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Thermal Electromagnetic Radiation in Heavy-Ion Collisions

Thermal Electromagnetic Radiation in Heavy-Ion Collisions. Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA 34 th International School of Nuclear Physics “Probing the Extremes of Matter with Heavy Ions”

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Thermal Electromagnetic Radiation in Heavy-Ion Collisions

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  1. Thermal Electromagnetic Radiation in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA 34th International School of Nuclear Physics “Probing the Extremes of Matter with Heavy Ions” Erice (Sicily, Italy), 20.09.12

  2. 1.) Intro: EM Spectral Function + Fate of Resonances Im Pem(M) in Vacuum Im Πem(M,q;mB,T) • 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? e+e-→ hadrons √s = M

  3. 1.2 Phase Transition(s) in Lattice QCD Tpcc~155MeV [Fodor et al ’10] • cross-over(s) ↔ smooth EM emission rates across Tpc • chiral restoration in “hadronic phase”? (low-mass dileptons!) • hadron resonance gas - - ≈ qq / qq0

  4. Outline 2.) Spectral Function + Emission Temperature  In-Medium r + Dilepton Rates  Dilepton Mass Spectra + Slopes  Excitation Function + Elliptic Flow 3.) Chiral Symmetry Restoration  Chiral Condensate  Weinberg + QCD Sum Rules  Euclidean Correlators 4.) Conclusions

  5. 2.1 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

  6. 2.2 Dilepton Rates: Hadronic - Lattice - Perturbative dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem dRee/d4q 1.4Tc (quenched) q=0 • continuous rate through Tpc • 3-fold “degeneracy” toward~Tpc - [qq→ee] [HTL] [Ding et al ’10] [RR,Wambach et al ’99]

  7. 2.3 Dilepton Rates vs. Exp.: NA60 “Spectrometer” • Evolve rates over fireball expansion: Acc.-correctedm+m- Excess Spectra In-In(17.3GeV) [NA60 ‘09] [van Hees+RR ’08] Mmm [GeV] • invariant-mass spectrum directly reflects thermal emission rate!

  8. 2.4 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

  9. 2.5 Low-Mass e+e- Excitation Function: SPS - RHIC Pb-Au(8.8GeV) Au-Au min. bias QM12 Pb-Au(17.3GeV) • no apparent change of the emission source • consistent with “universal” medium effect around Tpc • partition hadronic/QGP depends on EoS, total yield ~ invariant

  10. 2.6 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 early QGP • emission [Holopainen et al ’11,…]

  11. 2.6.2 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.]

  12. Outline 2.) Spectral Function + Emission Temperature  In-Medium r + Dilepton Rates  Dilepton Mass Spectra + Slopes  Excitation Function + Elliptic Flow 3.) Chiral Symmetry Restoration  Chiral Condensate  Weinberg + QCD Sum Rules  Euclidean Correlators 4.) Conclusions

  13. 3.1 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

  14. 3.2 Spectral Functions + Weinberg Sum Rules • Quantify chiral symmetry breaking via observable spectral functions • Vector (r) - Axialvector (a1) spectral splitting [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘93] t→(2n+1)p t→(2n)p [ALEPH ’98,OPAL ‘99] rA/s rV/s pQCD pQCD • Updated “fit”: [Hohler+RR ‘12] • r+a1 resonance, excited states (r’+a1’), universal continuum (pQCD!)

  15. 3.2.2 Evaluation of Chiral Sum Rules in Vacuum • pion decay • constants • chiral quark • condensates • vector-axialvector splitting quantitative observable of • spontaneous chiral symmetry breaking • promising starting point to analyze chiral restoration

  16. 3.3 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]

  17. 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?

  18. 4.) Conclusions • Low-mass dilepton spectra in URHIC point at universal source • r-meson gradually melts into QGP continuum radiation • prevalent emission temperature around Tpc~150MeV (slopes, v2) • 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 • Future precise characterization of EM emission source at • RHIC/LHC + CBM/NICA/SIS holds rich info on QCD phase • diagram (spectral shape, source collectivity + lifetime)

  19. 2.3 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

  20. 4.5 QGP Barometer: Blue Shift vs. Temperature SPS RHIC • QGP-flow driven increase of Teff ~ T + M (bflow)2 at RHIC • high pt: high T wins over high-flow r’s → minimum (opposite to SPS!) • saturates at “true” early temperature T0 (no flow)

  21. 4.3.2 Revisit Ingredients Emission Rates Fireball Evolution • multi-strange hadrons at “Tc” • v2bulkfully built up at hadronization • chemical potentials for p, K, … • Hadron - QGP continuity! • conservative estimates… [Turbide et al ’04] [van Hees et al ’11]

  22. 4.1.3 Mass Spectra as Thermometer Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion Thermometer [NA60, CERN Courier Nov. 2009] • Overall slope T~150-200MeV (true T, no blue shift!)

