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Vector Mesons and Chiral Restoration in Hadronic Matter

Vector Mesons and Chiral Restoration in 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.

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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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