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RHIC Phenomenology:Quantum Chromo-Dynamicswith relativistic heavy ions
D. Kharzeev
BNL
School on Heavy Ion Phenomenology, Bielefeld, September 2005
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1/2 of all “elementary” particles of the Standard Modelare not observable;
they are confinedwithin hadronsby “color” interactions
Quarks and the Standard Model
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“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,
…Therefore there’s no knowing whom we are even talking about. In fact we better not say anything about him...
so he was called “red-haired” only theoretically
Theoretical notion of color:
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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 Plasmao links between General Relativity and QCD
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What is QCD?
QCD = Quark Model + Gauge Invariance
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local gauge transformation:
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QCD and the origin of mass
.i
Invariant under scale ( ) and chiral
transformations in the limit of massless quarks
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?
Left Right
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gluonsquarks
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QCD and quantum anomalies
trace of the energy-momentum tensor
Classical scale invariance is broken by quantum effects: scale anomaly
Hadrons get masses coupling runs with the distance
“beta-function”; describes the dependence of coupling on momentum
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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
numberof flavors
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Asymptotic freedom and Landau levels of 2D parton gas
BB
The effective potential: sum over 2D Landau levels
1. The lowest level n=0 of radius is unstable! 2. Strong fields Short distances
Paramagnetic response of the vacuum:
H
V
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QCD and the classical limit
.i
Classical dynamics applies when the action is largein units of the Planck constant (Bohr-Sommerfeld quantization)
=> Need weak coupling and strong fields weakfield
strongfield
(equivalent to setting )
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Building up strong color fields:small x (high energy) and large A (heavy nuclei)Bjorken x : the fraction of hadron’s momentum carried bya parton; high energies s open access to small x = Q2/s
Because the probability to emit an extra gluon is ~ s ln(1/x) ~ 1, the number of gluons at small x grows; the transverse area is limited transverse density becomes large
Large x
the boundaryof non-linearregime:partons ofsize 1/Q > 1/Qs
overlap
small x
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Strong color fields in heavy nuclei
At small Bjorken x, hard processes develop over.large longitudinal distances
All partons contribute coherently => at sufficiently small x and/or .large A strong fields, weak coupling!
Density of partons in the transverse plane as a new dimensionful parameter Qs
(“saturation scale”)
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Non-linear QCD evolutionand population growth
T. Malthus (1798)
r - rate of maximum population growth
time rapidity
Unlimited growth!
Linear evolution:
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Color glass condensate
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Resolving the gluon cloud at small x and short distances ~ 1/Q2
number of gluons “jets”: high momentum partons
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Population growth in a limited environment
Pierre Verhulst (1845)
Stable population:
K - maximum sustainable population; define
“logisticequation”
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x
t
The limit is universal (no dependence on the initial condition)
r = 1.5, N(0)=0.1, x(0)=0.1
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7 8 9
Generations
Population
Geometric (N)
Logistic (x=N/K)
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Population growth in a limited environment:a (short) path to chaos
“logistic map”
Discrete version: bifurcations leading to chaos
Fixedpoints
Rate of growth (the value of )
( limitof the popu-lation)
John von Neumann
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High energy evolution starts here.
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Semi-classical QCD: experimental tests
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Hadron multiplicities:the effect of parton coherence
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Semi-classical QCD and total multiplicities in heavy ion collisions
Expect very simple dependence of multiplicity.on atomic number A / Npart:
Npart:
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Classical QCD in action
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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
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Gluon multiplication in a limited (nuclear) environment
At large rapidity y (small angle) expect suppression of hard particles!
