theory of thermal electromagnetic radiation

Theory of Thermal Electromagnetic Radiation

Ralf RappCyclotron Institute +

Dept. of Physics & Astronomy Texas A&M UniversityCollege Station, Texas

USA

JET Summer School The Ohio State University (Columbus, OH)

June 12-14, 2013

1.) Intro-I: Probing Strongly Interacting Matter

• Bulk Properties: Equation of State

• Phase Transitions: (Pseudo-) Order Parameters

• Microscopic Properties: - Degrees of Freedom - Spectral Functions

Would like to extract from Observables:• temperature + transport properties of the matter• signatures of deconfinement + chiral symmetry restoration• in-medium modifications of excitations (spectral functions)

“Freeze-Out”QGPAu + Au

1.2 Dileptons in Heavy-Ion Collisions

Hadron GasNN-coll.

Sources of Dilepton Emission:

• “primordial” qq annihilation (Drell-Yan): NN→e+eX -

e+

e-

• thermal radiation - Quark-Gluon Plasma: qq → e+e , … - Hot+Dense Hadron Gas: → e+e , …

-

• final-state hadron decays: ,→ e+e , D,D → e+eX, … _

1.3 Schematic Dilepton Spectrum in HICs

qq

Characteristic regimes in invariant e+e mass, M2 = (pe++ pe)2

• Drell-Yan: primordial, power law ~ Mn

• thermal radiation: - entire evolution - Boltzmann ~ exp(-M/T)

T/qeeFB

ee

TdMdR

VdMddN

0

31 e

q0≈ 0.5GeV Tmax ≈ 0.17GeV , q0≈ 1.5GeV Tmax ≈ 0.5GeV

Thermal rate: Im Πem(M,q;B,T)

• Thermal e+e emission rate from hot/dense matter (em >> Rnucleus )

• Temperature? Degrees of freedom?• Deconfinement? Chiral Restoration?

1.4 EM Spectral Function + QCD Phase Structure

• Electromagn. spectral function

- √s ≤ 1 GeV : non-perturbative - √s > 1.5 GeV : pertubative (“dual”)

• Modifications of resonances ↔ phase structure: hadronic matter → Quark-Gluon Plasma?

√s = M

e+e → hadrons ~ Im em/ M2

)T,q(fMqdxd

dN Bee023

2em

44 Im Πem(M,q;B,T)

1.5 Low-Mass Dileptons at CERN-SPS

CERES/NA45 e+e [2000]

Mee [GeV]

• strong excess around M ≈ 0.5GeV, M > 1GeV• quantitative description?

NA60 [2005]

1.6 Phase Transition(s) in Lattice QCD

• different “transition” temperatures?!

• extended transition regions• partial chiral restoration in “hadronic phase”! (low-mass dileptons!) • leading-order hadron gas

Tpcconf ~170MeV

Tpcchiral ~150MeV

≈

qq

/ q

q

-

-

[Fodor et al ’10]

2.) Chiral Symmetry in QCD - Nonperturbative QCD, Chiral Breaking + Hadron Spectrum

3.) Thermal Electromagnetic Emission Rates - EM Spectral Function: Hadronic vs. Partonic Regimes

4.) Vector Mesons in Medium

- Many-Body Theory, Spectral Functions + Chiral Partners (-a1)

5.) Quark-Gluon Plasma Emission - Perturbative vs. Lattice-QCD Rates, “Quark-Hadron-Duality”

6.) Dilepton + Photon Spectra in Heavy-Ion Collisions - Space-Time Evolution, Phenomenology + Interpretation

7.) Summary and Conclusions

Outline

well tested at high energies, Q2 > 1 GeV2:

• perturbation theory (s = g2/4π << 1)

• degrees of freedom = quarks + gluons

2.1 Nonperturbative QCD

2

41

aq Gq)m̂Agi(q QCDL

(mu ≈ md ≈ 5 MeV )

Q2 ≤ 1 GeV2 → transition to “strong” QCD:

