1. Dileptons at RHIC Ralf Rapp Cyclotron Inst. + Physics Dept. Texas A&M University College Station, USA International CCAST Workshop “QCD and RHIC Physics” Beijing, 10.08.04 … and the Quest for Chiral Symmetry Restoration

2. 1. Introduction 2. Chiral Symmetry in QCD 3. E.M. Correlation Function + Thermal Radiation 4. Low-Mass Dileptons 4.1 Axial-/Vector Correlators 4.2 Medium Effects and Excitation Function 4.3 Lattice QCD 5. Intermediate-Mass Dileptons: QGP Radiation? 6. Perspectives for RHIC 7. Conclusions Outline

3. 1.) Introduction: Towards QGP Discovery So far: RHIC observables ↔ bulk properties of the produced matter: - energy density  ≈20GeVfm -3 ↔ jet quenching (high-p t ) - thermalization + EoS ↔ hydrodynamics (v 0,v 2 ) - partonic degrees of freedom ↔ coalescence (p/ , v 2 -scal) Future: need to understand microscopic properties (phase transition, “QGP” !?): - Deconfinement ↔ quarkonia (J/ , Y, …) - Chiral Symmetry Restoration ↔ dileptons ( - temperature ↔ photons )

4. 2.) Chiral Symmetry in QCD: Vacuum SU(2) L × SU(2) R invariant (m u,d ≈0) Spontaneous Breaking: strong qq attraction  Bose Condensate fills QCD vacuum! > > > > qLqL qRqR qLqL - qRqR - [cf. Superconductor: ‹ee›≠0 Magnet ‹ M ›≠0, … ] - Profound Consequences: energy gap: ↔ mass generation! massless Goldstone bosons  0,± “chiral partners” split,  M≈0.5GeV: J P =0 ± 1 ± 1/2 ±

5. 2.2 “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

6. 2.3 Dilepton Data at CERN-SPS Low Mass: CERES/NA45 Intermediate Mass: NA50 Central Pb-Pb 158 AGeV open charm Drell- Yan M ee [GeV] M  [GeV] strong excess around M≈0.5GeV little excess in  region factor ~2 excess open charm? thermal? …

7. 3.) Electromagnetic Emission Rates E.M. Correlation Function: e + e - γ Im Π em (M,q) Im Π em (q 0 =q) = O(1) = O(1) = O(α s ) = 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!

8. 3.2 Two Regimes of Thermal Dilepton Radiation q 0 ≈0.5GeV  T max ≈0.17GeV, q 0 ≈1.5GeV  T max =0.5GeV Thermal rate: qq

9. 4.) Low-Mass Dileptons + Chiral Symmetry Im Π em (M) ~ Im D  (M) vector-meson spectral functions dominated by  -meson → chiral partner: a 1 (1260) Chiral breaking: Q 2 < 3GeV 2 Vacuum At T c : Chiral Restoration pQCD cont.

10. + > >    B *,a 1,K 1... N, ,K … Constraints: - branching ratios B,M→  N,  -  N,  A  absorpt.,  N→  N - QCD sum rules, lattice 4.2 Vector Mesons in Medium: Many-Body Theory  -meson “melts” in hot and dense matter baryon density  B more important than temperature (i) SPS Conditions  B /  0 0 0.1 0.7 2.6 D  (M,q:  B,T)=[M 2 -m  2 -   -   B -   M ] -1

11. (ii) Vector Mesons at RHIC baryon effects important even at  Bnet =0 : sensitive to  Btot =   +  B,  more robust ↔ OZI - Dilepton Emission Rates Quark-Hadron Duality ?! in-med HG ≈ in-med QGP ! [qq→ee] [qq+O(  s )] ----

12. Lower SPS Energy enhancement increases! precision test by NA60!? 4.3 Low-Mass Dileptons in URHICs Top SPS Energy baryon effects important! BEVALAC/SIS Energy DLS enhancement increases still: DLS puzzle → HADES!?

13. 4.4 Current Status of a 1 (1260)    > > > > N(1520) … ,N(1900) … a1a1 + +... Exp: - HADES (  A): a 1 →(  +  - )  - URHICs (A-A) : a 1 → 

14. 4.5 Comparison of Hadronic Models to LGT calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched)

15. T i ≈300MeV, QGP-dominated Hydrodynamics (chem-eq) [Kvasnikowa,Gale+Srivastava ’02] 5.) Intermediate-Mass Dileptons: NA50 (SPS) 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!

16. low mass: thermal dominant int. mass: cc e + X, rescatt.? e - X [RR ’01] - [R. Averbeck, PHENIX] 6.) Dilepton Spectrum at RHIC MinBias Au-Au (200AGeV) run-4 results eagerly awaited … thermal

17. 8.) Conclusions Thermal Dileptons in QCD:  em (q 0,q,  B,T) - low mass:     , chiral restoration ↔  -a 1 degeneracy - intermediate mass: QGP radiation (open charm?!) ( - thermal photons ) extrapolations into phase transition region  in-med HG and QGP shine equally bright lattice calculations? deeper reason? phenomenology for URHIC’s promising; precision data+theory needed for definite conclusions much excitement ahead: PHENIX, NA60, HADES, ALICE,… and theory!

