The quark-gluon plasma shear viscosity from RHIC to LHC ∗ Ulrich Heinz Department of Physics The Ohio State University 191 West Woodruff Avenue Columbus, OH 43210 presented at University of Crete, Heraklion, Sep. 4, 2011 ——————————————————– Work done in collaboration with S.A. Bass, T. Hirano, P. Huovinen, Zhi Qiu, Chun Shen, and H. Song ∗ Supported by the U.S. Department of Energy (DOE)
Prologue: How to measure ( η /s ) QGP 0.16 Hydrodynamics converts Au+Au RHIC spatial deformation of initial state = ⇒ 0.14 20~30% momentum anisotropy of final state , 0.12 through anisotropic pressure gradients 0.10 0.08 p Shear viscosity degrades conversion efficiency 0.06 � y 2 − x 2 � ⇒ ε p = � T xx − T yy � ε x = � � 0.04 ideal � = � T xx + T yy � � y 2 + x 2 � /s = 0.08 � 0.02 /s = 0.16 of the fluid; the suppression of ε p is monoto- /s = 0.24 0.00 nically related to η/s . 0 1 2 3 4 5 6 7 (f m /c) The observable that is most directly related to the total hydrodynamic momentum anisotropy ε p is the total ( p T -integrated) charged hadron elliptic flow v ch 2 : dN i dφ p p 2 � � � p T dp T T cos(2 φ p ) ε p = � T xx − T yy � i dyp T dp T dφ p ⇒ v ch � T xx + T yy � ⇐ ⇒ ⇐ 2 dN i dφ p p 2 � � � p T dp T i T dyp T dp T dφ p Ulrich Heinz Heraklion, Sep.4, 2011 1(15)
Prologue: How to measure ( η /s ) QGP (ctd.) • If ε p saturates before hadronization (e.g. in PbPb@LHC (?)) ⇒ v ch 2 ≈ not affected by details of hadronic rescattering below T c but: v ( i ) dN i 2 ( p T ) , dyd 2 p T change during hadronic phase (addl. radial flow!), and these changes depend on details of the hadronic dynamics (chemical composition etc.) ⇒ v 2 ( p T ) of a single particle species not a good starting point for extracting η/s • If ε p does not saturate before hadronization (e.g. AuAu@RHIC), dissipative hadronic dynamics affects not only the distribution of ε p over hadronic species and in p T , but even the final value of ε p itself (from which we want to get η/s ) ⇒ need hybrid code that couples viscous hydrodynamic evolution of QGP to realistic microscopic dynamics of late-stage hadron gas phase ⇒ VISHNU (“Viscous Israel-Steward Hydrodynamics ’n’ UrQMD”) Note: this paper shows that UrQMD � = viscous hydro! (Song, Bass, Heinz, PRC83 (2011) 024912) Ulrich Heinz Heraklion, Sep.4, 2011 2(15)
Extraction of ( η /s ) QGP from AuAu@RHIC H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRL106 (2011) 192301 η /s η/ s MC-KLN η /s MC-Glauber hydro ( η /s) + UrQMD hydro ( η /s) + UrQMD hydro ( η /s)+UrQMD 0.0 0.0 0.0 0.25 0.25 (a) (b) 0.08 0.08 0.08 0.2 0.2 0.16 0.16 0.16 0.24 0.24 0.24 v 2 / ε v 2 / ε 0.15 0.15 (fm/c) max. 0.1 0.1 η /s τ 0 dN/dy Glauber / KLN . 0.0 0.4 810 0.0 0.4 810 1/2 1/2 2 2 . v 2 {2} / 〈ε v 2 {2} / 〈ε part 〉 part 〉 0.08 0.6 810 0.08 0.6 810 0.05 0.05 KLN Gl . 