School on Heavy Ion Phenomenology, Bielefeld, September 2005
RHIC Phenomenology:
Quantum Chromo-Dynamics
with relativistic heavy ions
D. Kharzeev
BNL
Quarks and the Standard Model
1/2 of all “elementary”
particles of
the Standard Model
are not observable;
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they are confined
within hadrons
by “color” interactions
Theoretical notion of color:
“The red-haired man”
by Daniil Kharms (1905-1942)
from “Blue Notebook No.10”
Once there was a red-haired man who had no eyes or ears.
Neither did he have any hair,
so he was called “red-haired” only theoretically
…
Therefore there’s no knowing whom we are even talking about.
In fact we better not say anything about him...
Outline
• Quantum Chromo-Dynamics the theory of strong interactions
• Classical dynamics and quantum anomalies
• QCD phase diagram
• A glimpse of RHIC data
• New facets of QCD at RHIC and LHC:
o Color Glass Condensate
o (strongly coupled) Quark-Gluon Plasma
o links between General Relativity and QCD
What is QCD?
QCD = Quark Model + Gauge Invariance
local gauge transformation:
.i
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QCD and the origin of mass
gluons
Invariant under scale (
quarks
) and chiral Left
Right
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transformations in the limit of massless
quarks
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Experiment: u,d quarks are almost massless…
… but then… all hadrons must be massless as well!
Where does the “dark mass” of the proton come from?
QCD and quantum anomalies
Classical scale invariance is broken by quantum effects:
scale anomaly
trace of the energymomentum tensor
Hadrons get masses
“beta-function”; describes the dependence
of coupling on momentum
coupling runs with the distance
Asymptotic Freedom
At short distances,
the strong force becomes weak
(anti-screening) one can access the “asymptotically
free” regime in hard processes
and in super-dense matter
(inter-particle distances ~ 1/T)
number
of colors
number
of flavors
Asymptotic freedom and
Landau levels of 2D parton gas
B
The effective potential: sum over 2D Landau levels
Paramagnetic response of the vacuum:
V
H
1. The lowest level n=0 of radius
2. Strong fields
Short distances
is unstable!
QCD and the classical limit
Classical dynamics applies when the action
is large
in units of the Planck constant (Bohr-Sommerfeld quantization)
(equivalent to setting
)
=> Need weak coupling and strong fields
weak
field
.i
strong
field
Building up strong color fields:
small x (high energy) and large A (heavy nuclei)
Bjorken x : the fraction of hadron’s momentum carried by
a parton; high energies s open access to small x = Q2/s
the boundary
of non-linear
regime:
Large x
partons of
size 1/Q > 1/Qs
overlap
small x
Because the probability to emit an extra gluon is ~ as ln(1/x) ~ 1,
the number of gluons at small x grows; the transverse area is limited
transverse density becomes large
Strong color fields in heavy nuclei
At small Bjorken x, hard processes develop over
.large longitudinal distances
Density of partons
in the transverse
plane as a new
dimensionful
parameter Qs
(“saturation scale”)
All partons contribute coherently => at sufficiently small x and/or
.large A strong fields, weak coupling!
Non-linear QCD evolution
and population growth
Color glass condensate
time
rapidity
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Linear evolution: T. Malthus (1798)
r - rate of maximum
population growth
Unlimited growth!
Resolving the gluon cloud
at small x and short distances ~ 1/Q2
number of gluons
“jets”: high momentum partons
Population growth in a limited environment
“logistic
equation”
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K - maximum sustainable population; define
r = 1.5, N(0)=0.1, x(0)=0.1
4
x
3.5
3
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Population
Pierre Verhulst (1845)
2.5
TIFF
Geometric (N)
Logistic (x=N/K)
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
9
Generations
Stable population:
The limit is universal (no dependence on the initial condition)
t
Population growth in a limited environment:
a (short) path to chaos
Discrete version: bifurcations leading to chaos
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John von Neumann
Fixed
points
(
limit
of the population)
“logistic map”
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Rate of growth
(the value of
)
High energy evolution
starts here.
Semi-classical QCD: experimental tests
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Hadron multiplicities:
the effect of parton coherence
Semi-classical QCD and
total multiplicities in heavy ion collisions
Expect very simple dependence of multiplicity
.on atomic number A / Npart:
Npart:
Classical QCD in action
Classical QCD dynamics in action
The data on hadron multiplicities in Au-Au and d-Au collisions
support the quasi-classical picture
Kharzeev & Levin, Phys. Lett. B523 (2001) 79
Gluon multiplication in
a limited (nuclear) environment
The ratio
of pA and
pp cross
sections
DK, Levin, McLerran;
DK, Kovchegov,Tuchin;
Albacete,Armesto,
Kovner,Wiedemann; …
transverse
momentum
At large rapidity y (small angle) expect
suppression of hard particles!
Quantum regime at short distances:
the effect of the classical background
1) Small x evolution leads to anomalous dimension
