(I): Matter in Extremis
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Transcript of (I): Matter in Extremis
威海 2007
Xin-Nian Wang - LBNL 1
(I): Matter in Extremis
Lawrence Berkeley National Laboratory
Xin-Nian Wang
高能物理前沿暑期论坛威海 July 31 – August 7, 2006
QCD and Heavy Ion Physics
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Phases of Matter
火 水 土(gas) (liquid) (solid)
Bose-Einstein condensate, fermionic condensate, superfluids, supersolids, paramagnetic,
ferromagnetic, liquid crystals, …
Quark-gluon Plasma (QGP)
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Quark-gluon Plasma (QGP)
Discovery of asymptotic freedom of QCD: Gross, Wilczek and Politzer (1973)
Weakly interacting quarks at high density and temperature
First concept of QGP in early universe, neutron star coreand change of the vacuum structure at high temperature
Lee and Wick,(1974); Collins and Perry (1975);Baym and Chin (1976)
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QCD Theory
• SU(3) gauge symmetry (non-Abelian)• Asymptotic freedom at short distance
• Confinement at long distance
• Scale invariance and anomaly• Chiral symmetry and its spontaneous
breaking• Goldstone boson and chiral condensate
• UA(1) symmetry and anomaly
22 3
2 2
4 /(11 )( )
ln( / )f
sQCD
nQ
Q
,1
1( )
2 4
fna
QCD a a af a
L i gA m F F
0
0F F
0F F
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Scale Anomaly and invariance at high T
( ) 3 0T x P
( ) ( )scaleJ x x T x
( ) ( )12s
ac l
sa aeJ x T x F F
BFF aas 4
12
2 40.015 GeVs F
Scale anomaly Break scale invariance
2s
Pc
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EOS in Lattice QCD
MeVTc 817031.7 0.3 /c GeV fm
F. Karsch ‘2001 SB limit
25%
Quasi-particle with dispersion given by HTL resummation
Blaizot, Iancu, Rebhan ‘2001
Super Yang-Mills 2 3/ 20
3 15/ 1 (3)(2 )
4 8SYM YMS S g N
Guber, Klebanov, Tseytlin ‘1998
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Confinement-deconfinement
Karsch, Laermann and Peikert 2001
( ) + V r rr
SU(3) non-Abelian gauge interaction confinement
Heavy quark potential:
J/ suppression
Q Q
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QCD Phase Diagram
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Strong coupling near Tc
( ) 312
asaF FT x P
2s
Pc
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Resonances in QGP above Tc?
J/ survives up to T=1.6Tc
Hatsuda et al
Could there be many other resonances? Shuryak & Zahed ‘04
dpAK
xdeJxJpD xpi
),(),(
)0,0(),(T),( 3
Maximum entropy method (MEM)
Hatsuda et al, 2004
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Cerenkov gluon radiation in near Tc?
Koch, Majumder & XNW’05
1cos
( )c
p
Dielectric constant
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Chiral Symmetry
Spontaneously broken:
0
Goldstone bosons (,K,)
(3) (3) (3)L RSU SU SU
F. Karsch ‘2001
MeVTc 8170
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QCD Phase Diagram
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Quark Matter in Neutron Stars
Spin-down
Spin-up
N. Glendenning ‘2000
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Heavy-ion Collisions
RHIC BNL
Au+Au up to 200 GeV/n
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Medium Response
41( ) (0) ( )
4iq x em emW q d xe A j j x A
1( )BF xqp
qxB
2
2
Dynamic System:
Hard probes: Medium response to strong interactionJet quenching
EM emission: Medium response to EM interaction
production, J/ suppression
Soft hadrons: Bulk properties of medium, collective behavior
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Energy Density in Heavy-ion Collisions
20
1energy desnity: TdE
dy R
540 GeVTdE
dy3
0( 1.0 fm/ ) 4.5 GeV/fmc
Above the critical density from lattice QCD
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Chemical equilibrium at freeze-out
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Non-central Heavy Ion Collisions
x
z
y
EZDC
ET
Centrality of the collisions
Impact Parameter (b)
EZDC
ET
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Elliptic Flow
Ideal Hydro calculation
2cos2 v
Pressure gradient anisotropy
)2cos2cos1( 210
vvNd
dNch
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A perfect fluid?
