1. The Versatility of Thermal Photons and Dileptons Ralf Rapp Cyclotron Institute + Department of Phys & Astro Texas A&M University College Station, USA TPD Workshop BNL (Upton, NY), 05.-07.12.11

2. 1.) Introduction: Components of EM Probes HICs Thermal Emission Rate micro-physics: → Electro-Magnetic spectral function Space-Time Evolution of Fireball macro-physics (equation of state:  (P)) → temperature + flow fields Equation of State - governed by micro-physics (deg. of freedom, interactions) - drives the macro-physics - encodes deconfinement + chiral restoration e+ e-e+ e- γ

3. 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions Outline

4. 2.) Transport: Electric Conductivity hadronic theories (T~150MeV): - chiral pert. theory (pion gas):  em / T ~ 0.11 e 2 - hadronic many-body theory:  em / T ~ 0.09 e 2 [Fernandez-Fraile+ Gomez-Nicola ’07] lattice QCD (T ~ (1.5-3) T c ):  em /T ~ (0.26±0.02) e 2 [Gupta ’04, Aarts et al ’07, Ding et al. ‘11] soft-photon limit of thermal emission rate EM Susceptibility ( → charge fluctuations):  Q 2    Q  2 = χ em = Π em (q 0 =0,q→0)

5. 2.2 Soft Photons at SPS: WA98 [Turbide,RR +Gale’04] Thermal Radiation + pQCD Add  →  Bremsstrahlung [Liu+RR’06]

6. 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions Outline

7. 3.) EM Spectral Function I: Fate of Resonances Electromagn. spectral function - √s ≤ 1 GeV : non-perturbative - √s > 1.5 GeV : perturbative (“dual”) Vector resonances “prototypes” - representative for bulk hadrons: neither Goldstone nor heavy flavor Modifications of resonances ↔ phase structure: - hadron gas → Quark-Gluon Plasma - realization of transition? √s = M e + e  → hadrons Im Π em (M,q;  B,T) Im  em (M) in Vacuum

8. 3.2 Phase Transition(s) in Lattice QCD different “transition” temperatures?! smooth transitions! (smooth e + e  rate) partial chiral restoration in “hadronic phase” ?! (low-mass dileptons!) leading-order hadron gas “T c conf ” ~170MeV “T c chiral ”~150MeV ≈  qq  /  qq  -

9. > >    B *,a 1,K 1... N, ,K … 3.3  Vector Mesons in Hadronic Matter D  (M,q;  B,T) = [M 2 - m  2 -   -   B -   M ] -1  -Propagator: [Chanfray et al, Herrmann et al, Asakawa et al, RR et al, Koch et al, Klingl et al, Post et al, Eletsky et al, Harada et al …]   =   B,  M  = Selfenergies:  Constraints: decays: B,M→  N,  scattering:  N →  N,  A, …  B /  0 0 0.1 0.7 2.6 SPS RHIC

10. 3.4 “Smoothness” of Dilepton Rates across “T c ” smooth transition hadrons ↔ QGP?! resonance melting + chiral mixing on-shell qq vs.  annihil. in transport code - dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em

11. 3.5 Dilepton Rates vs. Exp.: NA60 “Spectrometer” invariant-mass spectrum directly reflects thermal emission rate! Acc.-corrected  +   Excess Spectra In-In(158AGeV) [NA60 ‘09] M  [GeV] Thermal     Emission Rate Evolve rates over fireball expansion: [van Hees+RR ’08]

12. 3.5.2 Sensitivity of NA60 to Spectral Function Significant differences in low-mass region Overall slope T~150-200MeV (!) [CERN Courier Nov. 2009] Emp. scatt. ampl. + T-  approximation Hadronic many-body Chiral virial expansion

13. M  [GeV] 3.5.3 Sensitivity to Spectral Function II avg.   (T~150MeV) ~ 350-400 MeV    (T~T c ) ≈ 600 MeV → m  driven by baryons Breit-Wigner shape insufficient: Im   ~ - q 0  vac (1+   B /  0 )

14. 3.6 Low-Mass e + e  at RHIC: PHENIX vs. STAR “large” enhancement not accounted for by theory QGP radiation not an option… (very) low-mass region overpredicted?! (SPS?!)

