Thermalization of Charm Quarks in Infinite and Finite QGP Matter

1. Thermalization of Charm Quarks in Infinite and Finite QGP Matter Shanshan Cao Duke University

2. Outline • Introduction and motivation • Methodology • Langevin approach and criterion of equilibrium • Results of charm quark thermalization process • Summary • Outlook: a systematic study of heavy quark-medium interaction

3. Introduction – Why to Study Charm Quark • Mainly produced at early stage: act as a hard probe • Heavy: supposed to be influenced less by the medium (c: 1.27GeV vs. u,d a few MeV) • Surprisingly large v2 and small RAA of non-photonic electrons • Strong coupling between heavy quark and the medium • Can charm quark thermalize in the QGP medium?

4. Methodology – Energy Loss • Two ways for heavy quarks to lose energy: CollisionRadiation • Radiation is suppressed by the “dead cone effect”: (suppression of small angle radiation) • Bremsstrahlung dominates only for ultrarelativistic situation: (in our calculation ) c c θ g medium q q

5. Methodology – Langevin Approach • Heavy quark inside the medium: Brownian motion • Description: Langevin equation Langevin Equation: Fluctuation: Fluctuation-dissipation: Diffusion Coefficient:

6. Introduction – Study on Thermalization • Previous Study: Moore and Teaney: Langevin algorithm  7 fm/c for the relaxation time of charm quark thermalization Hees and Rapp: resonant heavy-light quark interaction  reduce relaxation time from 30 to a few fm/c Neither of them have checked whether charm quarks are indeed thermalized in the QGP medium • Our Study: Follow Moore and Teaney, extend to relativistic (3+1)D hydrodynamic scenario and check for thermalization

7. Methodology – Thermalization Criterion Energy Spectrum: Momentum Spectrum: (check the isotropy of the momentum space) Consider a Blue Shift:

8. Results for Static Medium T=300MeV, D(2πT)=6 Tmedium=300MeV, D(2πT)=6 pi=5GeV (in z) Energy spectrum z pi=5GeV Linear relation appears after 10 fm/c. Slope keeps varying until 30 fm/c. No linear relation between 2-8 fm/c

9. Results for Static Medium • A comparison of temperature parameters extracted from different spectra. Equilibrium criterion: Temperature parameters extracted from different ways merge and approach that of the medium.

10. QGP Medium • Generation of QGP medium: a fully 3D relativistic ideal hydrodynamics model • Initialization of charm quarks: the VNI/BMS parton cascade model • Simulate the charm quark diffusion with the Langevin algorithm in the local rest frame of the medium After freeze-out: free-streaming Free-streaming outside the medium

11. QGP Medium • At each time step, choose a temperature range of the QGP medium and select charm quarks which happen to be in the position of the medium within that temperature range • Boost the charm quarks into the local rest frame of the medium, extract their temperature and compare it with that of the medium Medium temperature: temperature range T-ΔtT+Δt

12. Results for the QGP Medium Not fully thermalized above Tc Close to full equilibrium Phys. Rev. C84, 064902 (2011) For “reasonable” diffusion coefficient, heavy quarks may remain off-equilibrium during the QGP lifetime.

13. Summary • Study the thermalization of charm quarks in the framework of the Langevin approach • Establish rigorous criterion for studying the thermalization process: extract and compare temperature from energy and momentum spectra • Charm quarks may interact strongly with the medium (v2and RAA), but this does not imply thermalization: they remain off-equilibrium during the QGP lifetime.

14. Outlook: A Systematic Study of Heavy Quark-Medium Interaction • Within the same framework, calculate RAA and v2 of heavy quark, heavy meson and heavy flavor decay electron • Systematically examine the model and parameter dependence of these observables, e.g., how the final state spectra are affected by medium geometry and flow, and relative contribution from charm vs. bottom quarks, etc. (arXiv:1205.2396) • Expected to be more directly compared to data from RHIC and LHC

15. Medium Geometry vs. Flow Effect • Both geometric asymmetry and collective flow generate positive v2 • Decouple the influence of QGP collective flow on heavy quark motion by solving Langevin equation in the global c.m. frame • Medium geometry dominates the high pT region, while the collective flow has a significant impact in the low pT region

16. Glauber vs. CGC Initial Condition of Medium • KLN-CGC model exhibits a larger eccentricity of the medium • No apparent difference in RAA, but significant larger v2 from KLN-CGC initialization

17. Charm vs. Bottom Contribution to Electron Spectrum • Uncertainty still exists in relative normalization of charm and bottom quark production from pQCD calculation • Choose two mixtures with b/c ratio around 1% in our simulation • Non-photonic electron spectrum follow c-decay electron behavior at low pT, but b-decay at high pT • v2 behavior varies with coupling strength and cannot be resolved by current experimental data

18. Outlook We will further study: • Heavy quark energy loss contributed by gluon radiation • Anomalous transport due to the strong chromo-electromagnectic field in the pre-equilibrium stage after heavy-ion collisions

19. Thank you!