0.16 0.9 810 0.16 0.9 810 〈 v 2 〉 / 〈ε part 〉 Gl 〈 v 2 〉 / 〈ε part 〉 KLN . 0.24 0.9 810 0.24 1.2 810 0 0 0 10 20 30 40 0 10 20 30 0 10 20 30 40 -2 ) -2 ) -2 ) (1/S) dN ch /dy (fm (1/S) dN ch /dy (fm (1/S) dN ch /dy (fm 1 < 4 π ( η /s ) QGP < 2 . 5 Zhi Qiu & UH, PRC84 (2011) 024911 • All shown theoretical curves correspond to parameter sets that correctly describe centrality dependence of charged hadron production as well as p T -spectra of charged hadrons, pions and protons at all centralities • v ch 2 /ε x vs. (1 /S )( dN ch /dy ) is “universal”, i.e. depends only on η /s but (in good approximation) not on initial-state model (Glauber vs. KLN, optical vs. MC, RP vs. PP average, etc.) • dominant source of uncertainty: ε Gl vs. ε KLN → x x − • smaller effects: early flow → increases v 2 ε by ∼ few % → larger η/s bulk viscosity → affects v ch 2 ( p T ) , but ≈ not v ch 2 Ulrich Heinz Heraklion, Sep.4, 2011 3(15)
Extraction of ( η /s ) QGP from AuAu@RHIC H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRL106 (2011) 192301 η /s η/ s MC-Glauber MC-KLN hydro ( η /s) + UrQMD η /s hydro ( η /s) + UrQMD hydro ( η /s)+UrQMD 0.0 0.0 0.0 0.25 0.25 (a) (b) 0.08 0.08 0.08 0.2 0.2 0.16 0.16 0.16 0.24 0.24 0.24 v 2 / ε v 2 / ε 0.15 0.15 (fm/c) max. 0.1 η /s τ 0 dN/dy 0.1 Glauber / KLN . 0.0 0.4 810 0.0 0.4 810 2 1/2 2 1/2 . v 2 {2} / 〈ε part 〉 v 2 {2} / 〈ε part 〉 0.08 0.6 810 0.08 0.6 810 0.05 0.05 KLN Gl . 0.16 0.9 810 0.16 0.9 810 〈 v 2 〉 / 〈ε part 〉 Gl 〈 v 2 〉 / 〈ε part 〉 KLN . 0.24 1.2 810 0.24 0.9 810 0 0 0 10 20 30 40 0 10 20 30 0 10 20 30 40 -2 ) -2 ) -2 ) (1/S) dN ch /dy (fm (1/S) dN ch /dy (fm (1/S) dN ch /dy (fm 1 < 4 π ( η /s ) QGP < 2 . 5 Zhi Qiu & UH, PRC84 (2011) 024911 • All shown theoretical curves correspond to parameter sets that correctly 0.35 describe centrality dependence of charged hadron production as well as ideal hydro, MC−KLN p T -spectra of charged hadrons, pions and protons at all centralities p • v ch 0.3 2 /ε x vs. (1 /S )( dN ch /dy ) is “universal”, i.e. depends only on η /s but (in good approximation) not on initial-state model (Glauber K 0.25 vs. KLN, optical vs. MC, RP vs. PP average, etc.) v 2 /ε 2 π • dominant source of uncertainty: ε Gl vs. ε KLN x x 0.2 • smaller effects: early flow → increases v 2 ε by ∼ few % → larger η/s single-shot, v 2 / ¯ ε part bulk viscosity → affects v ch 2 ( p T ) , but ≈ not v ch 0.15 e-by-e, � v 2 � / ¯ ε part 2 v ch 2 by < e-by-e hydro → decreases ∼ 5% → smaller η/s 0.1 ε 0 2 4 6 8 10 12 14 b (fm) Ulrich Heinz Heraklion, Sep.4, 2011 4(15)
