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Berndt Müller

H-QM Opening SymposiumGSI, November 9, 2006

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Genre:Comedy / Crime /

Romance / Thriller

Eating Takoyaki(squid balls) fresh

from the grill in Osaka/Japan

Nucleons + mesons

Quark-gluon

plasma

Nucleons + mesons

Melting nuclear matter (at RHIC / LHC / FAIR)

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What heat does to matter:Increases disorder (entropy)Speeds up reactionsOvercomes potential barriers

States / phases of matter:Solid [long-range correlations, shear elasticity]Liquid [short-range correlations]

Gas [few correlations]Plasma [charged constituents] (solid / liquid / gaseous)

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Matter governed by the laws of QCD can also take on different states:

Solid, e.g. crust of neutron starsLiquid, e.g. all large nucleiGas, e.g. nucleonic or hadronic gas (T 7 MeV)Plasma - the QGP (T > Tc 150 – 200 MeV)

The QGP itself may exist in different phases:Gaseous plasma (T Tc)Liquid plasma (T, near Tc, c ?)Solid, color superconducting plasma ( c)

5B

Hadronicmatter

Critical end point

Plasma

Nuclei

Chiral symmetrybroken

Chiral symmetryrestored

Color superconductor

Neutron stars

T

1st order line

Quark-Gluon

RHIC

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RHIC

2

30 LHC ?

170 340 510 MeV

27f4(2 8)Degrees of fr (2 3 ) 1 ( )eedom : N O g

quarksgluons

colorcolorspin spin flavor

Indication of weak coupling?

Lattice QCD (Bielefeld)

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a

2 ( ) ( )a a b a bG Qg g

2a aInduced color density

2 2 2 2( ) ,wit (6

h )FG Q

NgT gT

Static color charge (heavy quark) generates screened potential

a a rst er

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B

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Color correlation length

Time

Length (z)

Quasi-abelian

Non-abelian

Noise

M. Strickland, hep-ph/0511212

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Higgs

field

quark

Quark

condensate

quarkqq

qq

QCD mass disappears above Tc:(partial) chiral symmetry restoration

1

10

100

1000

10000

100000

1000000

u d s c b t

QCD massHiggs mass

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R. Gavai & S. Gupta, hep-lat/0510044

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ln ( , )XY iX Y

i i ii

Z T XY X Y

XS x s n22

3XS

XS X SC

S S

pQGP

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quarks gain QCD mass and become confined

Arrow of time

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STAR

…is hexagonal and 3.8 km long

Relativistic Heavy Ion Collider

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Phenomenology provides t he connect ion

Detectors Computers

BG-J

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final2

( )/( )

( )/

( / )

dN dys

dV dy

dN dy

R

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eq

( 1 fm/c) 33/fm

or ( ) 275 MeV

in Au+Au (200 GeV)

s

T

Bjorken formula

eqPre-equil. phase

Liberation of saturated low-x

glue fields (CGC)

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Some important results from RHIC:

Chemical equilibration (incl. s-quarks!) u, d, s-quarks become light and unconfined

Elliptic flow rapid thermalization, low viscosity

Collective flow pattern related to valence quarks

Jet quenching parton energy loss, high color opacity

Strong energy loss of c and b quarks (why?)

Charmonium suppression is not increased compared with lower (CERN-SPS) energies

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1 1 2

2 ch

( )exp

Y m m

Y T

Increase in flavor correlation length rc 1 fm ( ?) + gluon thermalization

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Suppression of hadrons

No suppression for photons

Cross section in p+p coll’s

Area density of p+p coll’s

in A+A

Yield in A+A

2

2

/( )

/AA T

AA T

AA NN T

d N dp dyR p

T d dp dy

Without nuclear effects:

RAA = 1.

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qq

Radiative energy loss:

2 2TE L k

Scattering centers = color chargesq q

g

L

2T

2 22

ˆ ( ) (0)ii

dq dxq d xk

dqFq F

Density of scattering centers

Range of color forceScattering power of the QCD medium:

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Pion gas

QGP

Cold nuclear matter

sQGP? ??

RHIC data

“Baier plot”

RHIC

Eskola et al.

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Where does the “lost” energy go?

p+p Au+Au

Lost energy of away-side jet is redistributed to angles away from 180° and low transverse momenta pT < 2 GeV/c ( Mach cone?).

