Thermal Electromagnetic Radiation in HeavyIon Collisions Ralf Rapp

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), 20. 09. 12

1. ) Intro: EM Spectral Function + Fate of Resonances Im Πem(M, q; m. B, T) • Electromagn. spectral function - √s < 2 Ge. V : non-perturbative - √s > 2 Ge. V : 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? Im Pem(M) in Vacuum e+e- → hadrons √s = M

- / qq - 0 ≈ qq 1. 2 Phase Transition(s) in Lattice QCD Tpcc ~155 Me. V [Fodor et al ’ 10] • cross-over(s) ↔ smooth EM emission rates across Tpc • chiral restoration in “hadronic phase”? (low-mass dileptons!) • hadron resonance gas

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

2. 1 Vector Mesons in Hadronic Matter [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; m. B , T) = [M 2 - mr 2 - rpp - r. B - r. M ] -1 Selfenergies: rpp = r p p r. B, r. M = r > B*, a 1, K 1. . . > r-Propagator: N, p, K… Constraints: decays: B, M→ r. N, rp, . . . ; scattering: p. N → r. N, g. A, … SPS RHIC / LHC r. B /r 0 0 0. 1 0. 7 2. 6

2. 2 Dilepton Rates: Hadronic - Lattice - Perturbative d. Ree /d. M 2 ~ ∫d 3 q f B(q 0; T) Im Pem [qq→ee] [HTL] • continuous rate through Tpc • 3 -fold “degeneracy” toward ~Tpc d. Ree/d 4 q 1. 4 Tc (quenched) q=0 [Ding et al ’ 10] [RR, Wambach et al ’ 99]

2. 3 Dilepton Rates vs. Exp. : NA 60 “Spectrometer” • Evolve rates over fireball expansion: Acc. -corrected m+m- Excess Spectra In-In(17. 3 Ge. V) [NA 60 ‘ 09] [van Hees+RR ’ 08] Mmm [Ge. V] • invariant-mass spectrum directly reflects thermal emission rate!

2. 4 Dilepton Thermometer: Slope Parameters Invariant Rate vs. M-Spectra cont. r Transverse-Momentum Spectra Tc=160 Me. V Tc=190 Me. V • Low mass: radiation from around T ~ Tpcc ~ 150 Me. V • Intermediate mass: T ~ 170 Me. V and above • Consistent with p. T slopes incl. flow: Teff ~ T + M (bflow)2

2. 5 Low-Mass e+e- Excitation Function: SPS - RHIC Pb-Au(8. 8 Ge. V) Au-Au min. bias QM 12 Pb-Au(17. 3 Ge. V) • no apparent change of the emission source • consistent with “universal” medium effect around Tpc • partition hadronic/QGP depends on Eo. S, total yield ~ invariant

2. 6 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation • Teffexcess = (220± 25) Me. V • QGP radiation? • radial flow? • v 2 g, dir comparable to pions! • under-predicted by early QGP emission [Holopainen et al ’ 11, …]

2. 6. 2 Thermal Photon Spectra + v 2 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 Me. V • small slope + large v 2 suggest main emission around Tpc • confirmed with hydro evolution [He at al in prep. ]

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

- / qq - 0 qq 3. 1 Chiral Condensate + r-Meson Broadening effective hadronic theory • h = mq h|qq|h > 0 contains quark core + pion cloud + p > = hcore + hcloud ~ > p • matches spectral medium effects: resonances + pion cloud • resonances + chiral mixing drive r-SF toward chiral restoration

3. 2 Spectral Functions + Weinberg Sum Rules • Quantify chiral symmetry breaking via observable spectral functions • Vector (r) - Axialvector (a 1) spectral splitting [Weinberg ’ 67, Das et al ’ 67; Kapusta+Shuryak ‘ 93] t→(2 n)p r. V/s [ALEPH ’ 98, OPAL ‘ 99] t→(2 n+1)p r. A/s p. QCD • Updated “fit”: [Hohler+RR ‘ 12] r + a 1 resonance, excited states (r’+ a 1’), universal continuum (p. QCD!)

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

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] r. V/s Percentage Deviation T [Ge. V] • r and r’ melting compatible with chiral restoration [Hohler +RR ‘ 12]

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?

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~150 Me. V (slopes, v 2) • mechanisms underlying r-melting (p cloud + resonances) find counterparts in hadronic -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)

2. 3 QCD Sum Rules: r and a 1 in Vacuum • dispersion relation: • lhs: hadronic spectral fct. [Shifman, Vainshtein+Zakharov ’ 79] • rhs: operator product expansion • 4 -quark + gluon condensate dominant vector axialvector

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 T 0 (no flow)

4. 3. 2 Revisit Ingredients Emission Rates • Hadron - QGP continuity! • conservative estimates… [Turbide et al ’ 04] Fireball Evolution • multi-strange hadrons at “Tc” • v 2 bulk fully built up at hadronization • chemical potentials for p, K, … [van Hees et al ’ 11]

4. 1. 3 Mass Spectra as Thermometer Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion Thermometer [NA 60, CERN Courier Nov. 2009] • Overall slope T~150 -200 Me. V (true T, no blue shift!)

