Thermal Dileptons + Photons: Baseline Approach 6/27/2018 Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA RIKEN/BNL Workshop on “Thermal Radiation” in Heavy-Ion Reactions BNL (Upton, NY), 05.-07.12.12

1.) Intro: 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 - HICs: correlate (mN,T) ↔ spectral shape e+e- → hadrons √s = M

1.2 Chiral Restoration in Lattice QCD ≈ qq / qq0 - - Tpcc ~155MeV [Fodor et al ’10] compatible with hadron resonance gas (also for thermodynamics!) chiral restoration in “hadronic phase”? (low-mass dileptons!) cross-over ↔ smooth EM emission rates across Tpc

Outline 2.) Spectral Function in Medium 6/27/2018 Outline 2.) Spectral Function in Medium  Effective Hadronic Theory in Medium  QGP Emission and Lattice QCD  Chiral Restoration 3.) Dilepton Spectra in Heavy-Ion Collisions  Nature of Emission Source from SPS to RHIC  Spectral Shapes and Temperatures  Radial and Elliptic Collectivity 4.) Conclusions

2.1 Baseline I: r Meson in Hadronic Matter [Pisarski, Chanfray et al, Herrmann et al, Asakawa et al, RR et al, Koch et al, Steele et al, Post et al, Eletsky et al, Harada et al …] r-Propagator: Dr (M,q;mB ,T) = [M 2 - mr2 - Srpp - SrB - SrM ] -1 > B*,a1,K1... Sp r r Selfenergies: Srpp = SrB,rM = Sp N,p,K… Constraints: decays: B,M→ rN, rp, ... ; scattering: pN → rN, gA, … rB /r0 0.1 0.7 2.6 SPS RHIC / LHC

2.2 Chiral Condensate + r-Meson Broadening -Im PV / s qq / qq0 - - effective hadronic theory 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 Sp > -

2.3 Baseline II: Perturbative + Lattice QGP Rates dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem rates smoothly match around Tpc: - compatible with cross-over - 3-fold “degeneracy” - [qq→ee] [HTL] [Braaten et al ‘91] [Ding et al ’10] dRee/d4q 1.4Tc (quenched) q=0 [RR,Wambach et al ’99]

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

2.5 Criteria for Chiral Restoration Vector (r) – Axialvector (a1) degenerate [Weinberg ’67, Das et al ’67, Kapusta+ Shuryak ‘94] pQCD QCD sum rules: medium modifications ↔ vanishing of condensates Degeneracy with thermal lattice-QCD Approach to perturbative rate (QGP) → Talk by Hohler

Outline 2.) Spectral Function in Medium 6/27/2018 Outline 2.) Spectral Function in Medium  Effective Hadronic Theory in Medium  QGP Emission and Lattice QCD  Chiral Restoration 3.) Dilepton Spectra in Heavy-Ion Collisions  Nature of Emission Source from SPS to RHIC  Spectral Shapes and Temperatures  Radial and Elliptic Collectivity 4.) Conclusions

3.1 Thermal Dilepton + Photon Emission Rates 6/27/2018 e+ e- γ Im Πem(M,q;mB,T) Im Πem(q0=q;mB,T) determined by the same spectral function finite photon rate ↔ divergent dilepton rate for M → 0 low mass: r -meson dominated ImPem ~ [ImDr + ImDw /10 + ImDf /5]

3.2 SPS I: Dielectrons with CERES/NA45 Evolve rates over fireball expansion: Pb-Au(17.3GeV) Pb-Au(8.8GeV) Excess Spectra established large enhancement consistent with a “r-melting” around Tpc large effects at lower beam energy: baryons! M→0: photon point!