15. 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions Outline

16. 4.) Criteria for Chiral Restoration Vector (  ) – Axialvector (a 1 ) degenerate [Weinberg ’67, Das et al ’67] pQCD QCD sum rules: medium modifications ↔ vanishing of condensates Agreement with thermal lattice-QCD Approach to perturbative rate (QGP)

17. 4.1 Axialvector in Medium: Dynamical a 1 (1260) + +... =           Vacuum: a 1 resonance In Medium: + +... [Cabrera,Jido, Roca+RR ’09] in-medium  +  propagators broadening of  -  scatt. Amplitude pion decay constant in medium:

18. nonpert. Wilson coeffs. (condensates) 0.2% 1% 4.2 QCD Sum Rules:  (770) in Nuclear Matter dispersion relation: lhs: OPE (spacelike Q 2 ): rhs: hadronic model (s>0): [Shifman,Vainshtein,+Zakharov ’79] [Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05] ~50% reduced in nuclear matter ◊ ← vacuum

19. 4.3 Hadronic - Perturbative QGP - Lattice QCD dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em Hadronic, pert. + lattice QCD tend to “degenerate” toward ~T c Quark-Hadron Duality at all M ?! (  degenerate axialvector SF!) [qq→ee] - [HTL] [RR,Wambach et al ’99] [Ding et al ’10] dR ee /d 4 q 1.4T c (quenched) q=0

20. 4.3.2 Euclidean Correlators: Lattice vs. Hadronic Euclidean Correlation fct. Hadronic Many-Body [RR ‘02] Lattice (quenched) [Ding et al ‘10] “Parton-Hadron Duality” of lattice and in-medium hadronic?!

21. 4.3.3 Back to Spectral Function suggests approach to chiral restoration + deconfinement -Im  em /(C T q 0 )

22. 2.) Transport Properties  EM Conductivity + Low-Energy Photons 3.) Spectral Properties  Vector Spectral Functions + the Fate of Resonances  Dilepton Invariant-Mass Spectra 4.) Chiral Restoration  Criteria: Axialvector, Lattice QCD, pert. QCD  QCD +Weinberg Sum Rules 5.) Fireball Properties  Lifetime, Temperature, Collectivity 6.) Conclusions Outline

23. 5.1 Low-Mass Dileptons: Chronometer first “explicit” measurement of interacting-fireball lifetime:  FB ≈ (6.5±1) fm/c search for critical slowing down! In-In N ch >30

24. 5.2 Intermediate-Mass Dileptons: Thermometer use invariant continuum radiation (M>1GeV): no blue shift, T slope = T ! independent of partition HG vs QGP (dilepton rate continuous/dual) initial temperature T i ~ 190-220 MeV at CERN-SPS Thermometer

25. 5.3 Dimuon p t -Spectra and Slopes: Barometer theo. slopes originally too soft increase fireball acceleration, e.g. a ┴ = 0.085/fm → 0.1/fm insensitive to T c =160-190MeV Effective Slopes T eff

26. 5.4 Direct Photons at RHIC v 2 ,dir as large as that of pions!? underpredcited by QGP-dominated emission ← excess radiation T eff excess = (220±25) MeV QGP radiation? radial flow? Spectra Elliptic Flow [Holopainen et al ’11,…]

27. 5.4.1 Revisit Ingredients multi-strange hadrons at “T c ” v 2 bulk fully built up at hadronization chemical potentials for , K, … Hadron - QGP continuity! Emission Rates Fireball Evolution [van Hees et al ’11] [Turbide et al ’04]

28. 5.4.2 Thermal Photon Spectra + v 2 : PHENIX both spectral slope and v 2 point at blue-shifted hadronic source… to be tested in full hydro thermal + prim.  [van Hees,Gale+RR ’11]

29. 6.) Conclusions: Potential of Thermal EM Radiation at RHIC Transport: conductivity, susceptibility (→ diffusion,  /s) Spectrometer: “prototype” in-med. spectral function, hadron-to-quark transition Chiral Restoration: Weinberg + QCD sum rules, lattice QCD (  B ~0!) + perturbative limit Thermometer: int.-mass dileptons (heavy-flavor subtracted) Chronometer: search for anomalous fireball lifetimes Barometer: p t spectra (M=0-2GeV) Quality control: rates (constraints, continuity), medium evolution, consistency with SPS, … Needed: NA60-quality data RHIC premiere facility for soft EM probes of transition region

