Workshop for Particle Correlations and Femtoscopy 2011 AM and T. Hirano, Phys. Lett. B 703, 583 (2011) Viscous Hydrodynamic Deformation in Rapidity Distributions of the Color Glass Condensate Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano Workshop for Particle Correlations and Femtoscopy 2011 September 24th 2011, The University of Tokyo, Japan

Introduction Quark-gluon plasma (QGP) at relativistic heavy ion collisions Hadron phase (crossover) sQGP QGP phase (wQGP?) RHIC experiments (2000-) The QGP quantified as a nearly-perfect fluid Viscosity is important in detailed analyses LHC experiments (2010-) Heavy ion collisions of higher energies Will the RHIC modeling work at LHC? Introduction

Color glass condensate Introduction Modeling a high-energy heavy ion collision Hydrodynamic stage Color glass condensate Hadronic cascade Initial condition Hydro to particles ｔ particles t Freezeout QGP phase hadronic phase Pre-equilibrium z 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) The First ALICE Result

The First ALICE Result Mid-rapidity multiplicity Motivation K. Aamodt et al. PRL105 252301 Pb+Pb, 2.76 TeV at η = 0 CGC Motivation The CGC is fit to RHIC data; What is happening at LHC? ALICE data (most central 0-5%) CGC in Heavy Ion Collisions

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; PRC 76, 041903 λ=0.38 Fixed via direct comparison with data λ=0.28 λ=0.18 : thickness function : momentum fraction of incident particles dN/dy dNch/dη gets steeper with increasing λ; RHIC data suggest λ~0.28 Initial condition from the CGC Initial condition from the CGC Hydrodynamic evolution Observed particle distribution Observed particle distribution A missing piece! CGC in Heavy Ion Collisions

CGC in Heavy Ion Collisions CGC + Hydrodynamic Model Initial condition from the CGC Hydrodynamic evolution Observed particle distribution A missing piece! In this work… We 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 Hydrodynamic Model

+ Hydrodynamic Model Full 2nd order viscous hydrodynamic equations 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) with Landau frame where local energy flux is the flow Model Input for Hydro

Model Input for Hydro Equation of state and transport coefficients Boundary conditions at the initial time Equation of State: Lattice QCD S. Borsanyi et al., JHEP 1011, 077 Shear viscosity: η = s/4π P. Kovtun et al., PRL 94, 111601 A. Hosoya et al., AP 154, 229 Bulk viscosity: ζeff = (5/2)[(1/3) – cs2]η Relaxation times: Kinetic theory AM and T. Hirano, NPA 847, 283 2nd order coefficients: Kinetic theory Initial flow: Bjorken flow (i.e. flow rapidity Yf = ηs) Energy distribution: MC-KLN type CGC (averaged over transverse area) Dissipative currents: Results

Results Distributions at isothermal hypersurface Tf = 0.16 TeV RHIC LHC Outward entropy flux Flattening Entropy production Enhancement If the true λ is larger at RHIC, it enhances dN/dy at LHC; Hydro effect is a candidate for explaining the “gap” at LHC Results

Results Hydrodynamic parameter dependences (at the LHC) CGC parameter dependence to be explored Entropy production is roughly proportional to viscous coefficients Shear viscous effects are dominant in the QGP phase Fix the real λ from rapidity distribution and centrality dependences Summary and Outlook

AM & T. Hirano, in preparation Summary and Outlook We solved full 2nd order viscous hydro in (1+1)-dimensions for the “shattered” color glass condensate Future prospect includes: Analyses on the CGC parameter dependences, rcBK, etc… Estimation of the effects of transverse flow via developing (3+1)-dimensional viscous hydrodynamic model, etc… 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

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