Global description of AuAu@RHIC spectra and v 2 VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC 83 (2011) 054910) MC-Glauber initialization MC-KLN initialization 7 3 10 10 2 p 200 A GeV Au+Au charged hadrons + 3 0%~5%*10 2 0%~10%*10 5 2 10 10 s = 0.08 s = 0.16 1.8 2 5%~10%*10 VISHNU PHENIX v {EP} s = 0.16 s = 0.24 2 10%~15%*10 (0-5%)+1.2 10%~20%*10 1.6 3 1 ) 10 10 -2 15%~20%*1 ) -2 ) (GeV (5-10%)+1.0 ) (GeV 20%~30%/10 1.4 1 0 10 10 20%~40% 2 30%~40%/10 (10-20%)+0.8 1.2 T dp T 3 40%~50%/10 -1 -1 10 dp 10 40%~60%/10 T 4 1 50%~60%/10 / dy p T (20-30%)+0.6 2 dy p v -3 -2 10 10 5 60%~70%/10 0.8 (30-40%)+0.4 dN/(2 6 70%~80%/10 2 dN/(2 60%~80%/10 -5 -3 10 10 0.6 (40-50%)+0.2 -7 -4 10 10 0.4 /s = 0.0 PHENIX (ideal hy dro) STAR /s = 0.08 0.2 (50-60%) -9 -5 10 10 M C-KLN /s = 0.16 (a) (b) M C-Glauber /s = 0.24 0 -11 -6 10 10 0.0 0.4 0.8 1.2 1.6 0.0 0.4 0.8 1.2 1.6 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 p (GeV) p (GeV) p (GeV) p (GeV) T T T T • ( η/s ) QGP = 0 . 08 for MC-Glauber and ( η/s ) QGP = 0 . 16 for MC-KLN work well for charged hadron, pion and proton spectra and v 2 ( p T ) at all collision centralities Ulrich Heinz Heraklion, Sep.4, 2011 5(15)
Global description of AuAu@RHIC spectra and v 2 VISHNU (H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, PRC 83 (2011) 054910) 7 3 1.2 10 10 p s = 0.08 p + VISHNU STAR v {2} 3 0%~5%*10 1.0 2 0%~10%*10 /s = 0.16 2 5 2 (5-10%)+ 0.6 10 10 2 5%~10%*10 (20-30%)+ 0.4 0.8 (30-40%)+ 0.2 10%~15%*10 (40-50%) 10%~20%*10 3 1 0.6 ) 10 10 -2 15%~20%*1 ) -2 ) (GeV / ) (GeV 2 0.4 20%~30%/10 v 1 0 10 10 20%~40% 2 30%~40%/10 0.2 T dp T 3 40%~50%/10 -1 -1 0.0 10 dp 10 M C-Glauber initializ ation M C-Glauber initializ ation 40%~60%/10 T 4 50%~60%/10 dy p p T Au + Au 200 A GeV dy p s = 0.16 -3 -2 10 10 1.0 5 60%~70%/10 /s = 0.24 0.8 dN/(2 6 70%~80%/10 2 dN/(2 60%~80%/10 -5 -3 10 10 0.6 / -7 -4 10 10 2 0.4 /s = 0.0 v PHENIX (ideal hy dro) 0.2 STAR /s = 0.08 -9 -5 10 10 M C-KLN /s = 0.16 0.0 MC-KLN initialization MC-KLN initialization (a) (b) M C-Glauber /s = 0.24 -11 -6 10 10 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 p (GeV) p (GeV) p (GeV) p (GeV) T T T T • ( η/s ) QGP = 0 . 08 for MC-Glauber and ( η/s ) QGP = 0 . 16 for MC-KLN work well for charged hadron, pion and proton spectra and v 2 ( p T ) at all collision centralities • A purely hydrodynamic model (without UrQMD afterburner) with the same values of η/s does almost as well (except for centrality dependence of proton v 2 ( p T ) ) = ⇒ Shen et al., arXiv:1105.3226 • Main difference: VISHNU develops more radial flow in the hadronic phase (larger shear viscosity), pure viscous hydro must start earlier than VISHNU ( τ 0 = 0 . 6 instead of 0.9 fm/ c ), otherwise proton spectra are too steep • These η/s values agree with Luzum & Romatschke, PRC78 (2008), even though they used EOS with incorrect hadronic chemical composition = ⇒ shows robustness of extracting η/s from total charged hadron v 2 Ulrich Heinz Heraklion, Sep.4, 2011 6(15)
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