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” Erice (Sicily, Italy),

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

1.2 Phase Transition(s) in Lattice QCD cross-over(s) ↔ smooth EM emission rates across T pc chiral restoration in “hadronic phase”? (low-mass dileptons!) hadron resonance gas T pc  ~155MeV ≈  qq  /  qq  0 - [Fodor et al ’10]

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

> >    B *,a 1,K 1... N, ,K … 2.1 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 /  SPS RHIC / LHC

2.2 Dilepton Rates: Hadronic - Lattice - Perturbative dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em continuous rate through T pc 3-fold “degeneracy” toward ~T pc [qq→ee] - [HTL] [RR,Wambach et al ’99] [Ding et al ’10] dR ee /d 4 q 1.4T c (quenched) q=0

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

2.4 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.

Au-Au min. bias 2.5 Low-Mass e + e  Excitation Function: SPS - RHIC 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 Pb-Au(17.3GeV) Pb-Au(8.8GeV)

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

2.6.2 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.]

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

3.1 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   > > -

3.2 Spectral Functions + Weinberg Sum Rules Quantify chiral symmetry breaking via observable spectral functions Vector (  ) - Axialvector (a 1 ) spectral splitting [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘93]  →(2n+1)  pQCD Updated “fit”: [Hohler+RR ‘12]  + a 1 resonance, excited states (  ’+ a 1 ’), universal continuum (pQCD!)  →(2n)  [ALEPH ’98,OPAL ‘99]  V /s  A /s

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

3.3 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]

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?

4.) Conclusions Low-mass dilepton spectra in URHIC point at universal source  -meson gradually melts into QGP continuum radiation prevalent emission temperature around T pc ~150MeV (slopes, v 2 ) 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 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)

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

4.5 QGP Barometer: Blue Shift vs. Temperature QGP-flow driven increase of T eff ~ T + M (  flow ) 2 at RHIC high p t : high T wins over high-flow  ’s → minimum (opposite to SPS!) saturates at “true” early temperature T 0 (no flow) SPS RHIC

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! conservative estimates… Emission Rates Fireball Evolution [van Hees et al ’11] [Turbide et al ’04]

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

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

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

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= MeV) enrich with (low-) p t cuts

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 = MeV Effective Slopes T eff

3.4.2 Back to Spectral Function suggests approach to chiral restoration + deconfinement

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?!)

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

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

3.2 Axialvector in Nucl. Matter: 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:

3.6 Strategies to Test For Chiral Restoration Lat-QCD Euclidean correlators eff. theory for VC + AV spectral functs. constrain Lagrangian (low T,  N ) vac. data + elem. reacts. (  A→eeX, …) EM data in heavy-ion coll. Realistic bulk evol. (hydro,…) Lat-QCD condensates +  ord. par. global analysis of M, p t, v 2 test VC  AV: chiral SRs constrain VC + AV : QCD SR Chiral restoration? Agreement with data?

4.1 Quantitative Bulk-Medium Evolution initial conditions (compact, initial flow?) EoS: lattice (QGP, T c ~170MeV) + chemically frozen hadronic phase spectra + elliptic flow: multistrange at T ch ~ 160MeV , K, p, , … at T fo ~ 110MeV v 2 saturates at T ch, good light-/strange-hadron phenomenology [He et al ’11]

“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 ±

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

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]

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

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 ~ MeV at CERN-SPS Thermometer

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 - 

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

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

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

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)

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!

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

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

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)