The ratioof pA andpp crosssections
transversemomentum
DK, Levin, McLerran;DK, Kovchegov,Tuchin;Albacete,Armesto,Kovner,Wiedemann; …
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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
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Phase diagram of high energy QCD
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Model predictions
I. Vitev nucl-th/0302002 v2D. Kharzeev, Yu. Kovchegov and
K. Tuchin, hep-ph/0307037
CGC at y=0Y=0
Y=3
Y=-3
Very high energy
As y grows
R. Debbe, BRAHMS Coll., Talk at DNP Meeting, Tucson,November 2003
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R.Debbe, BRAHMS,QM’04
Nuclear Modification of Hard Parton Scattering
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Color Glass Condensate: confronting the data
DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045
BRAHMSdata,
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Color Glass Condensate: confronting the data
DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045
BRAHMSdata, RCP
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Confronting the RHIC data
hadrons
charm
DK & K.Tuchin STAR Collaboration
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Centrality dependence
R.Debbe, BRAHMS, QM’04
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d
Au
Phenix Preliminary
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dAu
Phenix Preliminary
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dAu
Color Glass?Shadowing?
Cronin effect &anti-shadowing?
Phenix Preliminary
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Newly Found State of Matter Could Yield Insights Into Basic Laws of NatureBy 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…
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Shattered Glass Seeking the densest matter: the color glass condensate By David Appell April 19, 2004QuickTime™ and a
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How dense is the produced matter?
The initial energy density achieved:
meantransversemomentumof produced gluons
gluonformation time
the densityof the gluonsin the transverseplane and inrapidity
about100 timesnucleardensity !
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What happens at such energy densities?Phase transitions:
deconfinement
Chiral symmetryrestoration
UA(1) restoration
Data from lattice QCD simulations F. Karsch et al
critical temperature ~ 1012 K; cf temperature inside the Sun ~ 107 K
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Strongly coupled QCD plasma
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C. Bernard, T.Blum, ‘97
Bielefeld
Interactions are important!(strongly coupled Quark-Gluon Plasma)
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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)
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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
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Screening in Quark-Gluon PlasmaThese diagrams are enhanced at finite temperature: (scattering off thermal gluons and quarks)
This diagram is not:
=> At high enough T, screening wins
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Screening in the QGP
F.Karsch’s lecture; F.Zantow’s talk
T-dependence of the running coupling develops in the non-perturbative regionat T < 3 Tc
Strong force is screened bythe presence of thermal gluonsand quarks
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sQGP
Lecture by F.Karsch
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Percolation deconfinement, CGC?
Lecture byH. Satz
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A.Nakamura and S.Sakai, hep-lat/0406009
Perfect fluid
sQGP: more fluid than water?
KSS bound:strongly coupled SUSY QCD = classical supergravity
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Charge fluctuations in sQGP Lecture by F.Karsch
Hadron resonancegas
Dynamicalquarks
QQ bound states
S.Ejiri, F.Karsch and K.Redlich, 05
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Do we see the QCD matter at RHIC ?I. Collective flow => Lectures by J.-Y. OllitraultAu-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
Hydro limit
STAR
PHOBOS
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vv22
Azimuthal anisotropy as a measure of the interaction strength
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Azimuthal anisotropy defined
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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
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Jets (high momentum partons) - I
Jet d’EauGeneva
3-jet event, LEP Geneva
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Jets -II
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Niagara Falls Au-Au collision event, RHIC
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Geometry of jet suppression
Away-side suppression is larger out-of-plane compared to in-plane
STAR Collaboration
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Di-jet correlations ‘‘Mono-Jets’ from Au + Au at 200 GeVMono-Jets’ from Au + Au at 200 GeVDi-Jets from p + p at 200 GeVDi-Jets from p + p at 200 GeV
STAR Coll.,PRL90(2002)082302
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The emerging picture
Big question:
How does the producedmatter thermalize so fast?
Perturbation theory +Kinetic equations:Thermalization time too long (?)
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Recent idea:
Quantum Black Holesand
Relativistic Heavy Ions ?
DK & K.Tuchin, hep-ph/0501234
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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
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What is a black hole?
Rev. John Michell (1724-1793)
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.
Letter to the Royal Society, 1783:
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Who was John Michell?
