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r Mesons in Medium at RHIC + JLab

r Mesons in Medium at RHIC + JLab. Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, USA Theory Center Seminar Jefferson Lab (Newport News, VA), 28.03.11. 1.) Introduction: QCD Hadron and Phase Structure. e + e - → hadrons.

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r Mesons in Medium at RHIC + JLab

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  1. r Mesons in Medium at RHIC + JLab Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, USA Theory Center Seminar Jefferson Lab (Newport News, VA), 28.03.11

  2. 1.) Introduction:QCD Hadron and Phase Structure e+e-→ hadrons • Electromagn. spectral function • - √s ≤ 1 GeV: non-perturbative • - √s ≥ 2 GeV: pertubative (“dual”) • Disappearance of resonances • ↔ phase structure changes: • - hadron gas → Quark-Gluon Plasma • - realization of transition? √s=M • Thermal e+e- emission rate from • hot/dense matter (lem >>Rnucleus ) • Temperature? Degrees of freedom? • Deconfinement? Chiral Restoration? Im Πem(M,q;mB,T)

  3. 1.2 Intro-II:Low-Mass Dileptons at CERN-SPS CERES/NA45 [2000] NA60 [2005] mee [GeV] • strong excess around M ≈ 0.5GeV (andM > 1GeV) • little excess in r/wandf region

  4. Outline 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.) r Meson in Medium  Hadronic Lagrangian + Empirical Constraints  Many-Body Theory + Spectral Functions 4.) Dilepton Spectra in Heavy-Ion Collisions  Thermal Emission Rates, Lattice QCD  Phenomenology in URHICs 5.) Dilepton Spectra in Nuclear Photo-Production  Elementary Amplitude, CLAS Phenomenology 6.) Conclusions

  5. 2.1 Chiral Symmetry Breaking + Hadron Spectrum Condensates fill QCD vacuum: Quark Level: Const. Mass Observables: Hadron Spectrum D(1700) N(1520) D(1232) “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] M [GeV] JP=0±1± 1/2± 3/2± - • Mq* ~ ‹0|qq|0› • chiral breaking:|q2| ≤ 1 GeV 2 • energy gap • massless Goldstone mode • “chiral partners” split(½GeV)

  6. F2-Structure Function (spacelike) JLAB Data p d • x ≈ x • average → Quark-Hadron Duality • lower onset-Q2in nuclei? [Niculescu et al ’00] 2.2 Q2-Dependence of Chiral Breaking Axial-/Vector Mesons pQCD cont. • Weinberg Sum Rule(s) • spectral distributions!

  7. Outline 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.) r Meson in Medium  Hadronic Lagrangian + Empirical Constraints  Many-Body Theory + Spectral Functions 4.) Dilepton Spectra in Heavy-Ion Collisions  Thermal Emission Rates, Lattice QCD  Phenomenology in URHICs 5.) Dilepton Spectra in Nuclear Photo-Production  Elementary Amplitude, CLAS Phenomenology 6.) Conclusions

  8. 3.1 r-Meson in Vacuum and Hot/Dense Matter r Sp > Sp > Sp p p r • Vacuum: chiral p rLagrangian Srpp =+ • → P-wave pp phase shift, p el.-mag. formfactor • Hadronic Matter: effective Lagrangian for interactions with heat bath •  In-Medium r-Propagator r Dr (M,q;mB,T) = [M2 - mr2 -Srpp - Sr B -Sr M ]-1 Srpp = + • Pion Cloud [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Oset et al, …] R=D, N(1520), a1, K1 ... r • r-Hadron Scattering SrB,M = [Haglin, Friman et al, RR et al, Post et al, …] h=N, p, K … • constrain effective vertices: R→ r h, scattering data (pN→rN, gN/A)

  9. > 3.2 Scattering Processes from r Spectral Function↔ Cuts (imag. parts) of Selfenergy Diagrams: resonance excitation N B r p g N → D → p N N-1 Sp p r meson-exchange scattering D p gN → p N, p D N-1 r meson-exchange current gNN →NN, ND

  10. gN gA p-ex 3.3 Constraints from Nuclear Photo-Absorption g-absorption cross section in-mediumrspectral function [Urban,Buballa, RR+Wambach ’98] Nucleon Nuclei • quantitative determination of interaction vertex parameters • melting of 2.+3. resonances

  11. 3.4 rSpectral Function in Nuclear Matter rN→B* resonances (low-density approx.) In-med. p-cloud + rN→B* resonances In-med p-cloud + rN → N(1520) [Urban et al ’98] [Post et al ’02] [Cabrera et al ’02] rN=0.5r0 rN=r0 rN=r0 p N →r NPWA Constraints:g N ,g A • strong broadening + small upward mass-shift • empirical constraints important quantitatively

  12. rB /r0 0 0.1 0.7 2.6 3.5 r Spectral Function in Heavy-Ion Collisions Hot+Dense Matter Hot Meson Gas [RR+Gale ’99] [RR+Wambach ’99] • r-meson “melts” in hot /dense matter • medium effects dominated by baryons