Trigger jetAway-side jet

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(Colorless or colorful) sonic shockwave:H. Stöcker, Nucl. Phys. A 750:121-147 (2005),J. Casalderrey-Solana & E. Shuryak, hep-ph/0411315,J. Ruppert & B.M., Phys. Lett. B 618:123-130 (2005),T. Renk & J. Ruppert, hep-ph/0509036

Localized heating of medium:A.Chaudhouri, U. Heinz, nucl-th/0503028

(does not work!)

Large Angle Gluon Emission:Ivan Vitev, Phys.Lett.B630:78-84,2005Cherenkov ( -like) radiation:A. Majumder & X. N. Wang, nucl-th/0507062,V. Koch et. al., nuclt-th/0507063,I. Dremin, hep-ph/0507167

Trigger jet

Trigger jet

Trigger jet

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Mach cone requires collective mode with (k) < k and strong coupling fs 0.8.

T. Renk & J. Ruppert

N=4 SUSY YM at strong coupling

J. Friess et al.

hep-th/0607022

J. Ruppert

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Collision Geometry: Elliptic Flow

Elliptic flow (v2) :• Gradients of almond-shape surface will lead to preferential expansion in the reaction plane• Anisotropy of emission is quantified by 2nd

Fourier coefficient of angular distribution: v2

prediction of fluid dynamics

Reaction plane

x

z

y

Bulk evolution described by relativistic fluid dynamics,assumes that the medium is in local thermal equilibrium,but no details of how equilibrium was reached.I nput: (x, i) , P( ) , ( ,etc.) .

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spatial eccentricity

momentumanisotropyinitial energy density distribution:

Elliptic flow: early creation

Time evolution of the energy density:

Flow anisotropy must generated at the earliest stages of the expansion, and matter needs to thermalize very rapidly, before 1 fm/c.

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2 pT

Mass splitting characteristic property of hydrodynamics

Failure of ideal hydrodynamics tells us how hadrons form

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2

In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :

2 2 2 2v22

v3

v3v Btt

q tM q tp ppp

q q q

q qT, ,v

Emitting medium is composed of unconfined, flowing quarks.

Paul Sorensen

Chiho Nonaka

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QGP

D. Teaney

0/ /s s

Exciting theoretical discovery:

N=4 SUSY YM theory (g2Nc 1) and string – CFT duality give

/s = 1/(4 (Kovtun, Son, Starinets).

Absolute lower bound on /s !?

Boost invariant hydrodynamics with T0 0 ~ 1 requires /s 1/10.

QGP(T˜ Tc) = sQGP ?

( )

0 with

( trace)P u

T

uT uu Pg

Relativistic viscous hydrodynamics:

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tr3f

pnp

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Is strong coupling really necessary for small /s ?

Possible resolution:Color instabilities

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Unstable modes in plasmas occur generally when the momentum distribution of a plasma is anisotropic (Weibel-type instabilities).

22 22 1forx y s z

s

p p Q pQpz

py

px

beam

Conditions are satisfied in nuclear collisions:

Longitudinal expansion locally “red-shifts” the longitudinal momentum components of released small-x gluon fields (CGC) from initial state:

In EM case, instabilities saturate due to effect on charged particles. In YM case, field nonlinearities lead to saturation (competition with Nielsen-Oleseninstability?)

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Exponential growth saturates when

B2 > g2 T4.

Mrowczynski

Strickland et al.

Arnold et al.

Wavelength and growth rate of unstable modes can be calculated perturbatively:

kz ~ gQs , ~ gQs < kz

Turbulent power spectrum

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Expansion Anisotropy

0 0

0

132

1

3

1

2

Perturbed equilibrium distribution:

For shear flow of ultrarelat. flu

( ) ( ) 1 1 ( )

( ) exp[ / ]

5 /( )

2

( )

( )

(

id:

)

i jij ij

ij i j j i ij

f p f p f p

f p u p T

sp p u

ETu u

f

u

p

u

f p

Anisotropic momentum distributions generate instabilities of soft field modes. Growth rate ~ f1(p).

Formation of turbulent color fields is controlled by f1(p), i.e. ij(u) and /s.

But: turbulent color fields control the anomalous viscosity A.

QGP

X-space

QGP

P-space

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p

paB

mr

13

2 2( )

2 2 2 2

Classical expression for shear viscosity:

Momentum change in one coherent domain:

Anomalous (collisionless) mean free path:

Anomalous viscosity due to random col

f

a am

Af m

m

np

p gQ B r

p pr

g Q B rp

33 94

2 2 2 2 2 2

or ie s

3

f ld :

A

m m

sTnp

g Q B r g Q B r

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Take moments of with pz2( , , )( )r p p

p

D pp

f r p t C ft E

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1

3

2

3

4 ln 11

1 11

10

mc

A Cc

FNO

N

g

sT

gO

T

M. Asakawa, S.A. Bass, B.M.,

PRL 96:252301,2006

hep-ph/0608270

' ( '), ' ( , ) ,

= color force

( )

v

ta b

i ab j

a a a

ij dt F r t t U r rD F r t

F

p

g E B

2

= jet

' ( ') ( )

quenching parameter !!

