Thermal Dileptons from High to Low Energies 2/5/2018 Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA ISF Research Workshop on Study of High-Density Matter with Hadron Beams Weizmann Institute (Rehovot, Israel), 28.-31.03.17

1.) Intro: EM Spectral Function to Probe Fireball   Thermal Dilepton Rate Im Πem(M,q;mB,T) e+e- → hadrons r Im Pem(M) / M2 Hadronic Resonances - change in degrees of freedom - restoration of chiral symmetry Continuum - temperature Low-q0,q limit: transport coefficient (EM conductivity) Total yields: fireball lifetime e+ e- e+ e- M [GeV]

1.2 30 Years of Dileptons in Heavy-Ion Collisions <Nch>=120 Robust understanding across QCD phase diagram: QGP + hadronic radiation with melting r resonance

Outline 1.) Introduction 2.) Degrees of Freedom of the Medium 2/5/2018 Outline 1.) Introduction 2.) Degrees of Freedom of the Medium  Quark-to-Hadron Transition 3.) Chiral Symmetry Restoration  QCD +Weinberg Sum Rules  Other Multiplets 4.) Phenomenological Tool  Fireball Temperature  Fireball Lifetime (pA?) 5.) Conclusions

2.1 In-Medium r-Meson Spectral Functions Dr (M,q;mB,T) = 1 / [M2 – (mr(0))2 - Srpp - SrB - SrM ] Hot + Dense Matter [RR+Gale ’99] Hot Meson Gas rB/r0 0.1 0.7 2.6 mB =330MeV [RR+Wambach ’99] r-meson “melts” in hot/dense matter baryon density rB more important than temperature

2.2 Dilepton Rates and Degrees of Freedom dRee /dM2 ~ ∫d3q/q0 f B(q0;T) Im Pem /M2 r-meson resonance “melts” spectral function merges into QGP description Direct evidence for transition hadrons → quarks + gluons - [qq→ee] [HTL] [Ding et al ’10] dRee/d4q 1.4Tc (quenched) q=0 [RR,Wambach et al ’99]

Outline 1.) Introduction 2.) Degrees of Freedom of the Medium 2/5/2018 Outline 1.) Introduction 2.) Degrees of Freedom of the Medium  Quark-to-Hadron Transition 3.) Chiral Symmetry Restoration  QCD +Weinberg Sum Rules  Other Multiplets 4.) Phenomenological Tool  Fireball Temperature  Fireball Lifetime (pA?) 5.) Conclusions

3.1 QCD + Weinberg Sum Rules [Hatsuda+Lee’91, Asakawa+Ko ’93, Leupold et al ’98, …] r a1 Dr = rV -rA [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘94] accurately satisfied in vacuum In Medium: condensates from hadron resonance gas, constrained by lattice-QCD T [GeV]

3.1.2 QCD + Weinberg Sum Rules in Medium → Search for solution for axial-vector spectral function [Hohler +RR ‘13] quantitatively compatible with (approach to) chiral restoration strong constraints by combining SRs Chiral mass splitting “burns off”, resonances melt

3.2 Lattice-QCD Results for N(940)-N*(1535) Euclidean Correlator Ratios Exponential Mass Extraction “Nucleon” “N*(1535)” R = ∫(G+-G-)/(G++G-) [Aarts et al ‘15] also indicates MN*(T) → MN (T) ≈ MNvac

Outline 1.) Introduction 2.) Degrees of Freedom of the Medium 2/5/2018 Outline 1.) Introduction 2.) Degrees of Freedom of the Medium  Quark-to-Hadron Transition 3.) Chiral Symmetry Restoration  QCD +Weinberg Sum Rules  Other Multiplets 4.) Phenomenological Tool: Excitation Functions  Fireball Temperature  Fireball Lifetime (pA?) 5.) Conclusions

4.1 NA60 Dimuons at SPS (√s=17.3 GeV) Integrate rates over thermal fireball: Radiation Spectrum e+ e- r Low mass: r-meson melting, fireball lifetime High mass: QGP thermometer Tavg ~ 200 MeV q q -

4.2 Fireball Temperature Slope of Intermediate-Mass Excess Dileptons unique ``early” temperature measurement (no blue-shift!) Ts approaches Ti toward lower energies first-order “plateau” at BES-II/CBM/NICA?

4.3 Fireball Lifetime Excitation Function of Low-Mass Dilepton Excess Yield 1000 [RR+van Hees ‘14] [STAR ‘15] Low-mass excess tracks lifetime well (medium effects!) Tool for critical point search?

4.4 Dileptons at HADES: Coarse Graining Coarse-graining of hadronic transport to → extract thermodynamic variables → convolute with thermal dilepton rate Temperature + Baryon Density Dilepton Yield vs. Nucleon Flow [Huovinen et al. ’02, Endres et al ’15, Galatyuk et al ‘16] Au-Au (1.23AGeV) build-up of collectivity  EM radiation  “thermal” fireball fireball lifetime “only” tfb ~ 13 fm/c

4.4.2 Dileptons at HADES: Spectra + Lifetimes Coarse-Graining Results with in-Medium Spectral Functions Fair consistency with mass spectra and lifetime systematics