2) Qs is the only relevant dimensionful parameter in the CGC;
.thus everything scales in the ratio
3) Since
Tthe A-dependence is changed
Expect high pT suppression at sufficiently small x
Phase diagram of high energy QCD
Model predictions
I. Vitev nucl-th/0302002 v2
D. Kharzeev, Yu. Kovchegov and
K. Tuchin, hep-ph/0307037
CGC at y=0
Y=0
As y grows
Y=3
Y=-3
Very high energy
R. Debbe, BRAHMS Coll., Talk at DNP Meeting, Tucson,
November 2003
Nuclear Modification of Hard Parton Scattering
R.Debbe, BRAHMS,
QM’04
Color Glass Condensate: confronting the data
BRAHMS
data,
= 0, 1,
2.2, 3.2
DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045
Color Glass Condensate: confronting the data
BRAHMS
data, RCP
= 0, 1,
2.2, 3.2
DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045
Confronting the RHIC data
DK & K.Tuchin
STAR Collaboration
charm
hadrons
Centrality dependence
R.Debbe, BRAHMS, QM’04
Phenix Preliminary
Au
d
Phenix Preliminary
d
Au
Phenix Preliminary
d
Cronin effect &
anti-shadowing?
Color Glass?
Shadowing?
Au
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Newly Found State of Matter Could Yield Insights
Into Basic Laws of Nature
By JAMES GLANZ
Published: January 13, 2004
OAKLAND, Calif., Jan. 12 — A fleeting, ultradense state of matter,
comparable in some respects to a bizarre kind of subatomic pudding,
has been discovered deep within the core of ordinary gold atoms,
scientists from Brookhaven National Laboratory said at a conference
here Monday…
Shattered Glass
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Seeking the densest matter:
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the color glass condensate
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By David Appell
April 19, 2004
How dense is the produced matter?
The initial energy density achieved:
mean
transverse
momentum
of produced
gluons
gluon
formation
time
the density
of the gluons
in the transverse
plane and in
rapidity
about
100 times
nuclear
density !
What happens at such energy densities?
Phase transitions:
deconfinement
Chiral symmetry
restoration
UA(1) restoration
Data from lattice QCD simulations F. Karsch et al
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critical temperature ~ 1012 K; cf temperature inside the Sun ~ 107 K
Strongly coupled QCD plasma
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C. Bernard, T.Blum, ‘97
Bielefeld
Interactions are important!
(strongly coupled
Quark-Gluon Plasma)
Coulomb potential in QCD
Spectral representation in the t-channel:
If physical particles can be produced (positive spectral density),
then unitarity implies screening
Gluons Quarks
(transverse)
Coulomb potential in QCD - II
Missing non-Abelian effect: instantaneous Coulomb exchange
dressed by (zero modes of) transverse gluons
Negative sign
(the shift of the ground level
due to perturbations - unstable vacuum! ):
Anti-screening
Screening in Quark-Gluon Plasma
These diagrams are enhanced at finite temperature:
(scattering off thermal gluons and quarks)
This diagram is not:
=> At high enough T, screening wins
Screening in the QGP
Strong force is
screened by
the presence of
thermal gluons
and quarks
F.Karsch’s lecture; F.Zantow’s talk
T-dependence of
the running coupling
develops in
the non-perturbative region
at T < 3 Tc
sQGP
Lecture by F.Karsch
Percolation
deconfinement, CGC?
Lecture by
H. Satz
sQGP: more fluid than water?
Perfect fluid
A.Nakamura and S.Sakai,
hep-lat/0406009
KSS bound:
strongly coupled SUSY QCD = classical supergravity
Charge fluctuations in sQGP
Lecture by F.Karsch
Hadron resonance
gas
QQ bound states
S.Ejiri, F.Karsch and K.Redlich, 05
Dynamical
quarks
Do we see the QCD matter at RHIC ?
I. Collective flow =>
Lectures by J.-Y. Ollitrault
Au-Au collisions at RHIC produce strongly interacting matter
shear viscosity - to - entropy ratio
hydrodynamics: QCD liquid is more fluid than water,
SUSY Yang-Mills (AdS-CFT corr.) :
Hydro limit
STAR
PHOBOS
Azimuthal anisotropy as a measure of
the interaction strength
v2
Azimuthal anisotropy defined
Do we see the QCD matter at RHIC?
II. Suppression of high pT particles => Lectures by U.Wiedemann
consistent with the predicted parton energy loss from induced
gluon radiation in dense QCD matter
R
J/Y suppression -> F.Fleuret, H.Satz
Jets (high momentum partons) - I
Jet d’Eau
Geneva
3-jet event, LEP
Geneva
Jets -II
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Niagara Falls
Au-Au collision event, RHIC
Geometry of jet suppression
Away-side suppression is larger out-of-plane compared to in-plane
STAR Collaboration
Di-jet correlations
Di-Jets from p + p at 200 GeV
‘Mono-Jets’ from Au + Au at 200 GeV
STAR Coll.,
PRL90(2002)
082302
The emerging picture
Big question:
How does the produced
matter thermalize
so fast?
Perturbation theory +
Kinetic equations:
Thermalization time
too long (?)
Recent idea:
Quantum Black Holes
and
Relativistic Heavy Ions ?
DK & K.Tuchin, hep-ph/0501234
Outline
• What is a black hole?
• Why black holes decay
• Why black holes cannot be produced at RHIC
• Why black holes may anyway teach us about
the properties of QCD matter produced at RHIC
What is a black hole?
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Rev. John Michell (1724-1793)
Letter to the Royal Society, 1783:
If the semi-diameter of a sphere of the same density as
the Sun in the proportion of five hundred to one,
