1. Thermal Photons in Strong Interactions Ralf Rapp Cyclotron Inst. + Physics Dept. Texas A&M University College Station, USA College Station, 24.09.04

2. Introduction I: E.M. Probes in Strong Interactions 0 0.05 0.3 0.75  [GeVfm -3 ] 120 150-160 175 T [MeV] ½   2  0 5  0  hadron  PT many-body degrees of freedom? QGP (2 ↔ 2) (3-body,...) (resonances?) consistent extrapolate pQCD  -ray spectroscopy of atomic nuclei: collective phenomena DIS off the nucleon: - parton model, PDF’s (high Q 2 ) - nonpert. structure of nucleon [JLAB] thermal emission: - compact stars (?!) - heavy-ion collisions What is the electromagnetic spectrum of matter?

3. 1. Introduction 2. Thermal Photon Emission Rates 2.1 Generalities 2.2 Quark-Gluon Plasma: Complete LO 2.3 Hadronic Matter: - Meson Gas - Baryonic Contributions - Medium Effects 3. Relativistic Heavy-Ion Collisions 3.1 Nonthermal Sources 3.2 Thermal Evolution 3.3 Comparison to SPS and RHIC Data 4. High-Density QCD: Colorsuperconductor 5. Conclusions Outline

4. Introduction II: 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: depend. on T,  B,   ; medium effects, … system evolution: V(  ), T(  ),  B (  ) ; transverse expansion, … nonthermal sources: e + e - : Drell-Yan, open-charm;  : initial/ consistency! pre-equil.

5. 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

6. 2.2 Quark-Gluon Plasma “Naïve” Leading Order Processes: q + q (g) → g (q) + γ [Kapusta etal ’91, Baier etal ’92] O But: other contributions to 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) q gq

7. 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)

8. 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

9. 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]

10. 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]

11. 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

12. 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

13. 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]

14. 2.3.6 Hadron Gas vs. QGP Emission complete LO QGP rate ~2-3 above tree-level rate in-med HG + Meson-Ex (bottom-up) ≈ complete LO QGP (top-down) “quark-hadron duality” ?! Similar findings for thermal dilepton rates not yet understood …

15. 3. Relativistic Heavy-Ion Collisions Au + Au → X e + e - Signatures of the QGP? Suppression of J/  Mesons Decays of  -Mesons Photons …  J/ 

16. 3.1 Nonthermal Sources Initial hard production: pp → γX scaling with x T =2p T /√s, + power-law fit [Srivastava ’01] Nuclear Effects: pA →  X “Cronin”: gaussian k t -smear. cf. pA → πX AA: AA ≈ 2 pA

17. 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

18. 3.3 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 + Initial initial+Cronin at q t >1.5GeV  T 0 =205MeV suff., HG dom.

19. 3.3 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  ?!

20. 3.3 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

21. 4. Photon Emission from Colorsuperconductor Cold Quark Matter → (qq) Cooper pairs,  qq ≈100MeV  q » m s 2 : u-d-s symmetrically paired (Color-Flavor-Locking)   iral symmetry broken, Goldstone bosons, m  2 ~ m q 2 ≈ (10MeV) 2 Effective theory description of “hadronic” processes: γ γ Photon Emissivities  exceeds e + e - → γγ for T≥5MeV [Vogt,Ouyed+RR]

22. 5. Conclusions significant progress in E.-M. radiation from QCD matter: - QGP: soft collinear enhancement → complete leading order - HG: more complete (strangeness, baryons,  t-chan, FF’s) extrapolations into phase transition region  HG and QGP shine equally bright deeper reason? lattice calculations? phenomenology for URHIC’s compares favorably with existing data consistency with dileptons much excitement ahead: PHENIX, NA60, HADES, ALICE,… and theory!

23. Additional Slides

24. Photon Properties in Colorsuperconductors

25. (i)  (770) + > >    B *,a 1,K 1... N, ,K … Constraints: - branching ratios B,M→  N,  -  N,  A  absorpt.,  N→  N - QCD sum rules Significance of high  B at low M E lab =20-40AGeV optimal?! 2.2.2 1 ± Mesons:

26. 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

27. (i) Check:  in Vacuum and in Nuclei → ok !

28. (ii)  (1232) in URHICs  broadening: Bose factor,  →B  repulsion:  N -1,  NN -1 not yet included: (  N→ 

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

30. 2.2.6 Observables in URHICs (i) Lepton Pairs (ii) Photons Im Π em (M,q) Im Π em (q 0 =q) e+e-e+e- γ baryon density effects! [Turbide,Gale+RR ’03] consistent with dileptons  Brems with soft  at low q?