RHIC Phenomenology: Quantum Chromo-Dynamics with relativistic heavy ions D. Kharzeev BNL School on...

RHIC Phenomenology:Quantum Chromo-Dynamicswith relativistic heavy ions

D. Kharzeev

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

“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:

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

What is QCD?

QCD = Quark Model + Gauge Invariance

.i QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

local gauge transformation:

QCD and the origin of mass

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

gluonsquarks

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

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

Asymptotic freedom and Landau levels of 2D parton gas

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:

QCD and the classical limit

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 )

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

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”)

Non-linear QCD evolutionand population growth

T. Malthus (1798)

r - rate of maximum population growth

time rapidity

Unlimited growth!

Linear evolution:

Color glass condensate

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

Pierre Verhulst (1845)

Stable population:

K - maximum sustainable population; define

“logisticequation”

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The limit is universal (no dependence on the initial condition)

r = 1.5, N(0)=0.1, x(0)=0.1

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

High energy evolution starts here.

Semi-classical QCD: experimental tests

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

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; …

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 v2D. Kharzeev, Yu. Kovchegov and

K. Tuchin, hep-ph/0307037

CGC at y=0Y=0

Very high energy

As y grows

R. Debbe, BRAHMS Coll., Talk at DNP Meeting, Tucson,November 2003

R.Debbe, BRAHMS,QM’04

Nuclear Modification of Hard Parton Scattering

Color Glass Condensate: confronting the data

DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045

BRAHMSdata,

Color Glass Condensate: confronting the data

DK, Yu. Kovchegov, K. Tuchin, hep-ph/0405045

BRAHMSdata, RCP

Confronting the RHIC data

hadrons

DK & K.Tuchin STAR Collaboration

Centrality dependence

R.Debbe, BRAHMS, QM’04

Phenix Preliminary

Color Glass?Shadowing?

Cronin effect &anti-shadowing?

Phenix Preliminary

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…

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 !

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

Strongly coupled QCD plasma

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 PlasmaThese 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

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

Lecture by F.Karsch

Percolation deconfinement, CGC?

Lecture byH. Satz

A.Nakamura and S.Sakai, hep-lat/0406009

Perfect fluid

sQGP: more fluid than water?

KSS bound:strongly coupled SUSY QCD = classical supergravity

Charge fluctuations in sQGP Lecture by F.Karsch

Hadron resonancegas

Dynamicalquarks

QQ bound states

S.Ejiri, F.Karsch and K.Redlich, 05

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

PHOBOS

Hydro limit

PHOBOS

Azimuthal anisotropy as a measure of the interaction strength

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

J/Y suppression -> F.Fleuret, H.Satz

Jets (high momentum partons) - I

Jet d’EauGeneva

3-jet event, LEP Geneva

Jets -II

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 ‘‘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

The emerging picture

Big question:

How does the producedmatter thermalize so fast?

Perturbation theory +Kinetic equations:Thermalization time too long (?)

Recent idea:

Quantum Black Holesand

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?

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:

Who was John Michell?

Rev. John Michell (1724-1793)

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

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

“What we know is not much. What we do not know is immense.”

A. Einstein, 1915:

energy-momentumtensor

Einstein tensor:

Ricci tensor

K. Schwarzschild, 1916:A solution for a static isotropic gravitational field

singularity at r = 2GM !

Scwarzschild radius

The meaning of R = 2GM ?

Consider the following Michell-like “derivation”:

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

Black holes emitthermal radiationwith temperature

S.Hawking ‘74

acceleration of gravityat 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?

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

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

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?

Black holes radiate

Black holes emitthermal radiationwith temperature

S.Hawking ‘74

acceleration of gravityat 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 detectsa thermal radiation with temperature

W.Unruh ‘76

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,

t − x

ds2 = ρ 2dη 2 − dρ 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 inEuclidean space…

well, now we need some quantum mechanics, too:

The rate of tunnelingunder 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

Accelerated detector is effectively immersed into a heat bath at temperature TU=a/2

Unruh,76

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

The Schwinger formula

Dirac seaE

+ + + …

• 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

S(t) = −m

aarcsh(at) +

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

• 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

Pair production by a pulse

Aμ = 0,0,0,−E

tanh(k0t) ⎛

⎝ ⎜

⎠ ⎟

Consider a time dependent field E

• Constant field limit

k0 → 0

• Short pulse limit

k0 → ∞

a thermal spectrum with

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

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

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:

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

Electric fields? Lasers?

compilation by A.Ringwald

Condensed matter black holes?

Unruh ‘81;e.g. T. Vachaspati, cond-mat/0404480“slow light”?

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

Hagedorntemperature!

