Theory of Thermal Electromagnetic Radiation

Theory of Thermal Electromagnetic Radiation Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, Texas USA JET Summer School The Ohio State University (Columbus, OH) June 1-14, 013

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)

1. Dileptons in Heavy-Ion Collisions e + ρ Au + Au e - NN-coll. QGP Hadron Gas Freeze-Out Sources of Dilepton Emission: - primordial qq annihilation (Drell-Yan): NN e + e X thermal radiation - Quark-Gluon Plasma: qq - e + e, - Hot+Dense Hadron Gas: π + π e + e, _ final-state hadron decays: π 0,η γe + e, D,D e + e X,

1.3 Schematic Dilepton Spectrum in HICs qq Characteristic regimes in invariant e + e mass, M = (p e+ + p e ) Drell-Yan: primordial, power law ~ M n thermal radiation: - entire evolution - Boltzmann ~ exp(-m/t) Thermal rate: dn ee dree q VFB 1 e 3 0 dmdτ dm T / T Im Π em (M,q;µ B,T) q 0 0.5GeV T max 0.17GeV, q 0 1.5GeV T max 0.5GeV

1.4 EM Spectral Function + QCD Phase Structure Electromagn. spectral function - s 1 GeV : non-perturbative - s > 1.5 GeV : pertubative ( dual ) e + e hadrons ~ Im Π em / M Modifications of resonances phase structure: hadronic matter Quark-Gluon Plasma? s = M Thermal e + e emission rate from hot/dense matter (λ em >> R nucleus ) d dn 4 xd ee 4 α B = em f (q0,t ) 3 Im Π q π M em (M,q;µ B,T) Temperature? Degrees of freedom? Deconfinement? Chiral Restoration?

1.5 Low-Mass Dileptons at CERN-SPS CERES/NA45 e + e [000] NA60 µ + µ [005] M ee [GeV] strong excess around M 0.5GeV, M > 1GeV quantitative description?

1.6 Phase Transition(s) in Lattice QCD qq - / qq - T pc chiral ~150MeV T pc conf ~170MeV [Fodor et al 10] different transition temperatures?! extended transition regions partial chiral restoration in hadronic phase! (low-mass dileptons!) leading-order hadron gas

Outline.) 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 (ρ-a 1 ) 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

.1 Nonperturbative QCD L QCD = q ( i / + ga/ mˆ 1 4 q )q G aµν well tested at high energies, Q > 1 GeV : perturbation theory (α s = g /4π << 1) degrees of freedom = quarks + gluons (m u m d 5 MeV ) Q 1 GeV transition to strong QCD: effective d.o.f. = hadrons (Confinement) massive constituent quarks m q * 350 _ MeV ⅓ M p (Chiral Symmetry ~ 0 qq 0 condensate! Breaking) ⅔ fm

L QCD =. Chiral Symmetry in QCD Lagrangian q ( i / + ga/ mˆ 1 4 q )q G aµν (bare quark masses: m u m d 5-10MeV ) Chiral SU() V SU() A transformation: Up to O(m q ), L QCD invariant under q q RV ( αv ) q = exp( iαv τ / ) q R ( α ) q = exp( iγ α / ) q A A 5 A τ Rewrite L QCD using left- and right-handed quark fields q L,R =(1±γ 5 )/ q : L QCD L,R ul ur = ( ul,dl ) id/ ( ur,dr ) id ( mq ) d + / L d + O R q exp( iα τ / L,R ) q L,R q L g 1 4 Invariance under isospin and handedness G aµν q L

.3 Spontaneous Breaking of Chiral Symmetry - strong qq attraction Chiral Condensate fills QCD vacuum: qq = q q + q q 0 L R R L [cf. Superconductor: ee 0, Magnet M 0, ] Simple Effective Model: assume mean-field linearize: L = q ( i / free energy: ground state: eff Ω M * χ 0 q 1 L eff = q Deff( M*) q + ( M * m d p log N N V T 3 Ω = Z = f ( π ) = 0 0 q L q- R = q ( i / mq ) q 0 qq 0, expand: [m Gχ ])q + G χ M* = 4N q 0 qq, ) / 4G p + M * = 0 M* G( qq ) χ + δ ( qq ) Gχ M G * c 3 4 c N f G d 3 p ( π ) 3 p M * + M * 0 q R q- L Gap Equation

