1. Update on Search for Chiral Symmetry Restoration in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA 11 th Int. Conference on Nucleus-Nucleus Collisions San Antonio (Texas), 29.05.12

2. 1.) Intro: EM Spectral Function + Fate of Resonances Electromagn. spectral function - √s < 2 GeV : non-perturbative - √s > 2 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

3. 1.2 Phase Transition(s) in Lattice QCD cross-over(s) ↔ smooth e + e  rate chiral restoration in “hadronic phase”?! (low-mass dileptons!) hadron resonance gas “T c conf ” ~170MeV “T c chiral ”~155MeV ≈  qq  /  qq  - [Fodor et al ’10]

4. 2.) Chiral Symmetry Breaking in Vacuum  “Higgs Mechanism”, Condensates + Mass Gap in QCD  Hadron Spectrum, Chiral Partners + Sum Rules 3.) EM Spectral Function in Medium  Hadronic Theory  QGP + Lattice QCD 4.) EM Probes in Heavy-Ion Collisions  Spectro-, Thermo-, Chrono- + Baro-meter  Thermal Photons  P t Spectra + Collectivity 5.) Conclusions Outline

5. “Higgs” Mechanism in Strong Interactions: qq attraction  condensate fills QCD vacuum! Spontaneous Chiral Symmetry Breaking 2.1 Chiral Symmetry + QCD Vacuum : flavor + “chiral” (left/right) invariant > > > > qLqL qRqR qLqL - qRqR - - Profound Consequences: effective quark mass: ↔ mass generation! near-massless Goldstone bosons  0,± “chiral partners” split:  M ≈ 0.5GeV J P =0 ± 1 ± 1/2 ±

6. 2.2 Chiral (Weinberg) Sum Rules Quantify chiral symmetry breaking via observable spectral functions Vector (  ) - Axialvector (a 1 ) spectral splitting [Weinberg ’67, Das et al ’67]  →(2n+1)  pQCD Key features of updated “fit”: [Hohler+RR ‘12]  + a 1 resonance, excited states (  ’+ a 1 ’), universal continuum (pQCD!)  →(2n)  [ALEPH ‘98, OPAL ‘99]

7. 2.2.2 Evaluation of Chiral Sum Rules in Vacuum vector-axialvector splitting (one of the) cleanest observable of spontaneous chiral symmetry breaking promising starting point to search for chiral restoration pion decay constants chiral quark condensates

8. 2.3 QCD Sum Rules:  and a 1 in Vacuum dispersion relation: lhs: hadronic spectral fct. rhs: operator product expansion [Shifman,Vainshtein+Zakharov ’79] 4-quark + gluon condensate dominant vector axialvector

9. 2.) Chiral Symmetry Breaking in Vacuum  “Higgs Mechanism”, Condensates + Mass Gap in QCD  Hadron Spectrum, Chiral Partners + Sum Rules 3.) EM Spectral Function in Medium  Hadronic Theory  QGP + Lattice QCD 4.) EM Probes in Heavy-Ion Collisions  Spectro-, Thermo-, Chrono- + Baro-meter  Thermal Photons  P t Spectra + Collectivity 5.) Conclusions Outline

10. > >    B *,a 1,K 1... N, ,K … 3.1 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/LHC

11. 3.2 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:

12. 3.3 Vector Correlator in Thermal Lattice QCD Euclidean Correlation fct. Hadronic Many-Body [RR ‘02] Lattice (quenched) [Ding et al ‘10] “Parton-Hadron Duality” of lattice and in-medium hadronic?!

