1. Introduction to Dileptons and in-Medium Vector Mesons Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, Texas USA 2 Lectures at ECT* EM-Probes Workshop Trento, 04. + 06.06.05

2. 1.) Introduction 1.1 Electromagnetic Probes in Strong Interactions  -ray spectroscopy of atomic nuclei: collective phenomena, … DIS off the nucleon: - parton model, PDF’s (high q 2 < 0) - nonpert. structure of nucleon [JLAB] Drell-Yan: pp → eeX (q 2 > 0: symmetry, nucl. shadowing) thermal emission: - compact stars (GRBs?!) - heavy-ion collisions: [SPS, RHIC, LHC, FAIR]  (q 2 =0), e + e  (q 2 >0) What is the electromagnetic spectrum of QCD matter?

3. “Freeze-Out” QGP Au + Au Creating 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-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 , … _

4. 1.2 Objective: Use Dileptons to Probe the Nature of Strongly Interacting Matter Bulk Properties: Equation of State Microscopic Properties: - Degrees of Freedom - Spectral Functions Phase Transitions: (Pseudo-) Order Parameters  (some) Key Questions: Can we infer the temperature of the matter? establish in-medium modifications of  →  e  e  ? extract signatures of chiral symmetry restoration?

5. 1.3 Intro-III: EoS and Hadronic Modes All information encoded in free energy: EoS:,, correlation functions: : “hadronic” current ↔ iso/scalar  pairs! ↔ dileptons, photons! QCD Order Parameters and Hadronic Modes condensate: ‹qq› = ∂  ∂m q suscept.:  s =∂ 2  ∂m q 2 =   (q=0) =  2 D  (q=0) ~ (m  ) -2  decay const: f  2 =  ∫ ds/s ( Im  V  Im  A )  2 ImD  1.0 T/T c ss ‹qq› - lattice QCD [Weinberg ’67, Kapusta+Shuryak ’94] -

6. 1.4.1 Schematic Dilepton Spectrum in HICs qq Characteristic regimes in invariant e + e  mass, M 2 =(p e+ + p e  ) 2 : Drell-Yan: power law ~ M n ↔ high mass thermal ~ exp(-M/T): - QGP (highest T) ↔ intermediate mass - HG (moderate T) ↔ low mass

7. Central Pb-Pb 158 AGeV open charm (DD) Drell- Yan factor ~2 excess open charm? thermal? … Intermediate Mass: NA50 M  [GeV] final-state hadron decays saturate yield in p-A collisions 1.4.2 Dilepton Data at CERN-SPS Low Mass: CERES/NA45 M ee [GeV] strong excess around M≈0.5GeV little excess in  region

8. 2. Thermal Electromagnetic Emission Rates - Vacuum: Quarks vs. Hadrons, Vector Mesons 3. Chiral Symmetry in QCD - Spontaneous Breaking, Hadronic Spectrum, Restoration 4. (Light) Vector Mesons in Medium - Hadronic Many-Body Approach - Dropping Mass, Chiral Restoration?! 5. QGP Emission 6. Thermal Photons 7. Dilepton Spectra in Heavy-Ion Collisions - Space-Time Evolution; Comparison to SPS and RHIC Data 8. Summary and Conclusions Outline

9. 2.) Electromagnetic Emission Rates E.M. Correlation Function: e+ e-e+ e- γ Im Π em (M,q) Im Π em (q 0 =q) = O(1) = O(α s ) also: e.m susceptibility (charge fluct.): χ = Π em (q 0 =0,q→0) In URHICs: source strength: dependence on T,  B,  , medium effects, … system evolution: V(  ), T(  ),  B (  ), transverse expansion, … nonthermal sources: Drell-Yan, open-charm, hadron decays, … consistency!

10. 2.2 E.M. Correlator in Vacuum:  (e + e  → hadrons) e+e-e+e- h 1 h 2 … s ≥ s dual ~(1.5GeV) 2 : pQCD continuum s < s dual : Vector-Meson Dominance qqqq _   qq _  2     4    KK e+e-e+e-     

11. after freezeout  V ~ 1/  V tot thermal emission  FB ~ 10fm/c 2.3 The Role of Light Vector Mesons in HICs  ee [keV]  tot [MeV] (N ee ) thermal (N ee ) cocktail ratio   (770) 6.7 150 (1.3fm/c) 1 0.13 7.7   0.6 8.6 (23fm/c) 0.09 0.21 0.43   1.3 4.4 (44fm/c) 0.07 0.31 0.23  In-medium radiation dominated by  -meson! Connection to chiral symmetry restoration?! Contribution to invariant mass-spectrum:

12. 3.1 Chiral Symmetry and its Breaking in Vacuum 3.2 Consequences for the Hadronic Spectrum 3.3 Vector-Axialvector Correlation Functions and Chiral Restoration 3.) Chiral Symmetry in QCD

13. 3.1.1 Chiral Symmetry in QCD: Vacuum current quark masses: m u ≈ m d ≈ 5-10MeV Chiral SU(2) V × SU(2) A transformation: O Up to O (m q ), L QCD invariant under Rewrite L QCD using q L,R =(1±  5 )/2 q : Invariance under isospin and “handedness”

14. 3.1.2 Spontaneous Breaking of Chiral Symmetry strong qq attraction  Chiral Condensate fills QCD vacuum: > > > > qLqL qRqR qLqL - qRqR - [cf. Superconductor: ‹ee› ≠ 0, Magnet ‹ M › ≠ 0, … ] - mass generation, not observables! but: hadronic excitations reflect SBCS: “massless” Goldstone bosons   0,± (explicit breaking: f  2 m  2 = m q ‹qq› ) “chiral partners” split:  M ≈ 0.5GeV ! vector mesons  and  : J P =0 ± 1 ± 1/2 ± - chiral singlet !

15. 3.2.2 Hadron Spectra and SBCS in Vacuum Axial-/Vector Correlators pQCD cont. entire spectral shape matters Weinberg Sum Rule(s) “Data”: lattice [Bowman etal ‘02] Curve: Instanton Model [Diakonov+Petrov ’85, Shuryak] ● chiral breaking: |q 2 | ≤ 1 GeV 2 ● quark condensate: n vac ≈ (2N f ) fm -3 ! Constituent Quark Mass

16. 3.3.1 “Melting” the Chiral Condensate How? Excite vacuum (hot+dense matter) quarks “percolate” / liberated  Deconfinement ‹qq› condensate “melts”,  iral Symm. chiral partners degenerate Restoration (   - ,   - a 1, … medium effects → precursor!) 0 0.05 0.3 0.75  [GeVfm -3 ] 120, 0.5  0 150-160, 2  0 175, 5  0 T[MeV],  had   PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD - 1.0 T/T c mm ‹qq› - lattice QCD

17. 3.3.2 Low-Mass Dileptons + Chiral Symmetry How is the degeneration realized ? “measure” vector with e + e , but axialvector? Vacuum At T c : Chiral Restoration

18. E.M. Emission Rates: ● proportional to e.m. correlator (photon selfenergy) ● vacuum: separation in perturbative (qq) -- nonpert. ( , ,   ) at “duality scale” s dual ~ (1.5GeV) 2 ● in-med radiation: low-mass ↔   -meson, high-mass ↔ QGP Chiral Symmetry: ● spontaneously broken in the vacuum  mass generation! M q * ~ ‹qq› ≠ 0 (low q 2 ) ● hadronic spectrum: chiral partners split (  - ,   - a 1, …) ● excite vacuum → condensate melts → chiral restoration → chiral partners degenerate Upshot of Chapters 2 + 3 - -

19. 4.1 Hadronic Many-Body Theory for Vector Mesons -   -Meson in Vacuum -  -Selfenergies and Spectral Functions - Constraints and Consistency: Photo-Absorption, QCD Sum Rules, Lattice QCD 4.2 Vector Meson in URHICs: Hot+Dense Matter 4.3 Dropping   -Mass; Vector Manifestation of CS 4.4 Chiral Restoration?! 4.) Vector Mesons in Medium

20. 4.1 Many-Body Approach:   -Meson in Vacuum Introduce  as gauge boson into free  +  Lagrangian   e.m. formfactor  scattering phase shift   |F  | 2    -propagator:

21. 4.1.2  -Selfenergies in Hot + Dense Matter D  (M,q;  B,T)=[M 2 -m  2 -     -    B -    M ] -1 modifications due to interactions with hadrons from heat bath  In-Medium  -Propagator     [Chanfray etal, Herrmann etal, RR etal, Weise etal, Oset etal, …] (1) Medium Modifications of Pion Cloud  D  = [k 0 2 -  k 2 -   (k 0,k)] -1 In-med  -prop. → mostly affected by (anti-) baryons

22.  a1a1  G e.g.  +  → , a 1 (1260) →  +  fix coupling G via decay width  (a 1 →  ) > > R h (2) Direct   -Hadron Interactions:  + h → R (i) Meson Gas (h = , K,  )  Generic features: real parts cancel, imaginary parts add (ii)   -Baryon Interactions (h = N, , …) S-wave:  + N → N(1520),  (1700) →  + N, etc. e.g.:  (N(1520)→N  ) ≈ 25MeV,  (  (1700)→N  ) ≈ 130MeV Coupling constant → free decay: Decay Phase Space N(1520)  (1700)

23. 4.1.3 Constraints I: Nuclear Photo-Absorption total nuclear  -absorption in-medium    –spectral cross section function at photon point > >    ,N*,  * N -1  N →  N,   N →   meson exchange! direct resonance!