1 fm/cth
Constraint on thermalization time
Heinz ‘04
/ 0.1s
Constraint on shear viscosity:
Teaney ‘03
H2O : / 10s
0T
Ideal Hydrodynamic
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Shear viscosity
3
3 0( ) ( , )
(2 ) 2
d kT x k k f x k
k
( )P u u Pg
2( )
3ij i j j i ij k k ij k ku u u u
0
1lim ( , ), (0,0)
2i t
xy xydtdx e T t x T
Kubo relation
Energy-momentum tensor in microscopic picture
( , ) ([ ])u f x k C f Transport:
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?
Kapusta, Csernai & McLerran
Viscosity of QCD Matter
• Hadron gas at low temperature:
– Chiral perturbation theory:
• QGP at high temperature:
– Perturbative QCD2
0.022/
log(1/ )S S
s
Arnold,
Moore,Yaffe
4
4
15
16
f
s T
Prakash et al
Chen & Nakano
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OH2
Phase transition or strong coupling?
1/
4s
Small viscosity in SYM Policastro, Son & Starinets ‘02
Is it possible to measure /s from experiments?
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Quark Coalescence
n = number of constituent quarks
Rec. ModelsHwa & YangFries, Muller, BassKo et al
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Bifurcation of Spectra
Constituent quark recombination promote baryon production
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Shock Wave or Cherenkov Radiation
PHENIX
1cos
( )c
p
cos /M sc c
Velocity of sound:Index of refraction
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Orbital angular momentum
x
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Quark Polarization
4 ( )qq
pP
E E m
20 12 2 2
ˆ( )4 ( ) ( )
( )T
T s T TT T T q
d d d p x nC K x K x
d x d x d x E E m
Polarized cross section:xT
p
n
pf
Zuo-tang Liang & XNW PRL 94(2005)
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STAR Preliminary
Au+Au @ 200GeV (20-70%)
Au+Au @ 62GeV (0-80%)
Tp (GeV/c)
P
STAR Preliminary
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Summary
• Broken symmetries and their restoration at high T accompanied by phase transitions
• Intriguing properties of QGP near the critical point
• Study of soft hadrons from RHIC experiments:– High initial energy density above Tc reached– Chemical equilibrium at freeze-out– Strong collective flow indicating fluid property with low viscosity
• Partonic degree of freedom before hadronization
• Many other effects such a global quark polarization provide additional information
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(II): Hard Probes of Dense Matter
Lawrence Berkeley National Laboratory
Xin-Nian Wang
高能物理前沿暑期论坛
威海 July 31 – August 7, 2006
QCD and Heavy Ion Physics
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Xin-Nian Wang - LBNL 35
Medium Response
41( ) (0) ( )
4iq x em emW q d xe A j j x A
1( )BF xqp
qxB
2
2
Dynamic System:
Hard probes: Medium response to strong interactionJet quenching
EM emission: Medium response to EM interaction
Soft hadrons: Bulk properties of medium, collective behavior
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Jets in heavy-ion collisions
q
q
leadingparticle
leading particle
pQCD
Bjorken’82, XNW & Gyulassy’92
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Jet Tomography
Calibrated source
Absorptionproperties
Compute assisted
Correction
pQCDp+p, p+A
dE/dx Expansion dynamics QGP
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LPM interference in EM Radiation
EM field carried by afast moving electronv
EM Radiation by scattering:Interference between initialand final state radiation
Initial rad.
Final rad.
