1. (I): Matter in Extremis
QCD and Heavy Ion Physics
(I): Matter in Extremis
高能物理前沿暑期论坛
威海 July 31 – August 7, 2006
Xin-Nian Wang
Lawrence Berkeley National Laboratory

2. 火 水 土 Phases of Matter (gas) (liquid) (solid) Quark-gluon Plasma (QGP)
火 水 土
(gas)
(liquid)
(solid)
Bose-Einstein condensate, fermionic condensate,
superfluids, supersolids, paramagnetic,
ferromagnetic, liquid crystals, …
Human kind has always been fascinated by different forms of matter in nature, from the rudimentary forms like gas, liquid, and solid which make up the basic fabrics of our daily life, to the plethora of new forms of matter discovered in the last century.
The focus of current effort in high-energy nuclear physics is searching and studying a new form of nuclear matter called quark-gluon plasma.
Quark-gluon Plasma (QGP)

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 core
and change of the vacuum structure at high temperature
BJ scaling as discovered at SLAC
对QCD 的认识, 是一个缓慢的过程
Lee and Wick,(1974); Collins and Perry (1975);
Baym and Chin (1976)

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
对称, 破却 和他们的起死回生

5. Scale Anomaly and invariance at high T
Scale anomaly  Break scale invariance

6. EOS in Lattice QCD
F. Karsch ‘2001
SB limit
25%
Quasi-particle with dispersion given by HTL resummation
Blaizot, Iancu, Rebhan ‘2001
Super Yang-Mills
Guber, Klebanov, Tseytlin ‘1998

7. Confinement-deconfinement
SU(3) non-Abelian gauge interaction  confinement
Heavy quark potential:
Karsch, Laermann
and Peikert 2001
J/Y suppression

8. QCD Phase Diagram
Not a first order phase transition but rather a Rapid cross over near Tc. The properties of QGP near Tc is quite intriguing.

9. Strong coupling near Tc

10. Resonances in QGP above Tc?
Maximum entropy method (MEM)
Hatsuda et al
Hatsuda et al, 2004
J/Y survives up to T=1.6Tc
Could there be many other resonances?
Shuryak & Zahed ‘04

11. Cerenkov gluon radiation in near Tc?f f1 f2
Koch, Majumder & XNW’05
Dielectric constant

12. Chiral Symmetry Goldstone bosons (p,K,h) Spontaneously broken:
F. Karsch ‘2001

13. QCD Phase Diagram

14. Quark Matter in Neutron Stars
Spin-up
Spin-down
Accretion increase the angular momentum of the neutron star
N. Glendenning ‘2000

15. Heavy-ion Collisions
RHIC BNL
Au+Au up to 200 GeV/n

16. Medium Response Dynamic System:
Soft hadrons: Bulk properties of medium, collective behavior
EM emission: Medium response to EM interaction
g production, J/Y suppression
Hard probes: Medium response to strong interaction
Jet quenching
Dynamic System:

17. Energy Density in Heavy-ion Collisions
Above the critical density from lattice QCD

18. Chemical equilibrium at freeze-out

19. Non-central Heavy Ion Collisionsx z y
EZDC ET ET
EZDC
In heavy ion collisions, you are colliding two extended objects.
Centrality of the collisions
Impact Parameter (b)

20. Elliptic Flow
Ideal Hydro calculation
Pressure gradient anisotropy

21. A perfect fluid? Ideal Hydrodynamic Constraint on thermalization time
Heinz ‘04
Constraint on shear viscosity:
Teaney ‘03
H2O :

22. Shear viscosity Energy-momentum tensor in microscopic picture
Transport:
Kubo relation

23. Viscosity of QCD Matter
Hadron gas at low temperature:
Chiral perturbation theory:
QGP at high temperature:
Perturbative QCD
Prakash et al
Chen & Nakano
Arnold, Moore,Yaffe ?
Kapusta, Csernai & McLerran

24. Phase transition or strong coupling?
Small viscosity in SYM
Policastro, Son & Starinets ‘02
Is it possible to measure h/s from experiments?