24. Light-like  -Spectral Function, D  (q 0 =q), and Nuclear Photo-Absorption NANA  -ex [Urban,Buballa,RR+Wambach ’98] On the Nucleon On Nuclei 2.+3. resonance melt (parameter) (selfconsistent N(1520)→N  ) [Post,Mosel etal ’98] fixes coupling constants and formfactor cutoffs for  NB

25. 4.1.4  (770) 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 Consensus: strong broadening + slight upward mass-shift Constraints from (vacuum) data important quantitatively N=0N=0 N=0N=0  N =0.5  0 [Urban etal ’98] [Post etal ’02] [Cabrera etal ’02]

26. 4.1.5 QCD Sum Rules +  (770) in Nuclear Matter General idea: dispersion relation for correlation function lhs: operator product expansion for large spacelike Q 2 : Nonpert. Wilson coeffs (condensates) rhs: model spectral function at timelike s>0: Resonance + pQCD continuum  -Meson: [Shifman,Vainshtein +Zakharov ’79] 4-quark condensate!

27. Vacuum: =  2 - 0.2% 1% Comparison to hadronic many-body models roughly consistent sensitive to detailed shape Nuclear Matter: decreases  softening of  -propagator decreasing mass or increasing width - QCD Sum Rule Results:  (770) in Nuclear Matter [Leupold etal ’98]

28. 4.2 Vector-Meson Spectral Functions in High-Energy Heavy-Ion Collisions: Hot and Dense Matter

29. [RR+Gale ’99] 4.2.1  -Meson Spectral Functions at SPS   -meson “melts” in hot and dense matter baryon density  B more important than temperature reasonable agreement between models  B /  0 0 0.1 0.7 2.6 Hot+Dense Matter Hot Meson Gas [RR+Wambach ’99] [Eletsky etal ’01] Model Comparison [RR+Wambach ’99]

30. 4.2.2 Light Vector Mesons at RHIC baryon effects important even at  B,tot = 0 : sensitive to  Btot =   +  B (  -N and  -N interactions identical)  also melts,  more robust ↔ OZI - 

31. 4.2.3 Lattice Studies of Medium Effects calculated on lattice MEM 1-1- 0-0- extracted [Laermann, Karsch ’04]

32. 4.2.4 Comparison of Hadronic Models to LGT calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched)

33. 4.3 Scenarios for Dropping   -Meson Mass (3) Vector Manfestation of Chiral Symmetry (a) Vacuum: effective L  with  L ≡  (“VM”) (b) Finite Temperature: thermal  - and  -loop expansion → f  (T), m  (T) QCD-matching requires “intrinsic” T-dependence of bare m  (0), g   dropping  -mass [Harada+Yamawaki, ’01] (1) Naïve Quark Model: m  ≈ 2M q * → 0 at chiral restoration (problem: kinetic energy of bound state) (2) Scale Invariance of L QCD : implement into effective L had  universal scaling law [Brown+, Rho ’91]

34. 4.4 Dilepton Rates and Chiral Restoration dR ee /dM 2 ~ f B Im  em Hard-Thermal-Loop result much enhanced over Born rate “matching” of HG and QGP automatic! Quark-Hadron Duality at low mass ?! Degenerate axialvector correlator? [Braaten,Pisarski+Yuan ’90] [qq→ee] [qq+O(  s )-HTL] ----

35. 4.4.2 Current Status of a 1 (1260)    > > > > N(1520) … ,N(1900) … a1a1 + +... Exp: - HADES (  A): a 1 →(  +  - )  - URHICs (A-A) : a 1 → 

36. 5.1 Pertubative vs. Lattice QCD 5.2 Emission from “Resonances” 5.) Dilepton Emission from the QGP

37. Im [ ] = + + + … 5.1 Perturbative vs. Lattice QCD Baseline: qqqq _ e+ee+e But: small M → resummations finite-T perturbation theory (HTL) qq qq collinear enhancement: D q,g =(t-m D 2 ) -1 ~ 1/α s [Braaten,Pisarski+Yuan ‘91] large enhancement at low M not shared by lattice calculations: threshold + resonance structures (photon rate?!) [Bielefeld Group ‘02]