and by supposing light to be attracted by the same force
in proportion to its [mass] with other bodies,
all light emitted from such a body would be made
to return towards it, by its own proper gravity.
Who was John Michell?
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Rev. John Michell (1724-1793)
John Michell is a little short Man, of a black Complex
and fat; but having no Acquaintance with him,
can say little of him…
from a contemporary diary
What is a black hole?
Pierre-Simon LaPlace (1749-1827)
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“What we know is not much.
What we do not know is immense.”
"...[It] is therefore possible that the largest luminous bodies
the universe may, through this cause, be invisible."
-- Le Système du Monde, 1796
What is a black hole?
A. Einstein, 1915:
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Einstein tensor:
energymomentum
tensor
Ricci tensor
K. Schwarzschild, 1916:
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A solution for a static isotropic
gravitational field
singularity at r = 2GM !
Scwarzschild radius
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The meaning of R = 2GM ?
v
Consider the following Michell-like “derivation”:
m
M
if we could put v = c, would get R = 2GM
(cannot do that!)
But: it is the distance at which the energy in
the gravitational field is ~ mc2 … quantum effects?
Black holes radiate
S.Hawking ‘74
Black holes emit
thermal radiation
with temperature
acceleration of gravity
at the surface, (4GM)-1
Do we see black holes in the Universe?
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Cygnus X-1 binary system:
super-giant star orbiting around a black hole?
Can black holes be produced at RHIC?
RHIC:
M < 104 GeV
R > 10-2 fm
E = 200 GeV
No role
for classical
or quantum
gravity:
< 10-22
< 10-34
W. Busza, R.L. Jaffe, J. Sandweiss,
F. Wilczek, hep-ph/9910333
Can black holes anyway help us
to understand the physics at RHIC?
One new idea: use a mathematical correspondence between
a gauge theory and gravity in AdS space
Gauge theory
Gravity
Maldacena
deconfinement black hole formation
in AdS5xS3xT space
boundary
Witten; Polyakov;
Anti de Sitter space - solution of Einstein’s equations Gubser, Klebanov;
Son, Starinets, Kovtun;
with a negative cosmological constant L
(de Sitter space - solution with a positive L (inflation)) Nastase; …
What is the origin of gravitational effects?
In the AdS/CFT correspondence, gravity as described
in the Anti - de Sitter space emerges as a consequence
of the conformal invariance of the gauge theory
(e.g., N=4 SUSY Yang-Mills)
T
mn
Isometry group = SO(2,d-1) for AdSd
for AdS5 boundary is S3x Time;
SO(2,4) maps the boundary on itself and
acts as a conformal group in 3+1 dimensions hence the gauge theory defined on the boundary
is conformal (no asymptotic freedom, no confinement)
Are gravitational-like effects possible in QCD?
Tmn
Tmn
Black holes radiate
S.Hawking ‘74
Black holes emit
thermal radiation
with temperature
acceleration of gravity
at the surface, (4GM)-1
Similar things happen in
non-inertial frames
Einstein’s Equivalence Principle:
Gravity
Acceleration in a non-inertial frame
An observer moving with an acceleration a detects
a thermal radiation with temperature
W.Unruh ‘76
In both cases the radiation is
due to the presence of event horizon
Black hole: the interior is hidden from
an outside observer;
Schwarzschild metric
Accelerated frame: part of space-time is hidden
(causally disconnected) from
an accelerating observer;
Rindler metric
 = x t ,
2
2
2
1 tx
 = ln
2 tx
ds2 =  2d2  d 2  dx
2
Pure and mixed states:
the event horizons
mixed state
pure state
mixed state
pure state
Thermal radiation can be understood
as a consequence of tunneling
through the event horizon
Let us start with relativistic classical mechanics:
velocity of a particle moving
with an acceleration a
classical action:
it has an imaginary part in
Euclidean space…
well, now we need some
quantum mechanics, too:
The rate of tunneling
under the potential barrier:
This is a Boltzmann factor with
Accelerating detector
• Positive frequency Green’s function (m=0):
• Along an inertial trajectory
• Along a uniformly accelerated trajectory
x = y = 0,z = (t 2  a2 )1/ 2
Unruh,76
 detector is effectively immersed into a heat bath
Accelerated
at temperature TU=a/2
An example: electric field
The force:
The acceleration:
The rate:
What is this?
Schwinger formula for the rate of pair production;
an exact non-perturbative QED result
factor of 2: contribution from the field
The Schwinger formula
eE
e+
Dirac sea
+
+
+…
The Schwinger formula
• Consider motion of a charged particle in a constant
electric field E. Action is given by
Equations of motion
yield the trajectory
where a=eE/m is
the acceleration
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Classically forbidden
trajectory t  it E
• Action along the classical trajectory:
(
)
m
eE
S(t) =  arcsh(at)  2 at( 1 a2 t 2  2)  arcsh(at)
a
2a
• In Quantum Mechanics S(t) is an analytical function of t
m eE m 2
 • Classically forbidden paths contribute to Im S(t) =
 2 =
a
2a
2eE
• Vacuum decays with probability
V m =1 exp (e
2 Im S
) e
2 Im S
 m 2 / eE
=e
Sauter,31
Weisskopf,36
Schwinger,51
• Note, this expression can not be expanded in powers
of the coupling - non-perturbative QED!

