ATHIC 2008 Tsukuba Heavy Quark Diffusion with Relativistic

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, ar. Xiv: 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~200 Me. V) components (g, u, d, s) relativistic ideal hydrodynamics HQ g, u, d, s strongly coupled matter Heavy (M >> T~200 Me. V) 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 loss of heavy quarks 1. weak coupling (p. QCD) HQ q-hats > LQ q-hats indicates collision energy of HQ dominant mechanism low energy collision high energy radiation (Armesto ’ 06, Wicks ‘ 07) but poor convergence (Caron-Huot ‘ 08) 2. strong coupling (Ad. S/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=210 Me. V)

3. Hydro + HQ Model • Flowchart 0 fm…. QGP 0. 6 fm… Little Bang Initial Condition (pp + Glauber) Brownian Motion Local temperature and flow T(x), u(x) Full 3 D hydrodynamics (Hirano ’ 06) Heavy Quark Spectra _ c(b)→D(B)→e- +νe+π etc Electron Spectra time Experiment (PHENIX, STAR ’ 07)

• Comments <decayed electron in pp> Initial condition <HQ in pp> available only spectral shape above p. T~3 Ge. V Reliable at high p. T No nuclear matter effects in initial condition No quark coalescence effects in hadronization Where to stop in coexisting phase at 1 st order P. T. 3 choices (no/half/full coexisting phase)

4. Numerical Results • Profile of HQ Diffusion 2 time scales : stay time and relaxation time stay time : ~3 -4 fm <relaxation times> 22 72 <stay times> 6. 7 21 2. 2 7. 2 Charm ~ not yet fully thermalized Bottom ~ not thermalized at all

• HQ Spectra Nuclear modification factor Large p. T, γ large momentum loss large suppression

Elliptic flow High p. T (almost) no anisotropy At low p. T, large γ large anisotropy

• Electron Spectra Bottom ratio At p. T above 3 Ge. V, bottom origin electrons dominate.

Nuclear modification factor

Elliptic flow Poor statistics for both simulation and experiment at high p. T. But at least consistent. (Still preliminary, PHENIX : v 2~0. 05 -0. 1 for p. T~3 -5 Ge. V) Quite Large v 2

5. Conclusions and Outlook • Heavy quark can be described by relativistic Langevin dynamics with a parameter predicted by Ad. S/CFT. • Prediction for heavy quark correlations. • Latest experimental data for v 2 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 charm bottom