• effective d.o.f. = hadrons (Confinement)• massive “constituent quarks” mq* ≈ 350 MeV ≈ ⅓ Mp (Chiral Symmetry ~ ‹0|qq|0› condensate! Breaking)

↕ ⅔ fm_

2.2 Chiral Symmetry in QCD Lagrangian

2

41

aq Gq)m̂Agi(q QCDL

(bare quark masses: mu ≈ md ≈ 5-10MeV )

Chiral SU(2)V × SU(2)A transformation:

Up to OO(mq ), LQCD invariant under

Rewrite LQCD using left- and right-handed quark fields qL,R=(1±5)/2 q :

q)/i(q)(Rq VVV 2 exp

q)/i(q)(Rq AAA 25 exp

2

4

1aq

R

RRR

L

LLL G)m(

du

Di)d,u(du

Di)d,u(

OQCDL

R,LR,LR,L q)/i(q 2 exp Invariance under

isospin and “handedness”

qL

qL

g

2.3 Spontaneous Breaking of Chiral Symmetry

strong qq attraction Chiral Condensate

fills QCD vacuum: 0 LRRL qqqqqq >

>

>

>qLqR

qL-qR

-[cf. Superconductor: ‹ee› ≠ 0 , Magnet ‹M› ≠ 0 , … ]

-

Simple Effective Model: 2)qq(Gq)mi(q q effL

• assume “mean-field” , expand:

• linearize:

• free energy:

• ground state:

00 |qq|0 )qq(qq 0

G/)m*M(q*)M(Dq

G*M,Gq])Gm[i(q

q

q

4

22

21eff

0200eff

L

G*M*Mp

)(

pdNNlog

VT

fc 422

2223

3

Z

223

3

240

*Mp

*M

)(

pdGNN*M

*M fc

Gap

Equation

2.3.2 (Observable) Consequences of SBCS

• mass gap , not observable!

but: hadronic excitations reflect SBCS

• “massless” Goldstone bosons 0,±

(explicit breaking: f2 m2= mq ‹qq› )

• “chiral partners” split: M ≈ 0.5GeV ! chiral trafo: ,

• Vector mesons and :

JP=0± 1± 1/2±

0042 |qq|G*Mqq

AR )(NNRA 1535

q)()(q)(R jj

jjA 2

12

12

1505

chiral singlet

-

-iijkkii

jiijj

ij

jij

j

AiAiA

)a(

q)(qiq)i()i(q

)qR()qR()(R

1

5505 2221

21

21

21

• quantify chiral breaking?

2.3.3 Manifestation of Chiral Symmetry Breaking

Axial-/Vector Correlators

pQCD cont.

“Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85]

● chiral breaking: |q2| ≤ 1 GeV2

Constituent Quark Mass

2.4 Chiral (Weinberg) Sum Rules• Quantify chiral symmetry breaking via observable spectral functions

• Vector () - Axialvector (a1) spectral splitting

)Im(ImsdsI AVn

n 00002

31

210

21

222

|q)q(|αcI,|qq|mI

,fI,FrfI

sq

πA

[Weinberg ’67, Das et al ’67]

→(2n+1)

pQCD

pQCD

• Key features of updated “fit”: [Hohler+RR ‘12]

+ a1 resonance, excited states (’+ a1’), universal continuum (pQCD!)

→(2n) [ALEPH ‘98, OPAL ‘99]

2.4.2 Evaluation of Chiral Sum Rules in Vacuum

• vector-axialvector splitting (one of the) cleanest observable of spontaneous chiral symmetry breaking • promising (best?) starting point to search for chiral restoration

• pion decay constants

• chiral quark condensates 00002

31

210

21

222

|q)q(|αcI|qq|mI

fIFrfI

sq

πA

2.5 QCD Sum Rules: and a1 in Vacuum

• dispersion relation:

• lhs: hadronic spectral fct. • rhs: operator product expansion

[Shifman,Vainshtein+Zakharov ’79]2

2

20 Q

)Q(Π

sQ

)s(Ims

ds

• 4-quark + gluon condensate dominant








Outline

3.1 EM Correlator + Thermal Dilepton Rate

)(j)x(jexdi)Q(Π iQx 0emem4

em• EM Correlation Fct.:

e+

e

)T,q(fQQxdd

dN Bee023

2em

44

Im Πem(M,q;T,B)

*(q))j

Qj()f(fi|j|ff|j|i

)QPP(E)(

pd

E)(

pde

xd

dNV

eefi

fif

ff

i

iieeee

4emem

3

3

3

34

4

11

22222

• Quark basis:

• Hadron basis:

(T,B)

ssdduuj 31

31

32 em

jjj

ss)dduu()dduu(j

31

231

21

31

61

21

em

→ 9 : 1 : 2

[McLerran+Toimela ’85]

3.2 EM Correlator in Vacuum: e+e→ hadrons

)s(emIm)s(D

gm

V,, V

V Im

22

s,d,u

sqc

)s()e(Ns

1

122

e+

e

h1

h2…

s ≥ sdual ~ (1.5GeV)2

pQCD continuum

s < sdual Vector-Meson Dominance

q

q_

qq_

46

KK

e+

e

3.3 Low-Mass Dileptons + Chiral Symmetry

• How is the degeneration realized?• “measure” vector with e+e , axialvector?

VacuumT > Tc: Chiral Restoration

Im Πem(M,q)

3.4 Versatility of EM Correlation Function• Photon Emission Rate

)T,q(fqd

dRq B

0230 em

Im Πem(q0=q)

e+

e-

γ ~ O(O(ααs s ))

*

• EM Susceptibility ( → charge fluctuations)

Q2 Q 2 = χem = Πem(q0=0,q→0)

~ O(1) O(1))T,q(fMqd

dR Bee023

2

4 em

same correlator!

• EM Conductivity

em = lim(q0→0) [ -Im Πem(q0,q=0)/2q0 ]








Outline

4.1 Axial/Vector Mesons in Vacuum

Introduce a1 as gauge bosons into free + +a1 Lagrangian

2

21 g)(gintL

1202 )]M()m(M[)M(D )(

EM formfactor

scattering phase shift

2402 |)M(D|)m(|)M(F| )(

)M(DRe)M(DIm

)M(

1-tan

|F|2

-propagator:

• 3 parameters: m(0), g,

4.2 -Meson in Matter: Many-Body Theory

D(M,q;B,T) = [M2 – (m(0))2 - - B - M ]-1

interactions with hadrons from heat bath In-Medium -Propagator

[Chanfray et al, Herrmann et al, Urban et al, Weise et al, Koch et al, …]

• In-Medium Pion Cloud

>>

R=, N(1520), a1, K1...

h=N, , K …

=• Direct -Hadron

Scattering

= +

[Haglin, Friman et al, RR et al, Post et al, …]

• estimate coupling constants from R→ + h, more comprehensive constraints desirable

4.3 Constraints I: Nuclear Photo-Absorption total nuclear -absorption in-medium-spectral cross section function at photon point

>

>

,N*,*

N-1

)q,M(Dg

mq

)qq(qA

)q(

NN

A 044

2

4

00

0

0 medemem

abs

ImIm

N → N ,

N →

meson exchange

direct resonance

4.3.2 Spectral Function in Nucl. Photo-Absorption

NA

-ex

[Urban,Buballa,RR+Wambach ’98]

On the Nucleon On Nuclei

• 2.+3. resonances melt (selfconsistent N(1520)→N)

• fixes coupling constants and formfactor cutoffs for NB

4.4 -Meson Spectral Function in Nuclear Matter

In-med. -cloud ++N→B* resonances

+N→B* resonances (low-density approx.)

