Yukinao Akamatsu 赤松 幸尚 (Univ. of Tokyo) ATHIC 2008 Tsukuba Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid Yukinao Akamatsu 赤松 幸尚 (Univ. of Tokyo) Ref : YA, T. Hatsuda, and T. Hirano, arXiv:0809.1499[hep-ph]

Outline Introduction Langevin Dynamics of Heavy Quarks Hydro + HQ Model Numerical Results Conclusions and Outlook

1. Introduction Relativistic Heavy Ion Collision Light (m << T~200MeV) components (g, u, d, s) HQ relativistic ideal hydrodynamics g,u,d,s strongly coupled matter Heavy (M >> T~200MeV) components (c, b) long time scale  not thermalized in fluid  impurity Other impurities : J/Ψ (color singlet), Jet (too energetic)

2. Langevin Dynamics of Heavy Quarks <Energy loss of HQ> Heavy Quarks in Medium energy of HQ dominant mechanism low energy collision high energy radiation Energy loss of heavy quarks 1. weak coupling (pQCD) HQ q-hats > LQ q-hats  indicates collision (Armesto ’06, Wicks ‘07) but poor convergence (Caron-Huot ‘08) 2. strong coupling (AdS/CFT) drag force (Gubser ’06,’07, HKKKY ’06, Teaney ‘06) ,

Model of HQ in medium relativistic Langevin equation in the rest frame of matter assume isotropic noise the only input, dimensionless relaxation time of HQ 22 6.7 2.2 72 21 7.2 (at T=210MeV)

c(b)→D(B)→e- +νe+π etc 3. Hydro + HQ Model Flowchart 0 fm…. Little Bang 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 Electron Spectra Experiment (PHENIX, STAR ’07) time

Comments <decayed electron in pp> Initial condition <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 coexisting phase at 1st order P.T.  3 choices (no/half/full coexisting phase)

4. Numerical Results 22 6.7 2.2 72 21 7.2 Profile of HQ Diffusion 2 time scales : stay time and relaxation time stay time : ~3-4fm <relaxation times> 22 6.7 2.2 72 21 7.2 Charm ~ not yet fully thermalized Bottom ~ not thermalized at all <stay times>

HQ Spectra Nuclear modification factor Large pT, γ large momentum loss  large suppression

Elliptic flow High pT  (almost) no anisotropy At low pT, large γ large anisotropy

Electron Spectra Bottom ratio At pT above 3GeV, bottom origin electrons dominate.

Nuclear modification factor

Poor statistics for both simulation and experiment at high pT. Elliptic flow Poor statistics for both simulation and experiment at high pT. But at least consistent. (Still preliminary, PHENIX : v2~0.05-0.1 for pT~3-5GeV) Quite Large v2

5. Conclusions and Outlook Heavy quark can be described by relativistic Langevin dynamics with a parameter predicted by AdS/CFT. Prediction for heavy quark correlations. Latest experimental data for v2 seems to have larger elliptic flow. Theoretically, heavy quark energy loss at strong coupling (based more on field theory) should be reconsidered.

Back Up Slides

Average Temperature charm bottom

Momentum Loss charm bottom

RAA of Electrons from Charm/Bottom