1.  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 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 e + e  → hadrons Im Π em (M,q;  B,T) Thermal e + e  emission rate from hot/dense matter ( em >> R nucleus ) Temperature? Degrees of freedom? Deconfinement? Chiral Restoration?

3. 1.2 Intro-II: Low-Mass Dileptons at CERN-SPS CERES/NA45 [2000] m ee [GeV] strong excess around M ≈ 0.5GeV (and M > 1GeV) little excess in  and  region NA60 [2005]

4. 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.)  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 Outline

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

6. spectral distributions! 2.2 Q 2 -Dependence of Chiral Breaking Axial-/Vector Mesons pQCD cont. F 2 -Structure Function ( spacelike) JLAB Data   ≈ x average → Quark-Hadron Duality lower onset-Q 2 in nuclei? [Niculescu et al ’00] p d Weinberg Sum Rule(s)

7. 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.)  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 Outline

8. 3.1  -Meson in Vacuum and Hot/Dense Matter D  (M,q;  B,T) = [M 2 - m  2 -   -   B -   M ] -1     [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Oset et al, …] Pion Cloud  > > R= , N(1520), a 1, K 1... h=N, , K …   =   -Hadron Scattering   = + [Haglin, Friman et al, RR et al, Post et al, …] constrain effective vertices: R→  h, scattering data (  N→  N,  N/A) Vacuum: chiral  Lagrangian     + → P-wave  phase shift,  el.-mag. formfactor Hadronic Matter: effective Lagrangian for interactions with heat bath  In-Medium  -Propagator   

9. 3.2 Scattering Processes from  Spectral Function ↔ Cuts (imag. parts) of Selfenergy Diagrams:   N -1 >         meson-exchange scattering resonance excitation meson-exchange current  N →   N →  →  N  NN → 

10. 3.3 Constraints from Nuclear Photo-Absorption  -absorption cross section in-medium   spectral function NANA  -ex [Urban,Buballa, RR+Wambach ’98] Nucleon Nuclei melting of 2.+3. resonances quantitative determination of interaction vertex parameters

11. 3.4  Spectral Function in Nuclear Matter In-med.  -cloud +  N→B* resonances (low-density approx.) In-med  -cloud +  N → N(1520) Constraints:   N,  A  N →  N PWA strong broadening + small upward mass-shift empirical constraints important quantitatively N=0N=0 N=0N=0  N =0.5  0 [Urban et al ’98] [Post et al ’02] [Cabrera et al ’02]

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

13. 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.)  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 Outline

14. “Freeze-Out” QGP Au + Au 4.1 Strong-Interaction Matter in the Laboratory Hadron Gas NN-coll. Sources of Dilepton Emission: “primordial” (Drell-Yan) qq annihilation: NN→e + e  X - e+e+ e   emission from equilibrated matter (thermal radiation) - Quark-Gluon Plasma: qq → e + e , … - Hot+Dense Hadron Gas:       → e + e , … - final-state hadron decays:  ,  →  e + e , D D → e + e   X , … _

15. 4.2 Thermal Dilepton Emission Rate: e+ e-e+ e- Im Π em (M,q;  B,T)  Im  em ~ [Im D  + Im D  /10 + Im D  /5] M ≤ 1 GeV: non-perturbative M > 1.5 GeV: perturbative Im  em ~  N c ∑(e q ) 2 √s=M e+e-e+e-  e+e-e+e- qqqq -  ee→had /  ee→  ~ Im  em (M) / M 2  “Hadronic Spectrometer” (T ≤ T c ) “QGP Thermometer” (T > T c )

16. 4.2.2 Dilepton Rates: Hadronic vs. QGP dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em Hadronic and QGP rates tend to “degenerate” toward ~T c Quark-Hadron Duality at all M ?! (  degenerate axialvector SF!) [qq→ee] - [HTL] F 2 -Structure Function p d JLAB Data   [RR,Wambach et al ’99]

17. 4.3 Lattice-QCD Dilepton Rate low-mass enhancement in lattice rate! similar to hard-thermal-loop resummed perturbation theory [Kaczmarek et al ’10] [Braaten,Pisarski+Yuan ‘90] dR ee /d 4 q 1.4T c (quenched) q=0

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 T c ) and hadronic many-body (“T c ”) rates?!

