Some Like It Hot:
Boiling the QCD Vacuum
At RHIC and LHC
Berndt Müller
Emilio Segre Lecture in Physics
Tel Aviv University - May 29, 2011
Sunday, May 29, 2011
Hot, hotter, hottest …
2
Sunday, May 29, 2011
Hot, hotter, hottest …
Hollywood
2
Sunday, May 29, 2011
Hot, hotter, hottest …
Hell
Hollywood
2
Sunday, May 29, 2011
Hot, hotter, hottest …
Hell
Nucleons
+ mesons
Hollywood
Quarkgluon
plasma
Quark matter
2
Sunday, May 29, 2011
Part 1
The Hottest Stuff
on Earth
3
Sunday, May 29, 2011
Heating Things Up

What heat does to matter:
Increases disorder (entropy)
 Speeds up reactions
 Overcomes potential barriers


States / phases of matter:





Solid [long-range correlations, shear elasticity]
Liquid [short-range correlations]
Gas [few correlations]
Plasma [free charges] (solid / liquid / gaseous)
Quark matter / quark-gluon plasma [free color charges]
(liquid)
4
Sunday, May 29, 2011
QCD phase diagram
T
Critical end
point
QuarkGluon
Plasma
Hadronic
matter
1st order
line
Chiral symmetry
broken
Nuclei
Sunday, May 29, 2011
Chiral symmetry
restored
Color
superconductor
Neutron stars
µB
5
QCD phase diagram
RHIC
T
Critical end
point
QuarkGluon
Plasma
Hadronic
matter
1st order
line
Chiral symmetry
broken
Nuclei
Sunday, May 29, 2011
Chiral symmetry
restored
Color
superconductor
Neutron stars
µB
5
QCD phase diagram
LHC
RHIC
T
Critical end
point
QuarkGluon
Plasma
Hadronic
matter
1st order
line
Chiral symmetry
broken
Nuclei
Sunday, May 29, 2011
Chiral symmetry
restored
Color
superconductor
Neutron stars
µB
5
QCD phase diagram
LHC
RHIC
T
Critical end
point
QuarkGluon
Plasma
RHIC beam
energy scan
Hadronic
matter
1st order
line
Chiral symmetry
broken
Nuclei
Sunday, May 29, 2011
Chiral symmetry
restored
Color
superconductor
Neutron stars
µB
5
QCD equation of state
gluons
spin
165
color
330
RHIC
quarks
spin
500
color
flavor
MeV
Indication of
weak or strong
coupling?
Lattice QCD
6
Sunday, May 29, 2011
QCD equation of state
gluons
spin
165
color
330
RHIC
LHC
quarks
spin
500
color
flavor
MeV
Indication of
weak or strong
coupling?
Lattice QCD
6
Sunday, May 29, 2011
Color screening
Induced color density
φa
Static color charge
(heavy quark) generates
screened potential
7
Sunday, May 29, 2011
Quark masses
Higgs
quark
field
Quark
quark
condensate
8
Sunday, May 29, 2011
Quark masses
Higgs
quark
field
Quark
quark
condensate
Heat “melts” the quark condensate:
QCD mass disappears above Tc.
(Partial) chiral symmetry restoration
Sunday, May 29, 2011
8
Lattice QCD - 2010
Wuppertal - Budapest Coll.
9
Sunday, May 29, 2011
Below Tc - the HRG
Lines: Hadron resonance gas (HRG)
Data points: Lattice QCD (Wu-Bu)
LQCD lies above HRG for T > 140 MeV
10
Sunday, May 29, 2011
Below Tc - the HRG
Lines: Hadron resonance gas (HRG)
Hadrons up to at least 2.5 GeV
(maybe 3 GeV) mass contribute
Data points: Lattice QCD (Wu-Bu)
4
LQCD lies above HRG for T > 140 MeV
�
�
mcut = 3.0 GeV
��3P�� T 4
3
�
mcut = 2.5 GeV
�
2
�
�
1
mcut = 2.0 GeV
mcut = 1.7 GeV
�
�
�
T �MeV�
0
100 110 120 130 140 150 160 170
10
Sunday, May 29, 2011
When the Universe was hot…
Arrow of time
11
Sunday, May 29, 2011
When the Universe was hot…
Arrow of time
quarks gain QCD mass
and become confined
11
Sunday, May 29, 2011
The practical path to the QGP…
…is hexagonal and 3.8 km long
Relativistic Heavy Ion Collider
12
Sunday, May 29, 2011
The practical path to the QGP…
…is hexagonal and 3.8 km long
Relativistic Heavy Ion Collider
STAR
12
Sunday, May 29, 2011
Toward higher energies…
LHC
13
Sunday, May 29, 2011
Toward higher energies…
CMS
LHC
ATLAS
ALICE
13
Sunday, May 29, 2011
Space-time picture
Pre-equil. phase
Liberation of
saturated low-x glue
fields (CGC)
τeq ≈ 1 fm/c
RHIC:
s0 ≈ 33 fm-3
T0 ≈ 275 MeV
LHC:
s0 ≈ 75 fm-3
T0 ≈ 360 MeV
14
Sunday, May 29, 2011
Chemistry
Chemical freeze-out line
STAR Preliminary
39 GeV
11.5 GeV
STAR Preliminary
SPS
Td
Tχ
AGS
STAR Preliminary
7.7 GeV
15
Sunday, May 29, 2011
Freeze-out conditions
(GeV)
Kinetic freeze-out
RHIC
LHC
mor
e ce
ntra
l
16
Sunday, May 29, 2011
Probes of hot QCD matter
Which properties of hot QCD matter can we hope to determine from relativistic
heavy ion data (RHIC and LHC, maybe FAIR) ?
Tµν
⇔ ε , p, s
cS2 = ∂p / ∂ε
Equation of state: spectra, coll. flow, fluctuations
Speed of sound: multiparticle correlations
1
η = ∫ d 4 x Txy (x)Txy (0)
T
Shear viscosity: anisotropic collective flow
⎫
⎪
⎪
⎪⎪
−
− a+
−
a+
∫ dy i∂ A (y )A (0) ⎬
⎪
⎪
−
a+−
−
a+−
∫ dy F (y )F (0) ⎪⎪⎭
4π 2α s C R
−
a +i
−
a+
q̂ =
dy
F
(y
)F
i (0)
2
∫
Nc − 1
4π 2α s C R
ê =
N c2 − 1
4π 2α s C R
ê2 =
N c2 − 1
1
mD = − lim
ln E a (x)E a (0)
|x|→∞ | x |
Sunday, May 29, 2011
Momentum/energy diffusion:
parton energy loss, jet fragmentation
Color screening: Quarkonium states
17
Probes of hot QCD matter
Which properties of hot QCD matter can we hope to determine from relativistic
heavy ion data (RHIC and LHC, maybe FAIR) ?
Easy for
LQCD
Tµν
⇔ ε , p, s
cS2 = ∂p / ∂ε
Equation of state: spectra, coll. flow, fluctuations
Speed of sound: multiparticle correlations
1
η = ∫ d 4 x Txy (x)Txy (0)
T
Shear viscosity: anisotropic collective flow
⎫
⎪
⎪
⎪⎪
−
− a+
−
a+
∫ dy i∂ A (y )A (0) ⎬
⎪
⎪
−
a+−
−
a+−
∫ dy F (y )F (0) ⎪⎪⎭
4π 2α s C R
−
a +i
−
a+
q̂ =
dy
F
(y
)F
i (0)
2
∫
Nc − 1
4π 2α s C R
ê =
N c2 − 1
4π 2α s C R
ê2 =
N c2 − 1
Easy for
LQCD
Sunday, May 29, 2011
1
mD = − lim
ln E a (x)E a (0)
|x|→∞ | x |
Momentum/energy diffusion:
parton energy loss, jet fragmentation
Color screening: Quarkonium states
17
Probes of hot QCD matter
Which properties of hot QCD matter can we hope to determine from relativistic
heavy ion data (RHIC and LHC, maybe FAIR) ?
