Download - (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
威海 2007
Xin-Nian Wang - LBNL 2
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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Xin-Nian Wang - LBNL 3
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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Xin-Nian Wang - LBNL 4
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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Xin-Nian Wang - LBNL 5
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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Xin-Nian Wang - LBNL 6
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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Xin-Nian Wang - LBNL 7
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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Xin-Nian Wang - LBNL 8
QCD Phase Diagram
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Xin-Nian Wang - LBNL 9
Strong coupling near Tc
( ) 312
asaF FT x P
2s
Pc
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Xin-Nian Wang - LBNL 10
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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Xin-Nian Wang - LBNL 11
Cerenkov gluon radiation in near Tc?
Koch, Majumder & XNW’05
1cos
( )c
p
Dielectric constant
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Xin-Nian Wang - LBNL 12
Chiral Symmetry
Spontaneously broken:
0
Goldstone bosons (,K,)
(3) (3) (3)L RSU SU SU
F. Karsch ‘2001
MeVTc 8170
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Xin-Nian Wang - LBNL 13
QCD Phase Diagram
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Xin-Nian Wang - LBNL 14
Quark Matter in Neutron Stars
Spin-down
Spin-up
N. Glendenning ‘2000
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Xin-Nian Wang - LBNL 15
Heavy-ion Collisions
RHIC BNL
Au+Au up to 200 GeV/n
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Xin-Nian Wang - LBNL 16
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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Xin-Nian Wang - LBNL 17
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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Xin-Nian Wang - LBNL 18
Chemical equilibrium at freeze-out
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Xin-Nian Wang - LBNL 19
Non-central Heavy Ion Collisions
x
z
y
EZDC
ET
Centrality of the collisions
Impact Parameter (b)
EZDC
ET
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Xin-Nian Wang - LBNL 20
Elliptic Flow
Ideal Hydro calculation
2cos2 v
Pressure gradient anisotropy
)2cos2cos1( 210
vvNd
dNch
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Xin-Nian Wang - LBNL 21
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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Xin-Nian Wang - LBNL 22
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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Xin-Nian Wang - LBNL 23
?
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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Xin-Nian Wang - LBNL 24
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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Xin-Nian Wang - LBNL 25
Quark Coalescence
n = number of constituent quarks
Rec. ModelsHwa & YangFries, Muller, BassKo et al
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Xin-Nian Wang - LBNL 26
Bifurcation of Spectra
Constituent quark recombination promote baryon production
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Xin-Nian Wang - LBNL 27
Shock Wave or Cherenkov Radiation
PHENIX
1cos
( )c
p
cos /M sc c
Velocity of sound:Index of refraction
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Xin-Nian Wang - LBNL 28
Orbital angular momentum
x
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Xin-Nian Wang - LBNL 29
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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Xin-Nian Wang - LBNL 30
STAR Preliminary
Au+Au @ 200GeV (20-70%)
Au+Au @ 62GeV (0-80%)
Tp (GeV/c)
P
STAR Preliminary
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Xin-Nian Wang - LBNL 31
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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Xin-Nian Wang - LBNL 33
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Xin-Nian Wang - LBNL 34
(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
威海 2007
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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Xin-Nian Wang - LBNL 36
Jets in heavy-ion collisions
q
q
leadingparticle
leading particle
pQCD
Bjorken’82, XNW & Gyulassy’92
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Xin-Nian Wang - LBNL 37
Jet Tomography
Calibrated source
Absorptionproperties
Compute assisted
Correction
pQCDp+p, p+A
dE/dx Expansion dynamics QGP
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Xin-Nian Wang - LBNL 38
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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Xin-Nian Wang - LBNL 39
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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Xin-Nian Wang - LBNL 40
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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Xin-Nian Wang - LBNL 41
DIS off Nucleie-
, )) (( ,( )qh
q h hHdW
d f x p q Dxd
zz
x
pypedy
xf yixpBq )()0(
2
1
2)(
/( ) 0 (0) , , ( ) 02 2 2
h hip y zhq h h q h h q
S
z dyD z e Tr p S p S y
Frag. Func.
22 )(2)(2
1),,( xpqxpqpTreqpxH q
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Xin-Nian Wang - LBNL 42
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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Xin-Nian Wang - LBNL 43
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
2 ( , )2
( )
Aqg B Ts
Tc A B
T x xq
N q x
Quark energy loss
pT broadening (Guo’98)
Guo & XNW(2000)
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Xin-Nian Wang - LBNL 44
Single hadron suppression
NNAB
ABAB
NR
binary
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Xin-Nian Wang - LBNL 45
Centrality Dependence
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Xin-Nian Wang - LBNL 46
Dihadron suppression
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Xin-Nian Wang - LBNL 47
Energy Loss in Cold Nuclear Matter
0.5 GeV/fmdE
dx
in Au nuclei
e-Enke Wang & XNW (2000)
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Xin-Nian Wang - LBNL 48
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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Xin-Nian Wang - LBNL 49
Cherenkov radiation or shock wave
PHENIX
cos /M sc c
Velocity of sound:
1cos
( )c
p
Index of refraction
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Xin-Nian Wang - LBNL 50
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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Xin-Nian Wang - LBNL 51
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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Xin-Nian Wang - LBNL 52
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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Xin-Nian Wang - LBNL 53
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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Xin-Nian Wang - LBNL 54
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Back up slides
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Xin-Nian Wang - LBNL 56
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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Xin-Nian Wang - LBNL 57
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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Xin-Nian Wang - LBNL 58
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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Xin-Nian Wang - LBNL 59
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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Xin-Nian Wang - LBNL 60
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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Xin-Nian Wang - LBNL 61
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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Xin-Nian Wang - LBNL 62
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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Xin-Nian Wang - LBNL 63
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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Xin-Nian Wang - LBNL 64
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
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Xin-Nian Wang - LBNL 65
Azimuthal anisotropy I
0 1 2(1 cos 2 cos 2 )chdNN v v
d
Single hadron
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Xin-Nian Wang - LBNL 66
Flavor of Jet Quenching
Parton recombination -> Partonic degrees of freedom
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Xin-Nian Wang - LBNL 67
Elliptic Flow
py
px
Coordinate space: initial asymmetry
Momentum space: final asymmetry
)2cos2cos1( 210
vvNd
dNch
2cos2 v Pressure gradient diff
Hydro-dynamics calc.
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Xin-Nian Wang - LBNL 68