  13. Outline 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.) r Meson in Medium  Hadronic Lagrangian + Empirical Constraints  Many-Body Theory + Spectral Functions 4.) Dilepton Spectra in Heavy-Ion Collisions  Thermal Emission Rates, Lattice QCD  Phenomenology in URHICs 5.) Dilepton Spectra in Nuclear Photo-Production  Elementary Amplitude, CLAS Phenomenology 6.) Conclusions

  14. e+ e- r • Sources of Dilepton Emission: • “primordial” (Drell-Yan) qq annihilation: NN→e+e-X - • emission from equilibrated matter (thermal radiation) • - Quark-Gluon Plasma: qq → e+e- , … • - Hot+Dense Hadron Gas: p+p- → e+e- , … - _ • final-state hadron decays: p0,h → ge+e- , D D → e+e-X, … 4.1 Strong-Interaction Matter in the Laboratory Au + Au NN-coll. Hadron Gas “Freeze-Out” QGP

  15. M ≤ 1 GeV: non-perturbative M > 1.5 GeV: perturbative ImPem~ Nc∑(eq)2 ImPem~ [ImDr + ImDw /10 + ImDf /5] 4.2 Thermal Dilepton Emission e+ e- g* Rate: Im Πem(M,q;mB,T) see→had / see→mm~ ImPem(M) / M2 - e+ e- p p q q e+ e- r √s=M “Hadronic Spectrometer” (T ≤ Tc) “QGP Thermometer” (T > Tc)

  16. F2-Structure Function JLAB Data p d  4.2.2 Dilepton Rates: Hadronic vs. QGP dRee /dM2 ~ ∫d3q f B(q0;T) Im Pem • Hadronic and QGP rates tend to • “degenerate” toward~Tc • Quark-Hadron Duality at all M?! • ( degenerate axialvector SF!) - [qq→ee] [HTL] [RR,Wambach et al ’99]

  17. 4.3 Lattice-QCD Dilepton Rate [Kaczmarek et al ’10] dRee/d4q 1.4Tc (quenched) q=0 • low-mass enhancement in lattice rate! • similar to hard-thermal-loop resummed perturbation theory [Braaten,Pisarski+Yuan ‘90]

  18. 4.3.2 Euclidean Correlators: Lattice vs. Hadronic • Euclidean Correlation fct. Hadronic Many-Body vs. Lat. [’02] Lattice [Kaczmarek et al ‘10] • “Duality” of lattice (1.4 Tc) and hadronic many-body (“Tc”) rates?!

  19. 4.3.3 Back to Spectral Function -Im Pem /(C T q0) • corroborates approach to chiral restoration !?

  20. 4.4 Dileptons in Heavy-Ion Collisions • Evolve rates over fireball expansion: m+m-Spectra at CERN-SPS In-In(158AGeV) [NA60 ‘09] Thermal m+m- Emission Rate Mmm [GeV] • invariant-mass spectrum directly • reflects thermal emission rate: • - M<1GeV: r broadening • - M>1GeV: Tslope ~ 160-180 MeV [van Hees +RR ’08]

  21. approach seems to fail at RHIC 4.4.2 Conclusions from Dilepton “Excess” Spectra • thermal source (T~120-200MeV) • M<1GeV: in-medium r meson • - no significant mass shift • - avg. Gr(T~150MeV)~350-400MeV • Gr (T~Tc) ≈ 600 MeV → mr • - driven by baryons • M>1GeV: radiation around Tc • fireball lifetime “measurement”: • tFB ~ (6.5±1) fm/c (semicentralIn-In) [van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08] Mmm [GeV]

  22. Outline 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.) r Meson in Medium  Hadronic Lagrangian + Empirical Constraints  Many-Body Theory + Spectral Functions 4.) Dilepton Spectra in Heavy-Ion Collisions  Thermal Emission Rates, Lattice QCD  Phenomenology in URHICs 5.) Dilepton Spectra in Nuclear Photo-Production  Elementary Amplitude, CLAS Phenomenology 6.) Conclusions

  23. 5.1 Nuclear Photoproduction: rMeson in Cold Matter e+ e- g + A → e+e- X g r Eg ≈ 1.5-3 GeV [CLAS+GiBUU ‘08] • extracted “in-medium” r-width Gr≈ 220 MeV - small?!

  24. 5.2 Equilibrium Approach (a) Production Amplitude: t-channel [Oh+Lee ‘04] + resonances (r spectr. fct.!) gd→e+e- X r g + CLAS N gN→ rN [Riek et al ’08, ‘10] (b) Medium Effects: r propagator in cold nuclear matter - broadening much reduced with increasing 3-momentum Im Dr [1/MeV2] M[GeV]

  25. 5.2.2 Application to CLAS Data Eg ≈1.5-3 GeV,uniform production points, decay distribution with in-med Gr Density at rDecay Point • average qr ~ 2GeV  average rN(Fe) ~ 0.4r0 • free norm:c2 =1.08 vs.1.55 in-med vs. vac rspectral function • need low momentum cut + absolute cross section!