25. Quark Coalescence Rec. Models Hwa & Yang Fries, Muller, Bass Ko et al
n = number
of constituent
quarks
Rec. Models
Hwa & Yang
Fries, Muller, Bass
Ko et al

26. Bifurcation of Spectra
Constituent quark recombination promote baryon production

27. Shock Wave or Cherenkov Radiation
PHENIX q
Velocity of sound:
Index of refraction

28. Orbital angular momentumDx

29. Quark Polarization xT p n pf Polarized cross section:
Zuo-tang Liang & XNW PRL 94(2005)

30. (GeV/c) Au+Au @ 200GeV (20-70%) Au+Au @ 62GeV (0-80%) STAR Preliminary

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

34. (II): Hard Probes of Dense Matter
QCD and Heavy Ion Physics
(II): Hard Probes of Dense Matter
高能物理前沿暑期论坛
威海 July 31 – August 7, 2006
Xin-Nian Wang
Lawrence Berkeley National Laboratory

35. Medium Response Dynamic System:
Hard probes: Medium response to strong interaction
Jet quenching
EM emission: Medium response to EM interaction
Dynamic System:
Soft hadrons: Bulk properties of medium, collective behavior

36. Jets in heavy-ion collisions
pQCD
leading
particle
Bjorken’82, XNW & Gyulassy’92 q q
leading particle

37. Jet Tomography QGP Absorption Compute assisted Calibrated properties
source
Absorption
properties
Compute assisted
Correction
pQCD
p+p, p+A
dE/dx
Expansion
dynamics
QGP

38. LPM interference in EM Radiationv
EM field carried by a
fast moving electron
Initial rad.
Final rad.
EM Radiation by scattering:
Interference between initial
and final state radiation
Landau-Pomeranchuck-Midgal interference
Formation time

39. Radiation in QCD: Colors matterpf pi k pi pf k a c k pi pf y
QED y
QCD
Gluon multiple scattering (BDMP’96)

40. Modified Jet Fragmentation
(Guo & XNW’00)
Suppression of leading particles (Huang, XNW’96)

41. Parton energy loss: A twisted story
Modified frag. function

42. Modified fragmentation function
Guo & XNW(2000)
Quark energy loss
pT broadening (Guo’98)

43. Detailed balance: thermal absorption
Enke Wang & XNW, PRL87(2001)
Thermal absorption important at lower E

44. Single hadron suppression

45. Centrality Dependence

46. Dihadron suppression

47. Jet quenching in hot and cold nuclear matter
Enke Wang & XNW, PRL 89 (2002) e-
in Au nuclei

48. Suppression of away-side jet
Initial Density about 30 times of that in a Cold Au Nucleus

49. Cones, Ridges & the Medium
STAR, PRL 93 (2004)
Au+Au 0-10%
preliminary
barrage of information

50. A Pedestrian Question:
What jet quenching really measures?

51. DIS: an Analogy e- Q2
s~ f(x,Q2)
x=Q2/2EmN

52. pT broadening and gluon distributionq

53. Gluon distribution in hot medium

54. Energy loss and pT broadening
Generalized jet
transport parameter
Total pt broadening:
Total energy loss:

55. A Theoretical Question:
What medium properties are imbedded in ?

56. Evolution of qhat k=E q High energy jet  small x p
Large momentum transfer
 large scale
(DLA)

57. Gluon Saturation in QGP
Evolution  growth of gluon distribution at small x
Nonlinear effect (gluon fusion) will
tame the growth of gluon distribution E q
Gluon Saturation p
QGP density is much larger than in nuclei
Saturation sets in at larger x and Qs2 is larger

58. E-dependence of qhat Nontrivial length dependence of qhat
J. Casalderrey-Solana and XNW, arXiv: [hep-ph].
Nontrivial length dependence of qhat

59. q-hat and Shear Viscosity h
Majumder, Muller and XNW (hep-ph/ )
Shear viscosity
This relation is strongly violated for strongly coupled medium
Where h/s does NOT reflect the transport of partons as quasi-particle
Jet quenching 

60. An Experimental Question:
How to measure ?

61. Single and Dihadron hadron suppression at RHIC
Hanzhong Zhang, Owens, Enke Wang and XNW, PRL 98 (2007)
zT=pTass/pTtrig

62. Sensitivity to initial density
h/s =

63. q-hat in a nucleus
Enke Wang & XNW PRL 89, (2002) e-

64. Surface emission?

65. Surface vs. Volume

66. 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 g-jets

67. (1) Direct measurement of qhatg

68. Utopia?
Lambda polarization surrounding the jet

69. 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/
With total 16 publications (in the last 8 years), this is one of
my most productive collaborations in my career!

