Uncertainties in the underlying e-by-e viscous fluid simulation Ulrich Heinz (The Ohio State University) Jet Workfest, Wayne State University, 24-25 August 213 Supported by the U.S. Department of Energy
What QGP tomographers need (3+1)-dimensional (color) charge density or temperature profiles of the medium (3+1)-dimensional flow velocity profiles information on deviations from local momentum isotropy Since these medium characteristics fluctuate significantly from event to event (due to quantum fluctuations in the initial state of the Little Bang ), providing this information in the form of an ensemble average is not sufficient = Event-by-event (3+1)-dimensional viscous fluid dynamics Jet Workfest, 8/24/213 1(23)
What QGP tomographers need (contd.) Questions that I will address in this talk: Which value of η/s? (η/s)(t)? Which initial conditions? Pre-equilibrium evolution? Questions that need to be addressed at lower than top RHIC energies: Which equation of state (EOS)? Questions that have been resolved in the last couple of years and that I won t discuss: EOS at RHIC and LHC (including early chemical freeze-out) Microscopic description of late hadronic rescattering stage and final decoupling Hydro-cascade interface Jet Workfest, 8/24/213 2(23)
Numerical precision: Gubser-Test Gubser (PRD82 (21) 8527) found analytical solution for relativistic Navier-Stokes equation with conformal EOS, boost-invariant longitudinal and non-zero transverse flow, corresponding to a specific transverse temperature profile. Marrochio, Noronha et al. (arxiv:137.613) found semianalytical generalization of this solution for Israel-Stewart theory. This solution provides a stringent test for numerical Irael-Stewart codes (very rapid and non-trivial transverse expansion!) MUSIC (H. Marrochio, J. Noronha, G. Denicol, M. Luzum, S. Jeon, C. Gale, arxiv:137.613) Jet Workfest, 8/24/213 3(23)
Numerical precision: Gubser-Test Gubser (PRD82 (21) 8527) found analytical solution for relativistic Navier-Stokes equation with conformal EOS, boost-invariant longitudinal and non-zero transverse flow, corresponding to a specific transverse temperature profile. Marrochio, Noronha et al. (arxiv:137.613) found semianalytical generalization of this solution for Israel-Stewart theory. This solution provides a stringent test for numerical Irael-Stewart codes (very rapid and non-trivial transverse expansion!) VISH2+1 (C. Shen, 213) U x 2. 1.5 1..5..5 1. 1.5 2. 5 4 3 2 1 1 2 3 4 5 x (fm) π yy (GeV/fm 3 ).2..2.4.6.8.1 5 4 3 2 1 1 2 3 4 5 x (fm) π xy (GeV/fm 3 ).1..1.2.3.4.5.6.7 5 4 3 2 1 1 2 3 4 5 x (fm) Jet Workfest, 8/24/213 4(23)
Global description of AuAu@RHIC spectra and v 2 dn/(2 dy p T dp T ) (GeV -2 ) 1 7 1 5 1 3 1 1 1-1 1-3 1-5 1-7 1-9 1-11 %~5%*1 3 5%~1%*1 2 1%~15%*1 15%~2%*1 2%~3%/1 3%~4%/1 2 4%~5%/1 3 5%~6%/1 4 6%~7%/1 5 7%~8%/1 6 PHENIX STAR MC-KLN MC-Glauber..5 1. 1.5 2. p T (GeV) VISHNU (H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRC83 (211) 5491) + (a) dn/(2 dy p T dp T ) (GeV -2 ) 1 3 1 2 1 1 1 1-1 1-2 1-3 1-4 1-5 1-6 %~1%*1 2 1%~2%*1 2%~4% 4%~6%/1 6%~8%/1 2 /s =. (ideal hydro) /s =.8 /s =.16 /s =.24 (b)..5 1. 1.5 2. p T (GeV) p v 2 / 2 1.8 1.6 1.4 1.2 1.8.6.4.2 MC-Glauber initialization MC-KLN initialization 2 A GeV Au+Au charged hadrons s =.8 s =.16..4.8 1.2 1.6 p T (GeV) s =.16 s =.24..4.8 1.2 1.6 2. p T (GeV) VISHNU PHENIX v 2 {EP} (-5%)+1.2 (5-1%)+1. (1-2%)+.8 (2-3%)+.6 (3-4%)+.4 (4-5%)+.2 (5-6%) (η/s) QGP =.8 for MC-Glauber and (η/s) QGP =.16 for MC-KLN work well for charged hadron, pion and proton spectra and v 2 (p T ) at all collision centralities Jet Workfest, 8/24/213 5(23)