.3. (Observable) Consequences of SBCS mass gap, not observable! but: hadronic excitations reflect SBCS massless Goldstone bosons π 0,± (explicit breaking: f π m π = m q qq ) chiral partners split: ΔM 0.5GeV! chiral trafo:, Vector mesons ρ and ω: J P =0 ± 1 ± 1/ ± = 0 0 4 qq G M* Δ qq Aπ σ R ) N( N R A 1535 µ µ µ ω α τ γ γ γ α τ γ ω α = + + )q ( ) ( q ) ( R j j j j A 1 1 1 5 0 5 chiral singlet - -iε ijk τ k i i j i i j j i j j i j j A i A i A ) a ( )q ( q i )q i ( ) i ( q q ) R ( q ) R ( ) ( R µ µ µ µ µ µ µ α ρ τ τ τ τ γ γ α ρ α τ γ τ γ γ α τ γ τ γ ρ α 1 5 5 0 5 1 1 1 1 + = + + = +

.3.3 Manifestation of Chiral Symmetry Breaking Constituent Quark Mass Axial-/Vector Correlators Data : lattice [Bowman et al 0] Theory: Instanton Model [Diakonov+Petrov; Shuryak 85] pqcd cont. chiral breaking: q 1 GeV quantify chiral breaking?

.4 Chiral (Weinberg) Sum Rules Quantify chiral symmetry breaking via observable spectral functions Vector (ρ) - Axialvector (a 1 ) spectral splitting I n = ds s π n (Im Π V [Weinberg 67, Das et al 67] Im Π A ) I I 0 1 f 3 π r = m = π FA, I 1 q 0 qq 0, I 1 = f π = cα s, 0 (qq) 0 τ (n)π [ALEPH 98, OPAL 99] τ (n+1)π pqcd pqcd Key features of updated fit : [Hohler+RR 1] ρ + a 1 resonance, excited states (ρ + a 1 ), universal continuum

.4. Evaluation of Chiral Sum Rules in Vacuum pion decay constants I 1 3 = fπ rπ FA I 1 = f π chiral quark condensates I = m 0 qq 0 I = cα 0 (qq) 0 0 q 1 s vector-axialvector splitting (one of the) cleanest observable of spontaneous chiral symmetry breaking promising (best?) starting point to search for chiral restoration

.5 QCD Sum Rules: ρ and a 1 in Vacuum dispersion relation: ds ImΠ ( s ) Πα α = s 0 Q + s Q (Q ) [Shifman,Vainshtein+Zakharov 79] lhs: hadronic spectral fct. rhs: operator product expansion 4-quark + gluon condensate dominant

(T,µ B ) 3.1 EM Correlator + Thermal Dilepton Rate γ*(q) e + e xd Q EM Correlation Fct.: Quark basis: Hadron basis: d dn 4 j Γ V ee ee 4 µ em = j µ em = = = dnee 4 Π d = e i 4 d x ( π ) α B = em f ( q0,t ) 3 Im Π π Q em (M,q;T,µ B ) Π µν em i em µ j 3 3 E 4 p f i i f ( π ) Π j iqx i E µ em ( 1± ν em (Q ) = i d x e j ( x )j ( 0) µ µ uγ u 1 dγ d 3 3 1 ( uγ 1 j µ µ ρ u dγ + µ 1 3 d ) + j µ ω 1 3 1 6 sγ f em ν µ s ( uγ 1 3 j µ φ µ d 3 3 p f f f i u + dγ πδ ( P µ f f d ) i ) ( 1 3 P j f µ e sγ Q ) 1 Q µ s 4 ν e [McLerran+Toimela 85] 9 : 1 : j )

e + 3. EM Correlator in Vacuum: e + e hadrons ρ π ρ Ι =1 e π + ππ 4π + 6π +... e + e q _ q h 1 h ρ +ω +φ KK _ qq ImΠ em ( s )= s N 1π c u,d,s m g V ρ, ω, φ V (e q ) α + s( s ) 1 + π ImD V ( s ) s s dual ~ (1.5GeV) pqcd continuum s < s dual Vector-Meson Dominance

3.3 Low-Mass Dileptons + Chiral Symmetry Vacuum T > T c : Chiral Restoration How is the degeneration realized? measure vector with e + e, axialvector?

