Probing QGP by Heavy FlavorsProbing QGP by Heavy Flavors

Variable Energy Cyclotron Center, Kolkata-700064..

Santosh Kumar DasTheoretical Physics Division

Outline of my talk…………..

Introduction

Formalism

Heavy flavor as a probe of QGP.

Summary and outlook.

Gay D. Moore and D. Teaney, PRC, 71,064904(2005)

Heavy Quark (HQ)

Light Quark (LQ)

Gluon

τ HQ > τLQ , τ HQ ~ (M/T) τLQ

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.

Water Light quarks and gluons

Heavy quarksPollen 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.

τLQ < τ < τHQτLQ < 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 Boltzmann Kinetic equation

colt

fpxE

Pt tpxf

,,.F

pfkpkpfkkpkdt

ftpR

col

,, 3

fPP

kkfp

kpfkpkpfkkpji

ji

2

2

1.)(,

colt

ftpf

t

,

kqkpqppqvqfqd

gkp ,,,3

3

)()2(

),(

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

fpBp

fpApt

fij

ji

i

i3

i k)k(pkdA ,

ji3

ij kk)k(pkdB ,

Where we have defined the kernels ,

Landau Kinetic equation. Landau Kinetic equation.

→ Drag Coefficient

→ Diffusion Coefficient

kqkpqppqvqfqd

gkp ,,,3

3

)()2(

),(

Non -equilibrium Equilibriumdistribution Function distribution

Function

Landau Kinetic Equation Fokker Planck Equation

reduced

replaced

fpBp

fpApt

fij

ji

i

For Collision Process the Ai and Bij can be calculated as following :

ii

cpqqpi ppppqfqpqpM

E

pd

E

qd

E

qd

EA

)(21

2222222

1 442

3

3

3

3

3

3

jiij ppppB )(2

1

Elastic processes

gcgc

qcqc

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

2

022

0 Fkkdd

dnkddkn f

gg

The average energy loss per collision

220

2

2

k

kF

kf /cosh

Where→ dead cone suppression factor

and → the formation time

Yu.L. Dokshitzer and D.E.Kharzeev, PLB,519(2001)199

Em /0

ω → the energy of the emitted gluon.

Radiative Energy Loss

SKD, J. Alam and P. Mohanty ,PRC, 82,014908,2010

2222

2222

2222

2

22 )(

)(

)( D

DsA

D

sAg

mqkks

mqqC

mqkk

qC

dkd

dn

(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. AlamPRD,83,114011,2011

.

raddX

dE

The radiative energy loss per unit length for heavy quark is

Where

= 1/ interaction rate ( inverse of interaction time).

pdx

dE

RadColleff

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.

TmD

Drag and Diffusion @LHC energy

At High temperature radiative loss dominate over collisional loss

SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

Drag and Diffusion @LHC energy

At High temperature radiative loss dominate over collisional loss

SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

Drag and diffusion @ finite baryonic chemical potentialDrag and diffusion @ finite baryonic chemical potential

For the process cg cg

Temperature

Drag (γ) Diffusion (D)

140 MeV 8.42 * 10 -3 fm -1 1.42 * 10 -3 GeV2 fm -1

190 MeV 1.86 * 10-2 fm-1 4.31 * 10-2 GeV2fm-1

SKD, J. Alam, P. Mohanty and B. Sinha PRC,81,044912(2010)

Probability that a charm /bottom quark is produced at r is parametrized as:

where

cossin 222 rrRLCharm/bottom quark propagates a length:

Geometric average of drag coefficients:

R

r

φ

φrcos φ

rsin

φ

L

222 RrsinrcosL

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

)(),0( 0 pfptf

00003 ,,, pfpptGpdtpf

0,, pptG

eXBDbc )()( C. Petersion et al PRD,27,105(1983)

SKD, J. Alam and P. MohantyPRC,80,054916(2009)

Nuclear Suppression Factor (RAA) :

pp

Tcoll

AuAu

TAA

dypddN

N

dypddN

R

2

2

A direct measure of the energy loss

If RAA = 1 No medium

If RAA< 1 Medium

RAA @ highest RHIC energyRAA @ highest RHIC energy

SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

RAA @ Low Energy RHIC(Finite baryonic chemical potential )RAA @ Low Energy RHIC(Finite baryonic chemical potential )

√SNN (GeV) dN/dy Ti (MeV) μq (GeV)

39 617 240 62

27 592 199 70

17.3 574 198 100

7.7 561 197 165

Radiative loss is

neglected

SKD, J. Alam, P. Mohanty and B. Sinha PRC,81,044912(2010)

RAA @ LHC EnergyRAA @ LHC Energy

SKD, J. Alam and P. Mohanty PRC, 82,014908,2010

ddydpdN

d

ddydpdN

d

pv

T

TT

HF

)2cos(

)2cos()(2

.....)2cos(2)cos(212 21

vvdydpp

dN

dyddpp

dN

TTTT

Overall shift

1+2v2

Elliptic Flow :

Major axis = 1+2v2

Minor axis = 1-2v2

1-2

v2

Polar Plots :

1+2v1cosφ 1+2v2cos(2φ)px

pyy

x px

py

px

pyy

x

V2 @ highest RHIC energyV2 @ highest RHIC energy

SKD and J. Alam arXiv-1008.2643

v 2

V2 @ LHC and Low Energy RHIC V2 @ LHC and Low Energy RHIC

LHCLow Energy RHIC

Hadronic Phase

S. Ghosh, SKD ,S. Sarkar, J. AlamPhys Rev D(R) 84,011503,2011

DD

DKDK

DD

BB

BKBK

BB

D (

GeV

2/f

m)

SKD, S. Ghosh ,S. Sarkar, J. Alam

arXiv:1109.3359 [hep-ph]

Summary & Outlook ……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.

RAA and V2 @ RHIC Energy RAA and V2 @ RHIC Energy

Where and → the energy fraction of the final state quark and anti-quark.sEx q /21 sEx q /22

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

qfl

22

2

2

2

4

1~

1

zC

dzd

d sF 212 xxz

s

m2

S. Klein, Rev. Mod. Phys 71 (1999)1501

where

and

2

222

2

2

1s

mq

dkd

dndkd

dn

R D

GB

g

g

c

218Tss

TTm sD 4

dtd

dt

dtd

dttqq

22

ETMss HFHF 62 Das and Alam

PRD, 82,051502(R),2010

dtt

dtt

vyl

vlx

y

x

p

p

0

0

)(~

)(~

exp

exp