1. Electromagnetic Probes of the Medium (Status of the Field) Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA INT Program (Week 8) on “Quantifying the Properties of Hot QCD Matter” INT (Seattle), 12.-16.07.10

2. 1.) Introduction: EM Probes + QCD Phase Diagram Electromag. Spectral Function - √s < 2 GeV : non-perturbative - √s ≥ 2 GeV : pertubative (dual) Phase structure tied to in-medium spectral functions - expect: hadron gas → QGP - realization of transition? Thermal dilepton emission rate ( EM >> R nucleus ) thermal  (M→0) → temperature, EM conductivity + susceptibility √s=M Im Π em (M,q;  B,T)

3. 1.) Introduction 2.) Chiral Symmetry  Spontaneous Chiral Symmetry Breaking  Chiral Partners, Sum Rules 3.) Light Vector Mesons in Medium  Lagrangian + Constraints  Spectral Function in Hot/Dense Matter 4.) Dilepton Phenomenology  Nuclear Photoproduction  High-Energy Heavy-Ion Collisions 5.) Conclusions Outline

4. 2.) 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]

5. spectral distributions! 2.3 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)

6. 2.4 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

7. 1.) Introduction 2.) Chiral Symmetry  Spontaneous Chiral Symmetry Breaking  Chiral Partners, Sum Rules 3.) Light Vector Mesons in Medium  Lagrangian + Constraints  Spectral Function in Hot/Dense Matter 4.) Dilepton Phenomenology  Nuclear Photoproduction  High-Energy Heavy-Ion Collisions 5.) Conclusions Outline

8. 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    3.2  -Meson in Vacuum and Hot/Dense Matter

9. 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

10. 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]

11. 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]

12. 1.) Introduction 2.) Resonances + Chiral Symmetry  Spontaneous Chiral Symmetry Breaking  Chiral Partners 3.) Light Vector Mesons in Medium  Lagrangian + Constraints  Spectral Function in Hot/Dense Matter 4.) Dilepton Phenomenology  Nuclear Photoproduction  High-Energy Heavy-Ion Collisions 5.) Conclusions Outline

13. 4.1 Nuclear Photoproduction:  Meson in Cold Matter  + A → e + e  X [CLAS+GiBUU ‘08] E  ≈1.5-3 GeV  e+ee+e  extracted “in-med”  -width   ≈ 220 MeV Microscopic Approach: Fe - Ti  N  product. amplitude in-med.  spectral fct. + M [GeV] [Riek et al ’08, ‘10] full calculation fix density 0.4  0  -broadening reduced at high 3-momentum; need low momentum cut!

14. 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)  “Hadronic Spectrometer” (T ≤ T c ) “QGP Thermometer” (T > T c )

15. 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]

16. 4.2.3 Dileptons in Heavy-Ion Collisions: Spectrometer thermal radiation dominant invariant-mass spectrum directly reflects thermal emission rate!  +   Spectra at CERN-SPS In-In(158AGeV) [NA60 ‘09] M  [GeV] Thermal     Emission Rate Evolve rates over fireball expansion: [van Hees+RR ’08]

17. “4  “ states dominate free EM correlator above M ≈ 1.1GeV lower estimate: use vacuum 4  correlator more realistic: O (T 2 ) medium effect → “chiral V-A mixing”: with 4.2.4 Intermediate-Mass Region [Eletsky+Ioffe ‘90] 44 22 55 33 [van Hees+RR ‘06]

18. 4.2.4.2 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 →     ) -

19. 4.2.5 Dimuon p t -Spectra and Slopes: Barometer modify fireball evolution: e.g. a ┴ = 0.085/fm → 0.1/fm both large and small T c compatible with excess dilepton slopes pions: T ch =175MeV a ┴ =0.085/fm pions: T ch =160MeV a ┴ =0.1/fm

20. M  [GeV] 4.2.6 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] currently fails at RHIC

21. 4.2.6 Origin of the Low-Mass Excess in PHENIX? - small T eff slope - why not in semi-central? - generic space-time argument:   maximal emission around T max ≈ M / 5.5 (for Im  em =const) Low mass (M<1GeV): T max < 200MeV Soft QGP Radiation? - “baked Alaska” ↔ small T - rapid quench+large domains ↔ central A-A -  therm +  DCC → e + e  ↔ M~0.3GeV, small p t Disoriented Chiral Condensate (DCC)? [Bjorken et al ’93, Rajagopal+Wilczek ’93] [Z.Huang+X.N.Wang ‘96]

22. 4.3 Axialvector in Medium: Dynamical a 1 (1260) + +... =           Vacuum: a 1 resonance In Medium: + +... in-medium  +  propagators broadening of  -  scattering amplitude [Cabrera et al. ’10]

23. 5.) 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-/baro-meter (CERES, NA50,NA60!) - corroborate melting of  toward expected 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

24. 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]

25. 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

26. 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 

27. 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

28. 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. 

29. 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]

30. 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

31. 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: