Probing QGP by Heavy Flavors

Probing QGP by Heavy Flavors Santosh Kumar Das Theoretical Physics Division Variable Energy Cyclotron Center, Kolkata-700064.

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

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

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 ?? • Early Production • It does not decide the bulk properties of the system rather act as a probe to extract information about the system.

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 is rate of collisions which change the momentum of the charmed quark from p to p-k

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

For Collision Process the Aiand Bij 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

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. The average energy loss per collision Where →dead cone suppression factor SKD, J. Alam and P. Mohanty ,PRC, 82,014908,2010 Yu.L. Dokshitzer and D.E.Kharzeev, PLB,519(2001)199 ω → the energy of the emitted gluon. Correction term (Gunion and Bertsch results) → the formation time and SKD and J. Alam PRD, 82,051502(R),2010 SKD and J. Alam PRD,83,114011,2011

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 ] The drag acting on the heavy quark 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. With this inputs we have solved the Fokker-Planks equation

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

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

rcos φ L φ rsin φ r φ R 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:

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 SKD, J. Alam and P. Mohanty PRC,80,054916(2009) C. Petersion et al PRD,27,105(1983)

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

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

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

RAA @ LHC Energy SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

Elliptic Flow : Polar Plots : 1+2v1cosφ 1+2v2cos(2φ) 1-2v2 1+2v2 Major axis = 1+2v2 Minor axis = 1-2v2 Overall shift

V2 @ highest RHIC energy v2 SKD and J. Alam arXiv-1008.2643

V2 @ LHC and Low Energy RHIC Low Energy RHIC LHC

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

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.

Thank You . . . .

RAA and V2 @ RHIC Energy

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)

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

Probing QGP by Heavy Flavors