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Langevin + Hydrodynamics Approach to Heavy Quark Diffusion in the QGP

2009/05/09 Heavy Ion Café @Tokyo. Langevin + Hydrodynamics Approach to Heavy Quark Diffusion in the 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

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Langevin + Hydrodynamics Approach to Heavy Quark Diffusion in the QGP

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  1. 2009/05/09 Heavy Ion Café @Tokyo Langevin + Hydrodynamics Approach to Heavy Quark Diffusion in the QGP Yukinao Akamatsu Tetsuo Hatsuda Tetsufumi Hirano (Univ. of Tokyo) Ref : Y.A., T.Hatsuda and T.Hirano, arXiv:0809.1499[hep-ph]

  2. Outline • Introduction • Langevin + Hydro Modelfor Heavy Quark • Numerical Calculations • Conclusions and Outlook

  3. Introduction 0 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 !

  4. Langevin + Hydro Model for Heavy Quark 1) Our model of HQ in medium in the (local) rest frame of matter Relativistic Langevin equation Assumeisotropic 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)

  5. 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

  6. 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

  7. 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)

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

  9. 3) Azimuthal Correlation Back to back correlation quenched & broadened 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

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

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

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

  13. 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,・・・

  14. Backup

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

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

  17. 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

  18. Numerical calculations for HQ Nuclear Modification Factor

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

  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.  Degree of HQ Thermalization Time measured by a clock co-moving with fluid element For γ=0-30 and initial pT=0-10GeV thermalized not thermalized _ (T=210MeV) 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 QBS

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