  23. 4.1.2 Sensitivity to Spectral Function In-Medium r-Meson Width • avg. Gr(T~150MeV)~370MeVGr (T~Tc) ≈ 600 MeV → mr • driven by (anti-) baryons Mmm [GeV]

  24. 5.1 Thermal Dileptons at LHC • charm comparable, accurate (in-medium) measurement critical • low-mass spectral shape in chiral restoration window

  25. 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

  26. 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

  27. 3.4.2 Back to Spectral Function • suggests approach to chiral restoration + deconfinement

  28. 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?!)

  29. 4.4 Elliptic Flow of Dileptons at RHIC • maximum structure due to • late r decays [He et al ‘12] [Chatterjee et al ‘07, Zhuang et al ‘09]

  30. 4.2 Low-Mass Dileptons: Chronometer In-In Nch>30 • first “explicit” measurement of interacting-fireball lifetime: • tFB≈ (7±1) fm/c

  31. p Sp Sp Sp r Sr Sr Sr 3.2 Axialvector in Nucl. Matter: 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:

  32. 3.6 Strategies to Test For Chiral Restoration eff. theory for VC + AV spectral functs. Lat-QCD Euclidean correlators vac. data + elem. reacts. (gA→eeX, …) constrain Lagrangian (low T, rN) constrainVC + AV : QCD SR Lat-QCD condensates + c ord. par. EM data in heavy-ion coll. test VC - AV: chiral SRs global analysis of M, pt, v2 Realistic bulk evol. (hydro,…) Agreement with data? Chiral restoration?

  33. 4.1 Quantitative Bulk-Medium Evolution • initial conditions (compact, initial flow?) • EoS: lattice (QGP, Tc~170MeV) + chemically frozen hadronic phase • spectra + elliptic flow: multistrange at Tch ~ 160MeV • p, K, p, L, … at Tfo ~ 110MeV • v2 saturates at Tch, good light-/strange-hadron phenomenology [He et al ’11]

  34. qR qL > > > > - - qL qR 2.1 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±

  35. 2.3.2 NA60 Mass Spectra: pt Dependence Mmm [GeV] • more involved at pT>1.5GeV: Drell-Yan, primordial/freezeout r , …

  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 • 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]

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

  38. 5.2 Intermediate-Mass Dileptons: Thermometer • use invariant continuum radiation (M>1GeV): no blue shift, Tslope = T ! Thermometer • independent of partition HG vs QGP (dilepton rate continuous/dual) • initial temperature Ti ~ 190-220 MeV at CERN-SPS

  39. 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 - -

  40. = = 5.3 Intermediate Mass Emission: “Chiral Mixing” [Dey, Eletsky +Ioffe ’90] • low-energy pion interactions fixed by chiral symmetry 0 0 0 0 • mixing parameter • degeneracy with perturbative • spectral fct. down to M~1GeV • physical processes at M≥ 1GeV: • pa1→ e+e- etc. (“4p annihilation”)

  41. 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

  42. 2.3.3 Spectrometer III: Before Acceptance Correction emp. ampl. + “hard” fireball hadr. many-body + fireball schem. broad./drop. + HSD transport chiral virial + hydro • Discrimination power much reduced • can compensate spectral “deficit” by larger flow: lift pairs into acceptance

  43. 4.2 Improved Low-Mass QGP Emission • LO pQCD spectral function: rV(q0,q) = 6∕9 3M2/2p [1+QHTL(q0)] • 3-momentum augmented lattice-QCD rate (finite g rate)

  44. 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!

  45. 2.3.6 Hydrodynamics vs. Fireball Expansion • very good agreement • between original • hydro [Dusling/Zahed] • and fireball [Hees/Rapp]

  46. 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]

  47. 3.5 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 • Agreement with thermal lattice-QCD • Approach to perturbative rate (QGP)

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