V iscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate

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

2. Outline • Introduction Models for relativistic heavy ion collisions • Hydrodynamic model for the CGC Non-boost invariant viscous hydro in the longitudinal direction • Results Hydro deformation of the CGC rapidity distribution at RHIC and LHC • Summary Summary and Outlook Introduction

3. Introduction • Quark-gluon plasma (QGP) at relativistic heavy ion collisions Hadron phase (crossover) QGPphase sQGP (wQGP?) 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 Introduction

4. Introduction • “Standard model” of a high-energy heavy ion collision particles ｔ t Freezeout Hadronic cascade Hydro to particles QGPphase Hydrodynamic stage hadronic phase Pre-equilibrium Initial condition z Color glass condensate Color glass condensate (CGC) Description of saturated gluons in the nuclei before a collision (τ < 0 fm/c) Relativistic hydrodynamics Description of collective motion of the QGP (τ ~ 1-10 fm/c) Introduction

5. Introduction • RHICexperiments (2000-) • LHCexperiments (2010-) The QGP is well-described by ideal hydro model Viscosityis important for 1st-principle-based inputs(equation of state, initial conditions, etc.) The CGC itself has also been successful in explaining multiplicity An unified picture would be necessary Heavy ion collisions of higher energies Will the RHIC modeling of heavy ion collisions be working intact at LHC? †he First ALICE Result

6. The First ALICE Result • Mid-rapidity multiplicity K. Aamodtet al. PRL105252301 Pb+Pb, 2.76 TeV at η = 0 CGC ALICE data (most central 0-5%) CGC; fit to RHIC data What is happening at LHC? CGC in Heavy Ion Collisions

7. CGC in Heavy Ion Collisions • Saturation scale in MC-KLN model D. Kharzeevet al., NPA 730, 448 H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903 : thicknessfunction λ=0.38 : momentum fraction of incident particles λ=0.28 λ=0.18 Fixed via directcomparison with data dNch/dη gets steeper with increasing λ; RHIC data suggest λ~0.28 dN/dy Initial condition from the CGC Observed particle distribution Initial condition from the CGC Hydrodynamic evolution Observed particle distribution secondary interactions! CGC in Heavy Ion Collisions

8. CGC in Heavy Ion Collisions • CGC + Hydrodynamic Model Initial condition from the CGC Hydrodynamic evolution Observed particle distribution secondary interactions! Motivation We need to estimate hydrodynamic effects with (i) non-boost invariant expansion for the CGC (ii) viscous corrections The first time the CGC rapidity distribution is discussed in terms of viscous hydrodynamics Viscous Hydrodynamic Model

9. Viscous Hydrodynamic Model • Decomposition of the energy-momentum tensor by flow • Stability condition + frame fixing where is the projection operator 2 equilibrium quantities 10 dissipative currents Energy density: Hydrostatic pressure: Energy density deviation: Bulk pressure: Energy current: Shear stress tensor: related in equation of state Thermodynamic stability demands This leaves and Identify the flow as local energy flux Viscous Hydrodynamic Model

10. Viscous Hydrodynamic Model • Physical meanings of and Naïve interpretation at the 1st order in gradient expansion Bulk viscosity: response to expansion + cooling Cross term in linear response theory Bulk pressure Shear viscosity: response to deformation Shear stress tensor - In actual calculations one includes 2nd order contributions for the sake of causality and stability Viscous Hydrodynamic Model

11. Viscous Hydrodynamic Model • Full 2nd order viscous hydrodynamicequations + Energy-momentum conservation AM and T. Hirano, NPA 847, 283 EoM for bulk pressure EoM for shear tensor All the terms are kept Solve in (1+1)-D relativistic coordinates (= no transverse flow) Note: (2+1)-D viscous hydro assumes boost invariance in the longitudinal direction Model Input for Hydro

12. Model Input for Hydro • Equation of state and transport coefficients • Initial conditions Equation of State: Lattice QCD S. Borsanyiet al., JHEP 1011, 077 P. Kovtunet al., PRL 94, 111601 Shear viscosity: η = s/4π A. Hosoyaet al., AP 154, 229 Bulk viscosity: ζ = (5/2)[(1/3) – cs2]η AM and T. Hirano, NPA 847, 283 Relaxation times: Kinetic theory & η, ζ 2nd order coefficients: Kinetic theory& η, ζ Energy distribution: MC-KLN type CGC model H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903 Dissipative currents: δTμν = 0 Initial flow: Bjorken flow (i.e. flow rapidity Yf = ηs) Initial time: τ = 1 fm/c Results

13. Results AM and T. Hirano, arXiv:1102.5053 • CGC initial distributions + longitudinal viscous hydro LHC RHIC Outward entropy flux Flattening Entropy production Enhancement 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 Results

14. Results AM and T. Hirano, arXiv:1102.5053 • CGC initial distributions + longitudinal viscous hydro LHC RHIC Outward entropy flux Flattening Entropy production Enhancement 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 Results

15. Results • Deviation from boost-invariant flow Flow rapidity: RHIC LHC τ = 30 fm/c τ = 50 fm/c Flows exhibit similar trends at RHIC and LHC Ideal flow ≈ viscous flow due to competition between decelerationbysuppression of total pressure P0 – Π + π at early stage and acceleration by enhancement of hydrostatic pressure P0 at late stage Results

16. 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 It could be accidental; isothermal entropic “freezeout” is coming soon Summary and Outlook

17. Summary and Outlook • We solved full 2nd 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 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 AM & T. Hirano, in preparation The End

18. The End • Thank you for listening! • Website: http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/index.html Appendices

19. Results • Parameter dependences • Comparison to boost-invariant flow (i) η/s = 0, ζeff/s = 0 (ii) η/s = 1/4π, ζeff/s = (5/2)[(1/3) – cs2]/4π (iii) η/s = 3/4π, ζeff/s = (15/2)[(1/3) – cs2]/4π Larger entropy production for more viscous systems preliminary Longitudinal viscous hydro expansion is essential Appendices

20. Introduction • Relativistic hydrodynamics: macroscopic theory defined on (in the limit of vanishing conserved currents) Flow Temperature Energy-momentum conservation driven by Law of increasing entropy Output Input • Initial conditions • Equation of state • Transport coefficients • Energy-momentum tensor • Flow field • Temperature field Introduction