Electromagnetic Probes of the Medium (Status of the Field)

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 • (lEM >> Rnucleus) • thermal g (M→0) → temperature, • EM conductivity + susceptibility √s=M Im Πem(M,q;mB,T)

3. Outline 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

4. 2.) 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(½ GeV)

5. F2-Structure Function (spacelike) JLAB Data p d • x ≈ x • average → Quark-Hadron Duality • lower onset-Q2in nuclei? [Niculescu et al ’00] 2.3 Q2-Dependence of Chiral Breaking Axial-/Vector Mesons pQCD cont. • Weinberg Sum Rule(s) • spectral distributions!

6. 2.4 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

7. Outline 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

8. 3.2 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. gN gA p-ex 3.3 Constraints from Nuclear Photo-Absorption g-absorption cross section in-mediumr–spectral function [Urban,Buballa, RR+Wambach ’98] Nucleon Nuclei • quantitative determination of interaction vertex parameters • melting of 2.+3. resonances

10. 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

11. 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

12. Outline 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

13. 4.1 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: + in-med. r spectral fct. product. amplitude full calculation fix density 0.4r0 Fe-Ti r g N [Riek et al ’08, ‘10] M[GeV] • r-broadening reduced at high 3-momentum; need low momentum cut!

14. 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~ Im Pem(M) - e+ e- p p q q e+ e- r √s=M “Hadronic Spectrometer” (T ≤ Tc) “QGP Thermometer” (T > Tc)

15. 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]

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

17. [van Hees+RR ‘06] 4.2.4 Intermediate-Mass Region • “4p“ states dominate free EM correlator • above M ≈ 1.1GeV • lower estimate: • use vacuum4p correlator • more realistic: • O(T2)medium effect → • “chiral V-A mixing”: • with 4p 2p [Eletsky+Ioffe ‘90] 3p 5p

18. 4.2.4.2 Intermediate-Mass Dileptons: Thermometer • QGP or Hadron Gas (HG) radition? • vary critical temperature Tcin 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” aroundTc! ) • Initial temperature Ti ~ 190-220 MeV at CERN-SPS

19. 4.2.5 Dimuon pt-Spectra and Slopes: Barometer pions: Tch=160MeV a┴ =0.1/fm pions: Tch=175MeV a┴ =0.085/fm • modify fireball evolution: • e.g. a┴ = 0.085/fm → 0.1/fm • both large and small Tccompatible • with excess dilepton slopes

20. currently fails at RHIC 4.2.6 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 aroundTc • 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]

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

22. p Sp Sp Sp r Sr Sr Sr 4.3 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]

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

24. 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]

25. 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

26. 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

27. 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

28. 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- , … _

29. 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

30. 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

31. |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