13. 3.3.2 Back to Spectral Function suggests approach to chiral restoration + deconfinement -Im  em /(C T q 0 )

14. 3.4 Dilepton Rates: Hadronic - Lattice - Perturbative dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  V 3-fold “degeneracy” 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

15. 3.5 Summary: 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)

16. 2.) Chiral Symmetry Breaking in Vacuum  “Higgs Mechanism”, Condensates + Mass Gap in QCD  Hadron Spectrum, Chiral Partners + Sum Rules 3.) EM Spectral Function in Medium  Hadronic Theory  QGP + Lattice QCD 4.) EM Probes in Heavy-Ion Collisions  Spectro-, Thermo-, Chrono- + Baro-meter  Thermal Photons  P t Spectra + Collectivity 5.) Conclusions Outline

17. 4.1 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]

18. M  [GeV] 4.1.2 Sensitivity to Spectral Function avg.   (T~150MeV) ~ 370 MeV    (T~T c ) ≈ 600 MeV → m  driven by baryons In-Medium  -Meson Width

19. 4.2 Low-Mass e + e  at RHIC: PHENIX vs. STAR “large” enhancement not accounted for by theory cannot be filled by QGP radiation… (very) low-mass region overpredicted… (SPS?!)

20. 4.3 Direct Photons at RHIC v 2 ,dir comparable to pions! under-predicted by ealry QGP emission ← excess radiation T eff excess = (220±25) MeV QGP radiation? radial flow? Spectra Elliptic Flow [Holopainen et al ’11,…]

21. 4.3.2 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]

22. 4.3.3 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]

23. 4.4 QGP Barometer: Blue Shift vs. Temperature QGP-flow driven increase of T eff ~ T + M (  flow ) 2 at RHIC temperature overcomes flowing late  ’s → minimum (opposite to SPS!) expect to be more pronounced at LHC RHIC SPS

24. 5.) Conclusions: Potential of Thermal EM Radiation Spectrometer: “prototype” in-medium spectral function, hadron-to-quark transition Chiral Restoration: Weinberg + QCD sum rules, lattice QCD (  B ~0!) + perturbative limit Quality control: rates (constraints, continuity), medium evolution, consistency SIS-SPS-RHIC-LHC, … Needed: high-quality data to determine spectral shape, then use with flow diagnostics (Non-) Redundancy of RHIC and LHC critical

25. 4.7 Elliptic Flow Diagnostics (RHIC) maximum structure due to late  decays [Chatterjee et al ‘07, Zhuang et al ‘09] [He et al ‘12]

26. 4.1.3 Mass Spectra as Thermometer Overall slope T~150-200MeV (true T, no blue shift!) [NA60, CERN Courier Nov. 2009] Emp. scatt. ampl. + T-  approximation Hadronic many-body Chiral virial expansion Thermometer

27. 2.3.2 NA60 Mass Spectra: p t Dependence more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

28. 5.2 Chiral Restoration Window at LHC low-mass spectral shape in chiral restoration window: ~60% of thermal low-mass yield in “chiral transition region” (T=125-180MeV) enrich with (low-) p t cuts

29. 4.3 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

30. 2.) Chiral Symmetry Breaking in Vacuum  “Higgs Mechanism”, Condensates + Mass Gap in QCD  Hadron Spectrum, Chiral Partners + Sum Rules 3.) EM Spectral Function in Medium  Hadronic Theory  QGP + Lattice QCD 4.) Highlights of EM Probes in Heavy-Ion Collisions  Spectro-, Thermo-, Chrono- + Baro-meter  Thermal Photons 5.) Low-Mass Dileptons at LHC  Mass Spectra + Collectivity 6.) Conclusions Outline

31. 5.1 Thermal Dileptons at LHC charm comparable, accurate (in-medium) measurement critical low-mass spectral shape in chiral restoration window

32. 2.2 EM Probes at SPS all calculated with the same e.m. spectral function! thermal source: T i ≈210MeV, HG-dominated,  -meson melting!

33. 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)

34. 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

35. 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 - 

36. 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”)

37. 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

38. 2.3.2 Acceptance-Corrected NA60 Spectra more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

39. 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]

40. 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

41. 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)

42. 4.4.1 Variations in QGP Radiation improvements in QGP rate insufficient

43. 4.4.2 Variations in Fireball Properties variations in space-time evolution only significant in (late) hadronic phase

44. 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!

45. 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!)

46. 2.3.6 Hydrodynamics vs. Fireball Expansion very good agreement between original hydro [Dusling/Zahed] and fireball [Hees/Rapp]

47. 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

48. 4.2 Low-Mass Dileptons: Chronometer first “explicit” measurement of interacting-fireball lifetime:  FB ≈ (7±1) fm/c In-In N ch >30