1. Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano V iscous Hydrodynamic Expansion of the Quark- Gluon Plasma for the Color Glass Condensate Standard and Novel QCD Phenomena at Hadron Colliders June 1 st 2011, ECT*, Trento, Italy AM and T. Hirano, arXiv:1102.5053 [nucl-th]

2. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Outline 1. Introduction Models for relativistic heavy ion collisions 2. Hydrodynamic model for the CGC Non-boost invariant viscous hydro in the longitudinal direction 3. Results Hydro deformation of the CGC rapidity distribution at RHIC and LHC 4. Summary Summary and Outlook Introduction 2

3. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Introduction Quark-gluon plasma (QGP) at relativistic heavy ion collisions Hadron phase QGP phase (crossover) sQGP(wQGP?) Introduction 3 Quantification of the space-time evolution of the QGP by modeling the heavy ion collisions Determination of the properties of the QCD matter from experimental data (e.g. transport coefficients) In this work, we discuss the role of hydrodynamic models on the color glass condensate Introduction 3

4. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Introduction “Standard model” of a high-energy heavy ion collision particles hadronic phase QGP phase Freezeout Pre- equilibrium Hydrodynamic stage Color glass condensate Hadronic cascade Initial condition Hydro to particles ｔ z t Color glass condensate (CGC) Relativistic hydrodynamics Description of saturated gluons in the nuclei before a collision (τ < 0 fm/c) Description of collective motion of the QGP (τ ~ 1-10 fm/c) 4 Introduction

5. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Introduction RHIC experiments (2000-) LHC experiments (2010-) †he First ALICE Result 5 The QGP is well-described by ideal hydro model Viscosity is important for 1 st -principle-based inputs (equation of state, initial conditions, etc.) Heavy ion collisions of higher energies Will the RHIC modeling of heavy ion collisions be working intact at LHC? The CGC itself has also been successful in explaining multiplicity 5 An unified picture would be necessary

6. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 The First ALICE Result Mid-rapidity multiplicity CGC in Heavy Ion Collisions ALICE data (most central 0-5%) CGC; fit to RHIC data What is happening at LHC? CGC Pb+Pb, 2.76 TeV at η = 0 K. Aamodt et al. PRL105 252301 6

7. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 CGC in Heavy Ion Collisions Saturation scale in MC-KLN model CGC in Heavy Ion Collisions Fixed via direct comparison with data dN ch /dη gets steeper with increasing λ; RHIC data suggest λ~0.28 D. Kharzeev et al., NPA 730, 448 dN/dy λ=0.28 λ=0.18 λ=0.38 Initial condition from the CGC Hydrodynamic evolution Observed particle distribution secondary interactions! Initial condition from the CGC Observed particle distribution H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903 : thickness function : momentum fraction of incident particles 7

8. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 CGC in Heavy Ion Collisions CGC + Hydrodynamic Model Viscous Hydrodynamic Model Initial condition from the CGC Hydrodynamic evolution Observed particle distribution secondary interactions! 8 The first time the CGC rapidity distribution is discussed in terms of viscous hydrodynamics We need to estimate hydrodynamic effects with (i) non-boost invariant expansion (ii) viscous corrections for the CGC Motivation

9. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Viscous Hydrodynamic Model Decomposition of the energy-momentum tensor by flow Stability condition + frame fixing 10 dissipative currents 2 equilibrium quantities Energy density deviation: Bulk pressure: Energy current: Shear stress tensor: Energy density: Hydrostatic pressure: Viscous Hydrodynamic Model where is the projection operator related in equation of state Thermodynamic stability demands Identify the flow as local energy flux This leaves and 9

10. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Viscous Hydrodynamic Model Physical meanings of and Viscous Hydrodynamic Model 10 Naïve interpretation at the 1 st order in gradient expansion Shear viscosity: response to deformation Bulk viscosity: response to expansion + cooling - In actual calculations one includes 2 nd order contributions for the sake of causality and stability Bulk pressure Shear stress tensor Cross term in linear response theory

11. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Viscous Hydrodynamic Model Full 2 nd order viscous hydrodynamic equations Model Input for Hydro EoM for bulk pressure EoM for shear tensor Energy-momentum conservation + AM and T. Hirano, NPA 847, 283 All the terms are kept 11 Solve in (1+1)-D relativistic coordinates (= no transverse flow) Note: (2+1)-D viscous hydro assumes boost invariance in the longitudinal direction

12. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Model Input for Hydro Equation of state and transport coefficients Initial conditions Results Equation of State: Lattice QCD Shear viscosity: η = s/4π 2 nd order coefficients: Kinetic theory & η, ζ Initial flow: Bjorken flow (i.e. flow rapidity Y f = η s ) Bulk viscosity: ζ = (5/2)[(1/3) – c s 2 ]η Relaxation times: Kinetic theory & η, ζ S. Borsanyi et al., JHEP 1011, 077 P. Kovtun et al., PRL 94, 111601 A. Hosoya et al., AP 154, 229 AM and T. Hirano, NPA 847, 283 Dissipative currents: δT μν = 0 Initial time: τ = 1 fm/c 12 Energy distribution: MC-KLN type CGC model H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903

13. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Results CGC initial distributions + longitudinal viscous hydro Results Outward entropy fluxFlattening Entropy productionEnhancement RHIC LHC If the true λ is larger at RHIC, it enhances dN/dy at LHC; Hydro effect is an important factor in explaining the LHC data If the true λ is larger at RHIC, it enhances dN/dy at LHC; Hydro effect is an important factor in explaining the LHC data 13 AM and T. Hirano, arXiv:1102.5053

14. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Results CGC initial distributions + longitudinal viscous hydro Results Outward entropy fluxFlattening Entropy productionEnhancement 14 RHIC LHC If the true λ is larger at RHIC, it enhances dN/dy at LHC; Hydro effect is an important factor in explaining the LHC data If the true λ is larger at RHIC, it enhances dN/dy at LHC; Hydro effect is an important factor in explaining the LHC data If the λ is unchanged at RHIC, dN/dy is still enhanced at LHC; Hydro effect is an important factor in explaining the LHC data If the λ is unchanged at RHIC, dN/dy is still enhanced at LHC; Hydro effect is an important factor in explaining the LHC data AM and T. Hirano, arXiv:1102.5053

15. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Results Deviation from boost-invariant flow RHICLHC Flows exhibit similar trends at RHIC and LHC τ = 30 fm/cτ = 50 fm/c deceleration by suppression of total pressure P 0 – Π + π at early stage and acceleration by enhancement of hydrostatic pressure P 0 at late stage Ideal flow ≈ viscous flow due to competition between Flow rapidity: Results 15

16. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Results Time evolution for the LHC settings No sizable modification the on rapidity distribution after 20 fm/c, unlike the flow profile Equal-time surface is close to isothermal surface for the current parameters 16 Summary and Outlook It could be accidental; isothermal entropic “freezeout” is coming soon

17. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Summary and Outlook We solved full 2 nd order viscous hydro in (1+1)-dimensions for the “shattered” color glass condensate Future prospect includes: – Detailed analyses on parameter dependences, rcBK, etc… – A (3+1)-dimensional viscous hydrodynamic model The End AM & T. Hirano, in preparation Non-trivial deformation of CGC rapidity distribution due to (i) outward entropy flux (non-boost invariant effect) (ii) entropy production (viscous effect) Viscous hydrodynamic effect may play an important role in understanding the seemingly large multiplicity at LHC 17

18. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 The End Thank you for listening! Website: http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/index.htmlhttp://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/index.html 18 Appendices

19. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Results Parameter dependences Comparison to boost-invariant flow 19 Larger entropy production for more viscous systems (ii) η/s = 1/4π, ζ eff /s = (5/2)[(1/3) – c s 2 ]/4π (iii) η/s = 3/4π, ζ eff /s = (15/2)[(1/3) – c s 2 ]/4π (i) η/s = 0, ζ eff /s = 0 Longitudinal viscous hydro expansion is essential preliminary Appendices

20. Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Next slide: / 18 Introduction Relativistic hydrodynamics: macroscopic theory defined on Flow Temperature 20 Energy-momentum conservation Law of increasing entropy (in the limit of vanishing conserved currents) driven by Input Output Initial conditions Equation of state Transport coefficients Energy-momentum tensor Flow field Temperature field Introduction