Pair production by a pulse
Consider a time dependent field


E
A = 0,0,0, tanh( k 0 t)
k0


E
m
• Constant field limit k0  0
• Short pulse limit
k0  
 spectrum with
a thermal

t
Chromo-electric field:
Wong equations
• Classical motion of a particle in the external nonAbelian field:
Ým = gFIÝqmn gfxÝn IxÝaA
mxÝ
m
a
abc
m
I =0
b c
The constant chromo-electric field is described by
A 0 a = Ez a 3, A i a = 0

Solution:
vector I3 precesses about 3-axis with I3=const
0
Ý
Ý
Ý
Ý
Ý
Ý
Ý
x = y = 0,mz = gEx I3

Effective Lagrangian: Brown, Duff, 75; Batalin, Matinian,Savvidy,77;
Nayak, van Nieuwenhuizen, 2005

An accelerated observer
consider an observer with internal degrees of freedom;
for energy levels E1 and E2 the ratio of occupancy factors
Bell, Leinaas:
depolarization in
accelerators?
For the excitations with transverse momentum pT:
but this is all purely academic (?)
Can one study the Hawking radiation
on Earth?
Gravity?
Take g = 9.8 m/s2;
the temperature is only
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Electric fields? Lasers?
compilation by A.Ringwald
Condensed matter black holes?
“slow light”?
Unruh ‘81;
e.g. T. Vachaspati,
cond-mat/0404480
Strong interactions?
Consider a dissociation of a high energy hadron of mass m into a final
hadronic state of mass M;
The probability of transition:
m
M
Transition amplitude:
In dual resonance model:
Unitarity:  P(mM)=const,
b=1/2 
universal slope
Hagedorn
temperature!
limiting acceleration
Fermi - Landau statistical model
of multi-particle production
Hadron production
at high energies
is driven by
statistical mechanics;
universal temperature
Enrico Fermi
1901-1954
Lev D. Landau
1908-1968
Where on Earth can one achieve the largest
acceleration (deceleration) ?
Relativistic heavy ion collisions! stronger color fields:

Hawking phenomenon in
the parton language
p The longitudinal frequency
k
of gluon fields in the initial
wave functions is typically very small:
Parton configurations are frozen,
Gauge fields are flat in the longitudinal direction G+- = 0
But: quantum fluctuations (gluon radiation
in the collision process) necessarily
induce
Gluons produced at mid-rapidity have
large frequency (c.m.s.)
=> a pulse of strong chromo-electric field
Production of gluons
1/Qs and quark pairs with
3D thermal spectrum
1) Classical Yang-Mills equations for
the Weizsacker-Williams fields are unstable
in the longitudinal direction =>
the thermal seed will grow
(a link to the instability-driven
thermalization?)
2) Non-perturbative effect, despite the weak
coupling (non-analytical dependence on g)
3) Thermalization time
c~1 (no powers of 1/g)
cf “bottom-up”
scenario
Deceleration-induced phase transitions?
• Consider Nambu-Jona-Lasinio model in Rindler space

n
L =  i (x)n (x) 
2N
2
2
(

(x)

(x))

(

(x)i


(x))


5
e.g.,Ohsaku,04
• Commutation relations:
 m (x),n (x)= 2gmn (x)

• Rindler space:
 = x t ,
2

2
2
1
2
 = ln
tx
tx
ds2 =  2d2  d 2  dx


2
Gap equation in an accelerated frame
• Introduce the scalar and pseudo-scalar fields

 (x) =   (x) (x)
N

 (x) =   (x)i 5 (x)
N
• Effective action (at large N):


Seff
 2  2
n
=  d x g
  iln det(i n    i 5 )
2 

4
• Gap equation:

2i
 =
a

d 2k 
sinh(  /a)
2
2
d

(K
(
a
/a))

(K
(
a
/a))
)


i

/
a
1/
2
i

/
a1/
2
2
2
(2 ) 

where


a 2 = k 2   2
Rapid deceleration induces phase transitions
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NambuJona-Lasinio model
(BCS - type)
Similar to phenomena in the vicinity of a large black hole:
Rindler space
Schwarzschild metric
A link between General Relativity and QCD?
solution to some of the RHIC puzzles?
Black holes
RHIC collisions
Additional slides
Classical QCD in action
Do we see the QCD matter at RHIC?
II. Suppression of high pT particles =>
consistent with the predicted parton energy loss from induced
gluon radiation in dense QCD matter
R
Strong color fields
(Color Glass Condensate)
as a necessary condition for
the formation of Quark-Gluon Plasma
The critical acceleration (or the Hagedorn temperature)
can be exceeded only if the density of partonic states
changes accordingly;
this means that the average transverse momentum
of partons should grow
CGC
QGP
sQGP: more fluid than water?
Perfect fluid
A.Nakamura and S.Sakai,
hep-lat/0406009
KSS bound:
strongly coupled SUSY QCD = classical supergravity
sQGP: more fluid than water
Kovtun, Son, Starinets,
hep-th/0405231
RHIC: a dedicated QCD machine
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Bogolyubov transformation
Second quantization:  (x) =  a  (x)  a  * (x)

i,in i,in

ai,in ,ai,in
where
Equivalently:

a
where
i,out



= 
ai,in | 0
ij
in
=0
 (x) =  ai,outi,out (x)  ai,out i,out * (x)