3.3 SPS II: Precision with m+m- at NA60 Acc.-corrected Excess Spectra In-In(17.3GeV) [NA60 ‘09] vs. Theoretical Input Rates r cont. Mmm [GeV] [van Hees+RR ’08] broadened r spectral function quantitatively confirmed invariant-mass spectrum directly reflects thermal emission rate! mass slope reveals emission temperature around Tpcc ~ 150 MeV

3.4 Low-Mass e+e- Excitation Function at RHIC PHENIX STAR QM12 tension between PHENIX and STAR (central Au-Au) non-central Au-Au consistent with “universal” source around Tpc partition hadronic/QGP depends on EoS → Talks by Wang, Vujanovic, Linnyk

3.4.2 Hadronic vs. QGP Emission at RHIC (Tc=180MeV) (Tpc=170MeV) smaller Tpc + lattice EoS enhance QGP + deplete hadronic yield corroborates prevalent emission source around Tpc

3.5 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation Teffexcess = (220±25) MeV “moderate” ~  T √(1+b)/(1-b)  suggests T < 200 MeV large v2 also suggests “later” emission (aka ~Tpc)

3.5.2 Thermal Photon Spectra + v2 + prim. g (Tc=180MeV) [van Hees,Gale+RR ’11] M → 0 limit of dilepton rates (continuous across Tc!) flow blue-shift, e.g. b=0.3: T ~ 220MeV / 1.35 ~ 160 MeV confirms bulk emission around Tpc compatible with hydro evolution if bulk-v2 saturates at Tpc [He at al in prep.] → Talks by Skokov, Tuchin, Dusling

3.6 Elliptic Flow of Dileptons at RHIC maximum structure due to late r decays [He et al in prep.] [Chatterjee et al ‘07, Zhuang et al ‘09]

4.) Conclusions Low-mass dileptons at SPS+RHIC point at universal source, avg. emission temperatures T ~ 150MeV ~ Tpcc (slopes, v2) r-meson smoothly melts into QGP continuum radiation Mechanisms underlying r-melting (p cloud + resonances) find counterparts in hadronic S-terms, restoring chiral symmetry Quantitative studies relating r-SF to chiral order parameters with QCD and Weinberg-type sum rules ongoing Need conditions under which medium effects turn off Future precise characterization of EM emission source at RHIC, LHC + CBM/NICA/SIS holds rich info on QCD phase structure (spectral shape + disp. rel., source collectivity + lifetime)

4.1 How to Turn off Medium Effects pp collisions: cocktail - seems to work (but: no medium effect) Peripheral collisions - challenging: dense hadronic phase persists d-A collisions: forward vs. backward y (formation time effects?) High(er) pT - seems to work: NA60 m+m- Elementary projectiles on cold nuclei - seems to work: CLAS gA → e+e- X (Gr ≈ 220 MeV) full calculation fix density 0.4r0 Fe - Ti

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

3.4.3 Hadronic vs. QGP Photons at RHIC (Tc=180MeV) (Tpc=170MeV) smaller Tpc + lattice EoS enhance QGP + deplete hadronic yield corroborates prevalent emission source around Tpc

3.6 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)

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

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!)

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 pQCD Updated “fit”: [Hohler+RR ‘12] r + a1 resonance, excited states (r’+ a1’), universal continuum (pQCD!) t→(2n)p [ALEPH ’98,OPAL ‘99] rV/s rA/s

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

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

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]

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

4.3.2 Revisit Ingredients Emission Rates Fireball Evolution Hadron - QGP continuity! conservative estimates… multi-strange hadrons at “Tc” v2bulk fully built up at hadronization chemical potentials for p, K, … [Turbide et al ’04] [van Hees et al ’11]

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=125-180MeV) 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=160-190MeV

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

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

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?!)

4.2 Low-Mass Dileptons: Chronometer In-In Nch>30 first “explicit” measurement of interacting-fireball lifetime: tFB ≈ (6±1) fm/c

3.2 Axialvector in Nucl. Matter: Dynamical a1(1260) p a1 resonance Vacuum: + + . . . = r Sr Sp p r Sr Sp In Medium: + + . . . [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. 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. global analysis of M, pt, v2 test VC - AV: chiral SRs Realistic bulk evol. (hydro,…) Agreement with data? Chiral restoration?

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]

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

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]

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

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

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 - -

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

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

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

4.1 Nuclear Photoproduction: r Meson 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 ‘08] Microscopic Approach: Fe - Ti g N r production amplitude in-med. r spectral fct. + M [GeV] [Riek et al ’08, ‘10] full calculation fix density 0.4r0 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]