Fermi - Landau statistical model of multi-particle production

Enrico Fermi1901-1954

Lev D. Landau1908-1968

Hadron productionat high energiesis driven bystatistical mechanics;universal temperature

Where on Earth can one achieve the largestacceleration (deceleration) ?

Relativistic heavy ion collisions! -stronger color fields:

Hawking phenomenon in the parton language

The longitudinal frequency 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 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 cf “bottom-up” scenario c~1 (no powers of 1/g)

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,

t − x

ds2 = ρ 2dη 2 − dρ 2 − dx⊥2

• Rindler space:

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

⎝ ⎜

⎠ ⎟− i lndet(iγ ν∇ν −σ − iγ 5π )∫

• Gap equation:

=−2iλσ

(2π )2∫ dωsinh(πω /a)

π 2(K iω / a +1/ 2(α /a))2 − (K iω / a−1/ 2(α /a))2){ }

−∞

2 = k⊥2 + σ 2

Rapid deceleration induces phase transitions

Nambu-Jona-Lasinio model(BCS - type)

Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

Black holes

A link between General Relativity and QCD? solution to some of the RHIC puzzles?

RHIC collisions

Additional slides

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

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

A.Nakamura and S.Sakai, hep-lat/0406009

Perfect fluid

sQGP: more fluid than water?

KSS bound:strongly coupled SUSY QCD = classical supergravity

Kovtun, Son, Starinets, hep-th/0405231

sQGP: more fluid than water

RHIC: a dedicated QCD machine

Bogolyubov transformation

φ(x) = ai,inφi,in (x) + ai,in+φi,in

∑ * (x)Second quantization:

ai,in ,ai,in+

[ ] = δ ij

ai,in | 0in

Equivalently:

φ(x) = ai,outφi,out (x) + ai,out+φi,out

∑ * (x)

ai,out ,ai,out+

[ ] = δ ij

ai,out | 0out

Obviously:

ai,in = α ija j,out + β ji * a j ,out+

Therefore

ΓV →m =out 0 ai,inai,in+ 0

out= | β ij |2

Pair production by a pulse

Aμ = 0,0,0,−E

tanh(k0t) ⎛

⎝ ⎜

⎠ ⎟Consider a time dependent field

Narozhnyj,Nikishov, 70

φ±p,in (x) =

(2π )3 / 2 2ω−

e iω− t +ir p

φ±p,out (x) =

(2π )3 / 2 2ω+

α peiω− t +i

r r + β pe

−iω− t +ir p

• Constant filed limit

k0 → 0

• Short pulse limit

k0 → ∞

ΓV →m =ω−

| β p |2= exp −2πm⊥

⎣ ⎢

⎦ ⎥

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:

Hagedorn temperature• Probability conservation:

P(m → M)M

∑ = const

• Therefore,

2π≡ T ≤

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

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

S. Chandrasekhar QuickTime™ and a

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 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.

Jets (high momentum partons) - I

Jet d’EauGeneva

3-jet event, LEP Geneva

Jets -II

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:

∂ + ieAμ( )2φ(x) + m2φ(x) = 0

• Let AA(t). Then the eigenstates are

φ±p (x) =

(2π )3 / 2 2ω−

e ir p

r r g±(

r p , t)

ω± = limt →±∞

∂ttg(r p , t) + ω2(t)g(

r p , t) = 0;

ω 2(t) =r p 2 − 2epz Az + e2Az

2 + m2

• Note, in(x) are different from

out(x)

Recent idea:

Quantum Black Holesand

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):

Leff =eB

(2π )2m2 + pz

2 + 2 m2 + pz2 + 2eBn

∑ ⎧ ⎨ ⎩

⎫ ⎬ ⎭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.

+ + + …

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

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 tunnelingunder the potential barrier:

This is a Boltzmann factor with

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

Dirac seaE

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:

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!

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!

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

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

Fast thermalization

Rindler coordinates:

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)

Rapid deceleration induces phase transitions

Nambu-Jona-Lasinio model(BCS - type)

Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric

Hawking radiation

New link between General Relativity and QCD;solution to some of the RHIC puzzles?

RHIC event

Quark-Hadron phase transition

Order of the deconfinement phase transition -Implications for baryosynthesis

Topological fluctuations - primordial magnetic fields?

P, CP violation ?

The future: experimental facilities

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.LHC

PHENIX Collaboration

0.906<<1.042

dN/dy = A (Ncoll)

induced gluon radiation should be suppressed for heavy quarks; is it?

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

Heavy quarkonium as a probe

Talk by F. Karsch

the link between the observablesand the McLerran-Svetitskyconfinement 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 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!

Additional slides

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

RHIC Phenomenology: Quantum Chromo-Dynamics with relativistic heavy ions D. Kharzeev BNL School on...

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