Axel Drees, Stony Brook University, Lectures at Trento June 16-20, 2008

Electromagnetic Radiation form High Energy Heavy Ion Collisions

I. Lecture: Study high T and QCD in the LaboratoryII. Lecture: Quark matter formation at RHIC III. Lecture: EM radiation and pioneering experiments at SPS IV. Lecture: An new era: precision measurements with NA60V. Lecture: PHENIX at RHIC: the challenge of high energiesVI. Lecture: Medium modifications of open charm productionVII. Lecture: Modified meson properties: insights with low

energies VIII. Lecture: The quest to detect for thermal radiationIX. Lecture: Outlook into the future (mostly RHIC)

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Gravity General Relativity

Electro-weak Quantum Field Theory

Strong interaction (QCD)

Fundamental Forces in Nature

Standard model

Although we have fundamental theories for all forces we need ~20 parameters, constants of unknown origin to describe nature.

Two outstanding puzzles:

• unseen quarks confinement

• broken symmetries existence of massive particles

Both connected to complex structure of vacuum

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Vacuum low resolution

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Vacuum high resolution

Vacuum is see of qq pairs (+ gg pairs + ..)Vacuum expectation value for u or d quarks <qq > ~ - (230 MeV)3

Vacuum density of u and d pairs ~ 3 fm-3

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Quarks and gluons carry color the charge of QCD

In nature only color neutral objects exist

Bag model:

Confinement

qqq baryons

qq mesons

0.8 fm

Pressure of vacuum (B) compensated by internal pressure

bag constant B1/4 ~ 200 MeV

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String Models

r

String with tension ~ 1 GeV/fm

QCD potential:

Need infinite energy to separate quarks

confinement

QCDV r rr

g

VQCD

r

r < rbag

r > rbag

r

1/r

(relation to <qq> ??)1 fm

1S 2S 3S 4Sbb

1S 1P 2Scc charmonuim and bottonium states

explore QCD potential

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Chiral Symmetry Chirality (handedness) or helicity

for massless particles chirality is conserved

QCD with 3 massless quarks (flavors)

symmetry

qR does not couple to qL

Masses break symmetry

if mass 0 qR couples to qL

(3) (3)L RSU SU

QCD ( ) ( ) ( )R L L R R LL L q L q m q q q q

spinmomentum

sp

sp

left handed right handed

left-handed

right-handed

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Masses of Quarks spontaneous breaking of electro-weak interaction

current mass of quark

for u & d quarks mou ~ mo

d ~ 5 MeV s quark mo

s ~ 175 MeV

explicitly breaking of chiral symmetry

spontaneous breaking of chiral symmetry constituent mass of quarks

for u & d quarks mu ~ md ~ 300 MeV (~1/3 mproton ) s quark mo

s ~ 500 MeV

spontaneous breaking of chiral symmetry

qq

q

q

coupling G

q couples toqq see

0q qm m G qq

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Symmetry Breaking

Spontaneously

Explicit

external force

VV

ground state

potential symmetricground state symmetric

potential symmetricsymmetry broken

for ground state

massless Goldstone bosonshere (2 flavors)

massive V

potential asymmetricMass small ~ 140 MeV

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1) all hadrons have well defined parity chiral symmetry qRqR = qLqL expect J doublets

2) characteristic mass scale of hadrons

1 GeV mass gap to quark condensate

except pseudoscaler mesons

Goldstone bosons: and

Consequences of Spontaneous Symmetry Breaking

1

1+ a1 (1270 MeV)

1- (770 MeV)

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current quark mass generated by spontaneous symmetry breaking (Higgs mass) contributes ~5% to the visible (our) mass

Origin of Mass

1

10

100

1000

10000

100000

1000000

u d s c b t

QCD Mass

Higgs Mass

constituent quark mass ~95% generated by

spontaneous chiral symmetry breaking (QCD mass)

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Fundamental Puzzles of Hadrons

Confinement Quarks do not exist as free particles

Large hadron masses Free quark mass ~ 5-7 MeV Quarks become “fat” in hadrons constituent mass ~ 330 MeV

Complex structure of hadrons Sea quarks and anti quarks Gluons

“spin crisis” Spin of protons not carried by quarks!

