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The heavy quark potential and jet quenching parameter in a Super Yang-Mills Plasma

Ziqiang Zhang

Huazhong Normal University

Zhang,Hou, Ren,Yin JHEP1107:035(2011)Zhang,Hou, Ren, [arxiv1210.5187]

HPT 2012, Wuhan

2

Outline

Motivations AdS/CFT correspondence Heavy quark potential and jet quenching

parameter Summary and discussion

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Motivations

Many interesting phenomena in QCD lie in the stronglycoupled region

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Lattice QCD: a first-principle computation.

However, there are technical difficulties in thecomputations if the system has

1.Finite baryon chemical potential2.Real time dynamics…

Maldacena conjecture: Maldacena, Witten

(x)])0,([

4

)2

1 tension(string

1

bulk in the theory string IIB Type boundary on the YM SUSY 4

0string

)()(

22

04

xZe

gN

gN

N

xOxxd

sc

YMc

actionty supergravi classical][

|)]()0,([

and limit In the

sugra

)()0,(][

0string 0

sugra

I

exxZ

N

xxI

c

‘t Hooft coupling

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QCD versus N=4 Super Yang-Mills from gravity dual

QCD Super YM

3 >>1

t’Hooft coupling 5.5-18.8 >>1

Quarks Fundamental Adjoint

Conformal symmetry NoYes at zero T

No at nonzero T

Supersymmetry NoYes at zero T

No at nonzero T

cN

Maldacena conjecture (cont.)

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AdS/CFT applied to RHIC physics

Viscosity ratio, /s. Thermodynamics. Jet quenching

Photon production Friction Heavy quarkonium Hardron spectrum (ADS/QCD)

)0(

4

3ss

Liu, Rajagopal and Wiederman

4

1

s Policastro, Son and Starinet

Gubser

32

3

4

54

3

ˆ Tq

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The gravity dual of a Wilson loop at large and large cN

][min)(tr CSeCW

C

xAdxi

PeCW)(

)(

the min.area of string world

sheet in the

Heavy quark potential

Heavy quark potential probes confinement

hadronic phase and meson melting in plasma

line] single[2-lines] parallel[),( minmin SSTTrF t

x1

z

t

z

5AdS

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Jet quenching parameter

2

[ ] exp( )4 2

A q L LW C

Jet quenching parameter describes the energy-loss of a jet of fast moving heavy quarks in QGP for TL<<1

Nestor Armesto ,et, al, JHEP 0609 (2006) 039

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The type B superstring N=4 SYMⅡ

Wilson loop expectationThe path integral of the string-sigma action

Leading order Classical limit

Sub-leading orderOne loop correction

Strong coupling expansion

Semi-classical expansion

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Heavy quark potential leading order from AdS/CFT

S.J.Rey , Nucl.Phys.B 527,171(1998)

where g0(rT) is a monotonic decreasing function corresponds to the leading order

Maldacena PRL.80, (1998) 4859

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3/2

3

3( )4

5( )4

q T

Jet quenching leading order from AdS/CFT

Liu, Rajagopal & Wiedemann, PRL,97,182301(2006)

Dipole amplitude: two parallel Wilson lines in the light cone:

1x

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Leading orders are strictly valid when ,

3CN

That is why we compute their next order corrections!

cN

Finite corrections may be essential for more precise theoretical predictions.

Real QCD, 5.5 6

Strong coupling expansion

Semi-classical expansion

[ ]ln [ ] , 0 ... [ ]eff

b CW C i S X S C

X = the solution of the classical equation of motion;

b[C] comes from the fluctuation of the string world sheet around X

,

Next order corrections

Formulation:

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, 0 X X X g g g

...)()()0,(),( )2()2( FB SXSXSXSBosonic and fermionic fluctuations decouple.

ZeCW XiS )0,(][ FB ZZZ

Formulation:

55in action gsuperstrin the),(

2

1SAdSXS

action Goto-Nambu the toequivalent is and

string bosonic a ofaction Polyakov2

1)0,( 2

XX

GggdXS

Quadratic expansion in

Metsaev and Tseytlin

g and ,X

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M. Cvetic,et,al. Nucl. Phys. B 573,149 (2000)55Schwarzschid AdS S

)(det2

1

3

8det

4

11det

4

11-det

22

5)2(22

3

)2(22)2(22

R

RR

ZZZ FB

)()det2det(-24det

4

11det

4

11-det

22

52)2(22

1

)2(22)2(22

R

RR

Z

Partition function at finite T with fluctuation underlying the heavy quark potential

Straight line：

Parallel lines：

Hou, Liu, Ren, PRD80,2009

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The other A refer to the correspondence operators too

The one loop effective action

[ ,0] lneffS S X i Z

Partition function at finite T with fluctuation underlying the jet quenching parameter.

Zhang,Hou, Ren, arxiv1210.5187

Z=

where

I.M.Gelfand, et, al, J.Math.Phys.,1,48(1960)2 2 2

1 1 1

det [ , ]

det [ , ]

H u v

H u v

( , )i iu v are 2 independent solutions 。

( ) ( ) ( ) ( )[ , ]

[ , ]i i i i

i ii i

u a v b u b v au v

W u v

Reduce evaluating functional determinants to a set of 2nd order ordinary differential equations, which are solved numerically

Wronskian determinant

Computing of the determinant ratio

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Heavy quark potential including the next order correction

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Zhang,Hou, Ren,Yin JHEP1107:03 （ 2011）

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Heavy quark potential discussion

1.In the weak coupling, the heavy quark potential at T>0 is of Yukawa type, that is non-vanishing for arbitrarily large r. 2.To the leading order of strong coupling, the magnitude of the potential drops to zero at a finite r.

3. The term decreases the screening radius.

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Zhang,Hou, Ren,Yin JHEP1107:03 （ 2011）

Chu,Hou, Ren,JHEP0908,(2009)

3/2

3 1/2 1

3( )4 [1 1.97 ( )]

5( )4

q T O

Jet quenching parameter including the next order correction

=3

0

/2

3

3( )4

5( )4

q T

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Zhang,Hou, Ren, arxiv1210.5187

Jet quenching parameter discussion

2.The negative sign of sub-leading order is consistent with a monotonic behavior from strong coupling to weak coupling.

1.Sub-leading order gives rise to 32% reduction of from the leading order amount in this case.

Take 6

2

0

3/

3 2

3( )4 4.48 /

5( )4

T GeV fmq

q

22

2exp 1 15 /q GeV fm

Nestor Armesto ,et, al, JHEP 0609 (2006) 039

13,

2c SYMN

Choose T=300MeV

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Summary and discussion

AdS/CFT provides a useful way to address the physics

at strong coupling .

The partition function of Wilson loop with fluctuations in strongly coupling N=4 SYM plasma are derived.

We computed the jet quenching parameter and heavy quark potential up to sub-leading orders.

The applicability of these AdS/QCD results demands phenomenological work to explain them in a way which can be translated to real QCD.

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Thanks