19. 4.3.3 Back to Spectral Function corroborates approach to chiral restoration !? -Im  em /(C T q 0 )

20. 4.4 Dileptons in Heavy-Ion Collisions invariant-mass spectrum directly reflects thermal emission rate: - M<1GeV:  broadening - M>1GeV: T slope ~ 160-180 MeV  +   Spectra at CERN-SPS In-In(158AGeV) [NA60 ‘09] M  [GeV] Thermal     Emission Rate Evolve rates over fireball expansion: [van Hees +RR ’08]

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

22. 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking + Chiral Partners 3.)  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 Outline

23. 5.1 Nuclear Photoproduction:  Meson in Cold Matter  + A → e + e  X [CLAS+GiBUU ‘08] E  ≈ 1.5-3 GeV  e+ee+e  extracted “in-medium”  -width   ≈ 220 MeV - small?!

24. 5.2 Equilibrium Approach  N  (a) Production Amplitude : t-channel [Oh+Lee ‘04] + resonances (  spectr. fct.!) [Riek et al ’08, ‘10] (b) Medium Effects:  propagator in cold nuclear matter - broadening much reduced with increasing 3-momentum   N→  N  d → e + e  X Im D  [1/MeV 2 ] M  [GeV] + CLAS

25. average q  ~ 2GeV  average  N (Fe) ~ 0.4  0 free norm:  2 =1.08 vs. 1.55 in-med vs. vac  spectral function need low momentum cut + absolute cross section! Density at  Decay Point 5.2.2 Application to CLAS Data E  ≈1.5-3 GeV, uniform production points, decay distribution with in-med  

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

27. X.) Axialvector in Medium: Dynamical a 1 (1260) + +... =           Vacuum: a 1 resonance In Medium: + +... in-medium  +  propagators broadening of  -  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  broadening in (baryonic) medium, suppresed at large momentum (CLAS!) Dileptons in heavy-ion collisions: - spectro- /thermo-meter (CERES, NA50,NA60) -  melting at “T c ” = 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 T c in fireball evolution partition QGP vs. HG depends on T c (spectral shape robust: dilepton rate “dual” around T c ! ) Initial temperature T i ~ 190-220 MeV at CERN-SPS green: T c =190MeV red: T c =175MeV (default) blue: T c =160MeV qq →      →     (e.g.  a 1 →     ) -

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

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

32. 3.5.2 Rho, Omega + Phi Freezeout from p t -Spectra sequential freezeout  →  →  consistent with mass spectra  freezeout = fireball freezeout adjust  and  freezeout contribution to fit p t -spectra 

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

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

35. 5.2.5 NA60 Dimuons: p t -Slopes in-medium radiation “harder” than hadrons at freezeout?! (thermal radiation softer by Lorentz-1/  smaller T ch helps (larger T fo ) non-thermal sources (DY, …)? additional transverse acceleration? hadron spectra (pions)? T ch =175MeV T ch =160MeV a ┴ =0.1/fm T ch =160MeV a ┴ =0.085/fm pions: T ch =175MeV a ┴ =0.085/fm pions: T ch =160MeV a ┴ =0.1/fm

36. 2.2 Chiral + Resonance Scheme  N + N(1535) -  a 1   N(1520) - N(1900) +  (1700) - (?)  (1920) + SS PP SS SS SS SS PP SS SS (a 1 ) S add S-wave pion → chiral partner P-wave pion → quark spin-flip importance of baryon spectroscopy

37. 3.1 Axial/Vector Mesons in Vacuum Introduce  a 1 as gauge bosons into free  +  +a 1 Lagrangian   EM formfactor  scattering phase shift   |F  | 2    -propagator:

38. 3.3 “Non-Thermal Dilepton Sources → relevant at M, q t ≥ 1.5 GeV (?) primordial qq annihilation (Drell-Yan): NN → e + e  X  mesons at thermal freeze-out (“blast-wave”): - extra Lorentz-  factor relative to thermal radiation - q t -spectra + yield fixed by fireball model primordial (“hard”)  mesons: - schematic jet-quenching with  abs fit to pions - late decays:  ,  →  e + e , DD → e + e  X , J/  →e + e , … _ f.o. + prim. 

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

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