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Hydrodynamic Expansion with QCD Critical Point

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## Hydrodynamic Expansion with QCD Critical Point

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**Hydrodynamic Expansionwith QCD Critical Point**Nagoya University Chiho NONAKA In collaboration with M.Asakawa(Osaka), S.A.Bass(Duke) and B.Mueller(Duke) April 21, 2008 @BNL**RHIC**T QGP phase critical end point 1sr order crossover GSI Hadron phase CSC B Stephanov,hep-lat/0701002 Where is the QCP? • Lattice QCD, Effective models…**energy scan**t focusing QCP Search in HIC • The QCD critical point search from phenomenology and experiments t M. Stephanov, K. Rajagopal, and E.Shuryak, PRL81 (1998) 4816**UrQMD**Full 3-d Hydrodynamics EoS :1st order phase transition QGP + excluded volume model Hadronization Cooper-Frye formula final state interactions Monte Carlo TC TSW t fm/c TC:critical temperature TSW:Hydro UrQMD 3D Hydro+UrQMD Model Nonaka and Bass PRC75:014902(2007) • Relativistic Heavy Ion Collision • Schematic sketch t hydrodynamical expansion collision thermalization hadronization freeze-out • 3D Hydro + UrQMD • Success of hydrodynamic models at RHIC: --PT spectra, rapidity distribution, elliptic flow • Limitation of Hydro Ex. Elliptic flow at forward/backward rapidity, HBT • Extension of Hydro --Viscosity effect of hadron phase --Final state interactions**UrQMD**Full 3-d Hydrodynamics EoS :1st order phase transition QGP + excluded volume model Hadronization Cooper-Frye formula final state interactions Monte Carlo TC TSW t fm/c TC:critical temperature TSW:Hydro UrQMD Realistic Equation of States • 3D Hydro + UrQMD • equation of states • bag model • freezeout process • Viscosity effect of • hadron phase • Final state interactions • initial conditions • parametrization Realistic EOS with QCD critical point**T**QGP Hadronic h r EOS with QCD Critical Point Nonaka and Asakawa, PRC71,044904(2005) • Singular part near QCD critical point + Non-singular part • Non-singular part QGP phase and hadron phase • Singular part • Mapping (r, h) (T, B) • Matching with known QGP and hadronic entropy density • Thermodynamical quantities 3d Ising Model QCD Same Universality Class**Comparison with Bag Model**• Isentropic trajectories on T- plane Bag Model + Excluded Volume Approximation (No Critical Point) With QCD critical point = Usual Hydro Calculation Not Focused Focused**Where is the QCP?**• Location of the QCD critical point, critical region around the QCD critical point • Fluctuations • NA49, STAR, PHENIX… Search of the QCD critical point from experiments**CEP: attractor of isentropic trajectories**Similar correlation length and fluctuation is observed near QCP. Consequence of QCP? CERES:Nucl.Phys.A727(2003)97 Fluctuations CERES 40,80,158 AGeV Pb+Au collisions Mean PT Fluctuation No unusually large fluctuation or non-monotonic behavior**NA49**QCP? • Suggestion of QCD critical end point? • Fluctuation Conservation**Consequences?**steeper spectra at high PT NA49, PRC73,044910(2006)**QCP**CF Location of QCP? Search of the QCD critical point from experiments • SPS energyregion • Location of QCP • (B,T)=(550,159) • Critical Region • Chemical freezeout point • Hadron ratios are fixed. • (B,T)=(406,145) • from statistical model • Hadronization • emission time distribution**QCP**CF Critical Region • ) QGP phase 0.8 -0.8 T QCD critical endpoint (B,T)=(550,159) hadron phase • Entropy density B**Signature of QCP**• decreases (Bag) • increases (QCE) with QCE steeper spectra at high PT**Consequences?