the heavy quark potential and jet quenching parameter in a super yang-mills plasma
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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. Outline. - PowerPoint PPT PresentationTRANSCRIPT
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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
4
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
5
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.)
6
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
7
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
9
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
10
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
11
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
12
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
13
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:
14
, 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
15
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
17
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
18
20
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.
20
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
21
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
23
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.