In-med. -cloud + +N → N(1520)

Constraints:N , A N →N PWA

• Consensus: strong broadening + slight upward mass-shift• Constraints from (vacuum) data important quantitatively

N=0

N=0

N=0.50

[Urban et al ’98]

[Post et al ’02]

[Cabrera et al ’02]

4.5-Meson Spectral Functions “at SPS”

• -meson “melts” in hot/dense matter• baryon densityB more important than temperature

B/0

0 0.1 0.7 2.6

Hot + Dense Matter

[RR+Gale ’99]

Hot Meson Gas

[RR+Wambach ’99]

B =330MeV

4.6 Light Vector Mesons “at RHIC + LHC”

• baryon effects remain important at B,net = 0:

sensitive to B,tot= + B (-N = -N, CP-invariant)

• also melts, more robust ↔ OZI

- [RR ’01]

4.7 Intermediate Mass: “Chiral Mixing”

)q()q()()q( ,A

,VV

00 1

)q()q()()q( ,V

,AA

001 =

=

• low-energy pion interactions fixed by chiral symmetry

• mixing parameter

2

2

3

3

2 6224

fT)(f

)(kd

fk

k

[Dey, Eletsky +Ioffe ’90]

0

0 0

0

• degeneracy with perturbative spectral fct. down to M~1GeV

• physical processes at M ≥ 1GeV: a1 → e+e etc. (“4 annihilation”)

4.8 Axialvector in Medium: Dynamical a1(1260)

+ + . . . =

Vacuum:

a1

resonance

InMedium: + + . . .

[Cabrera,Jido, Roca+RR ’09]

• in-medium + propagators• broadening of - scatt. Amplitude• pion decay constant in medium:

4.9 QCD + Weinberg Sum Rules in Medium

T [GeV]

[Hatsuda+Lee’91, Asakawa+Ko ’93, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]

)(sdsI AVn

n 2

122

02

1 q)q(αcI,mfI,fI sπ

[Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘94]

• melting scenario quantitatively compatible with chiral restoration• microscopic calculation of in-medium axialvector to be done

[Hohler et al ‘12]s [GeV2]

V,A/sVacuum T=140MeV T=170MeV

4.10 Chiral Condensate + -Meson Broadening

qq

/ q

q 0

-

-

effective hadronic theory

• h = mq h|qq|h > 0 contains quark core + pion cloud

= hcore + h

cloud ~ + +

• matches spectral medium effects: resonances + pion cloud

• resonances + chiral mixing drive -SF toward chiral restoration

>>

-








Outline

• marked low-mass enhancement

• comparable to recent lattice-QCD computations

Im [ ] = + + + …

5.1 QGP Emission: Perturbative vs. Lattice QCD

Baseline:q

q

_

e+

e

small M → resummations,finite-T perturbation theory (HTL)

q

q

collinear enhancement: Dq,g=(t-mD

2)-1 ~ 1/αs

[Braaten,Pisarski+Yuan ‘91]

[Ding et al ’10]

dRee/d4q 1.45Tc

q=0

5.2 Euclidean Correlators: Lattice vs. Hadronic

]T/q[)]T/(q[

)T;q,q(dq

)T;q,( VV 221

2 0

00

0

0sinh

cosh • Euclidean Correlation fct.

)T,(G

)T,(G

V

V

free

Hadronic Many-Body [RR ‘02] Lattice (quenched) [Ding et al‘10]

• “Parton-Hadron Duality” of lattice and in-medium hadronic …

5.2.2 Back to Spectral Function

• suggestive for approach to chiral restoration and deconfinement

-Im

em

/(C

T q

0)

5.3 Summary of Dilepton Rates: HG vs. QGP

dRee /dM2 ~ ∫d3q f B(q0;T) Im em

• Lattice-QCD rate somwhat below Hard-Thermal Loop

• hadronic → QGP toward Tpc: resonance melting + chiral mixing

• Quark-Hadron Duality at all Mee?! (QGP rates chirally restored!)