ˆ

!

ii mdt F t qF t F

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Possible effects on QGP probes:

Longitudinal broadening of jet cones (observed – “ridge”)

Anomalous diffusion of charm and bottom quarks (observed)

Synchrotron-style radiation of soft, nonthermal photons ?

Field induced quarkoniumdissociation ?

No unstable modes for quarks: quasi-particle picture of QGP is compatible with low viscosity

z

yx

B

JetJet

Au+Au 20-30%

a

b

c c

b

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LHC

ATLAS

CMS

ALICE

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Heavy ion physics at the LHC is only ~2 years away

LHC will provide quantitative tests of the models developed to describe the RHIC data:

Saturation of the initial gluon density(Almost) ideal hydrodynamic evolution of matter (v2)Scaling of parton energy loss with path lengthColor screening, quark recombination

Major new probes: contained jets and b-quarks, permitting much improved control of theoretical predictions.

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Bulk physics probes 10-4 < x < 10-3

100 GeV jets similar to 2 GeV hadrons at RHIC

Forward/backward regions provide access to very small x 10-5

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~ 1/Q2

2 1 / 3

2 2 2

(parton density

, )= r 1

a ea sA

A

xG x Q A x

R Q Q

2sat ( , )Q x A

Glassy gluons are liberated – quark pairs are produced rapidly.

“Glasma” turns into a quark-gluon plasma..

Nonlinear interactions among classical fields lead to the saturation of gluon density in the transverse plane.

“Color Glass Condensate”

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ECM

3

2

Geometric scaling à la Golec-Biernat & Wüsthoff

1/

2 2 0sat 0 2

with 0.288, 0.79

( , )A

x AQ x A Q

x R

(Armesto et al. hep-ph/0407018)

From fit to HERA e-p and NMC nuclear photoabsorption data.

2 2sat,/ A AdN dy Q R

LHC RHICin in3 500 MeVT T

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Photon- or Z0-tagged jets [g+q q+ (Z)]:Study of jets with known energy.

Fully resolved jets (ET > 100 GeV): Measurement of full medium-modified fragmentation function.

Tri-jets: Study of gluon propagation.

Jets initiated by c- and b-quarks., ’, ’’ spectroscopy:

Improved test of color screening.

Nuclear parton distributions down to x ~ 10-5 -10-6

(in p+A collisions): probe of gluon saturation.

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Do we have a coherent theoretical framework ?

High-pT hadrons: YES, but…High-pT di-hadrons: MAYBE

-jet correlations: YES, but…Single jets: YES, but…Tri-jets: NOHeavy quarkonia: NOHigh invariant mass lepton pairs: YES, but…High pT photons: MAYBE

There are many research challenges for theorists !

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AA

Vitev et al (GLV)

LHC

Armesto et al (ASW)

Extrapolations to LHC energy vary widely due to modeling differences:

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Detector

Deeper penetration of higher-pT probe leades to

increased “punch-through”of away side jet.

T. Renk

Vertex distribution for trigger hadrons of pT – 25 GeV/c in Pb+Pb @ LHC

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Jet energy is not lost, but just redistributed inside the jet cone to larger kt than in vacuum fragmentation (LPM effect).

Separation of fully evolved jet from background will become possible at LHC for large jet energies.

kT

Medium modifications of jet shape can tell us about the mechanism of energy loss of the initiating parton.

Are jets induced by b-quarks modified differently than those induced by light quarks/gluons?

400 GeV2

TdE

dy

Distributed over ~300 particles.

Soft background:

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Outlook

The RHIC program has shown that

• equilibrated matter is rapidly formed in heavy ion collisions;

• wide variety of probes available at collider energies;

• systematic study of matter properties is possible.

QGP appears to be a turbulent color liquid with novel and unanticipated transport properties.

Experimental surprises have become a gold mine for theorists:

• extreme opaqueness of matter to colored probes;

• large enhancement of baryon production;

• collective flow phenomena indicating strong coupling;

• connection to string theory and AdS/CFT duality.

Exciting times for HI physics at the LHC lie ahead !

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THE ENDOF THIS TALK - BUT

THE BEGINNINGFOR H-QM