Rev. John Michell (1724-1793)
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John Michell is a little short Man, of a black Complexion, and fat; but having no Acquaintance with him, can say little of him… from a contemporary diary
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What is a black hole?
Pierre-Simon LaPlace (1749-1827)
"...[It] is therefore possible that the largest luminous bodies in the universe may, through this cause, be invisible." -- Le Système du Monde, 1796
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“What we know is not much. What we do not know is immense.”
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What is a black hole?
A. Einstein, 1915:
energy-momentumtensor
Einstein tensor:
Ricci tensor
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K. Schwarzschild, 1916:A solution for a static isotropic gravitational field
singularity at r = 2GM !
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Scwarzschild radius
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The meaning of R = 2GM ?
Consider the following Michell-like “derivation”:
m
M
v
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?
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Black holes radiate
Black holes emitthermal radiationwith temperature
S.Hawking ‘74
acceleration of gravityat the surface, (4GM)-1
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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?
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Can black holes be produced at RHIC?
W. Busza, R.L. Jaffe, J. Sandweiss, F. Wilczek, hep-ph/9910333
RHIC:M < 104 GeVR > 10-2 fmE = 200 GeV
No rolefor classicalor quantumgravity:
< 10-22
< 10-34
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Can black holes anyway help usto understand the physics at RHIC?
One new idea: use a mathematical correspondence between a gauge theory and gravity in AdS space
Gauge theory Gravity
Anti de Sitter space - solution of Einstein’s equationswith a negative cosmological constant (de Sitter space - solution with a positive inflation
Maldacena
deconfinement -black hole formationin AdS5xS3xT space
Witten; Polyakov;Gubser, Klebanov;Son, Starinets, Kovtun;Nastase; …
boundary
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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)
Isometry group = SO(2,d-1) for AdSd
for AdS5 boundary is S3x Time;SO(2,4) maps the boundary on itself andacts as a conformal group in 3+1 dimensions -hence the gauge theory defined on the boundaryis conformal (no asymptotic freedom, no confinement) Are gravitational-like effects possible in QCD?
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Black holes radiate
Black holes emitthermal radiationwith temperature
S.Hawking ‘74
acceleration of gravityat the surface, (4GM)-1
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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 detectsa thermal radiation with temperature
W.Unruh ‘76
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In both cases the radiation is due to the presence of event horizon
Accelerated frame: part of space-time is hidden (causally disconnected) from an accelerating observer; Rindler metric
Black hole: the interior is hidden from an outside observer; Schwarzschild metric
€
ρ2 = x 2 − t 2,
€
=1
2ln
t + x
t − x
€
ds2 = ρ 2dη 2 − dρ 2 − dx⊥2
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Pure and mixed states:the event horizons
mixed state pure state mixed state pure state
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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 inEuclidean space…
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well, now we need some quantum mechanics, too:
The rate of tunnelingunder the potential barrier:
This is a Boltzmann factor with
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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
Accelerated detector is effectively immersed into a heat bath at temperature TU=a/2
Unruh,76
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An example: electric fieldThe 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
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The Schwinger formula
e+
e-
Dirac seaE
+ + + …
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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 QuickTime™ and a
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where a=eE/m isthe acceleration Classically forbidden
trajectory
€
t → −itE
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€
S(t) = −m
aarcsh(at) +
eE
2a2at( 1+ a2t 2 − 2) + arcsh(at)( )
• Action along the classical trajectory:
• In Quantum Mechanics S(t) is an analytical function of t
• Classically forbidden paths contribute to
€
ImS(t) =mπ
a−
eEπ
2a2=
πm2
2eE
• Vacuum decays with probability
€
ΓV →m =1− exp −e−2 Im S( ) ≈ e−2 Im S = e−πm 2 / eE
• Note, this expression can not be expanded in powers of the coupling - non-perturbative QED!