30. 2.3.2 NA60 Mass Spectra: pt Dependence more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

31. 4.1.2 Mass-Temperature Emission Correlation generic space-time argument:   T max ≈ M / 5.5 (for Im  em =const) thermal photons: T max ≈ (q 0 /5) * (T/T eff ) 2 → reduced by flow blue-shift! T eff ~ T * √(1+  )/(1  )

32. 4.7.2 Light Vector Mesons at RHIC + LHC baryon effects important even at  B,tot = 0 : sensitive to  Btot =   +  B (  -N and  -N interactions identical)  also melts,  more robust ↔ OZI - 

33. 5.3 Intermediate Mass Emission: “Chiral Mixing” = = low-energy pion interactions fixed by chiral symmetry mixing parameter [Dey, Eletsky +Ioffe ’90] 0 0 0 0 degeneracy with perturbative spectral fct. down to M~1GeV physical processes at M≥ 1GeV:  a 1 → e + e  etc. (“4  annihilation”)

34. 3.2 Dimuon p t -Spectra and Slopes: Barometer modify fireball evolution: e.g. a ┴ = 0.085/fm → 0.1/fm both large and small T c compatible with excess dilepton slopes pions: T ch =175MeV a ┴ =0.085/fm pions: T ch =160MeV a ┴ =0.1/fm

35. 2.3.2 Acceptance-Corrected NA60 Spectra more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

36. 4.4.3 Origin of the Low-Mass Excess in PHENIX? QGP radiation insufficient: space-time, lattice QGP rate + resum. pert. rates too small - “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A -  therm +  DCC → e + e  ↔ M~0.3GeV, small p t must be of long-lived hadronic origin Disoriented Chiral Condensate (DCC)? Lumps of self-bound pion liquid? Challenge: consistency with hadronic data, NA60 spectra! [Bjorken et al ’93, Rajagopal+Wilczek ’93] [Z.Huang+X.N.Wang ’96 Kluger,Koch,Randrup ‘98]

37. 2.2 EM Probes at SPS all calculated with the same e.m. spectral function! thermal source: T i ≈210MeV, HG-dominated,  -meson melting!

38. 2.3.3 Spectrometer III: Before Acceptance Correction Discrimination power much reduced can compensate spectral “deficit” by larger flow: lift pairs into acceptance hadr. many-body + fireball emp. ampl. + “hard” fireball schem. broad./drop. + HSD transport chiral virial + hydro

39. 4.2 Improved Low-Mass QGP Emission LO pQCD spectral function:  V (q 0,q) = 6 ∕ 9 3M 2 /2  1+Q HTL (q 0 )] 3-momentum augmented lattice-QCD rate (finite  rate)

40. 4.4.1 Variations in QGP Radiation improvements in QGP rate insufficient

41. 4.4.2 Variations in Fireball Properties variations in space-time evolution only significant in (late) hadronic phase

42. 4.1 Nuclear Photoproduction:  Meson in Cold Matter  + A → e + e  X [CLAS+GiBUU ‘08] E  ≈1.5-3 GeV  e+ee+e  extracted “in-med”  -width   ≈ 220 MeV Microscopic Approach: Fe - Ti  N  product. amplitude in-med.  spectral fct. + M [GeV] [Riek et al ’08, ‘10] full calculation fix density 0.4  0  -broadening reduced at high 3-momentum; need low momentum cut!

43. 1.2 Intro-II: EoS and Particle Content Hadron Resonance Gas until close to T c - but far from non-interacting: short-lived resonances R: a + b → R → a + b,  R ≤ 1 fm/c Parton Quasi-Particles shortly above T c - but large interaction measure I(T) =  -3P  both “phases” strongly coupled (hydro!): - large interaction rates → large collisional widths - resonance broadening → melting → quarks - broad parton quasi-particles - “Feshbach” resonances around T c (coalescence!)

44. 2.3.6 Hydrodynamics vs. Fireball Expansion very good agreement between original hydro [Dusling/Zahed] and fireball [Hees/Rapp]

45. 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