22 2
2
( )
4
( )i f
fi
k k v
k
d I e
d
k
vv
k
d
v
k
(
22
1 )2
21
( ) ( )
4i ii i
i i i
i t k rk k v k k vd I e
d d ke
v k v
Landau-Pomeranchuck-Midgal interference(1 cos ) /i i fL L
2
2f
Formation time
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Radiation in QCD: Colors matter
pi pf
ka
c
k
pi pf
pfpi
k
Gluon multiple scattering (BDMP’96)
accaS TTTTk
kR
2
)1( 2
caS TTkq
kqR ,
)(
)(22
)2(
dy
dN
y0
QCD
dy
dN
y0
QED
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Modified Jet Fragmentation
(Guo & XNW’00)
0 ( ) ( , ),h a h aD z D z E
Suppression of leading particles (Huang, XNW’96)
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Parton energy loss: A twisted story
e-
4
( , , ) () )( q h h
D
qh h twist
H x p qdW dW
dxd
f xz d
D zz
( ), () ( , ) q hq
hH x D zx px qfd
2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q Modified frag. function
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Modified fragmentation function
22 2
40
( , )21( ) ( ) (virtual)
2 1 ( )
Aqg Lh s sT
q h q h AT c A
T x xzdz z dD z D C g h
z z z N q x
1 2
_2 1
1 2 2 1( ) ( )
(1
)2
( , ) (0) ( ) ( ) ( )2 2
1 1 ( ) ( )
B L T
L L
i x x p y ix p y y
ix p y ix p
L
y y
Aqg
dyT x x dy dy A F y F y y Ae
e y y ye
2 1 22
40 0
1 (1 ) ( , )
( )
Q
s
Aqg L
s Aq
TT
E zd dz
E
T x x
f x
Quark energy loss
2 ( , )2
( )
Aqg B Ts
Tc A B
T x xq
N q x
pT broadening (Guo’98)
Guo & XNW(2000)
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Detailed balance: thermal absorption
Thermal absorption important at lower E
Enke Wang & XNW, PRL87(2001)
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Single hadron suppression
NNAB
ABAB
NR
binary
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Centrality Dependence
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Dihadron suppression
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Jet quenching in hot and cold nuclear matter
0.5 GeV/fmdE
dx
in Au nuclei
e-Enke Wang & XNW, PRL 89 (2002)
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Suppression of away-side jet
0
13.8 3.9 GeV/fmdE
dx
cold matter
0.5 GeV/fmdE
dx
0 0.2 fm/c
Initial Density about 30 times of that in a Cold Au Nucleus
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Cones, Ridges & the Medium
Au+Au 0-10%preliminary
STAR, PRL 93 (2004) 252301
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A Pedestrian Question:
What jet quenching really measures?
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DIS: an Analogye-
x=Q2/2EmN~ f(x,Q2)
Q2
1( , ) (0) ( )
2 2ixp ydy
f x Q e A y A
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pT broadening and gluon distribution
2 22
ˆ qdq dq q
dq
2 2 2
2 2 ( ) ( , )
1 (2 ) 2R T T
Tc
g C d q qdx x x q
N Ep
4 22 4
4 2
12 (( ) ) (0) ( )
2 (2 ) 1iqR
c
d q g Ck q d e p A A p
s N
E
pq
21( , ) (0) ( , )
2T Tixp i i
T T i T
dx q d e p F F p
p
q ξξ ξ
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Gluon distribution in hot medium
( , )
( )(1 ) [1 cos( )](0) ( )T Lix p i
Aqg L p
LAq
x F Fe e xT x x
dyx
pf
yd
3
3( )
(2 ) 2
d pO f p p O p
p
[ ( ) ( ) [1 co( s( )( ) )] ]T T L LT L Tx G x x x G xd x yyy x p
1 2
_2 1
1 2 2 1( ) ( )
(1
)2
( , ) (0) ( ) ( ) ( )2 2
1 1 ( ) ( )
B L T
L L
i x x p y ix p y y
ix p y ix p
L
y y
Aqg
dyT x x dy dy A F y F y y Ae
e y y ye
1( , ) (0) ( )
2 2ixp ydy
f x Q e A y A
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Energy loss and pT broadening
2 ( , )ˆ( ,0,
( ))
2A
qg B TsT A
c q B
T xq
xq dy
N f xE y
2 2
24
ˆ ˆ( ,0,1 (1 )
[1 cos( )]) ( ,2 2 (1 )
, )c s TT
TLq E y q E x y
N z ydy d dz
Ez z
2 1 22
40 0
1 ( ( , )
( )
1 )( )
Q
Radq gq s
Aqg
T
Ls A
qT
E zdz P z d dz
T x x
E f x
2ˆ( , , ) ( ) ( ( ) )s
L T L T Lc
q E x y y x x G x xN
Generalized jettransport parameter
Total pt broadening:
Total energy loss:
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A Theoretical Question:
What medium properties are imbedded in ?q̂
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Evolution of qhat
2 2 22
2 2ˆ( , ) ( ) ( , )
1 (2 ) 2R T T
Tc
g C d q qq E dx x x q
N Ep
High energy jet small x
Large momentum transfer large scale
22
4 ( )1
s AT T
c
Cx G x
N
2 22
2
( , ) 1( , )
ln(1/ ) ln 2
xG xxG x
x
(DLA)
k=E
p
q
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Gluon Saturation in QGP
Evolution growth of gluon distribution at small x
E
p
q
Nonlinear effect (gluon fusion) willtame the growth of gluon distribution
Gluon Saturation2
2
2
22( , ) min
( ))
41
1( ,s s
ss
c
cc
QxG x Q L
N QL
N
QGP density is much larger than in nuclei
Saturation sets in at larger x and Qs2 is larger
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E-dependence of qhatJ. Casalderrey-Solana and XNW, arXiv:0705.1352 [hep-ph].