38. 5.2 QGP Dileptons from Bound States → based on finite-T lattice potentials approach to “zero-binding line”  ~ stable-mass    -resonance [Shuryak+Zahed ‘04] double-peak structure due to zero-binding line + mixed phase factor 1.5-2 enhancement at M≈1.5GeV; depends on quark width Dilepton Spectrum ratio to pert. qq rate M ee /m q _ [Casalderrey+ Shuryak ‘04]

39. 6.) Thermal Photon Emission Rates Quark-Gluon Plasma q g q O But: other contributions in O(α s ) collinear enhanced D g =(t-m D 2 ) -1 ~1/α s [Aurenche etal ’00, Arnold,Moore+Yaffe ’01] Bremsstrahlung Pair-ann.+scatt. + ladder resummation (LPM) “Naïve” LO: q + q (g) → g (q) + γ [Kapusta,Lichard+Seibert ’91, …, Turbide,RR+Gale’04] Hot and Dense Hadron Gas    γ     a 1,   Im Π em (q 0 =q) ~ Im D  (q 0 =q) Low energy: vector dominance High energy: meson exchange Emission Rates Total HG ≈ in-med QGP ! to be understood…

40. 7.1 Space-Time Evolution of URHIC’s - Formation and Freezeouts - Trajectories in the QCD Phase Diagram 7.2 Comparison to Data - Dileptons at SPS (√s = 17, 8 GeV) - Photons at SPS (√s = 17 GeV) - RHIC (√s = 200 GeV) 7.) Dilepton Spectra in Relativistic Heavy-Ion Collisions

41. 7.1.1 Hadron Production in Heavy-Ion Collisions → well described by hadron gas in thermal+chemical equilibrium: SPS / RHIC: “chemical freezeout” close to phase boundary  need to construct “evolution” before: up to earliest “formation” time  0 ↔ T 0 > T chem after: down to thermal freezeout  f ↔ T fo < T chem [Braun-Munzinger etal ‘03]

42. Caveat: conserve hadron ratios after chem. f.o.  chemical potentials for , K, N,…:  ,K,N > 0 for T < T chem 7.1.2 Trajectories in the Phase Diagram Basic assumption: entropy (+baryon-number) conservation  fixes T(  B ) in the phase diagram Time scale: hydrodynamics, e.g. V FB (  )=(z 0 +v z   )  (R ┴0 + 0.5a ┴  2 ) 2  N [GeV]  [fm/c] Thermal Dilepton Emission Spectrum

43. Lower SPS Energy enhancement increases! confirms importance of baryonic effects (predicted) 7.2.1 Low-Mass Dileptons at SPS Top SPS Energy QGP contribution small medium effects! drop. mass or broadening?!

44. T i ≈300MeV, more QGP contr. Hydrodynamics (chem-eq) [Kvasnikowa,Gale+Srivastava ’02] 7.2.2 Intermediate-Mass Dileptons at SPS: NA50 e.m. corr. continuum-like: Im Π em ~ M 2 (1 +  s /  +…) T i ≈210MeV, HG-dominated Thermal Fireball (chem-off-eq) [RR+Shuryak ’99] QGP + HG!

45. 7.2.3 Photon Spectra at the SPS: WA98 Hydrodynamics: QGP + HG [Huovinen,Ruuskanen+Räsänen ’02] T 0 ≈260MeV, QGP-dominated still true if pp→  X included [Turbide,RR+Gale’04] Expanding Fireball + pQCD pQCD+Cronin at q t >1.5GeV  T 0 =205MeV suff., HG dom.

46. low mass: thermal dominant int. mass: cc e + X, rescatt.? e - X [RR ’01] - [R. Averbeck, PHENIX] 7.3 Dilepton Spectrum at RHIC MinBias Au-Au (200AGeV) run-4 results eagerly awaited … thermal

47. 8.) Conclusions Thermal E.M. Radiation from QCD matter - Low-mass dileptons: in-med  ( ,  ) ↔ Chiral Restoration!? - Intermediate mass: qq annihilation ↔ QGP Radiation!? - similar for photons but M=0 extrapolations into phase transition region  in-med HG and QGP shine equally bright (“duality”) deeper reason? lattice calculations? axialvector mode? phenomenology for URHICs so far promising - importance of model constraints - precision data+theory needed for definite conclusions much excitement ahead: PHENIX, NA60, CERES, HADES, ALICE, … and theory! -