Theory Update on Electromagnetic Probes II Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA CATHIE/TECHQM Workshop BNL (Upton, NY),

1.) Intro: Probing Strongly Interacting Matter Electromagnetic Probes: penetrating: EM >> R nuc Equilibrium: EM spectral function Im  EM (q 0,q;  B,T)  Information via EM Spectral Function: degrees of freedom (parton vs. hadron) transport properties (EM conductivity, susceptibility) relation to order parameters (chiral symmetry) measure of temperature

1.) Introduction 2.) EM Emission + Vector Mesons  Thermal Rate and Conductivity  Chiral Symmetry Breaking   and a 1 Meson in Medium 3.) Dilepton Spectra in A-A  Thermal Emission at SPS  The RHIC Problem 4.) Conclusions Outline

2.1 Thermal Electromagnetic Emission EM Current-Current Correlation Function: e+ e-e+ e- γ Im Π em (M,q) Im Π em (q 0 =q) Thermal Dilepton and Photon Production Rates: Im  em ~ [ImD  + ImD  /10 + ImD  /5] Low Mass:   -meson dominated

2.2 Electric Conductivity pion gas (chiral pert. theory)  em / T ~ 0.01 for T ~ MeV [Fernandez-Fraile+Gomez-Nicola ’07] quenched lattice QCD  em / T ~ 0.35 for T = (1.5-3) T c [Gupta ’04] soft-photon limit

Weinberg Sum Rule(s) 2.3 Chiral Symmetry Breaking + Hadron Spectrum Axial-/Vector Correlators pQCD cont. “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] Constituent Quark Mass chiral breaking: |q 2 | ≤ 1 GeV 2 Gellmann-Oakes-Renner: m  2 f  2 = m q ‹0|qq|0› - Condensates fill QCD vacuum:

> >    B *,a 1,K 1... N, ,K … 2.4  -Meson in Medium: Hadronic Interactions D  (M,q;  B,T) = [M 2 - m  2 -   -   B -   M ] -1  -Propagator: [Chanfray et al, Herrmann et al, RR et al, Koch et al, Klingl et al, Mosel et al, Eletsky et al, Ruppert et al, Sasaki et al …]   =   B,  M  = Selfenergies:  Constraints: decays: B,M→  N,  scattering:  N →  N,  A, …  B /  [RR,Wambach et al ’99]  Meson “Melting” Switch off Baryons

2.4.2  Meson in Cold Nuclear Matter: JLab  + A → e + e  X  e+ ee+ e  Nuclear Photo-Production: [CLAS/JLab ‘08] [Riek et al ’08] Theoretical Approach: M ee  [GeV] Fe - Ti  N  elementary production amplitude in-medium  spectral function + M [GeV] E  =1.5-3 GeV

2.6 Axialvector in Medium: Dynamical a 1 (1260) =           Vacuum: a 1 resonance In Medium: in-medium  +  propagators broadening of  -  scattering amplitude [Cabrera,Jido,Roca+RR ’09]

3.) Dilepton Spectra in A-A Thermal Dilepton Emission Rate: e+ e-e+ e- Im Π em (M,q;  B,T) Thermal Sources: Relevance: - Quark-Gluon Plasma: high mass + temp. qq → e + e , … M > 1.5 GeV, T >T c - Hot + Dense Hadron Gas: M ≤ 1 GeV       → e + e , … T ≤ T c - qqqq _ e+ee+e  e+ee+e   Im Π em ~ Im D 

3.1 Dilepton Rates: Hadronic vs. QGP dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em Hard-Thermal-Loop [Braaten et al ’90] enhanced over Born rate Hadronic and QGP rates “degenerate” around ~T c Quark-Hadron Duality at all M ?! (  degenerate axialvector SF!) [qq→ee] [HTL] -

3.2 Dilepton “Excess” Spectra  at SPS “average”   (T~150MeV) ~ MeV    (T~T c ) ≈ 600 MeV → m  fireball lifetime:  FB ~ (6.5±1) fm/c [van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08] Thermal Emission Spectrum:

3.2.2 NA60 Data vs. In-Medium Dimuon Rates acceptance-corrected data directly reflect thermal rates! M  [GeV] [RR,Wambach et al ’99] [van Hees +RR ’07]

3.2.3 NA60 Excess Spectra vs. Theory Thermal source does very well Low-mass enhancement very sensitive to medium effects Intermediate-mass: total agrees, decomposition varies [CERN Courier Nov. 2009]

3.2.4 NA60 Dimuons: Sensitivity to QGP and T c vary critical and chemical-freezeout temperature (T fo ~ 130 MeV fix) spectral shape robust: “duality” of dilepton rate around “T c ”! intermediate mass (M>1GeV): QGP vs. hadronic depends on T c Intermediate Mass Region “EoS-B” “EoS-C”

3.2.5 EM Probes in Central Pb-Au/Pb at SPS consistency of virtual+real photons (same  em ) very low-mass di-electrons ↔ (low-energy) photons [Srivastava et al ’05, Liu+RR ‘06] Di-Electrons [CERES/NA45] Photons [WA98] [Turbide et al ’03, van Hees+RR ‘07]

3.3 Low-Mass Dileptons at RHIC: PHENIX Successful approach at SPS fails at RHIC Excess concentrated: - at low mass - in central collisions - at low p t (T eff ~ 100 MeV) Inclusive Mass Spectrum Centrality Dependence of Excess

3.3.2 Origin of the Low-Mass Excess in PHENIX? - small T eff slope - why not in semi-central? - generic space-time argument:   maximal emission around T max ≈ M / 5.5 (for Im  em =const) Low mass (M<1GeV): T max < 200MeV Soft QGP Radiation? - “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A -  therm +  DCC → e + e  ↔ M~0.3GeV, small p t Disoriented Chiral Condensate (DCC)? [Bjorken et al ’93, Rajagopal+Wilczek ’93] [Z.Huang+X.N.Wang ‘96]

3.3.3 Low-Mass Excess from DCC? Dileptons from a DCC-DCC annihilation [Witham+RR ‘08] too small DCC-thermal to be evaluated …

3.3.4 Comparison of Thermal Emission Calculations Chiral Reduction + Hydro Hadronic Many-Body + Fireball Decomposition at M=0.5(0.2)GeV: Hadronic LO-QGP NLO-QGP Dusling+Zahed 6 (6) 5.5 (2) 10 (25) RR+van Hees 20 (15) 4 (3) --

4.) Conclusions Electromagnetic Probes - versatile tool (spectral fcts., transport, temp., lifetime!) Chiral Symmetry Breaking (Restoration) - chiral partners:  - a 1 (degeneracy at T c ) Thermal Dilepton Rates - melting  toward T c : quark-hadron duality?! hadron liquid?! Dilepton Spectra - quantitative agreement at SPS - failure at RHIC thus far (QGP not favored; DCC??)

2.3.2 Acceptance-Corrected NA60 Spectra more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

X.) Example for Comprehensive Analysis: NA60  thermal medium radiating from around T c with melted , well-bound J/  with large collectivity Dileptons Charmonium Flow Charmonium Production