Outline

6.1 Space-Time Evolution + Equation of State

• 1.order → lattice EoS: - enhances temperature above Tc

- increases “QGP” emission - decreases “hadronic” emission

• initial conditions affect lifetime

• simplified: parameterize space-time evolution by expanding fireball

• benchmark bulk-hadron observables

• Evolve rates over fireball expansion:

[He et al ’12]

Au-Au (200GeV)

)p(Acc),T;q,M(qxdd

dNq

qdM)(Vd

dMdN e

tM,B

thermee

FB

thermee

fo

44

0

3

0

6.1.2 Bulk Hadron Observables: Fireball Model

• Mulit-strange hadrons freeze-put at Tpc

• Bulk-v2 saturates at ~Tpc

[van Hees et al ’11]

6.2 Di-Electron Spectra from SPS to RHIC

• consistent excess emission source

• suggests “universal” medium effect around Tpc

• FAIR, LHC?

QM12

Pb-Au(17.3GeV)

Pb-Au(8.8GeV)

Au-Au (20-200GeV)

[cf. also Bratkovskaya et al, Alam et al, Bleicher et al, Wang et al …]

6.3 In-In at SPS: Dimuons from NA60• excellent mass resolution and statistics • for the first time, dilepton excess spectra could be extracted!

+ full acceptance correction…

[Damjanovic et al ’06]

6.3.2 NA60 Multi-Meter: Accept.-Corrected Spectra

• Thermal source!• Low-mass: good sensitivity to medium effects, T~130-170MeV• Intermediate-mass: T ~ 170-200 MeV > Tpc

• Fireball lifetime FB = (6.5±1) fm/c

[CERN Courier Nov. 2009]

Emp. scatt. ampl. + T- approximation

Hadronic many-body

Chiral virial expansion

Thermometer

Spectrometer

Chronometer

6.3.3 Spectrometer

• in-med + 4 + QGP • invariant-mass spectrum directly reflects thermal emission rate!

+ Excess Spectra In-In(17.3AGeV) [NA60 ‘09]

M[GeV]

Thermal Emission Rate

[van Hees+RR ’08]

dMRd

Vqd

dRq

qdM)(Vd

dMdN

FB

fo

440

3

0

thermtherm

M[GeV]

6.4 Conclusions from Dilepton “Excess” Spectra

• thermal source (T~120-230MeV)

• in-medium meson spectral function

- avg. (T~150MeV) ~ 350-400 MeV

(T~Tpc) ≈ 600 MeV → m

- “divergent” width ↔ Deconfinement?!

• M > 1.5 GeV: QGP radiation

• fireball lifetime “measurement”: FB ~ (6.5±1) fm/c (In-In)

[van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ’08, Santini et al ‘10]

6.5 The RHIC-200 Puzzle in Central Au-Au

• PHENIX, STAR and theory:

- consistent in non-central collisions

- tension in central collisions

6.6 Direct Photons at RHIC

• v2,dir as large as for pions!?

• underpredcited by QGP-dominated emission

← excess radiation

• Teffexcess = (220±30) MeV

• QGP radiation?• radial flow?

Spectra Elliptic Flow

[Holopainen et al ’11, Dion et al ‘11]

6.6.2 Thermal Photon Radiation

thermal + prim.

[van Hees,Gale+RR ’11]

• flow blue-shift: Teff ~ T √(1+)/(1) , ~0.3: T ~ 220/1.35 ~ 160 MeV

• “small” slope + large v2 suggest main emission around Tpc

• other explanations…? [Skokov et al ‘12; McLerran et al ‘12]

6.7 Direct Photons at LHC

• similar to RHIC (not quite enough v2)

• non-perturbative photon emission rates around Tpc?

● ALICE

[van Hees et al in prep]

SpectraElliptic Flow

• Spontaneous Chiral Symmetry Breaking in QCD Vacuum: - ‹qq› ~ mq* ≠ 0 , chiral partners split (-, -a1, …)

- low-mass dileptons dominated by

7.) Conclusions

• Hadronic Medium Effects: - “melting” of (constraints!) hadronic liquid!? - connection to chiral symmetry: QCD/chiral sum rules (a1)

• Extrapolate EM Emission Rates to Tpc ~ 170MeV in-med HG and QGP shine equally bright (“duality”) !