71. Cherenkov radiation or shock wave
PHENIX q
Index of refraction
Velocity of sound:

72. Degrees of freedom in sQGP?
Koch, Majumder & Randrup ‘05
Bound state QGP or hadronic gas
Ideal quarks
Gavai & Gupta ‘05
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

73. 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)

74. g Outlook: an example Direct g-tagged events: Eg~Ejet
Measure directly Dh/a(z)
Azimuthal anisotropy
jet g
X.-N.W&Huang
PRC55(97)3047

75. 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/Y suppression  deconfinement
Microscopic picture of sQGP
Quasi-particle, bound states?

76. UA(1) Anomaly U(1) and UA(1) Symmetry:
(Classically) conserved current:
Spontaneous chiral symmetry breaking  9th Goldstone boson (h0)
A0m not a conserved current
UA(1) is broken in
quantum theory:
Chiral anomaly
UA(1) charge is not conserved for topologically nontrivial vacuum and <FF~> is not zero.
Alder&Jackiw
Topological susceptibility

77. Partial restoration of UA(1)
Z. Huang & XNW
UA(1) restored phase could lead to false vacuum
Massive parity violation
Kharzeev & Pisarski

78. Chiral Symmetry Chirality of massless quarks: Chiral symmetry:
Or alternatively:
Conserved currents:
Two conserved currents. The combination of them give vector and axial vector cuurents
Uv transform vector currents among themselves, while U_A transform between vector and axial vector currents
Spontaneously broken:
Goldstone bosons (p,K,h)

79. Running of as(Q) SU(3) Gauge Symmetry Non-abelian interaction
S Bethke J.Phys. G26 (2000) R27
Anti-screening of color
It is therefore possible to use perturbative method to calculate physical observables. It is has been extremely successful in many cases,
Asymptotic freedom
Gross,Wilczek;Politzer (73)

80. Ideal Gas Approximation
Leading orders in perturbation (Kapusta)
Failure of simple perturbation: (non-convergenceg g~1) (Arnold & Zhai ’94)
Expand contributions from soft modes k~ gT in terms of g.
This also prompts one to try to calculate the EOS for a quark gluon gas. P=Tlog(Z/V)

81. Resummation of HTL
Resummation of Hard Thermal Loops (Braaten & Pisarski)
Effective theory integrating out “hard” (k~T) loops
Resummation of HTP
(Weldon’94) = + …
Debye mass

82. Quasi-partciles & Self-consistent Resummation
Quasi-particles with dispersion given by HTL
Self-consistent resummation:
Dyson’s equation
Phi- thermal dynamic potential

83. Scale Anomaly Scale invariance (massless quarks)
QCD interaction  renormalization of g(l)
Break scale invariance  scale anomaly
Classically conserved dilation current
Bag constant
Gluon condensate

84. QCD Phase transition Ideal quark and gluon gas P T4 Tc4 e T4 Tc4
Massless pion gas
First order phase transition: P
Tc4 T4
P=Tlog(Z/V)
Apparently, this model is too simplistic, it ignore strong interaction close to Tc, other hadron mass could decrease which will also contribute to the pressure e T4
Tc4

85. Azimuthal anisotropy I
Single hadron

86. Flavor of Jet Quenching
Parton recombination ->
Partonic degrees of freedom

87. Elliptic Flow Coordinate space: initial asymmetry Hydro-dynamics calc.
Pressure gradient diff
Hydro-dynamics calc. py px
Momentum space:
final asymmetry