Sauter,31Weisskopf,36Schwinger,51
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Pair production by a pulse
€
Aμ = 0,0,0,−E
k0
tanh(k0t) ⎛
⎝ ⎜
⎞
⎠ ⎟
Consider a time dependent field E
t
• Constant field limit
€
k0 → 0
• Short pulse limit
€
k0 → ∞
a thermal spectrum with
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Chromo-electric field:Wong equations
• Classical motion of a particle in the external non-Abelian field:
€
m˙ ̇ x μ = gF qμν ˙ x ν Ia
€
˙ I a − gfabc ˙ x μ AμbI c = 0
The constant chromo-electric field is described by
€
A0a = −Ezδ a3, A i
a = 0
Solution: vector I3 precesses about 3-axis with I3=const
€
˙ ̇ x = ˙ ̇ y = 0,m˙ ̇ z = gE˙ x 0I3
Effective Lagrangian: Brown, Duff, 75; Batalin, Matinian,Savvidy,77; Nayak, van Nieuwenhuizen, 2005
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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 inaccelerators?
For the excitations with transverse momentum pT:
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but this is all purely academic (?)
Take g = 9.8 m/s2; the temperature is only
Can one study the Hawking radiationon Earth?
Gravity?QuickTime™ and a
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Electric fields? Lasers?
compilation by A.Ringwald
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Condensed matter black holes?
Unruh ‘81;e.g. T. Vachaspati, cond-mat/0404480“slow light”?
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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
Transition amplitude:
In dual resonance model:
Unitarity: P(mM)=const,
b=1/2universal slope
limiting acceleration
M
Hagedorntemperature!
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Fermi - Landau statistical model of multi-particle production
Enrico Fermi1901-1954
Lev D. Landau1908-1968
Hadron productionat high energiesis driven bystatistical mechanics;universal temperature
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Where on Earth can one achieve the largestacceleration (deceleration) ?
Relativistic heavy ion collisions! -stronger color fields:
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Hawking phenomenon in the parton language
k
The longitudinal frequency of gluon fields in the initial wave functions is typically very small:
p
Parton configurations are frozen,Gauge fields are flat in the longitudinal direction G+- = 0
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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 and quark pairs with 3D thermal spectrum
1/Qs
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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 cf “bottom-up” scenario c~1 (no powers of 1/g)
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Deceleration-induced phase transitions?
• Consider Nambu-Jona-Lasinio model in Rindler space
e.g.,Ohsaku,04
€
L =ψ iγ ν (x)∇νψ (x) +λ
2N(ψ (x)ψ (x))2 + (ψ (x)iγ 5ψ (x))2
[ ]
• Commutation relations:
€
γ (x),γν (x){ } = 2gμν (x)
€
ρ2 = x 2 − t 2,
€
=1
2ln
t + x
t − x
€
ds2 = ρ 2dη 2 − dρ 2 − dx⊥2
• Rindler space:
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Gap equation in an accelerated frame• Introduce the scalar and pseudo-scalar fields
€
(x) = −λ
Nψ (x)ψ (x)
€
(x) = −λ
Nψ (x)iγ 5ψ (x)
• Effective action (at large N):
€
Seff = d4 x −g −σ 2 + π 2
2λ
⎛
⎝ ⎜
⎞
⎠ ⎟− i lndet(iγ ν∇ν −σ − iγ 5π )∫
• Gap equation:
€
=−2iλσ
a
d2k
(2π )2∫ dωsinh(πω /a)
π 2(K iω / a +1/ 2(α /a))2 − (K iω / a−1/ 2(α /a))2){ }
−∞
∞
∫
where
€
2 = k⊥2 + σ 2
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Rapid deceleration induces phase transitions
QuickTime™ and aTIFF (LZW) decompressor
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Nambu-Jona-Lasinio model(BCS - type)
Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric
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Black holes
A link between General Relativity and QCD? solution to some of the RHIC puzzles?