Global description of AuAu@RHIC spectra and v 2 VISHNU (H. Song, S.A. Bass, UH, T. Hirano, C. Shen, PRC83 (211) 5491) dn/(2 dy p T dp T ) (GeV -2 ) 1 7 1 5 1 3 1 1 1-1 1-3 1-5 1-7 1-9 1-11 %~5%*1 3 5%~1%*1 2 1%~15%*1 15%~2%*1 2%~3%/1 3%~4%/1 2 4%~5%/1 3 5%~6%/1 4 6%~7%/1 5 7%~8%/1 6 PHENIX STAR MC-KLN MC-Glauber..5 1. 1.5 2. p T (GeV) + (a) dn/(2 dy p T dp T ) (GeV -2 ) 1 3 1 2 1 1 1 1-1 1-2 1-3 1-4 1-5 1-6 %~1%*1 2 1%~2%*1 2%~4% 4%~6%/1 6%~8%/1 2 /s =. (ideal hydro) /s =.8 /s =.16 /s =.24 (b)..5 1. 1.5 2. p T (GeV) p v 2 / v 2 / 1.2 1..8.6.4.2. 1..8.6.4.2 s =.8 /s =.16 s =.16 /s =.24 MC-Glauber initialization VISHNU STAR v 2 {2} (5-1%)+.6 (2-3%)+.4 (3-4%)+.2 (4-5%) MC-Glauber initialization Au + Au 2 A GeV. MC-KLN initialization MC-KLN initialization..2.4.6.8 1...2.4.6.8 1. 1.2 1.4 1.6 p T (GeV) p T (GeV) p p (η/s) QGP =.8 for MC-Glauber and (η/s) QGP =.16 for MC-KLN work well for charged hadron, pion and proton spectra and v 2 (p T ) at all collision centralities Jet Workfest, 8/24/213 6(23)
Differences in evolution for η/s=.8 and.2 (for tomographers) (Au+Au@RHIC2, -5%, ensemble averaged) Chun Shen 211, unpublished Freeze-out surface Evolution of central temperature 4 15 MC-Glb. η/s =.8 MC-KLN η/s =.2 35 3 T (MeV) τ (fm/c) 1 MC-Glb. η/s =.8 MC-KLN η/s =.2 5 25 2 15 2 4 r (fm) 6 8 1 2 4 6 8 τ τ (fm/c) 1 12 14 Only small differences (?). Much less uncertainty than between hydro I and hydro II in Renk s analysis Jet Workfest, 8/24/213 7(23)
v 2 (p T ) in PbPb@LHC: ALICE vs. VISHNU v2 Data: ALICE, preliminary (Snellings, Krzewicki, Quark Matter 211) Dashed lines: Shen et al., PRC84 (211) 4493 (VISH2+1, MC-KLN, (η/s) QGP =.2) Solid lines: Song, Shen, UH 211 (VISHNU, MC-KLN, (η/s) QGP =.16).3.2.1 π + K + p ALICE Preliminary VISHNU (η/s) QGP =.16 VISH2+1 η/s =.2 5 1% 1 2% 2 3%.2 v2.1 3 4% 4 5% 5 6% 1. 2. 1. 2. 1. 2. 3. p T (GeV) p T (GeV) p T (GeV) VISHNU yields correct magnitude and centrality dependence of v 2 (p T ) for pions, kaons and protons! Same (η/s) QGP =.16 (for MC-KLN) at RHIC and LHC! Jet Workfest, 8/24/213 8(23)
Pre-equilibrium dynamics (I) Match pre-equilibrium T µν to viscous hydrodynamic form, at varying matching times τ match. Extreme case: pre-equilibrium = free-streaming = large τ match slow thermalization; short τ match fast thermalization. Studydependenceoffinalobservablesonτ match andcomparewithpurehydrocalculation that assumes no evolution at all between τ = and τ therm =.7fm/c. The following study by Jia Liu uses MC-KLN initial conditions for the gluon phase-space distribution. Viscous hydro evolution with η/s =.2. Jet Workfest, 8/24/213 9(23)
Pre-equilibrium dynamics (II) p T -spectra for thermal pions (left) and thermal protons (right) (Jia Liu, 213): (1/2π)(dN/dypTdpT) (GeV 2 ) 1 3 1 2 1 1 1 τ s =.4fm/c τ s =.7fm/c τ s = 1.fm/c τ s = 1.3fm/c τ s = 1.6fm/c pure hydro from.7 fm/c.2.4.6.8 1 1.2 1.4 1.6 1.8 2 p T (GeV/c) Pb-Pb@276GeV MC-KLN Centrality: 1% 2% Number of events: 4 η/s=.2 (1/2π)(dN/dypTdpT) (GeV 2 ) 1 1 1 1 1 τ s =.4fm/c τ s =.7fm/c τ s = 1.fm/c τ s = 1.3fm/c τ s = 1.6fm/c pure hydro from.7 fm/c.5 1 1.5 2 2.5 p T (GeV/c) Pb-Pb@276GeV MC-KLN Centrality: 1% 2% # of events: 4 η/s=.2 Jet Workfest, 8/24/213 1(23)
