Probing QGP by Heavy Flavor

1. Probing QGP by Heavy Flavor Santosh Kumar Das Variable Energy Cyclotron Center, Kolkata-700064. The 3rd Asian Triangle Heavy Ion Conference, Wuhan, China, October 18 – 20, 2010

2. Outline of my talk………….. • Introduction • Non-Equilibrium processes • Heavy flavors suppression and elliptic flow • Summary and outlook.

3. Introduction At very high temperature and density hadrons melt to a new phase of matter for which the word “Quark-Gluon-Plasma” was coined. • To be able to talk about the thermodynamic phase, phase transitions , temperature and so on, the system under consideration must • consist of large number of particle • it needs to reach local equilibrium ,

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

5. 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. Water Light quarks and gluons Pollen grain Heavy quarks τLQ <τ< τHQ This time interval can be treated within the scope of Fokker Planck Equation. • Why Heavy quark ?? • It does not decide the bulk properties of the system rather act as a probe to extract information about the system. • Early Production

6. Boltzmann Kinetic equation • The plasma is uniform ,i.e., • the distribution function is • independent of x. • Without application of any • external force, i.e F=0 ( The interaction with other heavy quarks are neglected. ) is rate of collisions which change the momentum of the charmed quark from p to p-k

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

8. For Collision Process the Aiand Bij can be calculated as following : Elastic processes • Among these diagram only (a) and (d) contain • divergence in the t-channel. • We have introduce a mass into the internal gluon • propagator in the t-channel-exchange diagrams, • to shield the infrared divergence. B. Svetitsky PRD 37(1987)2484

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

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

11. Drag and Difussion @LHC energy Das, Alam and Mohanty ,PRC, 82,014908,2010 At High temperature radiative loss dominate over collisional loss

12. Drag and diffusion @ finite baryonic chemical potential For the process cg  cg Das, Alam, Mohanty and Sinha PRC,81,044912(2010)

13. With the initial condition We solve the initial-value problem . The full solution with an arbitrary initial condition follows as Where is greens function for the Fokker-Planck equation Das, Alam and Mohanty,PRC,80,054916,2009

14. RAA and V2 @ highest RHIC energy Simultaneously reproduction of both RAA and v2 for the same set of in put within pQCD formalism for the highest RHIC energy Das, Alam and Mohanty ,PRC, 82,014908,2010 Das and Alam, arXiv-1008.2643

15. RAA @ Low Energy RHIC(Finite baryonic chemical potential ) Radiative loss is neglected Das, Alam, Mohanty and Sinha PRC,81,044912(2010)

16. RAA @ LHC Energy

17. V2 @ LHC and Low Energy RHIC Low Energy RHIC LHC

18. 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 both partonic and hadronic 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.

19. Thank You . . . .

20. RAA and V2 @ RHIC Energy

21. I) LPM effect : Suppression of bremsstrahlung and pair production. • Formation length ( ) : The distance over which interaction is spread out • 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 freduce  Radiation drops proportional • (II) Dead cone Effect :Suppression of radiation due to mass S. Klein, Rev. Mod. Phys 71 (1999)1501 and where 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)