RHIC collisions
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Additional slides
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Classical QCD in action
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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
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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 stateschanges accordingly;this means that the average transverse momentum of partons should grow
CGC QGP
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A.Nakamura and S.Sakai, hep-lat/0406009
Perfect fluid
sQGP: more fluid than water?
KSS bound:strongly coupled SUSY QCD = classical supergravity
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Kovtun, Son, Starinets, hep-th/0405231
sQGP: more fluid than water
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RHIC: a dedicated QCD machine
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QuickTime™ and aTIFF (Uncompressed) decompressor
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Bogolyubov transformation
€
φ(x) = ai,inφi,in (x) + ai,in+φi,in
i
∑ * (x)Second quantization:
where
€
ai,in ,ai,in+
[ ] = δ ij
€
ai,in | 0in
= 0
Equivalently:
€
φ(x) = ai,outφi,out (x) + ai,out+φi,out
i
∑ * (x)
where
€
ai,out ,ai,out+
[ ] = δ ij
€
ai,out | 0out
= 0
Obviously:
€
ai,in = α ija j,out + β ji * a j ,out+
( )j
∑
Therefore
€
ΓV →m =out 0 ai,inai,in+ 0
out= | β ij |2
j
∑
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Pair production by a pulse
€
Aμ = 0,0,0,−E
k0
tanh(k0t) ⎛
⎝ ⎜
⎞
⎠ ⎟Consider a time dependent field
E
t
Narozhnyj,Nikishov, 70
€
φ±p,in (x) =
1
(2π )3 / 2 2ω−
e iω− t +ir p
r r
€
φ±p,out (x) =
1
(2π )3 / 2 2ω+
α peiω− t +i
r p
r r + β pe
−iω− t +ir p
r r
( )
• Constant filed limit
€
k0 → 0
• Short pulse limit
€
k0 → ∞
€
ΓV →m =ω−
ω+
| β p |2= exp −2πm⊥
k0
⎡
⎣ ⎢
⎤
⎦ ⎥
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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) = 2π | T(m → M) |2 ρ (M)
• Unruh effect:
€
| T(m → M) |2≅ exp(−2πM /a)
• Using the dual resonance model, the density of hadronic states:
€
ρ(M) ≈ exp(4πb1/ 2M /61/ 2)
where b is universal slope of Regge trajectories
€
=1/2πbstring tension:
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Hagedorn temperature• Probability conservation:
€
P(m → M)M
∑ = const
• Therefore,
€
a
2π≡ T ≤
61/ 2
4πb1/ 2≡ THagedorn
• The string tension cannot create acceleration bigger than
€
acr = 3/2b−1/ 2
and, thus, produce pairs at temperature bigger than
€
THagedorn
• One needs stronger field to get larger temperature, e.g.
€
ECGC ≅ Qs2(s, A) /g
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Pair production in GR• The same problem of quantization in external field!
€
Dμ Dν gμν φ(x) + m2φ(x) = 0
• In Schwartzschild metric
€
φωlm (x) = r−1Rωl (r)Ylm (θ,ϕ )exp(±iωt)
€
Rωl ≈exp(iωr*) + α ωl exp(−iωr*),r* → −∞
βωl exp(iωr*),r* → ∞
⎧ ⎨ ⎩
€
r* = r + rg ln(r /rg −1)(tortoise coordinate)
• Black hole emission rate:
€
| βωl |2∝ exp(−2πω /κ )
where GM is acceleration of gravity at the surface of black hole, T=1/(8GM)
Hawking, 75
in
out
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What is a black hole?
S. Chandrasekhar QuickTime™ and a
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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, …
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Picking apart the 'Big Bang' brings a big mystery By Dan Vergano, USA TODAYAn 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.