3.4 Versatility of EM Correlation Function Photon Emission Rate drγ α q em B γ 0 = f (q 0,T ) 3 Im Π d q π em (q 0 =q) ~ O(α s ) γ* e + e - dr d ee 4 q = α em 3 π M f B (q 0,T ) Im Π em (M,q) same correlator! ~ O(1) EM Susceptibility ( charge fluctuations) Q Q = χ em = Π em (q 0 =0,q 0) EM Conductivity σ em = lim(q 0 0) [ -Im Π em (q 0,q=0)/q 0 ]

4.1 Axial/Vector Mesons in Vacuum Introduce ρ, a 1 as gauge bosons into free π +ρ +a 1 Lagrangian int µ µ π ρ L πρ = g ρ µ ρ -propagator: ( π D π ) 1 g ρ ρ µ ρ π π ( 0) 1 (mρ ) Σρππ ( M ( M ) = [ M )] π F π EM formfactor π ( M ) = (m ( 0) ρ ππ scattering phase shift δ ππ ( M ) = tan -1 ) 4 D Im D Re D ρ ρ ρ ( M ) ( M ) ( M ) F π δ ππ 3 parameters: m ρ (0), g, Λ ρ

ρ 4. ρ-meson in Matter: Many-Body Theory interactions with hadrons from heat bath In-Medium ρ-propagator D ρ (M,q;µ B,T) = [M (m ρ (0) ) - Σ ρππ - Σ ρb - Σ ρm ] -1 In-Medium Pion Cloud [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Koch et al, ] ρ Σ π Σ ρππ = + Σ π Σ π Direct ρ-hadron Scattering Σ ρβ,μ = ρ > R=Δ, N(150), a 1, K 1... [Haglin, Friman et al, RR et al, Post et al, ] > h=n, π, K estimate coupling constants from R ρ + h, more comprehensive constraints desirable

4.3 Constraints I: Nuclear Photo-Absorption total nuclear γ -absorption in-medium ρ -spectral cross section function at photon point σ abs γa (q A 0 ) = 4πα ImΠ q ρ 0 N em (q 0 = q ) = 4πα q ρ 0 em N m g 4 ρ ρ ImD med ρ ( M = 0,q ) ρ > Δ,N*,Δ* N -1 > γ N Β direct resonance ρ Σ π Σ π γ N π N,Δ meson exchange

4.3. ρ Spectral Function in Nucl. Photo-Absorption On the Nucleon On Nuclei γn γa π-ex fixes coupling constants and formfactor cutoffs for ρnb.+3. resonances melt (selfconsistent N(150) Nρ) [Urban,Buballa,RR+Wambach 98]

4.4 ρ-meson Spectral Function in Nuclear Matter In-med. π-cloud + ρ+n B* resonances [Urban et al 98] ρ+n B* resonances (low-density approx.) [Post et al 0] In-med. π-cloud + ρ+n N(150) [Cabrera et al 0] ρ N =0.5ρ 0 ρ N =ρ 0 ρ N =ρ 0 Constraints: γ N, γ A π N ρ N PWA Consensus: strong broadening + slight upward mass-shift Constraints from (vacuum) data important quantitatively

4.5 ρ-meson Spectral Functions at SPS Hot + Dense Matter Hot Meson Gas µ B =330MeV ρ B /ρ 0 0 0.1 0.7.6 [RR+Wambach 99] [RR+Gale 99] ρ-meson melts in hot/dense matter baryon density ρ B more important than temperature

4.6 Light Vector Mesons at RHIC + LHC baryon effects remain important at ρ B,net = 0: sensitive to ρ B,tot = ρ Β + ρ B - (ρ-n = ρ-n, CP-invariant) ω also melts, φ more robust OZI [RR 01]

4.7 Intermediate Mass: Chiral Mixing low-energy pion interactions fixed by chiral symmetry [Dey, Eletsky +Ioffe 90] = 0 0 Π µν V (q ) = ( 1 ε ) Π 0, µν V (q ) + ε Π 0, µν A (q ) = 0 0 Π µν A 0, µν A (q ) = ( 1 ε ) Π (q ) + ε Π 0, µν V (q ) mixing parameter π 3 ε = 4 d k 3 f ( π ) ω k f π ( ω k ) T 6 f π degeneracy with perturbative spectral fct. down to M~1GeV physical processes at M 1GeV: πa 1 e + e etc. ( 4π annihilation )

4.8 Axialvector in Medium: Dynamical a 1 (160) Vacuum: In π ρ π ρ Σ π Σ ρ + +... = Σ π Σ ρ Σ π Σ ρ a 1 resonance Medium: + +... in-medium π + ρ propagators [Cabrera,Jido, Roca+RR 09] broadening of π-ρ scatt. Amplitude pion decay constant in medium:

4.9 QCD + Weinberg Sum Rules in Medium s [GeV ] [Hohler et al 1] melting scenario quantitatively compatible with chiral restoration microscopic calculation of in-medium axialvector to be done [Hatsuda+Lee 91, Asakawa+Ko 93, Klingl et al 97, Leupold et al 98, Kämpfer et al 03, Ruppert et al 05 I n = ds π s n ( ρ V ρ A ) [Weinberg 67, Das et al 67; Kapusta+Shuryak 94] I 1 = fπ, I0 = fπ mπ, I1 = cαs (qq) ρ V,A /s T [GeV] Vacuum T=140MeV T=170MeV

4.10 Chiral Condensate + ρ-meson Broadening qq - / qq - 0 effective hadronic theory Σ h = m q h qq h - > 0 contains quark core + pion cloud = Σ h core + Σ h cloud ~ + + matches spectral medium effects: resonances + pion cloud resonances + chiral mixing drive ρ-sf toward chiral restoration > > Σ π Σ π ρ

5.1 QGP Emission: Perturbative vs. Lattice QCD Baseline: q _ q e + e small M resummations, finite-t perturbation theory (HTL) [Braaten,Pisarski+Yuan 91] Σ q Im [ ] = + + + Σ q dr ee /d 4 q 1.45T c q=0 collinear enhancement: D q,g =(t-m D ) -1 ~ 1/α s marked low-mass enhancement comparable to recent lattice-qcd computations [Ding et al 10]

5. Euclidean Correlators: Lattice vs. Hadronic Euclidean Correlation fct. dq Π ( τ,q;t ) = 0 ρv (q π cosh [q ( / T )],q;t ) 0 τ 1 sinh[q / T ] V 0 0 0 Lattice (quenched) [Ding et al 10] Hadronic Many-Body [RR 0] G G V free V ( τ,t ) ( τ,t ) Parton-Hadron Duality of lattice and in-medium hadronic

5.. Back to Spectral Function -Im Π em /(C T q 0 ) suggestive for approach to chiral restoration and deconfinement

5.3 Summary of Dilepton Rates: HG vs. QGP dr ee /dm ~ d 3 q f B (q 0 ;T) Im Π em Lattice-QCD rate somwhat below Hard-Thermal Loop hadronic QGP toward T pc : resonance melting + chiral mixing Quark-Hadron Duality at all M ee?! (QGP rates chirally restored!)

6.1 Space-Time Evolution + Equation of State Evolve rates over fireball expansion: therm dnee dm τ therm fo = M d q dn d V ( ) ee τ FB τ ( M,q;T, q 4 4 d xd q µ 0 τ 0 3 B,M ) Acc( p e t ± ) 1.order lattice EoS: - enhances temperature above T c - increases QGP emission - decreases hadronic emission Au-Au (00GeV) initial conditions affect lifetime simplified: parameterize space-time evolution by expanding fireball benchmark bulk-hadron observables [He et al 1]

6.1. Bulk Hadron Observables: Fireball Model Mulit-strange hadrons freeze-put at T pc Bulk-v saturates at ~T pc [van Hees et al 11]

6. Di-Electron Spectra from SPS to RHIC Pb-Au(8.8GeV) Au-Au (0-00GeV) QM1 Pb-Au(17.3GeV) consistent excess emission source suggests universal medium effect around T pc FAIR, LHC? [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 [Damjanovic et al 06] for the first time, dilepton excess spectra could be extracted! + full acceptance correction

6.3. NA60 Multi-Meter: Accept.-Corrected Spectra Spectrometer Chronometer Emp. scatt. ampl. + T-ρ approximation Hadronic many-body Chiral virial expansion Thermometer [CERN Courier Nov. 009] Thermal source! Low-mass: good sensitivity to medium effects, T~130-170MeV Intermediate-mass: T ~ 170-00 MeV > T pc Fireball lifetime τ FB = (6.5±1) fm/c

6.3.3 Spectrometer µ + µ Excess Spectra In-In(17.3AGeV) [NA60 09] therm µµ dn dm τ fo 3 M d q drµµ = dτ VFB( τ ) V q 4 4 0 d q τ 0 therm dr dm µµ Thermal µ + µ Emission Rate M µµ [GeV] [van Hees+RR 08] in-med ρ + 4π + QGP invariant-mass spectrum directly reflects thermal emission rate!