These phenomena must have occurred with formation of hadrons

nuclear matter p, n

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~ 10 s after Big Bang

Hadron Synthesisstrong force binds quarks and gluons in massive objects: protons, neutrons mass ~ 1 GeV/c2

~ 100 s after Big Bang

Nucleon Synthesisstrong force binds protons and neutrons bind in nuclei

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~ 10 s after Big Bang T ~ 200 MeV

Hadron Synthesisstrong force binds quarks and gluons in massive objects: protons, neutrons mass ~ 1 GeV/c2

~ 100 ps after Big Bang T ~ 1014 GeV

Electroweak Transition explicit breaking of chiral symmetry

inflation

Planck scale T ~ 1019 GeV End of Grand Unification

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“Travel” Back in Time QGP in Astrophysics

early universe after ~ 10 s possibly in neutron stars

Quest of heavy ion collisions

create QGP as transient state in heavy ion collisions verify existence of QGP Study properties of QGP study QCD confinement and how hadrons get their masses

neutron stars

Quark Matter

Hadron Resonance Gas

Nuclear Matter

SIS

AGS

SPS

RHIC& LHC

early universe

B

T

TC~170 MeV

940 MeV 1200-1700 MeVbaryon chemical potential

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Estimating the Critical Energy Density

• normal nuclear matter 0

• critical density: naïve estimation nucleons overlap R ~ rn

nuclear matter p, n

Quark-Gluon Plasma q, g

density or temperature

distance of two nucleons:2 r0 ~ 2.3 fm

size of nucleon rn ~ 0.8 fm

30 334

3 0

30

30.16

4

0.15 /

Afm

R r

GeV fm

303

3

30.5 3.1

4

0.5 /

c

n

c

fmr

GeV fm

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Critical Temperature and Degrees of Freedom

In thermal equilibrium relation of pressure P and temperature T

Assume deconfinement at mechanical equilibrium Internal pressure equal to vacuum pressure B = (200 MeV)4

Energy density in QGP at critical temperature Tc

Noninteracting system of 8 gluons with 2 polarizations and 2 flavor’s of quarks (m=0, s=1/2) with 3 colors

24 4 44 3 12

907 2 7

( ) 8 ( ) 378 8

232 2

total

total gluon q q

P g T T or P T

g g g g

4 200140

4 2c c

B MeVT T MeV

3( ) 0.6 /c cT GeV fm

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Critical energyC = 62 TC4

critical temperature TC

QCD calculations perturbative QCD calculations applicable only for

large momentum transfer small coupling

for small momentum transfer large coupling only solution numerical QCD calculations on lattice

results from lattice QCD establish the QCD phase transition

TC ~ 155-175 MeV C ~ 0.3-1.0 GeV/fm3

jump in energy density:

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The QCD phase transition

Change of order parameter:

deconfinement: Polyakov loop L ~ e-Fq

chiral symmetry: Quark condensate qq

chiral restoration and deconfinement

at same critical temperature TC ~ 170 MeV

temperature

deconfinement

chiral symmetry restoration

Polyakov loopresponse function

chiral susceptibility

different quark mass mq

165 MeV 175 MeV

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QCD Potential from Lattice Calculations

As temperature increases towards TC the QCD potential vanishes at large distances

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Restoration of Chiral Symmetry

Temperature axis:

sharp transition at TC (similar to lattice QCD results)

baryon density axis:

smooth transition at nuclear matter density

In hot and dense matter chiral symmetry is restored

model calculation (Nambu, Jona-Lasinio)

approaching of chiral symmetry restoration should strongly modify hadron properties like and m

)(8)/(1 42 TOfTqqqqoT

ooqqqq

33.01

oqqqq 7.0

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String Theory (AdS/CFT Correspondence)

Standard model describes all phenomena in nature, but is a disjoint framework Forces:

Gravity general relativity (classical)Electromagnetic, Weak, and Strong gauge theory

(quantum) Matter:

6 quarks, 6 leptons, plus Higgs

In string theory strings are basis of all forces

Open strings: gauge theory

Closed strings: gravity

A new approach to calculate properties of the QGP

10-34 m

(Next slides based on talk by Makoto Natsuume at RHIC/AGS Users Meeting 2008)

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Duality of Theories that Look Different

Tool in string theory for 10 years Strong coupling in one theory corresponds to weak coupling in

other theory

AdS/CFT duality (Anti deSitter Space/ Conformal field theory)

(N=4 SYM)

(in QCD)

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Relevance for Heavy Ion Collisions

New matter formed at RHIC resembles fluid QGP near phase boundary seems a strongly coupled plasma

Lower bound on Viscosity/Entropy from AdF/CFT duality4 BS k

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Exploring the Phase Diagram of QCD Quark Matter: Many new phases of matter Asymptotically free quarks &

gluons Strongly coupled plasma Superconductors, CFL ….

Experimental access to “high” T and moderate region: heavy ion collisions Pioneered at SPS and AGS Ongoing program at RHIC

Quark Matter

Hadron Resonance Gas

Nuclear Matter

sQGP

B

T

TC~170 MeV

940 MeV 1200-1700 MeVbaryon chemical potential

tem

per

atu

re

Mostly uncharted territory

Overwhelming evidence:Strongly coupled quark matter

produced at RHIC

Study high T and QCD in the Laboratory