Viscous Hydrodynamic Expansion of Quark-Gluon Plasma

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 1st2011, ECT*, Trento, Italy

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate 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 / 18 2 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Introduction

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Introduction Quark-gluon plasma (QGP) at relativistic heavy ion collisions Hadron phase (crossover) QGP phase 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 3 Introduction / 18 3 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Introduction

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

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Introduction RHIC experiments (2000-) The QGP is well-described by ideal hydro model Viscosity is 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 LHC experiments (2010-) Heavy ion collisions of higher energies Will the RHIC modeling of heavy ion collisions be working intact at LHC? / 18 5 5 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy he First ALICE Result

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

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate CGC in Heavy Ion Collisions Saturation scale in MC-KLN model D. Kharzeev et al., NPA 730, 448 H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903 : thickness function : momentum fraction of incident particles =0.38 =0.28 =0.18 Fixed via direct comparison with data dNch/d gets steeper with increasing ; RHIC data suggest ~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 / 18 7 Next slide: 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 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 (ii) viscous corrections for the CGC The first time the CGC rapidity distribution is discussed in terms of viscous hydrodynamics / 18 8 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Viscous Hydrodynamic Model

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Viscous Hydrodynamic Model Decomposition of the energy-momentum tensor by flow 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 Stability condition + frame fixing Thermodynamic stability demands This leaves and Identify the flow as local energy flux / 18 9 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Viscous Hydrodynamic Model

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Viscous Hydrodynamic Model Physical meanings of and Na ve interpretation at the 1storder 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 2ndorder contributions for the sake of causality and stability / 18 10 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Viscous Hydrodynamic Model

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Viscous Hydrodynamic Model Full 2ndorder viscous hydrodynamic equations + AM and T. Hirano, NPA 847, 283 Energy-momentum conservation 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 / 18 11 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Model Input for Hydro

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Model Input for Hydro Equation of state and transport coefficients S. Borsanyi et al., JHEP 1011, 077 Equation of State: Lattice QCD P. Kovtun et al., PRL 94, 111601 A. Hosoya et al., AP 154, 229 Shear viscosity: = s/4 Bulk viscosity: = (5/2)[(1/3) cs2] AM and T. Hirano, NPA 847, 283 Relaxation times: Kinetic theory & , 2ndorder coefficients: Kinetic theory & , Initial conditions Energy distribution: MC-KLN type CGC model H. J. Drescher and Y. Nara, PRC 75, 034905; 76, 041903 Dissipative currents: T = 0 Initial flow: Bjorken flow (i.e. flow rapidity Yf= s) Initial time: = 1 fm/c / 18 12 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Results

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

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

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Results Flow rapidity: Deviation from boost-invariant flow RHIC LHC = 30 fm/c = 50 fm/c Flows exhibit similar trends at RHIC and LHC Ideal flow viscous flow due to competition between deceleration by suppression of total pressure P0 + at early stage and acceleration by enhancement of hydrostatic pressure P0at late stage / 18 15 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Results

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate 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 / 18 16 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Summary and Outlook

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Summary and Outlook We solved full 2ndorder viscous hydro in (1+1)-dimensions for the shattered color glass condensate 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 Future prospect includes: AM & T. Hirano, in preparation Detailed analyses on parameter dependences, rcBK, etc A (3+1)-dimensional viscous hydrodynamic model / 18 17 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy The End

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

Akihiko Monnai (The University of Tokyo) Viscous Hydrodynamic Expansion of the Quark-Gluon Plasma for the Color Glass Condensate Results Parameter dependences (i) /s = 0, eff/s = 0 (ii) /s = 1/4 , eff/s = (5/2)[(1/3) cs2]/4 (iii) /s = 3/4 , eff/s = (15/2)[(1/3) cs2]/4 Larger entropy production for more viscous systems preliminary Comparison to boost-invariant flow Longitudinal viscous hydro expansion is essential / 18 19 Next slide: Standard and Novel QCD Phenomena at Hadron Colliders, June 1, ECT*, Trento, Italy Appendices

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