4.5 Lifetime from Dileptons vs. HBT Radii Rlong qualitatively consistent, quantitatively much smaller

5.) Conclusions Explicit evidence for parton-hadron transition: r melting Progress in understanding mechanisms of chiral restoration - evaporation of chiral mass r-a1 splitting (sum rules, MYM) Dilepton radiation as a precision tool to measure - fireball lifetime (low mass), including pA - early temperature (intermediate mass; no blue-shift) Coarse-graining enables to extend thermal-radiation tool to lower energies

5.3 Low-Mass Dileptons in p-Pb (5.02GeV) Thermal radiation at ~10% of cocktail follows excess-lifetime systematics

Outline 1.) Introduction 2.) Degrees of Freedom of the Medium 2/5/2018 Outline 1.) Introduction 2.) Degrees of Freedom of the Medium  Quark-to-Hadron Transition 3.) Chiral Symmery Restoration  QCD +Weinberg Sum Rules  Other Multiplets 4.) Transport Properties  Electric Conductivity 5.) Phenomenological Tool  Fireball Lifetime + Temperature (Excitation Fct.)  Fireball in pA? 6.) Conclusions

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+GiBUU ‘08] Microscopic Approach: Fe - Ti g N r product. 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!

2.1 In-Medium Vector Mesons at RHIC + LHC Anti-/baryon effects melt the r meson w also melts, f more robust ↔ OZI

4.3 Comparison to Data: RHIC Ideal Hydro Viscous Hydro [van Hees et al, ‘11, ’14] [Paquet et al ’16] same rates + intial flow  similar results from various evolution models

3.2 Massive Yang-Mills in Hot Pion Gas Temperature progression of vector + axialvector spectral functions supports “burning” of chiral-mass splitting as mechanism for chiral restoration [as found in sum rule analysis]

4.1 Initial Flow + Thermal Photon-v2 Bulk-Flow Evolution Direct-Photon v2 Ideal Hydro 0-20% Au-Au initial radial flow: - accelerates bulk v2 - harder radiation spectra (pheno.: coalescence, multi-strange f.o.) much enhances thermal-photon v2 [He et al ’14]

[Holt,Hohler+RR in prep] 4.2 Thermal Photon Rates Hadronic emission rate close to QGP-AMY semi-QGP much more suppressed [Pisarski et al ‘14] ``Cocktail” of hadronic sources (available in parameterized form) Sizable new hadronic sources: pr → gw , pw → gr , rw → gp [Heffernan et al ‘15] [Holt,Hohler+RR in prep]

3.2 Massive Yang-Mills Approach in Vaccum Gauge r + a1 into chiral pion lagrangian: problems with vacuum phenomenology → global gauge? Recent progress: - full r propagator in a1 selfenergy - vertex corrections to preserve PCAC: [Urban et al ‘02, Rischke et al ‘10] [Hohler +RR ‘14] enables fit to t-decay data! local-gauge approach viable starting point for addressing chiral restoration in medium

4.3.2 Photon Puzzle!? Tslopeexcess ~240 MeV blue-shift: Tslope ~ T √(1+b)/(1-b)  T ~ 240/1.4 ~ 170 MeV

2.2 Transverse-Momentum Dependence pT -Sliced Mass Spectra mT -Slopes x 100 spectral shape as function of pair-pT entangled with transverse flow (barometer)

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

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

4.1 Prospects I: Spectral Shape at mB ~ 0 STAR Excess Dileptons [STAR ‘14] rather different spectral shapes compatible with data QGP contribution?

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)

2.3 Low-Mass e+e- Excitation Function: 20-200 GeV P. Huck et al. [STAR], QM14 compatible with predictions from melting r meson “universal” source around Tpc

3.3.2 Effective Slopes of Thermal Photons Thermal Fireball Viscous Hydro [van Hees,Gale+RR ’11] [S.Chen et al ‘13] thermal slope can only arise from T ≤ Tc (constrained by closely confirmed by hydro hadron data) exotic mechanisms: glasma BE? Magnetic fields+ UA(1)? [Liao at al ’12, Skokov et al ’12, F. Liu ’13,…]

3.1.2 Transverse-Momentum Spectra: Baro-meter Effective Slope Parameters SPS RHIC QGP HG [Deng,Wang, Xu+Zhuang ‘11] qualitative change from SPS to RHIC: flowing QGP true temperature “shines” at large mT

2.2 Chiral Condensate + r-Meson Broadening 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 > - r

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

4.4 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.) Electric Conductivity Similar behavior for different transport? h/s ~ (2pT) DsHF ~ sEM/T Probes soft limit of EM spectral function sEM(T) = - e2 limq0→0 [ ∂/∂q0 Im PEM(q0,q=0;T) ] Need density-squared contributions Non-trivial for vertex corrections (usually evaluated with vacuum propagators) Start out with pion gas: dress pions in r-cloud + vertex corrections [Atchison+RR in prog.]

4.2 Low-Energy Limit of Spectral Function Pion Gas Perturbative QGP T=150MeV ar = 0.7 ar = 1.2 ar = 2.7 0 2 4 6 8 10 q0 [MeV] [Moore+Robert ‘06] conductivity peak strongly smeared out suggestive for strongly coupled system

4.3 Conductivity: Comparison to other Approaches in-med. p gas → [Greif et al ‘16] in-medium pion gas well above SYM limit interactions with anti-/baryons likely to reduce it

3.3.2 Fireball vs. Viscous Hydro Evolution [van Hees, Gale+RR ’11] [S.Chen et al ‘13] very similar!