Easy for
LQCD
Tµν
⇔ ε , p, s
cS2 = ∂p / ∂ε
Equation of state: spectra, coll. flow, fluctuations
Speed of sound: multiparticle correlations
1
η = ∫ d 4 x Txy (x)Txy (0)
T
Hard for
LQCD
4π 2α s C R
ê2 =
N c2 − 1
Sunday, May 29, 2011
⎫
⎪
⎪
⎪⎪
−
− a+
−
a+
∫ dy i∂ A (y )A (0) ⎬
⎪
⎪
−
a+−
−
a+−
∫ dy F (y )F (0) ⎪⎪⎭
4π 2α s C R
−
a +i
−
a+
q̂ =
dy
F
(y
)F
i (0)
2
∫
Nc − 1
4π 2α s C R
ê =
N c2 − 1
Easy for
LQCD
Shear viscosity: anisotropic collective flow
1
mD = − lim
ln E a (x)E a (0)
|x|→∞ | x |
Momentum/energy diffusion:
parton energy loss, jet fragmentation
Color screening: Quarkonium states
17
Part 2
The Liquid QGP
18
Sunday, May 29, 2011
Elliptic Flow (v2)
Reaction
plane
v2 = cos(2ϕ)
coefficient of the
azimuthal distribution
z
y
x
Hydrodynamics:
Flow is generated by ∇P
∇P( ) > ∇P(↕)
19
Sunday, May 29, 2011
v2(pT) vs. hydrodynamics
20
Sunday, May 29, 2011
v2(pT) vs. hydrodynamics
Mass splitting characteristic
property of hydrodynamics
20
Sunday, May 29, 2011
v2(pT) vs. hydrodynamics
Failure of ideal
hydrodynamics
tells us how
hadrons form
Mass splitting characteristic
property of hydrodynamics
20
Sunday, May 29, 2011
Bulk hadronization
Sudden recombination
Fast hadrons
experience a
rapid transition
from medium to
vacuum for fast
hadrons
pB ≈ 3pQ
T,µ,v
pM ≈ 2 pQ
M
QGP
Vacuum
21
Sunday, May 29, 2011
Bulk hadronization
Sudden recombination
Fast hadrons
experience a
rapid transition
from medium to
vacuum for fast
hadrons
pB ≈ 3pQ
T,µ,v
M
QGP
Vacuum
pM ≈ 2 pQ
⎛ pt ⎞
v ( pt ) = 2v ⎜ ⎟
⎝ 2⎠
M
2
Q
2
⎛ pt ⎞
v ( pt ) = 3v ⎜ ⎟
⎝ 3⎠
B
2
Q
2
21
Sunday, May 29, 2011
Quark number scaling of v2
1 M
Q ⎛ pt ⎞
v2 ( pt ) = v2 ⎜ ⎟
⎝ 2⎠
2
1 B
Q ⎛ pt ⎞
v2 ( pt ) = v2 ⎜ ⎟
⎝ 3⎠
3
22
Sunday, May 29, 2011
Quark number scaling of v2
1 M
Q ⎛ pt ⎞
v2 ( pt ) = v2 ⎜ ⎟
⎝ 2⎠
2
Emitting medium is composed of
unconfined, flowing quarks.
Sunday, May 29, 2011
1 B
Q ⎛ pt ⎞
v2 ( pt ) = v2 ⎜ ⎟
⎝ 3⎠
3
22
Quark number scaling of v2
1 M
Q ⎛ pt ⎞
v2 ( pt ) = v2 ⎜ ⎟
⎝ 2⎠
2
Emitting medium is composed of
unconfined, flowing quarks.
Sunday, May 29, 2011
1 B
Q ⎛ pt ⎞
v2 ( pt ) = v2 ⎜ ⎟
⎝ 3⎠
3
22
Historical note
23
Sunday, May 29, 2011
Event by event
Initial state generated in A+A collision is grainy
event plane ≠ reaction plane
eccentricities ε1, ε2, ε3, ε4, etc. ≠ 0
flows v1, v2, v3, v4,...
