1. Chiral Symmetry Restoration in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA High Energy/Nuclear Physics Seminar Rice University (Houston, TX), 06.11.12

2. 1.) Intro-I: Probing Strongly Interacting Matter Bulk Properties: Equation of State Microscopic Properties: - Degrees of Freedom - Spectral Functions Phase Transitions: (Pseudo-) Order Parameters  Would like to extract from Observables: temperature + transport properties in-medium spectral functions signatures of deconfinement + chiral symmetry restoration

3. 1.2 EM Spectral Function + Fate of Resonances Electromagnetic spectral function - √s < 2 GeV : non-perturbative - √s > 2 GeV : perturbative (“dual”) Vector resonances “prototypes” - representative for bulk hadrons: neither Goldstone nor heavy flavor Medium modifications of resonances - QCD phase structure - where in the diagram? √s = M e + e  → hadrons Im Π em (M,q;  B,T) Im  em (M) in Vacuum

4. 1.3 Phase Transition(s) in Lattice QCD different “transition” temperatures?! smooth transitions (smooth e + e  rate!) chiral restoration in “hadronic phase”?! (low-mass dileptons!) hadron resonance gas approx. “T c conf ” ~170MeV “T c chiral ”~150MeV ≈  qq  /  qq  - [Fodor et al ’10]

5. 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  Excitation Function  Thermal Photons 5.) Conclusions Outline

6. well tested at high energies, Q 2 > 2 GeV 2 : perturbation theory (  s = g 2 /4π << 1) degrees of freedom = quarks + gluons 3 charges (r,g,b), rich of symmetries 2.1 Nonperturbative QCD (m u,d ≈ 5MeV) Q 2 ≤ 2 GeV 2 → 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 _

7. “Higgs” Mechanism in Strong Interactions: qq attraction  condensate fills QCD vacuum! Spontaneous Chiral Symmetry Breaking 2.2 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 ±

8. Spectral shape matters for chiral symmetry breaking! 2.3 Mass Gap and Chiral Partners Axial-/Vector Correlators pQCD cont. “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] ● Chiral breaking: |q 2 | ≤ 2 GeV 2 Constituent Quark Mass

9. 2.4 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]

10. 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

11. 2.5 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 ● typically 0.5% deviation

12. 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  Excitation Function  Thermal Photons 5.) Conclusions Outline

13. > >    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

14. 3.2 QCD Sum Rules at Finite Temperature  and  ’ melting compatible with chiral restoration  V /s Percentage Deviation T [GeV] [Hohler +RR ‘12] [Hatsuda+Lee’91, Asakawa+Ko ’93, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]

15. 3.3 Chiral Condensate +  -Meson Broadening  qq  /  qq  0 - effective hadronic theory  h = m q  h|qq|h  > 0 contains quark core + pion cloud =  h core +  h cloud ~ + matches spectral medium effects: resonances + pion cloud resonances + chiral mixing drive  -SF toward chiral restoration   > > -

16. 3.4 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?!

17. 3.4.2 Back to Spectral Function suggests approach to chiral restoration + deconfinement -Im  em /(C T q 0 )

18. 3.5 Dilepton Rates: Hadronic - Lattice - Perturbative dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  V 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

19. 3.6 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 Thermal lattice-QCD Approach to perturbative rate (QGP)

20. 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-, Baro- + Chrono-meter  Excitation Function  Thermal Photons 5.) Conclusions Outline

21. 4.1 Pioneering e + e  Measurements at SPS: CERES first quantitative measurement of excess yield and shape consistent with a “melting” of the  resonance around T pc indications for larger effects at lower beam energy: baryons! hints for large very-low mass excess (photons! conductivity?!) Pb-Au(17.3GeV)Pb-Au(8.8GeV) Excess Spectra Evolve rates over fireball expansion:

22. 4.2 Increasing Precision: NA60 “Spectrometer” invariant-mass spectrum directly reflects thermal emission rate! Acc.-corrected  +   Excess Spectra In-In(158AGeV) [NA60 ‘09] M  [GeV] Thermal     Emission Rates [van Hees+RR ’08]

23. 4.3 Dilepton Thermometer: Slope Parameters Low mass: radiation from around T ~ T pc  ~ 150MeV Intermediate mass: T ~ 170 MeV and above Consistent with p T slopes incl. flow: T eff ~ T + M (  flow ) 2 Invariant Rate vs. M-Spectra Transverse-Momentum Spectra T c =160MeV T c =190MeV  cont.

24. M  [GeV] 4.4 Sensitivity to Spectral Function avg.   (T~150MeV) ~ 370 MeV    (T~T c ) ≈ 600 MeV → m  driven by baryons In-Medium  -Meson Width

25. 4.5 Low-Mass Dileptons: Chronometer first “explicit” measurement of interacting-fireball lifetime:  FB ≈ (7±1) fm/c In-In N ch >30

26. STAR 4.6 Low-Mass e + e  Excitation Function at RHIC tension between PHENIX and STAR (central Au-Au) no apparent change of the emission source (?) consistent with “universal” medium effect around T pc partition hadronic/QGP depends on EoS, total yield ~ invariant QM12 PHENIX

27. 4.7 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,…]

28. 4.7.2 Thermal Photon Spectra + v 2 hadronic emission close to T pc essential (continuous rate!) flow blue-shift: T eff ~ T √(1+  )/(1  ) e.g.  =0.3: T ~ 220/1.35~ 160 MeV small slope + large v 2 suggest main emission around T pc confirmed with hydro evolution thermal + prim.  [van Hees,Gale+RR ’11] [He at al in prep.]

29. 5.) Conclusions  -meson gradually melts into QGP continuum radiation Mechanisms underlying  -melting (  cloud + resonances) find counterparts in hadronic  -terms, which restore chiral symmetry Quantitative studies relating  -SF to chiral order parameters with QCD and Weinberg-type sum rules ongoing Low-mass dilepton spectra in URHICs point at universal source, with avg. emission temperatures around T pc ~150MeV (slopes, v 2 ) Future precise characterization of EM emission source at RHIC/LHC + CBM/NICA/SIS holds rich info on QCD phase diagram (spectral shape + disp. rel., source collectivity + lifetime)

30. 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

31. 4.4 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?!)

32. 4.1.2 Sensitivity of NA60 to Spectral Function Significant differences in low-mass region Overall slope T~150-200MeV (true T, no blue shift!) [CERN Courier Nov. 2009] Emp. scatt. ampl. + T-  approximation Hadronic many-body Chiral virial expansion Thermometer

33. 3.3 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:

34. 4.5.2 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]

35. 5.1 Thermal Dileptons at LHC charm comparable, accurate (in-medium) measurement critical low-mass spectral shape in chiral restoration window

36. 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

37. 5.3 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

38. 5.4 Elliptic Flow Diagnostics (RHIC) maximum structure due to late  decays

39. 2.3.2 NA60 Mass Spectra: p t Dependence more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

40. 2.2 EM Probes at SPS all calculated with the same e.m. spectral function! thermal source: T i ≈210MeV, HG-dominated,  -meson melting!

41. 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  )

42. 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 - 

43. 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

44. 2.3.2 Acceptance-Corrected NA60 Spectra more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

45. 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]

46. 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!

47. 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!)

48. 2.3.6 Hydrodynamics vs. Fireball Expansion very good agreement between original hydro [Dusling/Zahed] and fireball [Hees/Rapp]

49. 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