From
Quark-Gluon Plasma
to the
Perfect Liquid
Berndt Mueller – Duke University
Krakow School of Theoretical Physics
Zakopane, 14-22 June 2007
1
Part I
Q uark-G luon
P lasm a
2
Matter at extreme conditions
•
•
Squeeze slowly → Cold, dense matter
Squeeze fast → Hot, “dense” matter
(1) is much more difficult to do than (2):
Cold matter beyond nuclear matter density (ρB > ρ0 = 0.15 fm-3)
exists only in the core of collapsed (neutron) stars.
(2) Happened once: t < 20 µs after inflation.
Can also be achieved by colliding nuclei at high energy.
30 years of history: Bevalac, AGS, SPS, RHIC → LHC.
Goal: energy density ε » MN ρ0 = 0.14 GeV/fm3.
3
Quantum chromodynamics
LQCD = −
+ĺ
+ĺ
1
4
ĺ
a
µν
G G
a
a µν
ć
a a
Ψγ  ∂ µ + g ĺ Aµ t Ψ
a
č
ř
m f ΨΨ
µ
f
f
4
Cosmic Connection
5
Degrees of freedom

At extreme (energy) density, particle masses can be
neglected relative to the kinetic energy:
δ π
Ε
2
2
ε = νň
ωιτη Ε = π + µ
3 Ε /Τ
(2π ) ε ± 1
2
ě7 / 8(fermions)
π
4
ε =ν
aT
with a = 
30
 1 (bosons)
3
Quarks: ν = 2 × 2 × N C × N F = 12 N F
Gluons: ν = 2 × ( N − 1) = 16
2
C
6
Hadrons or partons?
If QCD had NF light quark flavors, there would be (NF2-1)
nearly massless Goldstone bosons (“pions”):
νπ = N −1
2
F
For large NF the pions win out over quarks, but
for NF=3 the quarks and gluons win out:
→ at high T matter is composed of a colored
plasma of quarks and gluons, not of hadrons!
7
QCD phase diagram
RHIC
T
Critical end
point (?)
QuarkGluon
Tc ~ 170 MeV
Plasma
Chiral symmetry
restored
Hadronic
matter
1st order
line
Chiral symmetry
broken
Nuclei
Color
superconductor
Neutron stars
µB
8
From hadrons to QGP
ε=
π2
30
νT
4
QGP = quark-gluon plasma
ψψ ≈ 0
QCD equation
of state from
lattice QCD
Hadron gas
ψψ
0
9
Crossover of phases
Susceptibilities peak at Tc, but do not diverge. Vacuum
properties change smoothly, but rapidly → “crossover”
A okietal.(N ature 2006)
10
A fuzzy transition?
Fodoretal.(N ature 2006)
11
Quasi-particles in the QGP
Physical excitation modes at high T are not elementary quarks and
gluons, but “dressed” quarks and gluons:
T
Compton scattering
on a thermal gluon!
(k,ω )
Propagator of transversely polarized gluons
1
1 ćω k  ω + k ů
2 
D(k , ω ) = ω − k − ( gT ) ę1 −  −  ln

2
 2čk ω ř ω−kű
−1
2
2
→ Effective mass of gluon:
1
m ľ ľ ľ→
gT
3
1
k →0
*
mG ľ ľ ľ→
gT
2
*
G
k →0
12
Lattice - susceptibilities
χ XY
∂2
=
ln Z (T , µi ) = XY − X Y
∂µ X ∂µY
XS ≈ ĺ xi si ni
i
R. Gavai & S. Gupta, hep-lat/0510044
C XS = #
XS − X
S
2
− S
S
2
A .M ajum der
pQGP
13
Color screening
−Ń 2φ a = g ρGa (φ b ) + g ρQa (φ b )
Induced color density
with
µ = ( gT ) ,
2
G
2
ρ a = − µ 2φ a
NF
µ =
( gT ) 2
6
2
Q
φa
Static color charge
(heavy quark) generates
screened potential
α s −µr
φ =t
e
r
a
a
14
Plasma two-stream instability
r
v
r
v
15
Turbulent color fields
C olorcorrelation
length
M .Strickland,hep-ph/0511212
Tim e
N onabelian
Q uasiabelian
N oise
Length (z)
16
Quark masses
H iggs
1000000
quark
QCD mass
Higgs mass
100000
field
10000
1000
100
Q uark
10
qq
quark
1
u
d
s
c
b
t
qq
condensate
Q C D m ass disappears above T c:
(partial)chiralsym m etry restoration
17
The QCD EoS (at µ=0)
The precise value of Tc is still under debate:
Tc = 170 ± 20 MeV with 20 - 30 MeV width.
EoS near Tc is far from ideal ultrarelativistic gas!
Sound velocity cs2 = ∂P/∂ε << 1/3.
18
Into the T-µB plane
Tc ( µ B )
First order phase
transition line
Fodor& K atz (2001)
Controls net baryon density
19
Is there a phase transition?
Almost
certainly:
NOT
20
A triple point ?
Fodoretal.hep-lat/0701022
21