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Jets (high momentum partons) - I
Jet d’EauGeneva
3-jet event, LEP Geneva
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Jets -II
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Niagara Falls Au-Au collision event, RHIC
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Semi-classical QCD and total multiplicities in heavy ion collisions
Expect very simple dependence of multiplicity.on atomic number A / Npart:
Npart:
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Quantization in external field• Condier charged scalar field coupled to external electric field E. Klein-Gordon equation:
€
∂ + ieAμ( )2φ(x) + m2φ(x) = 0
• Let AA(t). Then the eigenstates are
€
φ±p (x) =
1
(2π )3 / 2 2ω−
e ir p
r r g±(
r p , t)
€
ω± = limt →±∞
ω(t)
€
∂ttg(r p , t) + ω2(t)g(
r p , t) = 0;
€
ω 2(t) =r p 2 − 2epz Az + e2Az
2 + m2
where
• Note, in(x) are different from
out(x)
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Recent idea:
Quantum Black Holesand
Relativistic Heavy Ions ?
DK & K.Tuchin, hep-ph/0501234
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Effective Lagrangian• Effective Lagrangian in constant magnetic field: sum over Landau levels (generalization to E≠0 is straightforward):
€
Leff =eB
(2π )2m2 + pz
2 + 2 m2 + pz2 + 2eBn
n=1
∞
∑ ⎧ ⎨ ⎩
⎫ ⎬ ⎭dpz
−∞
∞
∫
• In weak fields:
€
Leff ≈e4
360π 2m4
r E 2 −
r B 2( ) + 7
r E ⋅
r B ( )[ ] + ...
Heisenberg,Euler, 36
• Note that
€
ImLeff = 0 in all orders of this expansion.
+ + + …
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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 detectsa thermal radiation with temperature
W.Unruh ‘76
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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
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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…
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well, now we need some quantum mechanics, too:
The rate of tunnelingunder the potential barrier:
This is a Boltzmann factor with
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An example: electric fieldThe 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
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The Schwinger formula
e+
e-
Dirac seaE
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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 inaccelerators?
For the excitations with transverse momentum pT:
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but this is all purely academic (?)Take g = 9.8 m/s2; the temperature is only
Where on Earth can one achieve the largestacceleration (deceleration) ?
Relativistic heavy ion collisions!
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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
Transition amplitude:
In dual resonance model:
Unitarity: P(mM)=const, b=1/2universal slope
limiting acceleration
Hagedorntemperature!
M
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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 stateschanges accordingly;this means that the average transverse momentum of partons should grow
CGC QGP
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Quantum thermal radiation at RHIC
The event horizon emerges due to the fastdecceleration of the colliding nucleiin strong color fields;
Tunneling throughthe event horizon leads to the thermalspectrum
Rindler and Minkowski spaces
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Fast thermalization
Rindler coordinates:
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collision point Qs
horizons
Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell in t=2Qs
(period of Euclidean motion)
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Rapid deceleration induces phase transitions
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Nambu-Jona-Lasinio model(BCS - type)
Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric
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Hawking radiation
New link between General Relativity and QCD;solution to some of the RHIC puzzles?
RHIC event
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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 ?
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The future: experimental facilities
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QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.LHC
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PHENIX Collaboration
0.906<<1.042
dN/dy = A (Ncoll)
induced gluon radiation should be suppressed for heavy quarks; is it?
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Direct photons as a probe What is the origin of the “B/ puzzle”?
0-10% Central 200 GeV AuAu
PHENIX Preliminary
1 + (γ pQCD x Ncoll) / γ phenix
backgrd Vogelsang NLO
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Heavy quarkonium as a probe
Talk by F. Karsch
the link between the observablesand the McLerran-Svetitskyconfinement criterion
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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
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Summary
1. Quantum Chromo-Dynamics isan established and consistent field theory of strong interactions
but it’s properties are far from being understood2. High energy nuclear collisions test the predictions of strong field QCD and probe the properties of super-dense matter3. New connections between field theory and General Relativity (black holes,…)
All of this directly tested by experiment!
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Additional slides
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Classical QCD in action
The data on hadron multiplicities in Au-Au and d-Au collisions support the semi-classical picture
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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