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Chiral Symmetry Restoration in Heavy-Ion Collisions

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.

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Chiral Symmetry Restoration in Heavy-Ion Collisions

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  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 Im Pem(M) in Vacuum Im Πem(M,q;mB,T) • 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? e+e-→ hadrons √s = M

  4. 1.3 Phase Transition(s) in Lattice QCD - - ≈ qq / qq “Tcchiral”~150MeV “Tcconf” ~170MeV [Fodor et al ’10] • different “transition” temperatures?! • smooth transitions (smooth e+e- rate!) • chiral restoration in “hadronic phase”?! • (low-mass dileptons!) • hadron resonance gas approx.

  5. Outline 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

  6. Q2≤ 2GeV2 → transition to “strong” QCD: • effective d.o.f. = hadrons (Confinement) • massive “constituent quarks” • mq* ≈ 350 MeV ≈ ⅓ Mp (Chiral Symmetry • ~ ‹0|qq|0› condensate! Breaking) ↕⅔fm 2.1 Nonperturbative QCD • well tested at high energies, Q2>2GeV2: • perturbation theory (as = g2/4π<< 1) • degrees of freedom = quarks + gluons • 3 charges (r,g,b), rich of symmetries (mu,d ≈ 5MeV) _

  7. qR qL > > > > - - qL qR 2.2 Chiral Symmetry + QCD Vacuum : flavor + “chiral” (left/right) invariant • “Higgs” Mechanism in Strong Interactions: • qqattraction  condensate fills QCD vacuum! • Spontaneous Chiral Symmetry Breaking - • Profound Consequences: • effective quark mass: • ↔ mass generation! • near-massless Goldstone bosons p0,± • “chiral partners” split: DM ≈ 0.5GeV JP=0±1± 1/2±

  8. 2.3 Mass Gap and Chiral Partners Axial-/Vector Correlators Constituent Quark Mass “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] pQCD cont. • Spectral shape matters for • chiral symmetry breaking! ● Chiral breaking:|q2| ≤ 2 GeV2

  9. 2.4 Chiral (Weinberg) Sum Rules • Quantify chiral symmetry breaking via observable spectral functions • Vector (r) - Axialvector (a1) spectral splitting [Weinberg ’67, Das et al ’67] t→(2n+1)p t→(2n)p [ALEPH ‘98, OPAL ‘99] pQCD pQCD • Key features of updated “fit”: [Hohler+RR ‘12] • r+a1 resonance, excited states (r’+a1’), universal continuum (pQCD!)

  10. 2.4.2 Evaluation of Chiral Sum Rules in Vacuum • pion decay • constants • chiral quark • condensates • vector-axialvector splitting (one of the) cleanest observable of • spontaneous chiral symmetry breaking • promising (best?) starting point to search for chiral restoration

  11. 2.5 QCD Sum Rules: r and a1 in Vacuum • dispersion relation: [Shifman,Vainshtein+Zakharov ’79] • lhs:hadronic spectral fct. • rhs:operator product expansion • 4-quark + gluon condensate dominant vector axialvector ●typically 0.5% deviation

  12. Outline 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

  13. 3.1 Vector Mesons in Hadronic Matter > rB /r0 0 0.1 0.7 2.6 > [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 …] Dr (M,q;mB ,T) = [M 2 - mr2 -Srpp -SrB -SrM ] -1 r-Propagator: B*,a1,K1... r Sp r SrB,rM= Selfenergies: Srpp= N,p,K… Sp Constraints:decays:B,M→ rN, rp, ... ; scattering:pN→rN, gA, … SPS RHIC/LHC

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

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

  16. 3.4 Vector Correlator in Thermal Lattice QCD • Euclidean Correlation fct. Lattice (quenched) [Ding et al ‘10] Hadronic Many-Body [RR ‘02] • “Parton-Hadron Duality” of lattice and in-medium hadronic?!

  17. 3.4.2 Back to Spectral Function -Im Pem /(C T q0) • suggests approach to chiral restoration + deconfinement

  18. 3.5 Dilepton Rates: Hadronic - Lattice - Perturbative dRee /dM2 ~ ∫d3q f B(q0;T) Im PV • Hadronic, pert. + lattice QCD • tend to “degenerate” toward~Tc • Quark-Hadron Duality at all M?! • ( degenerate axialvector SF!) dRee/d4q 1.4Tc (quenched) q=0 - [qq→ee] [HTL] [Ding et al ’10] [RR,Wambach et al ’99]

  19. 3.6 Summary: Criteria for Chiral Restoration • Vector (r) – Axialvector (a1) 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. Outline 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

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

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

  23. 4.3 Dilepton Thermometer: Slope Parameters Invariant Rate vs. M-Spectra Transverse-Momentum Spectra cont. Tc=160MeV Tc=190MeV r • Low mass: radiation from around T ~ Tpcc ~ 150MeV • Intermediate mass: T ~ 170 MeV and above • Consistent with pT slopes incl. flow: Teff ~ T + M (bflow)2

