Langevin + Hydrodynamics Approach to Heavy Quark Diffusion in the QGP Yukinao Akamatsu Tetsuo Hatsuda Tetsufumi Hirano (Univ. of Tokyo) /05/09 Heavy Ion Ref : Y.A., T.Hatsuda and T.Hirano, arXiv: [hep-ph]

Outline Introduction Langevin + Hydro Model for Heavy Quark Numerical Calculations Conclusions and Outlook 2

Introduction 00.6fmO(10) fm CGC Glasma Hydrodynamics Hadron Rescattering Observed Medium composed of light particles (u,d,s,g) Others : jets, J/Psi, etc Heavy quarks (c,b) --- heavy compared to temperature tiny thermal pair creation no mutual interaction  Good probe ! 3 Local thermalization assumed Strongly coupled QGP (sQGP)  How can we probe ?

4 Langevin + Hydro Model for Heavy Quark 1) Our model of HQ in medium Relativistic Langevin equation the only input, dimensionless Assume isotropic Gaussian white noise in the (local) rest frame of matter in the (local) rest frame of matter 2) Energy loss of heavy quarks Weak coupling (pQCD) Poor convergence (Caron-Huot ‘08) Strong coupling (SYM by AdS/CFT  sQGP) N=4 SYM theory [ for naïve perturbation] (Gubser ’06, Herzog et al. ’06, Teaney ’06) “Translation” to sQGP (Gubser ‘07) Satisfy fluctuation-dissipation theorem (leading order)

0 fm…. 0.6 fm… Little Bang Initial Condition Brownian Motion Heavy Quark Spectra Full 3D hydrodynamics Electron Spectra + …. T(x), u(x) Local temperature and flow (pp + Glauber) (Hirano ’06) c(b) → D(B) → e - +ν e +π etc _ time QGP Experiment (PHENIX, STAR ’07) 5 3) Heavy Quark Langevin + Hydro Model O(10)fm… generated by PYTHIA (independent fragmentation)

6 Numerical Calculations Experimental result  γ=1-3 AdS/CFT γ=2.1±0.5 Different freezeouts at 1 st order P.T. Bottom dominant 1) Nuclear Modification Factor ・ Initial (LO pQCD): good only at high p T ・ CNM, quark coalescence : tiny at high pT

7 Poor statistics, but at least consistent with γ=1-3. (Still preliminary, PHENIX : v 2 ~ for p T ~3-5GeV) 2) Elliptic Flow

thermalized not thermalized  Degree of HQ Thermalization Experimental result γ=1-3  charm : nearly thermalized, bottom : not thermalized Relaxation time Stay time

9 3) Azimuthal Correlation Observables : c, b  D, B  single electron, muon charged hadron e-h, μ-h correlation : two peaks (near & away side) e-μ correlation : one peak (away side only) no contribution from vector meson decay Back to back correlationquenched & broadened diffusion

10 electron - (charged) hadron correlation (e - π, K, p) = (trigger - associate) Quenching of backward (0.5π-1.5π) signal Q BS ・ More quenching & broadening with larger γ ・ Mach cone : not included ZYAM

11 electron - muon correlation (trigger - associate) Quenching of backward (0-2π) signal Q BS ・ High p T associate : energy loss ・ Low p T associate : fluctuation ・ Energy loss  quenching ・ Fluctuation  broadening ・ More quenching & broadening with larger γ electron, muon : mid-rapidity (< 1.0)

12 electron - muon correlation electron : mid pseudo-rapidity (< 0.35) muon : forward pseudo-rapidity (1.4~2.1) (trigger - associate)

13 Heavy quark can be described by relativistic Langevin dynamics with a drag parameter predicted by AdS/CFT (for R AA ). V 2 has large statistical error. But at least consistent. Heavy quark correlations in terms of lepton-hadron, electron-muon correlations are sensitive to drag parameter. Possible update for initial distribution with FONLL pQCD quark coalescence, CNM effects, ・・・ Conclusions and Outlook Y. Morino (PhD Thesis) arXiv: [nucl-ex] (Fig.7.12)

14 Backup

15 Weak coupling calculations for HQ energy loss RHIC, LHC γ~0.2 γ~2.5

16 Fluctuation-dissipation theorem Ito discretization  Fokker Planck equation Generalized FD theorem A Little More on Langevin HQ

Initial condition available only spectral shape above p T ~ 3GeV No nuclear matter effects in initial condition No quark coalescence effects in hadronization Where to stop in mixed phase at 1 st order P.T.  3 choices (no/half/full mixed phase) Reliable at high pT 17 f 0 =1.0/0.5/0.0 Notes in our model

18 Numerical calculations for HQ Nuclear Modification Factor

19 γ=30 : Surface emission dominates at high pT only at low p T Elliptic Flow

20 Subtlety of outside production proportion of ts=0 for pT>5GeV Gamma=0.3_ccbar:1.2%Gamma=0.3_bbbar:0.70% Gamma=1_ccbar:4.2%Gamma=1_bbbar:0.93% Gamma=3_ccbar:25%Gamma=3_bbbar: 2.2% Gamma=10_ccbar: 68%Gamma=10_bbbar: 15% Gamma=30_ccbar:90%Gamma=30_bbbar:46% Gamma=0.3_eb:0.75% Gamma=0.3_mb:0.97% Gamma=1_eb:1.7% Gamma=1_mb:2.0% Gamma=3_eb:5.3% Gamma=3_mb:5.1% Gamma=10_eb:31% Gamma=10_mb:30%

21 DEFINITIONVALUE Stay timet s =Σ Δt| FRF 3-4 [fm] TemperatureT=Σ(TΔt| FRF ) / t s~ 210 [MeV] For γ=0-30 and initial p T =0-10GeV (T=210MeV) thermalized not thermalized Time measured by a clock co- moving with fluid element _  Degree of HQ Thermalization Experimental result γ=1-3  charm : nearly thermalized, bottom : not thermalized

22 QQbar Correlation

23 Other numerical calculations muon - (charged) hadron correlation Quenching of backward (0.5π-1.5π) signal Q BS