**steeper spectra at high PT NA49, PRC73,044910(2006)**Where is the QCP?**• Location of the QCD critical point, critical region around the QCD critical point • Fluctuations • NA49, STAR… • Anti-p/p ratio • Focusing effect in isentropic trajectories • Clear signature • Narrow collision energy window is needed. Search of the QCD critical point from experiments**Equation of State**• QCD critical point (B,T)=(550,159) entropy density trajectories**T**= 159 MeV, m = 550 MeV QCP: E E 2 1 0=0.6 fm/c 0=0.5 =1.5 0 3D Hydro+UrQMD with QCP • Initial Conditions • Energy density • Baryon number density • Parameters • Flow • EOS: QCP, Bag Model • Switching temperature • longitudinal direction: H() vL=Bjorken’s solution); vT=0 TSW=150 [MeV]**1**2 RHIC Isentropic Trajectories in Hydro • T and B in one volume element close to center Hydro with Bag Model Hydro with QCD critical point T [MeV] [MeV] • Tf=110 MeV • Behavior of isentropic trajectories in hydro with QCP is different from • one in hydro with bag model. • Focusing effect appears in hydro with QCD critical point.**PT Spectra in 3D Hydro**Hydro with QCD critical point Hydro with Bag Model • Tf=110 MeV • PT slope is almost the same.**1**2 3D Hydro + UrQMD Hydro with Bag Model Hydro with QCD critical point T [MeV] UrQMD UrQMD B [MeV] Switching temperature: 150 MeV**At TSW**Because of focusing effect PT Spectra QCD critical point Bag Model**p Spectra**work in progress • Narrow collision energy window is needed. NA49: anti-p spectra • Careful choice for initial condition of hydro calculation**Focusing**Summary • 3D Hydro + UrQMD Model with the QCD critical point • Isentropic trajectories • PT spectra, hadron ratio • From experiments information of the QCD critical point location, critical region, existence… • Physical observables • Anti-p/p ratio:promising and clear signature • Fluctuations • Balance function**T**= 143.7 MeV, m = 652.0 MeV QCP: E E 0=0.6 fm/c 0=0.5 =1.5 3D Hydro+UrQMD with QCP • Initial Conditions • Energy density • Baryon number density • Parameters • Flow • EOS: QCP, Bag Model • Switching temperature • longitudinal direction: H() vL=Bjorken’s solution); vT=0 TSW=150 [MeV]**T**= 143.7 MeV, m = 652.0 MeV QCP: E E 1 2 1 2 1 2 T [MeV] RHIC B [MeV] Isentropic Trajectories in Hydro • T and B in one volume element close to center Hydro with QCD critical point Hydro with Bag Model T [MeV] B [MeV] • Tf=110 MeV • Behavior of isentropic trajectories in hydro with QCP is different from • one in hydro with bag model. • Focusing effect appears in hydro with QCD critical point.**PT Spectra in 3D Hydro**Hydro with QCD critical point Hydro with Bag Model • Tf=110 MeV • PT slope is almost the same.**1**2 1 2 3D Hydro + UrQMD Hydro with Bag Model Hydro with QCD critical point T [MeV] T [MeV] UrQMD UrQMD B [MeV] B [MeV] Switching temperature: 150 MeV**PT Spectra**QCD critical point Bag Model • PT slope is almost the same. • Larger difference of different initial conditions appears in the case of QCP.**T [MeV]**B [MeV] At TSW Because of focusing effect Hadron Ratios QCD critical point Bag Model**Focusing**Summary • 3D Hydro + UrQMD Model with the QCD critical point • Isentropic trajectories • PT spectra, hadron ratio • The QCD critical point search • Energy scan parameter sets of and nB in initial conditions • Switching temperature dependence • Location of QCD critical point • Physical observables • Fluctuations • Balance function**Equation of State**QCD critical point entropy density baryon number density**Isentropic Trajectories**• Isentropic