1. Probing QGP by Heavy Flavors Santosh Kumar Das Theoretical Physics Division

2. Outline of my talk…………..  Introduction  Formalism  Heavy flavor as a probe of QGP.  Summary and outlook.

3. Gay D. Moore and D. Teaney, PRC, 71,064904(2005) Heavy Quark (HQ) Light Quark (LQ) Gluon τ HQ > τ LQ, τ HQ ~ (M/T) τ LQ LQ thermalizes faster than HQ The propagation of heavy quarks through the QGP can be treated as interactions between equilibrium and non equilibrium degrees of freedom. Introduction The FP equation provides an appropriate framework for such processes.

4. Water Light quarks and gluons Heavy quarks Pollen grain Fokker-Planck equation is use to study the evolution of charm and bottom quark. Just like evolution of pollen grain on the background of water molecule, where water molecule are in equilibrium and the pollen grains executes Brownian motion in the water. Fokker-Planck equation is use to study the evolution of charm and bottom quark. Just like evolution of pollen grain on the background of water molecule, where water molecule are in equilibrium and the pollen grains executes Brownian motion in the water. τ LQ < τ < τ HQ This time interval can be treated within the scope of Fokker Planck Equation. Why Heavy quark ??  Early Production  It does not decide the bulk properties of the system rather act as a probe to extract information about the system.

5. Boltzmann Kinetic equation is rate of collisions which change the momentum of the charmed quark from p to p-k  The plasma is uniform,i.e., the distribution function is independent of x.  Without application of any external force, i.e F=0

6. Where we have defined the kernels, Landau Kinetic equation. → Drag Coefficient → Diffusion Coefficient Non -equilibrium Equilibrium distribution Function Landau Kinetic Equation Fokker Planck Equation reduced replaced

7. For Collision Process the A i and B ij can be calculated as following : Elastic processes We have introduce a mass into the internal gluon propagator in the t and u-channel-exchange diagrams, to shield the infrared divergence. B. Svetitsky PRD 37(1987)2484

8. The average energy loss per collision Where → dead cone suppression factor and → the formation time Yu.L. Dokshitzer and D.E.Kharzeev, PLB,519(2001)199 ω → the energy of the emitted gluon. Radiative Energy Loss SKD, J. Alam and P. Mohanty,PRC, 82,014908,2010 (Gunion and Bertsch results)Correction term Source to the heavy quark radiative processes are cg → cgg and cq → cqg SKD and J. Alam PRD, 82,051502(R),2010 But we start with the common mass less process like gg → ggg, then we will generalized it for massive. SKD and J. Alam PRD,83,114011,2011

9. The radiative energy loss per unit length for heavy quark is Where  = 1/   interaction rate ( inverse of interaction time). The drag acting on the heavy quark [Using Einstein's fluctuation-dissipation theorem ] With this inputs we have solved the Fokker-Planks equation Radiative Energy Loss (Contd.) Collisional and radiative process are not independent from each other, since collision contribution is less compare to the radiative, we take it as a perturbation to the radiative process.

10. Drag and Diffusion @LHC energy At High temperature radiative loss dominate over collisional loss SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

11. Drag and Diffusion @LHC energy At High temperature radiative loss dominate over collisional loss SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

12. Drag and diffusion @ finite baryonic chemical potential For the process cg  cg Temperature Drag ( γ ) Diffusion (D) 140 MeV8.42 * 10 -3 fm -1 1.42 * 10 -3 GeV 2 fm -1 190 MeV1.86 * 10 -2 fm -1 4.31 * 10 -2 GeV 2 fm -1 SKD, J. Alam, P. Mohanty and B. Sinha PRC,81,044912(2010)

13. Probability that a charm /bottom quark is produced at r is parametrized as: where Charm/bottom quark propagates a length: Geometric average of drag coefficients: R r φ φ rcos φ rsin φ L

14. With the initial condition We solve the initial-value problem. The full solution with an arbitrary initial condition follows as Where is the Greens function for the Fokker-Planck equation C. Petersion et al PRD,27,105(1983) SKD, J. Alam and P. Mohanty PRC,80,054916(2009)

15. Nuclear Suppression Factor (R AA ) : A direct measure of the energy loss If R AA = 1 No medium If R AA < 1 Medium

16. R AA @ highest RHIC energy SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

17. R AA @ Low Energy RHIC(Finite baryonic chemical potential ) √S NN (GeV) dN/dyT i (MeV)μ q (GeV) 39 61724062 27 59219970 17.3 574198100 7.7 561197165 Radiative loss is neglected SKD, J. Alam, P. Mohanty and B. Sinha PRC,81,044912(2010)

18. R AA @ LHC Energy SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

19. Overall shift 1+2v 2 Elliptic Flow : Major axis = 1+2v 2 Minor axis = 1-2v 2 1-2v 2 Polar Plots : 1+2v 1 cosφ1+2v 2 cos(2φ)

20. V2 @ highest RHIC energy SKD and J. Alam arXiv-1008.2643 v2v2

21. V 2 @ LHC and Low Energy RHIC LHC Low Energy RHIC

22. Hadronic Phase S. Ghosh, SKD,S. Sarkar, J. Alam Phys Rev D(R) 84,011503,2011 D (GeV2/fm ) SKD, S. Ghosh,S. Sarkar, J. Alam arXiv:1109.3359 [hep-ph]

23. Summary & Outlook …… We have calculated the drag and diffusion coefficients for both radiative and collisional energy loss with finite chemical potential. Using drag, diffusion and initial distribution as input, we have solved the FP Equation. Nuclear modification factor and elliptic flow has been calculated using the FP solution for partonic medium. The effect of non zero baryonic chemical potential on nuclear modification factor is highlighted. Comparison of the experimental data with the results is satisfactory. Prediction for both LHC and low energy RHIC has been given.

25. RAA and V 2 @ RHIC Energy

26. Where and → the energy fraction of the final state quark and anti-quark. Radiation from heavy quarks suppress in the cone from θ = 0 (minima) to θ=2 √γ (maxima) I) LPM effect : Suppression of bremsstrahlung and pair production. Formation length ( ) : The distance over which interaction is spread out 1)It is the distance required for the final state particles to separate enough that they act as separate particles. 2) It is also the distance over which the amplitude from several interactions can add coherently to the total cross section. As q ┴ increase  l f reduce  Radiation drops proportional (II) Dead cone Effect : Suppression of radiation due to mass S. Klein, Rev. Mod. Phys 71 (1999)1501 where and

27. Das and Alam PRD, 82,051502(R),2010