6.4 Conclusions from Dilepton Excess Spectra thermal source (T~10-30MeV) in-medium ρ meson spectral function - avg. Γ ρ (T~150MeV) ~ 350-400 MeV Γ ρ (T~T pc ) 600 MeV m ρ - divergent width Deconfinement?! M > 1.5 GeV: QGP radiation fireball lifetime measurement : τ 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] M µµ [GeV]

6.5 The RHIC-00 Puzzle in Central Au-Au PHENIX, STAR and theory: - consistent in non-central collisions - tension in central collisions

6.6 Direct Photons at RHIC Spectra Elliptic Flow excess radiation T eff excess = (0±30) MeV QGP radiation? radial flow? v γ,dir as large as for pions!? underpredcited by QGP-dominated emission [Holopainen et al 11, Dion et al 11]

6.6. Thermal Photon Radiation thermal + prim. γ [van Hees, Gale+RR 11] flow blue-shift: T eff ~ T (1+β)/(1 β), β~0.3: T ~ 0/1.35 ~ 160 MeV small slope + large v suggest main emission around T pc other explanations? [Skokov et al 1; McLerran et al 1]

6.7 Direct Photons at LHC Spectra Elliptic Flow ALICE [van Hees et al in prep] similar to RHIC (not quite enough v ) non-perturbative photon emission rates around T pc?

7.) Conclusions Spontaneous Chiral Symmetry Breaking in QCD Vacuum: - qq - ~ m q * 0, chiral partners split (π-σ, ρ-a 1, ) - low-mass dileptons dominated by ρ Hadronic Medium Effects: - melting of ρ (constraints!) hadronic liquid!? - connection to chiral symmetry: QCD/chiral sum rules (a 1 ) Extrapolate EM Emission Rates to T pc ~ 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 First-Order EoS + HTL Rate In-In (17.3GeV) T in =190MeV T c =T ch =175MeV Lattice EoS + Lat-QGP Rate T in =30MeV T pc =T ch =175MeV [van Hees+RR 08] M µµ [GeV] partition QGP/HG changes, low-mass spectral shape robust [cf. also Ruppert et al, Dusling et al ]

6.3.6 Chronometer In-In N ch >30 direct measurement of fireball lifetime: τ FB (6.5±1) fm/c non-monotonous around critical point?

6.4 Summary of EM Probes at SPS In(158AGeV)+In M µµ [GeV] calculated with same EM spectral function!

6.1 Fireball Evolution in Heavy-Ion Collisions Thermal Dilepton Spectrum: therm dnee dm τ therm fo = M d q dn d V ( ) ee τ FB τ ( M,q;T, q 4 4 d xd q µ 0 τ 0 Isentropic Trajectories in the Phase Diagram 3 B,M ) Acc( p e t ± ) µ N [GeV] τ [fm/c] chemical freezeout T chem ~ T c ~170MeV, thermal freezeout T fo ~ 10MeV conserve entropy + baryon no.: T i T chem T fo

6.3. NA60 Data Before Acceptance Correction Discrimination power of model calculations improved, but can compensate spectral deficit by larger flow: lift pairs into acceptance emp. ampl. + fireball hadr. many-body + fireball chiral virial + hydro schem. broad./drop. + HSD transport

6.3.7 Dimuon p t -Spectra + Slopes: Barometer slopes originally too soft increase fireball acceleration, e.g. a = 0.085/fm 0.1/fm insensitive to T c = 160-190 MeV Effective Slopes T eff

6. Mass vs. Temperature Correlation generic space-time argument: dn 3 3 dn = M d xd q dmdτ q 4 0 d xd Im Π M ee ee em M / T 3 / V e 4 FB(T ) ( MT ) q dn ee! M / T! 5.5 dm dt " Im# em (M,T) e T T max M / 5.5 (for Im Π em =const) thermal photons: T max (q 0 /5) * (T/T eff ) reduced by flow blue-shift! T eff ~ T * (1+β)/(1 β)

.4.4 Weinberg (Chiral) Sum Rules + Order Parameters Moments Vector Axialvector I I I I n 1 I 0 1 = ds π = = = 1 3 f 0 π = cα f s π r s π n (qq) (Im Π F A V Im Π [Weinberg 67, Das et al 67] A ) In Medium: energy sum rules at fixed q [Kapusta+Shuryak 93] correlators (rhs): effective models (+data) order parameters (lhs): lattice QCD promising synergy!

