Thermalization of Charm Quarks in Infinite and Finite QGP Matter

Shanshan Cao Duke University

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

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?

c

q q

g

c

medium

θ

Methodology – Energy Loss• Two ways for heavy quarks to lose energy:

Collision Radiation

• Radiation is suppressed by the “dead cone effect”: (suppression of small angle radiation)

• Bremsstrahlung dominates only for ultrarelativistic situation: (in our calculation )

Methodology – Langevin Approach

Langevin Equation:

Fluctuation:

Fluctuation-dissipation:

Diffusion Coefficient:

• Heavy quark inside the medium: Brownian motion

• Description: Langevin equation

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

Methodology – Thermalization CriterionEnergy Spectrum:

Momentum Spectrum:

(check the isotropy of the momentum space)

Consider a Blue Shift:

Linear relation appears after 10 fm/c. Slope keeps varying until 30 fm/c.

No linear relation between 2-8 fm/c

Energy spectrum

Results for Static MediumT=300MeV, D(2πT)=6

pi=5GeV z

Tmedium=300MeV, D(2πT)=6pi=5GeV (in z)

• A comparison of temperature parameters extracted from different spectra.

Equilibrium criterion:Temperature parameters extracted from different ways merge and approach that of the medium.

Results for Static Medium

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

Free-streaming outside the medium

After freeze-out: free-streaming

• 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 rangeT-Δt T+Δt

QGP Medium

Results for the QGP Medium

For “reasonable” diffusion coefficient, heavy quarks may remain off-equilibrium during the QGP lifetime.

Close to full equilibriumNot fully thermalized above Tc

Phys. Rev. C84, 064902 (2011)

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 (v2 and RAA), but this does not imply thermalization: they remain off-equilibrium during the QGP lifetime.

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

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

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

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

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

Thank you!