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Vector Mesons and Chiral Restoration in Hadronic Matter

This workshop discusses the behavior of r-mesons in dense hadronic matter, probing chiral restoration with electromagnetic baryonic transitions. Topics include in-medium spectral functions, dilepton rates, and constraints from nuclear interactions. The event also covers the implications of QCD and Weinberg sum rules, providing insights into the transition from hadrons to quarks and gluons.

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Vector Mesons and Chiral Restoration in Hadronic Matter

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  1. Vector Mesons and Chiral Restorationin Hadronic Matter Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, TX, USA ECT* Workshop on “Space- and Timelike Electromagnetic Baryonic Transitions” ECT* Trento (Italy), 08.-12.05.17

  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] • Continuum - temperature • Hadronic Resonances - change in degrees of freedom - restoration of chiral symmetry

  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.) In-Medium Spectral Functions  Hadronic Many-Body Theory + Constraints  Hadron-to-Quark Transition 3.) Phenomenological Applications  Dilepton Spectra in Heavy-Ion Collisions  Dilepton Production off Nuclei 4.) Chiral Symmetry Restoration  QCD +Weinberg Sum Rules  Other Multiplets 5.) Conclusions

  5. 2.1 r-Meson in Matter: Many-Body Theory r Sp > Sp > Sp interactions with hadrons from heat bath  In-Medium r-Propagator r Dr(M,q;mB,T) = [M2 – (mr(0))2 - Srpp - SrB - SrM ]-1 • In-Medium Pion Cloud Srpp = + [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Koch et al, …] R=D, N(1520), a1, K1, … r • Direct r-Hadron Scattering SrB,M = [Haglin, Friman et al, RR et al, Post et al, …] h=N, p, K, … • estimate couplings fromR→ r + h, r + g • comprehensively: scattering data (pN→rN, gN/A,…)

  6. gN gA p-ex 2.2 Constraints I: Nuclear Photo-Absorption On the Nucleon On Nuclei • constrain rNB couplings and non-resonant pion cloud background • 2.+3. resonances melt (selfconsistent N(1520)→Nr) [Urban,Buballa,RR+Wambach ’98]

  7. 2.3 Constraints II: pN→rN Scattering HADES -p-0p background (LpNN=400MeV) p - total 3/2- (D13+…) 1/2- (S11+…) [Urban,Buballa, RR+Wambach ’98] • strong constraint on pion cloud coupling to nucleons • similarly small cutoff in pN → D → pN scattering!

  8. Hot Meson Gas rB/r0 0 0.1 0.7 2.6 [RR+Gale ’99] 2.4 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 strongly broadens in hadronic matter • baryon density rB dominant effect

  9. 2.5 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]

  10. Outline 1.) Introduction 2.) In-Medium Spectral Functions  Hadronic Many-Body Theory + Constraints  Hadron-to-Quark Transition 3.) Phenomenological Applications  Dilepton Spectra in Heavy-Ion Collisions  Dilepton Production off Nuclei 4.) Chiral Symmetry Restoration  QCD +Weinberg Sum Rules  Other Multiplets 5.) Conclusions

  11. 3.1 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 - qq

  12. 3.2 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: production amplitude + in-med. r spectral fct. r g N [Riek et al ’08, ‘10] M[GeV] M[GeV] • r-broadening reduced at high 3-momentum; need low momentum cut

  13. Outline 1.) Introduction 2.) In-Medium Spectral Functions  Hadronic Many-Body Theory + Constraints  Hadron-to-Quark Transition 3.) Phenomenological Applications  Dilepton Spectra in Heavy-Ion Collisions  Dilepton Production off Nuclei 4.) Chiral Symmetry Restoration  QCD +Weinberg Sum Rules  Other Multiplets 5.) Conclusions

  14. 4.1 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]

  15. 4.2 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

  16. 4.3 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

  17. 5.) Conclusions • In-medium r spectral function: - rooted in vacuum spectroscopy and reactions - strongly broadened via interactions w/ baryons (“core” + “cloud”) • Explicit evidence for parton-hadron transition: - rmelting describes dilepton spectra in heavy-ion collisions • Progress in understanding mechanisms of chiral restoration: - evaporation of chiral r-a1 mass splitting (sum rules, MYM) - similar behavior for p-s, N(940)-N(1535), …

  18. 2.2 Transverse-Momentum Dependence pT -Sliced Mass Spectra mT -Slopes x100 • spectral shape as function of pair-pT • entangled with transverse flow (barometer)

  19. 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?

  20. 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?

  21. 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

  22. 4.4.2 Dileptons at HADES: Spectra + Lifetimes Coarse-Graining Results with in-Medium Spectral Functions • Fair consistency with mass spectra and lifetime systematics

  23. 4.5 Lifetime from Dileptons vs. HBT Radii • Rlong qualitatively consistent, quantitatively much smaller

  24. 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

  25. 5.3 Low-Mass Dileptons in p-Pb (5.02GeV) • Thermal radiation at ~10% of cocktail • follows excess-lifetime systematics

  26. 2.1 In-Medium Vector Mesons at RHIC + LHC • Anti-/baryon effects melt the r meson • w also melts, f more robust ↔ OZI

  27. 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

  28. 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]

  29. 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]

  30. 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]

  31. 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

  32. 4.3.2 Photon Puzzle!? • Tslopeexcess ~240 MeV • blue-shift: Tslope ~ T √(1+b)/(1-b) T ~ 240/1.4 ~170 MeV

  33. 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]

  34. 4.2 Low-Mass Dileptons: Chronometer In-In Nch>30 • first “explicit” measurement of interacting-fireball lifetime: tFB≈ (7±1) fm/c

  35. 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)

  36. 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

  37. 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

  38. 3.3.2 Fireball vs. Viscous Hydro Evolution [van Hees, Gale+RR ’11] [S.Chen et al ‘13] • very similar!

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