6. Low-Mass Di-Electrons: CERES/NA45 Top SPS Energy (T i ~ 00MeV T fo ~110 MeV) Lower SPS Energy (T i ~ 170MeV T fo ~100MeV) QGP contribution small medium effects! drop. mass or broadening?! [RR+Wambach 99] enhancement increases!? supports importance of baryonic effects

6.1. Emission Profile of Thermal EM Radiation generic space-time argument: dn 3 3 dn = M d xd q ee dmdτ q 4 4 0 d xd q VFB(T ) dn ee! M / T 5. 5 " Im# em(m,t) e T dm dt ee em M / T 3 / e ( MT ) T max M / 5.5 (for Im Π em =const) Additional T-dependence from EM spectral function Latent heat at T c not included (penalizes T > T c, i.e. QGP) Im Π M

4.6 ρ -Hadron Interactions in Hot Meson Gas resonance-dominated: ρ + h R, selfenergy: Σ ρ hr 3 = d k h DR( k + q ) v hr [ f ( ωk ) ± 3 ρ ( π ) f R ( ω R )] ρ > > R h Effective Lagrangian (h = π, K, ρ) L µ e.g. µν, A=a 1,h 1 πρa = G A ( fix G via Γ(a 1 ρπ) ~ G v PS 0.4GeV, Generic features: cancellations in real parts imaginary parts strictly add up ν π ) ρ

.5 Dimuon p t -Spectra and Slopes: Barometer pions: T ch =175MeV a =0.085/fm pions: T ch =160MeV a =0.1/fm vary fireball evolution: e.g. a = 0.085/fm 0.1/fm both large and small T c compatible with excess dilepton slopes

4.3.3 Acceptance-Corrected NA60 Spectra [van Hees + RR 08] rather involved at p T >1.5GeV: Drell-Yan, primordial/freezeout ρ,

4.5 EM Probes in Central Pb-Au/Pb at SPS Di-Electrons [CERES/NA45] Photons [WA98] consistent description with updated fireball (a T =0.045 0.085/fm) very low-mass di-electrons (low-energy) photons [Liu+RR 06, Alam et al 01] [van Hees+RR 07]

Model Comparison of ρ-sf in Hot/Dense Matter ImΣ V ~ ImT VN ρ N + ImT Vπ ρ π ~ σ VN,Vπ + dispersion relation for ReT V [Eletsky,Belkacem,Ellis,Kapusta 01] [RR+Wambach 99] [Eletsky etal 01] first sight: reasonable agreement second sight: differences! ρ B vs. ρ N Implications for NA60 interpretation?!

3.8 Axialvector in Medium: Explicit a 1 (160) a 1 Σ π Σ ρ Σ π > > N(150) > > Δ,N(1900) + +... [RR 0] Exp: - HADES (πa): a 1 (π + π - )π - URHICs (A-A) : a 1 πγ f π = ds π s (ImΠ V ImΠ A )

3.3 The Role of Light Vector Mesons in HICs Contribution to invariant mass-spectrum: dnv dm ee dr = 3 4 d q d x 4 d q ee N V ( M ) ΓV M ee Δτ thermal emission τ FB ~ 10fm/c after freezeout τ V ~ 1/Γ V tot Γ ee [kev] Γ tot [MeV] (N ee ) thermal (N ee ) cocktail ratio ρ (770) 6.7 150 (1.3fm/c) 1 0.13 7.7 ω(78) 0.6 8.6 (3fm/c) 0.09 0.1 0.43 φ(100) 1.3 4.4 (44fm/c) 0.07 0.31 0.3 In-medium radiation dominated by ρ -meson! Connection to chiral symmetry restoration?!

4.5 Constraints II: QCD Sum Rules in Medium dispersion relation for correlator: lhs: OPE (spacelike Q ): = c Π (Q ) n α n Q n Π Nonpert. Wilson coeffs. (condensates) α (Q ) ds ImΠ = α Q s 0 Q [Hatsuda+Lee 91, Asakawa+Ko 9, Klingl et al 97, Leupold et al 98, Kämpfer et al 03, Ruppert et al 05] + s ( s ) [Shifman,Vainshtein +Zakharov 79] rhs: hadronic model (s>0): ImΠ ρ 4 mρ ( s ) = ImD ( s ) ρ gρ s α ( 1+ s ) Θ( s s 8π π dual ) 0.% 1%