Pre-equilibrium dynamics (III) v 2 /ε 2, v 3 /ε 3 for thermal pions (left) and thermal protons (right) (Jia Liu, 213): v n {Thermal Pion+}/ǫ n for Bumpy Events v n {Thermal Proton}/ǫ n for Bumpy Events vn/ǫn(τ).6.5.4.3.35.3.25.2.15.1.5.2.4.6.8 1 1.2 1.4 τ s (fm/c) ǫ 2 v 2 ǫ 3 v 3 v 2 /ǫ 2 (τ ) with variance v 3 /ǫ 3 (τ ) with variance Pb Pb@276GeV MC KLN Centrality: 1%~2% # of events: 4 η/s=.2 vn/ǫn(τ).6.5.4.3.35.3.25.2.15.1.5.2.4.6.8 1 1.2 1.4 τ s (fm/c) ǫ 2 v 2 ǫ 3 v 3 v 2 /ǫ 2 (τ ) with variance v 3 /ǫ 3 (τ ) with variance Pb Pb@276GeV MC KLN Centrality: 1%~2% # of events: 4 η/s=.2.2.195.2.238.197.143.1.1.1.4.6.8 1 1.2 1.4 1.6 Matching Time τ s (fm/c).1.4.7 1 1.3 1.6 Matching Time τ s (fm/c) Jet Workfest, 8/24/213 11(23)
Initial-state fluctuations Jet Workfest, 8/24/213 12(23)
MC-Glauber: fluctuating nucleon positions Schenke, Tribedy, Venugopalan, PRL18, 25231 (212) MC-Glauber Jet Workfest, 8/24/213 13(23)
MC-KLN: Q sat from fluctuating nucleon positions Schenke, Tribedy, Venugopalan, PRL18, 25231 (212) MC-KLN Jet Workfest, 8/24/213 14(23)
IP-Glasma: Adding sub-nucleonic quantum fluctuations Schenke, Tribedy, Venugopalan, PRL18, 25231 (212) IP-Glasma Jet Workfest, 8/24/213 15(23)
Each Little Bang evolves differently! Density evolution of a single b = 8 fm Au+Au collision at RHIC, with IP-Glasma initial conditions, Glasma evolution to τ =.2 fm/c followed by (3+1)-d viscous hydrodynamic evolution with MUSIC using η/s =.12 = 1.5/(4π) Schenke, Tribedy, Venugopalan, PRL 18 (212) 25231: 6-6 4-4 2-2 x [fm] -2 2 4 U. Heinz -4 6-6 y [fm] -6 4-4 2-2 x [fm] -2 2 4-4 6-6 y [fm] 6-12 -9-6 3 3 1 τ=5.2 fm/c ε [GeV/fm ] 4 2.8.6.4.2 τ=.2 fm/c ε [GeV/fm ] 3 8 3 τ=.1 fm/c ε [GeV/fm ] 12-3 x [fm] 3 6 9 12-12 -9-6 -3 3 Jet Workfest, 8/24/213 6 9 12 y [fm] 16(23)
The Little Bang fluctuation power spectrum: initial vs. final.6.5 Little Bang density power spectra -.2% -5% 2-3% 5-6% Solid: IP Glasma Dash dotted: MC Glauber Dashed: MC KLN Flow power spectrum for ultracentral PbPb Little Bangs (Data: CMS, Quark Matter 212; Theory: OSU 213).3.25 CMS poster QM212 (Wei Li) MCGlb. η/s =.8 MCKLN η/s =.2 εn.4.3.2.1 v n.2.15.1.5.2%@lhc.3 <p T <3 GeV 1 2 3 4 5 6 7 8 9 n. 1 2 3 4 5 6 7 8 9 n Higher flow harmonics get suppressed by shear viscosity Neither MC-Glb nor MC-KLN gives the correct initial power spectrum! R.I.P. A detailed study of fluctuations is a powerful discriminator between models! U. Heinz Jet Workfest, 8/24/213 17(23)
Anisotropic flow coefficients, eccentricity and flow fluctuations from IP-Glasma U. Heinz Jet Workfest, 8/24/213 18(23)
Towards a Standard Model of the Little Bang B. Schenke: QM212 With inclusion of sub-nucleonic quantum fluctuations and pre-equilbrium dynamics of gluon fields: outstanding agreement between data and model Rapid convergence on a standard model of the Little Bang! Schenke, Tribedy, Venugopalan, Phys.Rev.Lett. 18:25231 (212) Perfect liquidity reveals in the final state initial-state gluon field correlations of size 1/Q s (sub-hadronic)! U. Heinz Jet Workfest, 8/24/213 19(23) 13
What We Don t Know B. Schenke: QM212 Model doesn t distinguish between a constant η/s of.2 or a temperature dependent η/s with a minimum of 1/4π Need both RHIC and LHC to sort this out! U. Heinz Jet Workfest, 8/24/213 2(23) 14