24
Sunday, May 29, 2011
nd
2
order relat. hydrodynamics
∂ µT µν = 0 with
T µν = (ε + P)u µ uν − Pg µν + Π µν
η = Shear viscosity
λ
⎡ dΠ µν
⎤
du
µ νλ
ν µλ
µ ν
ν µ
µν
τΠ ⎢
+ u Π +u Π
=
η
∂
u
+
∂
u
−
trace
−
Π
⎥
dτ ⎦
⎣ dτ
(
)
(
)
Excellent approximation of Boltzmann
transport; negligible uncertainties due to:
● Bulk viscosity
● QCD Equation of state
Main input parameters:
● η/s
● Initial energy density profile
● Equilibration time τ0
25
Sunday, May 29, 2011
Elliptic flow “measures” ηQGP
Universal strong coupling limit of
non-abelian gauge theories with a
gravity dual:
η/s → 1/4π
η/s = 0
η/s = 1/4π
η/s = 2/4π
aka: the “perfect” liquid
26
Sunday, May 29, 2011
Elliptic flow “measures” ηQGP
Universal strong coupling limit of
non-abelian gauge theories with a
gravity dual:
η/s → 1/4π
η/s = 0
η/s = 1/4π
η/s = 2/4π
aka: the “perfect” liquid
Consistency check:
Triangular flow
26
Sunday, May 29, 2011
Elliptic flow “measures” ηQGP
Universal strong coupling limit of
non-abelian gauge theories with a
gravity dual:
η/s → 1/4π
η/s = 0
η/s = 1/4π
η/s = 2/4π
aka: the “perfect” liquid
Consistency check:
Triangular flow
✓
26
Sunday, May 29, 2011
vn @ LHC
Conclusions agree almost
(too ?) perfectly with RHIC
v2
RHIC
v3
LHC
27
Sunday, May 29, 2011
vn (n = 2,...,6)
0.2
v2
v3
v4
v5
v6
vn almost independent of rapidity
2.0-3.0 GeV
EP from FCalP(N)
vn
ATLAS Preliminary
0 Ldt = 8 !b
-1
0.1
0
0-5%
5-10%
10-20%
20-30%
30-40%
40-50%
vn
0.2
0.1
0
0
Sunday, May 29, 2011
0.5
1
|d|
1.5
2
0
0.5
1
|d|
1.5
2
0
0.5
1
|d|
1.5
2
28
Hunting for perfection...
Aihong Tang
[STAR] 2009
29
Sunday, May 29, 2011
Hunting for perfection...
My
best
bet
2009
Aihong Tang
[STAR] 2009
29
Sunday, May 29, 2011
Hunting for perfection...
Present
limits
2011
Aihong Tang
[STAR] 2009
29
Sunday, May 29, 2011
The scientific challenge
30
Sunday, May 29, 2011
The scientific challenge
No need to
worry, Lucy!
We are very
close to
proving....
....that the world
was once
(13.7 × 109 y ago)
a
perfect liquid.
30
Sunday, May 29, 2011
Part 3
The opaque QGP
31
Sunday, May 29, 2011
Radiative energy loss
ΔE  ρ L kT
2
q
q
2
L
q
q
g
Scattering centers
= color charges
dσ
−
+
−
+i
q̂ = ρ ∫ q dq
=
dx
F
(x
)F
(0)
i
∫
2
dq
2
2
32
Sunday, May 29, 2011
Jet quenching in Au+Au
Yield in A+A
No suppression for photons
Suppression of hadrons
Area density
of p+p coll’s
in A+A
Cross section
in p+p coll’s
Without nuclear effects:
RAA = 1.
33
Sunday, May 29, 2011
‹
Towards measuring q
Good fits for light hadrons can be
obtained for all energy loss models
with 3-D hydro evolution, but...
Bass, Gale, Majumder, Nonaka, Qin, Renk & Ruppert
34
Sunday, May 29, 2011
‹
Towards measuring q
Good fits for light hadrons can be
obtained for all energy loss models
with 3-D hydro evolution, but...
Transport parameter q̂
deviates by more than
factor 2 between different
implementations.
Bass, Gale, Majumder, Nonaka, Qin, Renk & Ruppert
Caused by differences in
the cut-offs in collinear
approximation used in all
implementations of gluon
radiation.
34
Sunday, May 29, 2011
‹
Towards measuring q
Good fits for light hadrons can be
obtained for all energy loss models
with 3-D hydro evolution, but...
Transport parameter q̂
deviates by more than
factor 2 between different
implementations.
Bass, Gale, Majumder, Nonaka, Qin, Renk & Ruppert
Caused by differences in
the cut-offs in collinear
approximation used in all
implementations of gluon
radiation.
Is pQCD the correct
theory for jet quenching?
34
Sunday, May 29, 2011
Jet quenching at LHC
Single-hadron suppression
rapidly decreases for large pT
RCP L,
Λ,K!K
L!