,ai,out

i
= 
ij
ai,out | 0
out
(

V m =out 0 ai,in ai,in 0
=0

2
=
|

|

ij
out
j

i,in
i
Obviously: ai,in =  a ij a j,out   ji * a j,out

j
Therefore
i,in
)
Pair production by
aEpulse


Consider a time dependent field
A m = 0,0,0, tanh( k 0 t)
k0


E
  p,in (x) =
1
e i  t ipr

(2 ) 3 / 2 2
1
i  t ipr
i  t ipr
  p,out (x) =
a
e


e
(
)
p
p
3/2
(2 )
2 
t
• Constant filed limit k0  0
• Short pulse limit


k0  
V m
 2m 

2
=
|  p | = exp


k

0 
Narozhnyj,
Nikishov, 70
Applications to heavy ions
• Consider breakdown of a high energy hadron of mass m into
a final hadronic state of invariant mass M.
• Transition probability:
P(m  M) = 2 | T(m  M) |2 (M)
• Unruh effect:

| T(m  M) |2  exp(2M /a)
• Using the dual resonance model, the density of hadronic
states: 
(M)  exp( 4 b1/ 2 M /61/ 2 )
where b is universal slope of Regge trajectories
 tension:  =1/2b
string
Hagedorn temperature
P(m  M) = const

• Probability conservation:
M
• Therefore,
a
61/ 2
T 
 THagedorn
1/ 2
2  4 b
• The string tension cannot create acceleration bigger than

acr = 3/2b1/ 2
and, thus, produce pairs at temperature bigger than THagedorn
 stronger field to get larger temperature, e.g.
• One needs
ECGC  Qs (s, A)/g
2

Pair production in GR
• The same problem of quantization in external field!
Dm Dn gmn  (x)  m 2 (x) = 0
1
• In Schwartzschild metric lm (x) = r Rl (r)Ylm (, )exp(it)
exp(i
r*)  a l exp(ir*),r*   in

Rl  
out
l exp(i
r*), r*  

• Black hole emission rate:
r* = r  rg ln( r /rg 1)
(tortoise coordinate)

| l |2 exp(2
 / )
Hawking, 75
where =1GM is acceleration of gravity at the

surface of black hole,
T=1/(8GM)
What is a black hole?
S. Chandrasekhar
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At One Trillion Degrees, Even Gold Turns Into
the Sloshiest Liquid
By KENNETH CHANG
Published: April 19, 2005
It is about a trillion degrees hot and flows like water.
Actually, it flows much better than water. Scientists at the
Brookhaven National Laboratory on Long Island announced
yesterday that experiments at its Relativistic Heavy Ion
Collider - RHIC, …
Picking apart the 'Big Bang' brings a big mystery
By Dan Vergano, USA TODAY
An atom-smashing fireball experiment has physicists puzzling
over existing theories about the moments after the "Big Bang" that
scientists say created the universe. Researchers conducted the
experiment over the past three years at the Energy Department's
Brookhaven National Laboratory in Long Island, New York.
Jets (high momentum partons) - I
Jet d’Eau
Geneva
3-jet event, LEP
Geneva
Jets -II
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Niagara Falls
Au-Au collision event, RHIC
Semi-classical QCD and
total multiplicities in heavy ion collisions
Expect very simple dependence of multiplicity
.on atomic number A / Npart:
Npart:
Quantization
in external
field
• Condier
charged scalar field
 coupled to external
electric field E. Klein-Gordon equation:
(
 ieAm )  (x)  m 2 (x) = 0
2
m
• Let Am=Am(t). Then the eigenstates are
 p (x) =
1

(2 )
3/2
2
e ipr g  ( p,t)
where

tt g( p,t)   2 (t)g( p,t) = 0;
  = lim  (t)

 2 (t) = p2  2epz Az  e 2 Az 2  m 2
• Note, in(x) are different from out(x)

t 
Recent idea:
Quantum Black Holes
and
Relativistic Heavy Ions ?
DK & K.Tuchin, hep-ph/0501234
Effective Lagrangian
• Effective Lagrangian in constant magnetic field:
sum over Landau levels (generalization to E≠0 is
straightforward):


eB  
2
2
2
2
Leff =
 m  pz  2 m  pz  2eBn  dpz
2 
(2 )  

n=1
• In weak fields:


Leff
e4

360 2 m 4
+
• Note that Im Leff = 0
(E
+
2
) (
)
 B 2  7 E  B  ...
Heisenberg,
Euler, 36
+…
in all orders of this expansion.
Similar things happen in
non-inertial frames
Einstein’s Equivalence Principle:
Gravity
Acceleration in a non-inertial frame
An observer moving with an acceleration a detects
a thermal radiation with temperature
W.Unruh ‘76
In both cases the radiation is
due to the presence of event horizon
Black hole: the interior is hidden from
an outside observer;
Schwarzschild metric
Accelerated frame: part of space-time is hidden
(causally disconnected) from
an accelerating observer;
Rindler metric
Thermal radiation can be understood
as a consequence of tunneling
through the event horizon
Let us start with relativistic classical mechanics:
velocity of a particle moving
with an acceleration a
classical action:
it has an imaginary part…
well, now we need some
quantum mechanics, too:
The rate of tunneling
under the potential barrier:
This is a Boltzmann factor with
An example: electric field
The force:
The acceleration:
The rate:
What is this?
Schwinger formula for the rate of pair production;
an exact non-perturbative QED result
factor of 2: contribution from the field
The Schwinger formula
eE
e+
Dirac sea
A quantum observer
consider an observer with internal degrees of freedom;
for energy levels E1 and E2 the ratio of occupancy factors
Bell, Leinaas:
depolarization in
accelerators?
For the excitations with transverse momentum pT:
but this is all purely academic (?)
Take g = 9.8 m/s2;
the temperature is only
Where on Earth can one achieve the largest
acceleration (deceleration) ?
Relativistic heavy ion collisions!
Why not hadron collisions?
Consider a dissociation of a high energy hadron of mass m
into a final hadronic state of mass M;
The probability of transition:
m
M
Transition amplitude:
In dual resonance model:
Unitarity:  P(mM)=const,
b=1/2 
universal slope
Hagedorn
temperature!
limiting acceleration
Color Glass Condensate as
a necessary condition for
the formation of Quark-Gluon Plasma
The critical acceleration (or the Hagedorn temperature)
can be exceeded only if the density of partonic states
changes accordingly;
this means that the average transverse momentum
of partons should grow
CGC
QGP
Quantum thermal radiation at RHIC
The event horizon
emerges due to the fast
decceleration
of the colliding nuclei
in strong color fields;
Tunneling through
the event horizon
leads to the thermal
spectrum
Rindler and Minkowski spaces
Fast thermalization
horizons
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collision point
0Qs
Rindler coordinates:
Gluons tunneling through the event horizons have thermal
distribution. They get on mass-shell in t=2Qs
(period of Euclidean motion)
Rapid deceleration induces phase transitions
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NambuJona-Lasinio model
(BCS - type)
Similar to phenomena in the vicinity of a large black hole:
Rindler space
Schwarzschild metric
New link between General Relativity and QCD;
solution to some of the RHIC puzzles?
Hawking radiation
RHIC event
Quark-Hadron phase transition
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Order of the deconfinement phase transition Implications for baryosynthesis
Topological fluctuations - primordial magnetic fields?
P, CP violation ?
The future: experimental facilities
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Qu i ck Ti me ™a nd a
TIF F (Un co mpre ss ed )d ec omp res so r
a re ne ed ed to s ee th i s pi c tu re.
LHC
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induced gluon radiation should be suppressed
for heavy quarks; is it?
0.906<a<1.042
dN/dy = A
(Ncoll)a
PHENIX Collaboration
Direct photons as a probe
PHENIX Preliminary
0-10% Central 200
1 + ( pQCD
x Ncoll) /  phenix
GeV
AuAu
backgrd
Vogelsang NLO
What is the origin of
the “B/ puzzle”?
Heavy quarkonium as a probe
Talk by F. Karsch
the link between the observables
and the McLerran-Svetitsky
confinement criterion
Heavy quark internal energy above T
Talks by
F.Karsch,
P. Petreczky,
K. Petrov,
F. Zantow,
O.Kaczmarek,
S. Digal
O.Kaczmarek, F. Karsch, P.Petreczky,
F. Zantow, hep-lat/0309121
Summary
1. Quantum Chromo-Dynamics is
an established and consistent field theory
of strong interactions
but it’s properties are far from being understood
2. High energy nuclear collisions test the predictions
of strong field QCD and probe
the properties of super-dense matter
3. New connections between field theory and
General Relativity (black holes,…)
All of this directly tested by experiment!
Additional slides
Classical QCD in action
The data on hadron multiplicities in Au-Au and d-Au collisions
support the semi-classical picture
Quantum regime at short distances:
the effect of the classical background
1) Small x evolution leads to anomalous dimension
2) Qs is the only relevant dimensionful parameter in the CGC;
.thus everything scales in the ratio
3) Since
Tthe A-dependence is changed
Expect high pT suppression at sufficiently small x