trajectories: nB/s=const. line • Behavior of focusing depends on the location of QCP on T-plane. • The focusing effect appears stronger in the case (T,)=(143,652). • The location of QCP is a parameter. Experiments**Comparison with Bag Model**• Isentropic trajectories on T- plane Bag Model + Excluded Volume Approximation (No Critical Point) With QCD critical point = Usual Hydro Calculation Not Focused Focused**Mean PT Fluctuation**preliminary PT < 1 GeV p K 1 0.567E-02 0.266E-01 0.156E-01 2 0.416E-02 0.242E-01 0.115E-01 *In this calculation, definition of mean Pt fluctuation is different from CERES.**Consequences**• Slowing out of equilibrium • Large fluctuation • Freeze out temperature at RHIC • Fluctuation Focusing CEP and Its Consequences Existence and location of CEP in phase diagram: Collision energy dependent experiments are indispensable. Work in Progress • Realistic hydro calculation with critical point**H**Q Sound Velocity • EoS Hydrodynamic Expansion Ex. Rischke et al. nucl-th/9504021 QGP hadron Mixed Effect of mixed phase?**Lattice QCD at finite T and B**• Multi-parameter reweighting technique • Fodor and Katz (JHEP 0203 (2002) 014) Overlap problem: The lattice size is small. hep-lat/0402006 • Allton et al. (Bielefeld-Swansea) Maezawa san’s talk**Still we need to study**• Hadronic Observables : NOT directly reflect properties at CEP • Fluctuation, Collective Flow • EOS • Focusing in nB/s trajectories • Dynamics (Time Evolution) Phenomenological Consequence ? M. Stephanov, K. Rajagopal, and E.Shuryak, PRL81 (1998) 4816 critical end point Divergence of Fluctuation Correlation Length If expansion is adiabatic.**slower (longer)**expansion r h faster (shorter) expansion along r = const. line h E Time Evolution • Berdnikov and Rajagopal’s Schematic Argument B. Berdnikov and K. Rajagopal, Phys. Rev. D61 (2000) 105017 Correlation Length longer than Leq • What’s missing: • Realistic Hydro Calculation with Realistic EOS**3-d Hydrodynamic Model**Hydrodynamic equation Baryon number density conservation Coordinates Lagrangian hydrodynamics Tracing the adiabatic path of each volume element Effects of phase transition of observables Algorithm Focusing on conservation law Flux of fluid**Trajectories on the phase diagram**• Lagrangian hydrodynamics temperature and chemical potential of volume element of fluid Effect of phase transition C.N et al., Eur. Phys.J C17,663(2000)**Jets in medium**Jet quenching mechanisms Ex. Nuclear modification factor in 3D hydro • pQCD • Mixed and hadron phase • AMY • gluon bremsstrahlung • parton path arXiv:0705.2575(hep-ph) with Qin, Ruppert, Turbide, Gale nucl-th/0703019 with Majumder nucl-th/0611027 with Renk and Ruppert**Soft + Hard**Soft Improved Cooper-Frye formula (Reco) • Full 3-d Hydrodynamic Model • QGP formation, EoS UrQMD t fm/c Final Interactions Interaction between Soft and Hard Hadronization Hard Fragmentation • Hard scattering & jet production • Propagation of jet in medium, • energy loss • Dynamical effect on jets • Jet correlations • First schematic attempt Hirano & Nara PRC66:041901,2002, PRL91:082301,2003**Non-Singular Part**• Hadron Phase • Excluded volume model • QGP Phase B=0 P PQGP PH Tc T B Nf=2 B:Bag constant (220 MeV)4**Isentropic Trajectories in Hydro**• Conservation law in ideal fluid Hydrodynamic expansion: nB/s =const. nB/s =const. lines on T-B plane: behavior of expansion**Trajectories on the phase diagram**• Lagrangian hydrodynamics temperature and chemical potential of volume element of fluid Effect of phase transition C.N et al., Eur. Phys.J C17,663(2000)