20081126 Komaba Seminar Heavy Quark Diffusion in the
2008/11/26 Komaba Seminar Heavy Quark Diffusion in the Quark-Gluon Fluid Yukinao Akamatsu Univ. of Tokyo Ref : Y. A. , T. Hatsuda and T. Hirano, ar. Xiv: 0809. 1499[hep-ph] 1
Outline • • • Introduction HQ Energy Loss Langevin HQ + Hydro Model Numerical Results : HQ Numerical Results : e± Conclusions and Outlook 2
Introduction 3
Relativistic Heavy Ion Collision 0 CGC 0. 6 fm Glasma O(10) fm Hydrodynamics Hadron Rescattering Observed What ? --- medium composed of light particles (u, d, s, g) Others : jets --- very energetic light quarks and gluons : heavy quarks (c, b) --- very heavy compared to temperature Dynamical Probe? : J/Psi --- almost colorless : photons --- electromagnetic interaction EM Probe Hard Probes 4
Hard Probes 1) Jet Quenching From slides of X. -N. Wang @Hard Probe ’ 08 q-hat ~ 4 -14 [Ge. V 2/fm] 5
2) Heavy Quark From slides of R. Rapp @SQM ’ 08 • p. QCD radiative E-loss with upscaled transport coeff. • Langevin with elastic p. QCD + resonances + coalescence • Langevin with upscaled p. QCD elastic Radiation vs. Collision q-hat ~ >14 [Ge. V 2/fm] (line) for rad. non-perturbative for coll. 6
Dynamical Probes? From slides of T. Gunji @SQM ’ 08 Survival of J/Psi ~ 2 Tc ? Hydro + J/y T. Gunji et al. PRC 76: 051901, 2007 EM Probe From slides of F. -M. Liu @SQM ’ 08 7
HQ Energy Loss 8
Collisional Energy Loss (E>>M>>T) (Braaten ‘ 91) (ET>>M 2) (ET<<M 2) 9
Radiative Energy Loss (BDMPS) (E>>M) μ : Debye mass λ : mean free path 10
Langevin HQ + Hydro Model 11
Heavy Quarks in Medium 1) Energy loss of heavy quarks weak coupling (p. QCD) Dominance Experiment Higher order Fast (v ~ c) Not alone × Radiation (g=g(m. D)) Fast (v ~ c) ? ? Collision (g=g(T)) Slow (v ~ 0) Not alone × Collision (g=g(m. D)) Slow (v ~ 0) OK by alone ? Radiation (g=g(T)) (Aichelin ’ 08) (Moore ’ 05, van Hees ‘ 05) (Caron-Huot ‘ 08) HQ q-hats > LQ q-hats àindicates collision (Armesto ’ 06, Wicks ’ 07) But even rad+coll cannot (Djordjevic ’ 06) Non-Perturbative method is required 12
strong coupling (Ad. S/CFT) drag force (= enegy loss d. E/dx) (Gubser ’ 06, ’ 07, HKKKY ’ 06, Teaney ‘ 06) , By comparing energy density & HQ pot. 2) 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 72 (at T=210 Me. V) 6. 7 2. 2 21 7. 2 13
HQs in Dynamical Medium 1) Flowchart 0 fm…. QGP 0. 6 fm… Little Bang Initial Condition Brownian Motion (pp + Glauber) Local temperature and flow T(x), u(x) Full 3 D hydrodynamics (Hirano ’ 06) Heavy Quark Spectra O(10)fm… _ c(b)→D(B)→e- +νe+π etc Electron Spectra time Experiment (PHENIX, STAR ’ 07) 14
2) Comments Initial condition <decayed electron in pp> <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) f 0=1. 0/0. 5/0. 0 15
Numerical Results : HQ 16
Profile of HQ Diffusion 2 time scales : stay time and relaxation time 1) stay time 3 -4 fm 17
2) relaxation time _ T ~ 0. 21 Ge. V 22 72 6. 7 2. 2 21 7. 2 18
3) pt loss 19
Nuclear Modification Factor : RAA 20
Elliptic Flow : v 2 21
HQ Correlation p. T 1>p. T 2 & p. T 1>p. Ttrig 1: trigger, 2: associate Gamma 0. 0 <Ts 1+Ts 2> 7. 5 fm 7. 2 fm 7. 0 fm 7. 7 fm 0. 3 1. 0 30. 0 7. 1 fm 6. 7 fm 7. 4 fm 6. 8 fm 6. 0 fm 7. 8 fm 7. 4 fm 6. 0 fm 4. 0 fm 7. 7 fm 7. 1 fm 6. 3 fm 0. 6 fm 7. 3 fm 4. 8 fm 22
Numerical Results : e± 23
Nuclear Modification Factor : RAA Experimental result γ=1 -3 Ad. S/CFT γ=2. 1± 0. 5 24
Elliptic Flow : v 2 Poor statistics, but at least consistent. (Still preliminary, PHENIX : v 2~0. 05 -0. 1 for p. T~3 -5 Ge. V) 25
Conclusions and Outlook 26
• Heavy quark can be described by relativistic Langevin dynamics with a parameter predicted by Ad. S/CFT (for RAA). • Prediction for heavy quark correlations More effort needed for e-h correlations • Latest experimental data for v 2 seems to have larger elliptic flow Within our model, coalescence even at high p. T is necessary ? • Theoretically, heavy quark energy loss at strong coupling should be reconsidered. 27
To Be Continued… 28
- Slides: 28