Nontrivial length dependence of qhat
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q-hat and Shear Viscosity
trC sT
2 22 2 2
ˆ1 4 2
9tr T Ttr cm T
d qdq q
E dq T
39ˆ2
TC
s q
Majumder, Muller and XNW (hep-ph/0703082)
Shear viscosity 1/ 3C
This relation is strongly violated for strongly coupled mediumWhere /s does NOT reflect the transport of partons as quasi-particle
Jet quenching ˆ( ) q T ˆ( )q E
1
4s
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An Experimental Question:
How to measure ?q̂
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Single and Dihadron hadron suppression at RHIC
00
zT=pTass/pT
trig
Hanzhong Zhang, Owens, Enke Wang and XNW, PRL 98 (2007)
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Sensitivity to initial density
22
20 0ˆ 1 2 GeVAq /s = 0.1-0.2
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q-hat in a nucleus
2ˆ 0.01 GeV /Fq fm
e-
20ˆ 1.3 GeV / ( =1 fm)Fq fm
Enke Wang & XNW PRL 89, 162301(2002)
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Surface emission?
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Surface vs. Volume
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A roadmap for future jet study
Re-constructed jets open up a whole new world for jet quenching study
Reconstructed jets: Single inclusive jets, di-jets or -jets
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(1) Direct measurement of qhat
2 ˆ( , )T q Edy yq
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Utopia?
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Jet quenching study in China
• Enke Wang(王恩科 ), et al.: Detailed balance in parton energy loss (PRL 87, 2001)
• Enke Wang (王恩科 ), et al: Jet tomography of cold and hot matter (PRL 89, 2002)
• Benwei Zhang (张本威 ) & Enke Wang (王恩科 ), et al: Heavy quark energy loss (PRL 93, 2004)
• Hanzhong Zhang (张汉中 ) & Enke Wang (王恩科 ) et al: NLO study of single and dihadron spectra suppression (PRL 98, 2007)
• Benwei Zhang (张本威 ) et al: Review on jet quenching, nucl-th/0302077
With total 16 publications (in the last 8 years), this is one of my most productive collaborations in my career!
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Cherenkov radiation or shock wave
PHENIX
cos /M sc c
Velocity of sound:
1cos
( )c
p
Index of refraction
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Degrees of freedom in sQGP?
2 223 3 BS
BSS
BS B SC
S S
Quark-gluon plasma: s quark has both B and S B & S strongly correlated, CBS=1
Hadron gas:K meson has B=0 B-S correlation is more complicated
Koch, Majumder & Randrup ‘05
Bound state QGP or hadronic gas
Ideal quarks
Gavai & Gupta ‘05
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Other Important Developments
• Gluon Saturation in heavy nuclei at small x (parallel 4: Kharzeev; Gay Ducati)
• High baryon density physics at lower energies (parallel 4: Bravina)
• Microscopic picture of strongly interacting QGP (parallel 4: Levai)
• Elastic versus radiative energy loss
• Heavy quark energy loss & quarkonium suppression (parallel 4: Armesto)
• Hard probes at LHC (parallel 4: Lokhtin, Kodolova, Safarik)
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Outlook: an example
• Direct -tagged events:
E~Ejet
• Measure directly Dh/a(z)• Azimuthal anisotropy
jet
X.-N.W&HuangPRC55(97)3047
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Summary
• Heavy-ion collisions can test many properties of QCD– Deconfinement phase transition– Chiral symmetry restoration
• Current RHIC data indicate formation of strongly interacting QGP– High energy density 20 GeV/fm (t0=1 fm/c)
from jet quenching, dN/dy, radial flow– Elliptic flow early thermalization, low viscosity– Parton recombination partonic matter– J/ suppression deconfinement
• Microscopic picture of sQGP– Quasi-particle, bound states?