  26. 5.3 Predictions for r Photoproduction 3-Momentum Cuts Transparency Ratio • low-momentum yield small, • but spectral broadening strong

  27. p Sp Sp Sp r Sr Sr Sr X.) Axialvector in Medium: Dynamical a1(1260) p a1 resonance + + . . . = Vacuum: r In Medium: + + . . . • in-medium p + r propagators • broadening of p-r scattering • amplitude [Cabrera et al. ’10]

  28. 6.) Conclusions • EM spectral function ↔ excitations of QCD vacuum • - ideal tool to probe hot/dense matter • Effective hadronic Lagrangian + many-body theory: • - strong r broadening in (baryonic) medium, • suppresed at large momentum (CLAS!) • Dileptons in heavy-ion collisions: • - spectro- /thermo-meter (CERES, NA50,NA60) • - r melting at “Tc” = 160-190 MeV • → quark-hadron duality?! hadron liquid?! • Sum rules + axialvector spectral function to tighten • relations to (partial) chiral restoration • Future experiments at RHIC-2, FAIR +LHC; JLAB?!

  29. 4.2.4 Intermediate-Mass Dileptons: Thermometer • QGP or Hadron Gas (HG) radition? • vary critical temperature Tc in fireball evolution - qq→m+m- pppp→m+m- (e.g. pa1→ m+m-) green: Tc=190MeV red: Tc=175MeV (default) blue: Tc=160MeV • partition QGP vs. HG depends on Tc • (spectral shape robust: dilepton rate “dual” around Tc! ) • Initial temperature Ti ~ 190-220 MeV at CERN-SPS

  30. 4.4 Sum Rules and Order Parameters • QCD-SRs [Hatsuda+Lee ’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05] • Weinberg-SRs: momentsVector-Axialvector [Weinberg ’67, Das et al ’67, Kapusta+Shuryak ‘93]  Promising synergy of lQCD and effective models

  31. 3.2.5 EM Probes in Central Pb-Au/Pb at SPS Di-Electrons [CERES/NA45] Photons [WA98] [Turbide et al ’03, van Hees+RR ‘07] • consistency of virtual+real photons (same Pem) • very low-mass di-electrons ↔ (low-energy) photons [Srivastava et al ’05, Liu+RR ‘06]

  32. 3.5.2 Rho, Omega + Phi Freezeout from pt-Spectra r • r freezeout = fireball freezeout • adjust w and f freezeout • contribution to fit pt-spectra • sequential freezeout f → w → r • consistent with mass spectra

  33. 3.5.3 Composition of Mass Spectra in qt-Bins low qt intermed. qt high qt • high qt ≥ 1.5GeV: • - medium effects reduced • - non-thermal sources take over

  34. check fireball evolution to fit slopes • of excess radiation (▼) • (thermal radiation softer by Lorentz-1/g) • increase a┴ = 0.085/fm → 0.1/fm • (viscous effects, larger grads. in In-In …) 3.5 Dimuon pt-Spectra and Slopes

  35. pions: Tch=160MeV a┴ =0.1/fm pions: Tch=175MeV a┴ =0.085/fm 5.2.5 NA60 Dimuons: pt-Slopes • in-medium radiation “harder” than • hadrons at freezeout?! • (thermal radiation softer by Lorentz-1/g) • smaller Tch helps (largerTfo) • non-thermal sources (DY, …)? • additional transverse acceleration? • hadron spectra (pions)? Tch=160MeV a┴ =0.1/fm Tch=175MeV Tch=160MeV a┴ =0.085/fm Tch=160MeV

  36. pS pS pS pS pS pP pP 2.2 Chiral + Resonance Scheme p s N+ N(1535)- r a1D+ N(1520)- N(1900)+ D(1700)-(?) D(1920)+ rS (a1)S rS • add S-wave pion → chiral partner • P-wave pion → quark spin-flip • importance of baryon spectroscopy

  37. |Fp|2 dpp 3.1 Axial/Vector Mesons in Vacuum Introduce r, a1 as gauge bosons into free p +r +a1Lagrangian p p r r-propagator: pEM formfactor ppscattering phase shift

  38. f.o.+prim. p 3.3 “Non-Thermal Dilepton Sources • → relevant at M,qt ≥ 1.5 GeV (?) • primordial qq annihilation (Drell-Yan): NN → e+e- X • r mesons at thermal freeze-out (“blast-wave”): • - extra Lorentz-g factor relative to thermal radiation • - qt-spectra + yield fixed by fireball model • primordial (“hard”) r mesons: • - schematic jet-quenching • with sabs fit to pions - • late decays: p0,h → ge+e- , • DD → e+e-X, J/y→e+e- , … _

  39. 2.2 Electric Conductivity • pion gas (chiral pert. theory) • sem / T ~ 0.01 for T ~ 150-200 MeV [Fernandez-Fraile+Gomez-Nicola ’07] • quenched lattice QCD • sem / T ~ 0.35 for T = (1.5-3) Tc [Gupta ’04] • soft-photon limit

  40. 3.2.3 NA60 Excess Spectra vs. Theory [CERN Courier Nov. 2009] • Thermal source does very well • Low-mass enhancement very sensitive to medium effects • Intermediate-mass: total agrees, decomposition varies

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