Yukinao Akamatsu Tetsuo Hatsuda Tetsufumi Hirano (Univ. of Tokyo) 2009/04/03 Quark Matter @Knoxville Langevin + Hydrodynamics Approach to Heavy Quark Propagation and Correlation in QGP Yukinao Akamatsu Tetsuo Hatsuda Tetsufumi Hirano (Univ. of Tokyo) Ref : Y.A., T.Hatsuda and T.Hirano, arXiv:0809.1499[hep-ph]

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

Introduction 0.6fm O(10) fm CGC Glasma Hydrodynamics Hadron Rescattering Observed Local thermalization assumed Medium composed of light particles (u,d,s,g) Strongly coupled QGP (sQGP)  How can we probe ? Others : jets, J/Psi, etc Heavy quarks (c,b) --- heavy compared to temperature tiny thermal pair creation 　　　　　　　　　　　 no mutual interaction Good probe !

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

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

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

2) Elliptic Flow Poor statistics, but at least consistent with γ=1-3. (Still preliminary, PHENIX : v2~0.05-0.1 for pT~3-5GeV)

22 6.7 2.2 72 21 7.2  Degree of HQ Thermalization Stay time Relaxation time 22 6.7 2.2 72 21 7.2 thermalized not thermalized Experimental result γ=1-3  charm : nearly thermalized, bottom : not thermalized

3) Azimuthal Correlation Back to back correlation Quenched diffusion 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

electron - (charged) hadron correlation (e - π, K, p) = (trigger - associate) ・More quenching with larger γ ・Partial quenching predicted Quenching of backward (0.5π-1.5π) signal QBS ZYAM γ QBS 0.3 1.01±0.16 1.0 0.88±0.11 3.0 0.55±0.09 10.0 0.21±0.07

electron - muon correlation (trigger - associate) ・More quenching with larger γ ・Partial quenching predicted Quenching of backward (0-2π) signal QBS ZYAM γ QBS 0.3 1.01±0.02 1.0 0.98±0.02 3.0 0.79±0.02 10.0 0.31±0.03

V2 has large statistical error. But at least consistent. Y. Morino (PhD Thesis) arXiv:0903.3504 [nucl-ex] (Fig.7.12) Conclusions and Outlook Heavy quark can be described by relativistic Langevin dynamics with a drag parameter predicted by AdS/CFT (for RAA). V2 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,・・・

Backup

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

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

Notes in our model Initial condition <decayed electron in pp> <HQ in pp> available only spectral shape above pT ~ 3GeV Reliable at high pT No nuclear matter effects in initial condition No quark coalescence effects in hadronization Where to stop in mixed phase at 1st order P.T.  3 choices (no/half/full mixed phase) f0=1.0/0.5/0.0

Numerical calculations for HQ Nuclear Modification Factor

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

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%

22 6.7 2.2 72 21 7.2 DEFINITION VALUE Stay time ts=Σ Δt|FRF 3-4 [fm]  Degree of HQ Thermalization Time measured by a clock co-moving with fluid element For γ=0-30 and initial pT=0-10GeV DEFINITION VALUE Stay time ts=Σ Δt|FRF 3-4 [fm] Temperature T=Σ(TΔt|FRF) / ts ~210 [MeV] 22 6.7 2.2 72 21 7.2 thermalized not thermalized _ (T=210MeV) Experimental result γ=1-3  charm : nearly thermalized, bottom : not thermalized

QQbar Correlation

Other numerical calculations muon - (charged) hadron correlation Quenching of backward (0.5π-1.5π) signal QBS γ QBS 0.3 0.89±0.13 1.0 0.77±0.11 3.0 0.49±0.07 10.0 0.12±0.06

electron - muon correlation with higher associate pT Quenching of backward (0-2π) signal QBS γ QBS 0.3 1.00±0.02 1.0 0.97±0.02 3.0 0.92±0.03 10.0 0.95±0.06 γ QBS 0.3 0.99±0.02 1.0 0.95±0.01 3.0 0.76±0.01 10.0 0.31±0.02

Summary of QBS