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Thermal Dileptons from High to Low Energies

Explore the emissions of thermal dileptons across a wide range of energies in heavy-ion collisions. Investigate the QCD phase diagram, chiral symmetry restoration, and medium properties using electromagnetic spectral functions. Learn about hadronic resonances, transport coefficients, and fireball properties. Gain insights into the parton-hadron transition and the behavior of low-mass dileptons. Discover the significance of fireball temperature, lifetime, and the search for critical points.

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Thermal Dileptons from High to Low Energies

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  1. Thermal Dileptons from High to Low Energies 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

  2. 1.) Intro: EM Spectral Function to Probe Fireball • Thermal Dilepton Rate ImΠem(M,q;mB,T) e+e-→ hadrons r Im Pem(M) / M2 e+ e- e+ e- M [GeV] • 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

  3. 1.2 30 Years of Dileptons in Heavy-Ion Collisions <Nch>=120 • Robust understanding across QCD phase diagram: QGP + hadronic radiation with meltingr resonance

  4. 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

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

  6. 2.2 Dilepton Rates and Degrees of FreedomdRee /dM2 ~ ∫d3q/q0 f B(q0;T) ImPem /M2 • r-meson resonance “melts” • spectral function merges into QGP description • Direct evidence for transition hadrons → quarks + gluons - [qq→ee] [HTL] dRee/d4q 1.4Tc (quenched) q=0 [Ding et al ’10] [RR,Wambach et al ’99]

  7. 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

  8. 3.1 QCD + Weinberg Sum Rules [Hatsuda+Lee’91, Asakawa+Ko ’93, Leupold et al ’98, …] r a1 [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘94] Dr = rV -rA • accurately satisfied in vacuum • In Medium: condensates from hadron resonance gas, constrained by lattice-QCD T [GeV]

  9. 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

  10. 3.2 Lattice-QCD Results for N(940)-N*(1535) Euclidean Correlator Ratios Exponential Mass Extraction “N*(1535)” “Nucleon” R=∫(G+-G-)/(G++G-) [Aarts et al ‘15] • also indicates MN*(T) → MN (T) ≈ MNvac

  11. 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

  12. 4.1 NA60 Dimuons at SPS (√s=17.3 GeV) e+ e- r • Integrate rates over thermal fireball: Radiation Spectrum High mass: QGP thermometer Tavg ~ 200 MeV Low mass: r-meson melting, fireball lifetime - qq

  13. 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?

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

  15. 4.4 Dileptons at HADES: Coarse Graining • Coarse-graining of hadronic transport to → extract thermodynamic variables → convolute with thermaldilepton rate Temperature + Baryon DensityDilepton 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

  16. 4.4.2 Dileptons at HADES: Spectra + Lifetimes Coarse-Graining Results with in-Medium Spectral Functions • Fair consistency with mass spectra and lifetime systematics

  17. 4.5 Lifetime from Dileptons vs. HBT Radii • Rlong qualitatively consistent, quantitatively much smaller

  18. 5.) Conclusions • Explicit evidence for parton-hadron transition: rmelting • 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

  19. 5.3 Low-Mass Dileptons in p-Pb (5.02GeV) • Thermal radiation at ~10% of cocktail • follows excess-lifetime systematics

  20. 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

  21. 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!

  22. 2.1 In-Medium Vector Mesons at RHIC + LHC • Anti-/baryon effects melt the r meson • w also melts, f more robust ↔ OZI

  23. 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

  24. 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]

  25. 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]

  26. 4.2 Thermal Photon Rates • ``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] • Hadronic emission rate close to QGP-AMY • semi-QGP much more suppressed [Pisarski et al ‘14]

  27. 3.2 Massive Yang-Mills Approach in Vaccum • Gauge r + a1 into chiral pion lagrangian: • problems with vacuum phenomenology → global gauge? • Recent progress: - full rpropagator 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

  28. 4.3.2 Photon Puzzle!? • Tslopeexcess ~240 MeV • blue-shift: Tslope ~ T √(1+b)/(1-b) T ~ 240/1.4 ~170 MeV

  29. 2.2 Transverse-Momentum Dependence pT -Sliced Mass Spectra mT -Slopes x100 • spectral shape as function of pair-pT • entangled with transverse flow (barometer)

  30. 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]

  31. 4.2 Low-Mass Dileptons: Chronometer In-In Nch>30 • first “explicit” measurement of interacting-fireball lifetime: tFB≈ (7±1) fm/c

  32. 4.1 Prospects I: Spectral Shape at mB ~ 0 STAR Excess Dileptons [STAR ‘14] • rather different spectral shapes compatible with data • QGP contribution?

  33. 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)

  34. 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

  35. 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,…]

  36. 3.1.2 Transverse-Momentum Spectra: Baro-meter Effective Slope Parameters RHIC SPS QGP HG [Deng,Wang, Xu+Zhuang ‘11] • qualitative change from SPS to RHIC: flowing QGP • true temperature “shines” at large mT

  37. 2.2 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 r - - qq / qq0

  38. 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

  39. 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]

  40. 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.]

  41. 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

  42. 4.3 Conductivity: Comparison to other Approaches in-med.pgas → [Greif et al ‘16] • in-medium pion gas well above SYM limit • interactions with anti-/baryons likely to reduce it

  43. 3.3.2 Fireball vs. Viscous Hydro Evolution [van Hees, Gale+RR ’11] [S.Chen et al ‘13] • very similar!

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