar. Xiv: 1410. 7739 To compare with usual per particle anisotropy: n=0: Relative multiplicity fluctuations n=2: Elliptic flow, n=3: Triangular flow v v 0(1) ( ) gives global 12 relative fluctuation indep. of v v 0(2) ( ) is odd parity with (2) (1)/60 v v 0(3) ( ) has alternating parities as A-A and analysis is symmetric =0 v Higher modes fall within statistical fluctuations 21

Principal components versus p. T Within AMPT: Construct a pair distrb in p. T

Principal components versus p. T Within AMPT: Construct a pair distrb in p. T bins Diagonalize the matrix: Vn (p. T 1, p. T 2). ALICE data for Vn (p. T 1, p. T 2) used in PCA PLB: 708 (2012) 249. n=0: Relative multiplicity fluctuations n=2: Elliptic flow, n=3: Triangular flow Ø v 0(1) (p. T) gives 12 fluctuation in total multip. Øv 0(2) (p. T) increases with p. T radial flow fuct. ØLO: v 2(1) & v 3(1) identical to measured v 2 & v 3 ØNLO: vn(1) have smaller magnitudes and increase with p. T PCA use all info (momenta) in 2 -particle azimuthal correlations 22

Summary & Conclusions v Ultimate goal: First principal calculation of non-equilibrium QCD for initial

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

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A Multi. Phase Transport model (AMPT) Inclusive hadron distribution – calculable in p. QCD

A Multi. Phase Transport model (AMPT) Inclusive hadron distribution – calculable in p. QCD ΔE Lin, Ko, Li, Zhang, SP, PRC 72 (2005) 064901 Energy loss Karsch, NPA 698 (2002) SPS RHIC LHC σ ~ 1/(t-μ 2)2 TC ~ 170 Me. V εC ~ 700 Me. V/fm 3 25

Hard jets & its energy loss in AMPT Momentum distribution of hard partons from

Hard jets & its energy loss in AMPT Momentum distribution of hard partons from LO p. QCD in p+p collision Gaussian NLO GRV 94 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)/parton 3ρ(r, τ ) From cascade Radiated gluons scatter in medium with σ ~ 1/(t-μ 2)2 Parton hadron duality: Ng → Nπ 26

AMPT with updated HIJING 2. 0 • GRV parametrization of parton distribution function Deng,

AMPT with updated HIJING 2. 0 • GRV parametrization of parton distribution function Deng, Wang, Xu, PLB 701 (2011) 133 PDF in nucleus: Impact parameter dependent shadowing sq = 0. 1 (fixed) from deep-inelastic- scattering data off nuclear targets. sg fitted to centrality dependence of measured d. Nch/dy in A+A collision.

d. Nch/dy in HIC at RHIC & LHC Parameters in AMPT In string fragmentation

d. Nch/dy in HIC at RHIC & LHC Parameters in AMPT In string fragmentation function, Default HIJING: a=0. 9, b=0. 5 Ge. V-2. s=0. 33, =3. 226 fm-1 = 1. 5 mb HIJING: d. Nch/dη||η| 0. 5 = 705 (RHIC) = 1775 (LHC) v Parton scattering leads to 15% reductions in particle multiplicity. v Hadron scattering insensitive to d. N/dη. AMPT hadron yield ratios at LHC SP, Bleicher, PLB 709 (2012) 82

Centrality dependence of d. Nch/dη Au+Au collisions at RHIC: Measured charged hadron multiplicity density

Centrality dependence of d. Nch/dη Au+Au collisions at RHIC: Measured charged hadron multiplicity density per participant pair constrains the gluon shadowing parameter sg = 0. 10 - 0. 17 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 [5]