4. 1. 2 Sensitivity to Spectral Function In-Medium r-Meson Width Mmm [Ge. V] • avg. Gr (T~150 Me. V) ~ 370 Me. V Gr (T~Tc) ≈ 600 Me. V → mr • driven by (anti-) baryons

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=125 -180 Me. V) • enrich with (low-) pt cuts

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 -190 Me. V

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 r decays [He et al ‘ 12] [Chatterjee et al ‘ 07, Zhuang et al ‘ 09]

4. 2 Low-Mass Dileptons: Chronometer In-In Nch>30 • first “explicit” measurement of interacting-fireball lifetime: t. FB ≈ (7± 1) fm/c

3. 2 Axialvector in Nucl. Matter: Dynamical a 1(1260) p + Vacuum: In Medium: r p r + + . . . p p r r a 1 = resonance + . . . [Cabrera, Jido, Roca+RR ’ 09] • in-medium p + r propagators • broadening of p-r scatt. Amplitude • pion decay constant in medium:

3. 6 Strategies to Test For Chiral Restoration eff. theory for VC + AV spectral functs. vac. data + elem. reacts. (g. A→ee. X, …) EM data in heavy-ion coll. Realistic bulk evol. (hydro, …) constrain Lagrangian (low T, r. N) constrain VC + AV : QCD SR global analysis of M, pt, v 2 test VC - AV: chiral SRs Agreement with data? Chiral restoration? Lat-QCD Euclidean correlators Lat-QCD condensates + c ord. par.

4. 1 Quantitative Bulk-Medium Evolution • initial conditions (compact, initial flow? ) • Eo. S: lattice (QGP, Tc~170 Me. V) + chemically frozen hadronic phase • spectra + elliptic flow: multistrange at Tch ~ 160 Me. V p, K, p, L, … at Tfo ~ 110 Me. V [He et al ’ 11] • v 2 saturates at Tch, good light-/strange-hadron phenomenology

2. 1 Chiral Symmetry + QCD Vacuum : flavor + “chiral” (left/right) invariant > q- R Spontaneous Chiral Symmetry Breaking > q. R > “Higgs” Mechanism in Strong Interactions: q. L > • qq attraction condensate fills QCD vacuum! -q L Profound Consequences: • effective quark mass: ↔ mass generation! • near-massless Goldstone bosons p 0, ± • “chiral partners” split: DM ≈ 0. 5 Ge. V JP=0± 1± 1/2±

2. 3. 2 NA 60 Mass Spectra: pt Dependence Mmm [Ge. V] • more involved at p. T>1. 5 Ge. V: Drell-Yan, primordial/freezeout r , …

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)? [Bjorken et al ’ 93, Rajagopal+Wilczek ’ 93] [Z. Huang+X. N. Wang ’ 96 - “baked Alaska” ↔ small T Kluger, Koch, Randrup ‘ 98] - rapid quench+large domains ↔ central A-A - ptherm + p. DCC → e+ e- ↔ M~0. 3 Ge. V, small pt • Lumps of self-bound pion liquid? • Challenge: consistency with hadronic data, NA 60 spectra!

2. 2 EM Probes at SPS • all calculated with the same e. m. spectral function! • thermal source: Ti≈210 Me. V, HG-dominated, r-meson melting!

5. 2 Intermediate-Mass Dileptons: Thermometer • use invariant continuum radiation (M>1 Ge. V): no blue shift, Tslope = T ! Thermometer • independent of partition HG vs QGP (dilepton rate continuous/dual) • initial temperature Ti ~ 190 -220 Me. V at CERN-SPS

4. 7. 2 Light Vector Mesons at RHIC + LHC • baryon effects important even at r. B, tot= 0 : sensitive to r. Btot= r. B + r-B (r-N and r-N interactions identical) • w also melts, f more robust ↔ OZI

5. 3 Intermediate Mass Emission: “Chiral Mixing” [Dey, Eletsky +Ioffe ’ 90] • low-energy pion interactions fixed by chiral symmetry = 0 0 • mixing parameter • degeneracy with perturbative spectral fct. down to M~1 Ge. V • physical processes at M≥ 1 Ge. V: pa 1 → e+e- etc. (“ 4 p annihilation”)

3. 2 Dimuon pt-Spectra and Slopes: Barometer pions: Tch=175 Me. V a┴ =0. 085/fm • modify fireball evolution: e. g. a┴ = 0. 085/fm → 0. 1/fm • both large and small Tc compatible with excess dilepton slopes pions: Tch=160 Me. V a┴ =0. 1/fm

2. 3. 3 Spectrometer III: Before Acceptance Correction emp. ampl. + “hard” fireball hadr. many-body + fireball chiral virial + hydro schem. broad. /drop. + HSD transport • Discrimination power much reduced • can compensate spectral “deficit” by larger flow: lift pairs into acceptance

4. 2 Improved Low-Mass QGP Emission • LO p. QCD spectral function: r. V(q 0, q) = 6∕ 9 3 M 2/2 p [1+QHTL(q 0)] • 3 -momentum augmented lattice-QCD rate (finite g rate)

4. 1 Nuclear Photoproduction: r Meson in Cold Matter g + A → e +e - X e+ g r • extracted “in-med” r-width Gr ≈ 220 Me. V Eg≈1. 5 -3 Ge. V e- [CLAS+Gi. BUU ‘ 08] • Microscopic Approach: product. amplitude g + in-med. r spectral fct. r Fe - Ti full calculation fix density 0. 4 r 0 N [Riek et al ’ 08, ‘ 10] M [Ge. V] • r-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: Thermal Dilepton and Photon Production Rates: Low Mass: e+ e- Im Πem(M, q) γ Im Πem(q 0=q) Im. Pem ~ [Im. Dr + Im. Dw /10 + Im. Df /5] r -meson dominated

3. 5 Summary: Criteria for Chiral Restoration • Vector (r) – Axialvector (a 1) degenerate [Weinberg ’ 67, Das et al ’ 67] p. QCD • QCD sum rules: medium modifications ↔ vanishing of condensates • Agreement with thermal lattice-QCD • Approach to perturbative rate (QGP)