Λ
K0
K±
0.1
Open charm mesons are as much
suppressed as light mesons
35
Sunday, May 29, 2011
0
Z,
photons, hadrons
36
Sunday, May 29, 2011
0
Z,
photons, hadrons
36
Sunday, May 29, 2011
Di-jets
37
Sunday, May 29, 2011
Di-jet asymmetry
38
Sunday, May 29, 2011
Parton shower in matter
39
Sunday, May 29, 2011
CMS data
ATLAS data
GY Qin & BM
PRL 106 (ʼ11)
ATLAS and CMS data differ in cuts on jet energy, cone angle, etc.
ATLAS results depend somewhat on precise cuts and background
corrections. Theory fits require 20% different parameters.
40
Sunday, May 29, 2011
pT balance
pT along jet primary axis balances for whole event
41
Sunday, May 29, 2011
pT balance
Di-jet momentum difference is balanced
by low-pT particles outside a wide cone.
42
Sunday, May 29, 2011
Fragmentation
Subleading jet fragments just like a lower energy jet
in pp collisions: jet loses energy, but is unmodified
43
Sunday, May 29, 2011
Part 4
QGP ≅ BH ?
44
Sunday, May 29, 2011
To the rescue?

Perturbative QCD seems to be compatible with some
aspects of jet quenching, but not with others:
Where are the radiated gluons?
 How is the lost energy thermalized so quickly?
 Why do charm quarks lose energy just like light quarks?


Perturbative QCD is incapable of explaining η/s ≤ 1/2π

Maybe a theory of strong coupling is needed ?
Toy model: Strongly coupled large-Nc super-Yang-Mills theory
 Exactly solvable by holographic duality: gravity on AdS5“+”

45
Sunday, May 29, 2011
Gauge-string duality
AdS5
r
UV
describes
virtuality scale
of quantum
field theory
z, χ
IR
46
Sunday, May 29, 2011
Thermal holography
AdS5+BH
r
z, χ
47
Sunday, May 29, 2011
Thermal holography
AdS5+BH
η

=
s 4π
r
z, χ
47
Sunday, May 29, 2011
Quark energy loss
Quark-gluon plasma
Deposited energy
and momentum
Trailing string
(flux tube)
Black hole
Sunday, May 29, 2011
48
Quark energy loss
v
χm
χh =
Upper and lower parts
of the training string are
causally disconnected
comoving field
radiated field
χ0 =
Quark-gluon plasma
Deposited energy
and momentum
Trailing string
(flux tube)
Black hole
Sunday, May 29, 2011
48
Quark energy loss
v
χm
χh =
Upper and lower parts
of the training string are
causally disconnected
comoving field
radiated field
χ0 =
If quark is sufficiently massive or
off-shell after scattering, it
travels above the string horizon.
Soft field is continuously
stripped off; quark emerges from
matter in a highly virtual state
with a truncated color field.
Sunday, May 29, 2011
Quark-gluon plasma
Deposited energy
and momentum
Trailing string
(flux tube)
Black hole
48
Lightning fast
Colliding shock waves create
thermal matter within τ ≈ 0.3 fm/c
(Chesler & Yaffe ʼ10)
49
Sunday, May 29, 2011
Lightning fast
Colliding shock waves create
thermal matter within τ ≈ 0.3 fm/c
(Chesler & Yaffe ʼ10)
A volume of diameter D
thermalizes perfectly after
τ ≈ D/2,
i.e. at the speed of light
(Balasubramanian et al. ʼ11)
Sunday, May 29, 2011
Τ
2.
1.
0.
0.
2.
D
4.
49
A puzzle
Fluctuations of conserved quantum numbers
of quarks above Tc behave “as if” quarks were free:
Baryon number kurtosis
B = baryon number
Q = electric charge
S = strangeness
S. Eijiri,
F. Karsch &
K. Redlich
Is this behavior compatible with strong coupling ?
50
Sunday, May 29, 2011
Paths to progress
Theorists solving a problem
Fortunately, experimental progress with
several facilities (RHIC, LHC, and soon
FAIR) producing data at an amazing rate,
is a greater challenge than rival theories.
Main challenges for the next few years:
• Constructing a solvable model that
consistently interpolates between
weak and strong coupling
• Understand the initial state and
thermalization
• Develop the theory of fluctuations
theory of jet quenching.
• Extend Lattice QCD to μB ≠ 0
and
real-time response functions
51
Sunday, May 29, 2011
Instead of a summary
52
Sunday, May 29, 2011
53
Sunday, May 29, 2011
THE END
53
Sunday, May 29, 2011