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UA(1) Anomaly
U(1) and UA(1) Symmetry:5, ii
AU e U e
(Classically) conserved current:0V 0 5A
Spontaneous chiral symmetry breaking 9th Goldstone boson (0)
A0 not a conserved current UA(1) is broken in
quantum theory: Chiral anomaly0
2
16f a
s a
nA F F
Alder&Jackiw
0
22 4
2
20 | ( ), (0) | 0
16f s
YM
nm i d x T FF x FF
f
Topological susceptibility2
YM
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Partial restoration of UA(1)
Z. Huang & XNW
UA(1) restored phase could lead to false vacuum 0 Massive parity violation Kharzeev & Pisarski
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Chiral Symmetry
Chirality of massless quarks: 5
1(1 )
2L 5
1(1 )
2R
Chiral symmetry: LiL Le
Ri
R Re
Conserved currents: 2
aaV 5 2
aaA
Spontaneously broken: 0
Goldstone bosons (,K,)(3) (3) (3)L RSU SU SU
Or alternatively: 5 / 2/ 2 , iiV AU e U e
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Running of s(Q)
S Bethke J.Phys. G26 (2000) R27
22 2 23
4( )
(11 ) ln( / )sf QCD
Qn Q
Gross,Wilczek;Politzer (73)
SU(3) Gauge SymmetryNon-abelian interaction
Anti-screening of color
Asymptotic freedom
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Ideal Gas Approximation
• Leading orders inperturbation (Kapusta)
• Failure of simple perturbation: (non-convergenceg g~1)(Arnold & Zhai ’94)
– Expand contributions from soft modes k~ gT in terms of g.
1/3
0
[ ]exp ( )T
Z d d d xL
)4
151(
3016 4
2
sT
g
ssfqq TTn
2
184
1
21
501
120
76
2
4224
2
432
0 2ln013.0007.0ln09.012.0095.01 g
TgggPP
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Resummation of HTL
• Resummation of Hard Thermal Loops (Braaten & Pisarski)
– Effective theory integrating out “hard” (k~T) loops
– Resummation of HTP
)(
)(
)(
)()(
22 pp
pe
pp
pepD
HTLL
LHTLT
T
xix
xxxD
HTLL 21
1ln
21)1( 22
)1(41
1ln)1(
4222
22 xxi
x
xx
xxD
HTLT
(Weldon’94)
p
px 0
= + + …
222 )6/1( Tgn fD
Debye mass
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Quasi-partciles & Self-consistent Resummation
• Quasi-particles with dispersion given by HTL
• Self-consistentresummation:
• Dyson’s equation
-1 -10 0 0
1 1Tr lnD Tr ln D
2 2HTL THL
)(10
1 DDD
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Scale Anomaly
• Scale invariance (massless quarks)
• QCD interaction renormalization of g()
– Break scale invariance scale anomaly
3/ 2( ) ( )
( ) ( )
x x
A x A x
( ) ( )scaleJ x x T x
( ) ( ) 0scaleJ x T x
Classically conserved dilation current
12as
aT F F
BFF aas 4
12
2 40.015 GeVs F
Gluon condensate
0 0, PB B
Bag constant
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QCD Phase transition
• Ideal quark and gluon gas
• Massless pion gas
• First order phase transition:
2416
30T
g
247
6120q q fn T
243
30T
3
P
( ) ( )q g c cP T P T
1/ 40.72cT B ( 0)
P
T4
T4
4B
Tc4
Tc4
,q g B ,
1
3 q gP B
威海 2007
Xin-Nian Wang - LBNL 86
Azimuthal anisotropy I
0 1 2(1 cos 2 cos 2 )chdNN v v
d
Single hadron
威海 2007
Xin-Nian Wang - LBNL 87
Flavor of Jet Quenching
Parton recombination -> Partonic degrees of freedom
威海 2007
Xin-Nian Wang - LBNL 88
Elliptic Flow
py
px
Coordinate space: initial asymmetry
Momentum space: final asymmetry
)2cos2cos1( 210
vvNd
dNch
2cos2 v Pressure gradient diff
Hydro-dynamics calc.
威海 2007
Xin-Nian Wang - LBNL 89