Other successes of the IP-Glasma initial-state model v n 2 1/2 v n 2 1/2.2.15.1.5.2.15.1.5 v 1 v 2 v 3 v 4 v 5 v 1 v 2 v 3 v 4 v 5 Gale, Jeon, Schenke, Tribedy, Venugopalan, arxiv:129.633 (PRL 212) RHIC 2GeV, 3-4% filled: STAR prelim. open: PHENIX RHIC 2GeV, 3-4% filled: STAR prelim. open: PHENIX η/s =.12 η/s(t).5 1 1.5 2 p T [GeV] P(v 2 / v 2 ), P(ε 2 / ε 2 ) P(v 3 / v 3 ), P(ε 3 / ε 3 ) P(v 4 / v 4 ), P(ε 4 / ε 4 ) 1 1 1 2-25% ε 2 IP-Glasma v 2 IP-Glasma+MUSIC v 2 ATLAS.1 p T >.5 GeV η < 2.5.1.5 1 1.5 2 2.5 3 v 2 / v 2, ε 2 / ε 2 1 1 1 2-25% ε 3 IP-Glasma v 3 IP-Glasma+MUSIC v 3 ATLAS.1 p T >.5 GeV η < 2.5.1.5 1 1.5 2 2.5 3 v 3 / v 3, ε 3 / ε 3 1 1 1 2-25% ε 4 IP-Glasma v 4 IP-Glasma+MUSIC v 4 ATLAS.1 p T >.5 GeV η < 2.5.1.5 1 1.5 2 2.5 3 v 4 / v 4, ε 4 / ε 4 Model describes RHIC data with lower effective specific shear viscosity η/s =.12 In contrast to MC-Glauber and MC-KLN, IP-Sat initial conditions correctly reproduce the final flow fluctuation spectrum, generated from initial shape fluctuations by viscous hydrodynamics U. Heinz Jet Workfest, 8/24/213 21(23)
Longitudinal fluctuations Pang, Wang & Wang (PRC86 (212) 24911) used 3+1-d ideal hydro to study (among other things) initial conditions that fluctuate along the rapidity direction, and found significant effects on spectrum and v 2 (p T ) at midrapidity (see plot). The origin of this effect is still poorly understood, and the effect of longitudinal fluctuations on η/s extraction deserve a detailed and systematic study. This requires (3+1)-d viscous hydro. U. Heinz Jet Workfest, 8/24/213 22(23)
Outlook Huge progress towards quantitatively precise description of medium evolution Strong interplay between QGP transport coefficients and initial-state fluctuations Enough and precise flow data are (or will be) available to constrain both transport coefficients and statistical properties of the initial-state fluctuations well enough to establish a Standard Model for the Little Bang (text book level) A precise understanding of the dynamical behaviour of the medium formed in pa and high-multiplicity pp collisions at the LHC will be essential for further constraining the initial-state fluctuation spectrum, but there is a very good chance that this will be completed within < 5 years. Extending the model towards lower than top RHIC energies requires more work on the EOS and extensive hybrid model simulations but will further tie down any loose ends of the Little Bang Standard Model I don t believe that during the next 5-1 years parton energy loss will be competitive in constraining bulk evolution dynamics and the initial fluctuation spectrum; I do, however, have a strong suspicion that the extraction of precise information about the internal structure of the medium from parton energy loss and jet modification will be strongly affected by the event-by-event fluctuations of the fireball medium, and that these must therefore be carefully constrained with soft probes, and they must be included in the analysis of jet data (and therefore in the modeling of jet quenching). Food for thought: At same multiplicity, central Cu+Cu collisions have a different fluctuation spectrum from peripheral Au+Au collisions. Is it really sufficient to run sphenix at one energy, for one collision system only? I doubt it. U. Heinz Jet Workfest, 8/24/213 23(23)