18. Additional Slides

19. 7.) Thermal Photons 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    a1,a1,  Im Π em (q 0 =q) ~ Im D vec (q 0 =q) Low energy: vector dominance High energy: meson exchange Emission Rates Total HG ≈ in-med QGP ! to be understood…

20. 7.2 Perspectives on Photon Data at RHIC large “pre-equilibrium” yield from parton cascade (no LPM) thermal yields ~ consistent QGP undersat. small effect Predictions for Central Au-Au PHENIX Data consistent with pQCD only disfavors parton cascade not sensitive to thermal yet

21. 4.2 Comparison to Data I: WA98 at SPS 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.

22. 4.2 Comp. to Data II: WA98 “Low-q t Anomaly” [Turbide,RR+Gale’04] Expanding Fireball Model current HG rate much below 30% longer  FB  30% increase Include   →  S-wave slight improvement in-medium “  ” or  ?!

23. 2. Thermal Photon Radiation 2.1 Generalities Emission Rate per 4-volume and 3-momentum γ   Im Π em (q 0 =q) T transverse photon selfenergy many-body language: kinetic theory: γ    2 |M| 2 in-medium effects, resummations, … cut

24. γ    γ    a1a1 a1a1 Photon-producing reactions: mostly at dominant (q 0 >0.5GeV) gauge invariance! q 0 <0.5GeV a 1 -strength problematic [Song ’93, Halasz etal ’98,…] 2.3.1 Hot Hadronic Matter:  -  -a 1 Gas Chiral Lagrangian + Axial/Vector-mesons, e.g. HLS or MYM: (g 0,m 0, ,  ) fit to m  a1,  ,a1 D/S and  a 1 →  γ) not optimal HLS MYM Kap.’91 (no a1)

25. quantitative analysis: account for finite hadron size improves a 1 phenomenology t-channel exchange: gauge invariance nontrivial [Kapusta etal ’91] simplified approach: [Turbide,Gale+RR ’04] 2.3.1.b Hadronic Formfactors with Factor 3-4 suppression At intermediate and High photon energies

26. 2.3.2 Further Meson Gas Sources (i) Strangeness Contributions: SU(3) F MYM (iii) Higher Resonances Ax-Vec: a 1,h 1 → , Vec: ,  ’,  ’’ →  other:  (1300) →  f 1 → , K 1 → K  K * → K  a 2 (1320) →  γ  KK K γ  K*K* K  ~25% of   →  ~40% of   →  (ii)  t-Channel γ     G  large! potentially important … [Turbide,Gale +RR ’04]

27. 2.3.3 Baryonic Contributions use in-medium  –spectral funct: constrained by nucl.  -absorption: > >    B *,a 1,K 1... N, ,K …  N →  N,   N →   NANA  -ex [Urban,Buballa,RR+Wambach ’98]

28. 2.3.3(b) Photon Rates from  Spectral Function: Baryons + Meson-Resonances baryonic contributions dominant for q 0 <1GeV (CERES enhancement!) also true at RHIC+LHC: at T=180MeV,  B =0  B =220MeV

29. 2.3.4 HG Emission Rates: Summary  B =220MeV [Turbide,RR+Gale ’04]  t-channel (very) important at high energy formfactor suppression (2-4) strangeness significant baryons at low energy

30. 2.3.5 In-Medium Effects many-body approach: encoded in vector-spectral function, relevant below M, q 0 ~ 1-1.5 GeV “dropping masses”: large enhancement due to increased phase space [Song+Fai ’98, Alam etal ’03] unless: vector coupling decreases towards T c (HLS, a→1) [Harada+Yamawaki ’01, Halasz etal ’98]

31. 3.2 Thermal Evolution: QGP→ Mix→ HG QGP: initial conditions [SPS]  0 =1fm/c →  0 =0.5fm/c: ~2-3 s=Cd QG T 3 ; d QG =40 → 32: ~2 pre-equilibrium?! HG: chemistry [LHC] T [GeV] conserved BB use entropy build-up of   >0 (N  =const) accelerated cooling HG: chemistry and trans. flow R~exp(3   ) for  → , … yield up at low q t, down above large blue shift from coll. flow

32. Photon Properties in Colorsuperconductors

33. 2.2.4 In-Medium Baryons:  (1232)  long history in nuclear physics ! (  A,  A ) e.g. nuclear photoabsorption: M ,   up by 20MeV  little attention at finite temperature   -Propagator at finite  B and T [van Hees + RR ’04] in-medium vertex corrections incl. g’  -cloud, (“induced interaction”) (1+ f  - f N ) thermal  -gas  →N(1440), N(1520),  (1600) + +...   > > > > > > > > NN -1  N -1

34. 3.3 Dilepton Spectrum at RHIC

35. 4.3 Perspectives on Data III: RHIC large “pre-equilibrium” yield from parton cascade (no LPM) thermal yields ~ consistent QGP undersat. small effect Predictions for Central Au-Au PHENIX Data consistent with initial only disfavors parton cascade not sensitive to thermal yet