• Phenomenology for URHICs: - versatile + precise tool (spectro, chrono, thermo + baro-meter) - SPS/RHIC (NA45,NA60,STAR): compatible w/ chiral restoration - tension STAR/PHENIX; LHC (ALICE) and CBM/NICA?

-

6.3.4 Sensitivity of Dimuons to Equation of State

• partition QGP/HG changes, low-mass spectral shape robust

[cf. also Ruppert et al, Dusling et al…]

6.3.5 NA60 Dimuons with Lattice EoS + Rate

• partition QGP/HG changes, low-mass spectral shape robust

First-Order EoS + HTL Rate Lattice EoS + Lat-QGP Rate

M[GeV][van Hees+RR ’08]

In-In (17.3GeV)

Tin =190MeV Tc =Tch =175MeV

[cf. also Ruppert et al, Dusling et al…]

Tin =230MeV Tpc =Tch =175MeV

6.3.6 Chronometer

• direct measurement of fireball lifetime: FB ≈ (6.5±1) fm/c

• non-monotonous around critical point?

In-In Nch>30

6.4 Summary of EM Probes at SPS

• calculated with same EM spectral function!

M[GeV]

In(158AGeV)+In

6.1 Fireball Evolution in Heavy-Ion Collisions

• “chemical” freezeout Tchem~ Tc ~170MeV, “thermal” freezeout Tfo ~ 120MeV

• conserve entropy + baryon no.: Ti → Tchem → Tfo

• time scale: hydrodynamics, fireball VFB() = (z0+vz ) (r0 + 0.5a┴ 2)2

N [GeV] [fm/c]

)p(Acc),T;q,M(qxdd

dNq

qdM)(Vd

dMdN e

tM,B

thermee

FB

thermee

fo

44

0

3

0

Thermal Dilepton Spectrum:

Isentropic Trajectories in the Phase Diagram

6.3.2 NA60 Data Before Acceptance Correction

• Discrimination power of model calculations improved, but …• can compensate spectral “deficit” by larger flow: lift pairs into acceptance

hadr. many-body + fireball

emp. ampl. + fireball

schem. broad./drop.+ HSD transportchiral virial

+ hydro

6.3.7 Dimuon pt-Spectra + Slopes: Barometer

• slopes originally too soft

• increase fireball acceleration, e.g. a┴ = 0.085/fm → 0.1/fm

• insensitive to Tc = 160-190 MeV

Effective Slopes Teff

6.2 Mass vs. Temperature Correlation• generic space-time argument:

Tmax ≈ M / 5.5

(for Im em =const)

23em44

33

0e /T/M

FBeeee )MT(

MIm

)T(Vqxdd

dNqxdd

qM

dMddN

55.T/Mee TdTdM

dN eT)(M,Im em

• thermal photons:

Tmax ≈ (q0/5) * (T/Teff)2

→ reduced by flow blue-shift!

Teff ~ T * √(1+)/(1)

2.4.4 Weinberg (Chiral) Sum Rules + Order Parameters

)Im(ImsdsI AVn

n

21

0

21

222

0

31

q)q(αcI

IfI

FrfI

s

π

Aππ

[Weinberg ’67, Das et al ’67]

• Moments VectorAxialvector

• In Medium: energy sum rules at fixed q [Kapusta+Shuryak ‘93]

• correlators (rhs): effective models (+data) • order parameters (lhs): lattice QCD

promising synergy!

Lower SPS Energy (Ti ~ 170MeV→ Tfo~100MeV)

• enhancement increases!?• supports importance of baryonic effects

6.2 Low-Mass Di-Electrons: CERES/NA45Top SPS Energy(Ti ~ 200MeV → Tfo~110 MeV)

• QGP contribution small• medium effects! • drop. mass or broadening?!

[RR+Wambach ‘99]

6.1.2 Emission Profile of Thermal EM Radiation• generic space-time argument:

Tmax ≈ M / 5.5

(for Im em =const)

23em44

33

0e /T/M

FBeeee )MT(

MIm

)T(Vqxdd

dNqxdd

qM

dMddN

55em eT)(M, .T/Mee TIm

dTdMdN

• Additional T-dependence from EM spectral function

• Latent heat at Tc not included

(penalizes T > Tc, i.e. QGP)

e.g. , A=a1,h1

fix G via (a1→) ~ G2 v2 PS ≈ 0.4GeV, …

>>

R

h

4.6 -Hadron Interactions in Hot Meson Gasresonance-dominated: + h → R, selfenergy:

Effective Lagrangian (h = , K, )

Generic features: • cancellations in real parts• imaginary parts strictly add up

)](f)(f[v)qk(D)(

kdR

Rk

hhRRhR

23

3

2

)(AGA L

2.5 Dimuon pt-Spectra and Slopes: Barometer

• vary fireball evolution: e.g. a┴ = 0.085/fm → 0.1/fm

• both large and small Tc compatible

with excess dilepton slopes

pions: Tch=175MeV a┴ =0.085/fm

pions: Tch=160MeV a┴ =0.1/fm

4.3.3 Acceptance-Corrected NA60 Spectra

• rather involved at pT>1.5GeV: Drell-Yan, primordial/freezeout , …

[van Hees + RR ‘08]

4.5 EM Probes in Central Pb-Au/Pb at SPS

• consistent description with updated fireball (aT=0.045→0.085/fm)• very low-mass di-electrons ↔ (low-energy) photons

[Liu+RR ‘06, Alam et al ‘01]

Di-Electrons [CERES/NA45] Photons [WA98]

[van Hees+RR ‘07]

Model Comparison of-SF in Hot/Dense Matter

• first sight: reasonable agreement• second sight: differences! B vs. N

• Implications for NA60 interpretation?!

[RR+Wambach ’99]

[Eletsky etal ’01]

• ImV ~ ImTVN N + ImTV ~ VN,V + dispersion relation for ReTV

[Eletsky,Belkacem,Ellis,Kapusta ’01]

3.8 Axialvector in Medium: Explicit a1(1260)

>

> >

>

N(1520)…

,N(1900)…

a1 + + . . .

Exp: - HADES (A): a1→(+-) - URHICs (A-A) : a1→

)Im(Ims

dsf AV 2

[RR ’02]

after freezeoutV ~ 1/V

tot

thermal emissionFB ~ 10fm/c

M

)M(Nqd

dRxdqd

dMdN eeV

VeeeeV 4

43

3.3 The Role of Light Vector Mesons in HICs

ee [keV] tot [MeV] (Nee )thermal (Nee )cocktail ratio

(770) 6.7 150 (1.3fm/c) 1 0.13 7.7

0.6 8.6 (23fm/c) 0.09 0.21 0.43

1.3 4.4 (44fm/c) 0.07 0.31 0.23

In-medium radiation dominated by -meson!

Connection to chiral symmetry restoration?!

Contribution to invariant mass-spectrum:

n

nn

Q

c)Q(Π 2

2

Nonpert. Wilson coeffs. (condensates)

0.2% 1%

4.5 Constraints II: QCD Sum Rules in Mediumdispersion relation

for correlator:

• lhs: OPE (spacelike Q2): • rhs: hadronic model (s>0):

[Shifman,Vainshtein+Zakharov ’79]

sQ

)s(Ims

dsQ

)Q(Π

20

2

2

[Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]

)ss()(s

)s(DImg

m)s(Im

sdual

18

2

4

theory of thermal electromagnetic radiation

Documents

chiral singlet

chiral trafo

gev tmax

gev thermal rate

qcd nonperturbative

invariant e e mass

mq qq chiral partners

hadronic phase