  24. 4.4 Sensitivity to Spectral Function In-Medium r-Meson Width • avg. Gr(T~150MeV)~370MeVGr (T~Tc) ≈ 600 MeV → mr • driven by baryons Mmm [GeV]

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

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

  27. 4.7 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation • Teffexcess = (220±25) MeV • QGP radiation? • radial flow? • v2g,dir comparable to pions! • under-predicted by ealry QGP • emission [Holopainen et al ’11,…]

  28. 4.7.2 Thermal Photon Spectra + v2 thermal + prim. g [van Hees,Gale+RR ’11] • hadronic emission close to Tpc essential (continuous rate!) • flow blue-shift: Teff ~ T √(1+b)/(1-b) • e.g. b=0.3: T ~ 220/1.35~ 160 MeV • small slope + large v2 suggest main emission around Tpc • confirmed with hydro evolution [He at al in prep.]

  29. 5.) Conclusions • r-meson gradually melts into QGP continuum radiation • Mechanisms underlying r-melting (p cloud + resonances) find • counterparts in hadronic S-terms, which restore chiral symmetry • Quantitative studies relating r-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 Tpc~150MeV (slopes, v2) • 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 pt-Spectra and Slopes: Barometer Effective Slopes Teff • theo. slopes originally too soft • increase fireball acceleration, • e.g. a┴ = 0.085/fm → 0.1/fm • insensitive to Tc=160-190MeV

  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 Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion Thermometer [CERN Courier Nov. 2009] • Significant differences in low-mass region • Overall slope T~150-200MeV (true T, no blue shift!)

  33. p Sp Sp Sp r Sr Sr Sr 3.3 Axialvector in Medium: Dynamical a1(1260) p a1 resonance + + . . . = Vacuum: r In Medium: + + . . . [Cabrera,Jido, Roca+RR ’09] • in-medium p + r propagators • broadening of p-r scatt. Amplitude • pion decay constant in medium:

  34. 4.5.2 Revisit Ingredients Emission Rates Fireball Evolution • multi-strange hadrons at “Tc” • v2bulkfully built up at hadronization • chemical potentials for p, K, … • Hadron - QGP continuity! [Turbide et al ’04] [van Hees et al ’11]

  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-) pt cuts

  37. 5.3 QGP Barometer: Blue Shift vs. Temperature RHIC SPS • QGP-flow driven increase of Teff ~ T + M (bflow)2 at RHIC • temperature overcomes flowing late r’s → minimum (opposite to SPS!) • expect to be more pronounced at LHC

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

  39. 2.3.2 NA60 Mass Spectra: pt Dependence Mmm [GeV] • more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

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

  41. 4.1.2 Mass-Temperature Emission Correlation • generic space-time argument: •  • Tmax ≈ M / 5.5 • (forImPem =const) • thermal photons: • Tmax≈ (q0/5) * (T/Teff)2 • → reduced by flow blue-shift! • Teff ~ T * √(1+b)/(1-b)

  42. 4.7.2 Light Vector Mesons at RHIC + LHC • baryon effects important even at rB,tot= 0 : • sensitive to rBtot= rB + rB (r-N and r-N interactions identical) • w also melts, f more robust ↔ OZI - -

  43. 3.2 Dimuon pt-Spectra and Slopes: Barometer pions: Tch=160MeV a┴ =0.1/fm pions: Tch=175MeV a┴ =0.085/fm • modify fireball evolution: • e.g. a┴ = 0.085/fm → 0.1/fm • both large and small Tccompatible • with excess dilepton slopes

  44. 2.3.2 Acceptance-Corrected NA60 Spectra Mmm [GeV] Mmm [GeV] • more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

  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 • 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] - “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A - ptherm + pDCC → e+ e- ↔ M~0.3GeV, small pt [Z.Huang+X.N.Wang ’96 Kluger,Koch,Randrup ‘98]

  46. 4.1 Nuclear Photoproduction: rMeson in Cold Matter g + A → e+e- X • extracted • “in-med” r-width • Gr≈ 220 MeV e+ e- Eg≈1.5-3 GeV g r [CLAS+GiBUU ‘08] • Microscopic Approach: + in-med. r spectral fct. product. amplitude full calculation fix density 0.4r0 Fe-Ti r g N [Riek et al ’08, ‘10] M[GeV] • r-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 Tc • - but far from non-interacting: • short-lived resonances R: • a + b → R → a + b,tR ≤ 1 fm/c • Parton Quasi-Particles shortly above Tc • - but large interaction measure I(T) = e -3P  both “phases” strongly coupled (hydro!): - large interaction rates → large collisional widths - resonance broadening → melting → quarks - broad parton quasi-particles - “Feshbach” resonances around Tc (coalescence!)

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

  49. e+ e- γ 2.1 Thermal Electromagnetic Emission EM Current-Current Correlation Function: Thermal Dilepton and Photon Production Rates: Im Πem(M,q) Im Πem(q0=q) r-meson dominated Low Mass: ImPem~ [ImDr + ImDw /10 + ImDf /5]

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