1. Properties of Vector Mesons in Matter - Theory and Phenomenology Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA 19. Quark Matter Conference Shanghai, China, 16.11.06

2. 1.) Introduction: Basic Questions Vector-meson propagators Broader Impact: Are ,  and  alike? cold vs. hot matter in-medium hadrons + equation of state phase transitions (condensates, f , susceptibilities, …) Phenomenology: production mechanism (elementary: p-A,  -A, thermal: A-A) competing sources (centrality, p T, √s, …) E.M. Correlation Function: Im  em ~ [ImD  +ImD  /10+ImD  /5]      qq _  4    KK

3. 2.) Constraints from QCD  Lattice  Sum Rules 3.) Hadronic Spectral Functions  Many-Body Theory  Bare Parameters  Dilepton Rates 4.) Dilepton Phenomenology in URHICs  SPS (NA60, NA45)  RHIC 5.) Conclusions Outline

4. 2.1 Lattice QCD: Susceptibilites Quark-number susceptibilities: [Allton etal. ’05] “dropping”  -mass at critical point? “smooth”  spectral function across phase diagram?! Isoscalar (“  ”) Isovector (“  ”)

5. 2.2 Sum Rules and Order Parameters [Weinberg ’67, Das etal ’67, Kapusta+Shuryak ‘93] QCD-SRs: - lhs: OPE (condensates!) - rhs: spectral function,   (0)= 1 ⁄ 9   (0) [Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl etal ’97, Leupold etal ’98, Kämpfer etal ‘03,Ruppert etal ’05]  Promising synergy of lQCD and effective models! 0.2% 1% Weinberg-SRs: moments Vector  Axialvector  Meson

6. > >   V B *,a 1,K 1... N, ,K … 3.) Medium Effects I: Hadronic Interactions D V  (M,q;  B,T) = [M 2 - m V 2 -  VP  -  VB -  VM ] -1 V-Propagator: [Chanfray etal, Herrmann etal, RR etal, Koch etal, Weise etal, Mosel etal, Eletsky etal, Oset etal, Lutz etal …]  VP =  VB,VM  = Selfenergies: V Constraints: decays: B,M→ VN, V  scattering:  N/A,  N→VN, …  B /  0 0 0.1 0.7 2.6 [RR,Wambach etal ’99]  Meson “Melting” Switch off Baryons

7. 3.2  Spectral Functions from Free V-N/-  Scattering fair model agreement (~ compatible with QCDSR)  -broadening somewhat less pronounced [RR+Wambach ’99] [Eletsky etal ’01] [Eletsky etal ’01]  -Meson  -Meson Im  V ~ ImT VN  N + ImT V    ~  VN,V  + dispersion relation for ReT V

8. 3.2 Medium Effects II: Dropping Mass Hidden Local Symmetry:  -mass ↔ “Higgs” mechanism Vector Manifestation of Chiral Symmetry:  L ↔  In-Medium: thermal  -loops, m  (0), g  →0 (renormalization group)  - dropping  -mass - vector dominance violated: a = 2 → 1 [Harada+ Yamawaki ‘01] ~(a-2) ~a    Open Issues: - “flash temperature” T f ~ 0.7 T c (  symm.!) - extrapolation to T c - no resonances, baryons [Sasaki+Harada ’06: P81]  EM Formfactor 0.85T c vac

9. 3.3 Dilepton Emission Rates “matching” HG -QGP at ~T c : “Quark-Hadron Duality” ?! (pQCD↔ chirally symmetric) anti-/baryons important at RHIC  -meson more stable Isovector (  ) at SPS [qq→ee] [qq+HTL] ---- Inclusive (  ) at RHIC

10. 4.) Dilepton Spectra in Heavy-Ion Collisions evolve over thermal fireball, isentropic QGP-Mix-HG central In-In: T 0-fo =195→120MeV, T c =175MeV,  FB =7fm Thermal Emission: +  +  absolute norm., melting  M>0.9GeV: “4  ”→  and  baryon effects essential [van Hees+ RR ‘06]

11. 4.2 Chiral Virial Approach vs. NA60 low-density expansion + chiral reduction also: compare fireball vs. hydrodynamics good agreement fireball - hydro (p T -spectra!) lack of broadening [van Hees+RR ‘06] [Dusling,Teaney+Zahed ’06]

12. 4.3 NA60 p T -Spectra vs. Hadronic Many-Body improved freezeout-  (  -factor!) + Drell-Yan (p T >1.5GeV) approx. agreement (local slopes?!) See parallel talks by H.van Hees, J.Ruppert

13. 4.4 Pb-Au Collisions at SPS: CERES/NA45 very low-mass di-electrons ↔ low-energy photons [Turbide etal.’03, Alam etal.‘01]

14. 4.5 Dileptons at RHIC low mass: thermal! (mostly in-medium  ) connection to Chiral Restoration: a 1 (1260)→ , 3  intermed. mass: QGP vs. cc → e + e - X (softening?) - [RR ’01] [R. Averbeck, PHENIX] QGP [Toia etal. ’06]

15. 5.) Conclusions Hot+Dense Hadronic Matter:  -broadening matured (melting at ~T c → hadronic liquid!?) Differences between  and  (critical point)?! NA45, NA60: - support “quark-hadron duality” - (anti-)baryon-induced medium effects Looking forward to further exciting developments … Chiral Restoration: - direct (exp.): measure axialvector (  ) - indirect (theo.): chiral + QCD sum rules HADES, RHIC, LHC, SPS-09, CBM, …, elementary reactions ( cf. working group reports RHIC-II [nucl-ex/0611009], CBM [in prep.])

16. “4  “ states dominate the vacuum e.m. correlator above M ≈ 1.1GeV lower estimate: use vacuum 4  correlator upper estimate: O (T 2 ) medium effect → “chiral V-A mixing”: with 4.2.3 Intermediate-Mass Region [Eletsky+Ioffe ‘90] [van Hees+RR ‘06] 44 22

17. [Leupold ’98, Ruppert etal ’05] 0.2% 1% 3.1.3 QCD Sum Rules +  (770) in Nuclear Matter dispersion relation for correlator: lhs: OPE (spacelike Q 2 ): rhs: hadronic model (s>0): [Shifman,Vainshtein +Zakharov ’79] 4-quark condensate!

18. 3.1.2  (770) Spectral Function in Nuclear Matter In-med  -cloud +   -N → B* resonances Relativist.   -N → B* (low-density approx) In-med  -cloud +  -N → N(1520) Constraints:  N,  A  N →  N PWA good agreement: strong broadening + small mass-shift up 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]

19. 3.1 Lattice QCD (QGP) T=1.5T c lQCD << pQCD at low mass (finite volume?) currently no thermal photons from lQCD vanishing electric conductivity!? but: [Gavai ’04] Dilepton Rate ~ Im  ( ,q=0)/  2 EM Correlator Im  ( ,q)/  2 [Bielefeld Group ’02, ‘05] 3.) Medium Effects and Thermal Dileptons

20. 4.6 Dropping-Mass Scenarios vs. NA60 thermal fireball with absolute normalization dropping mass disfavored? free  decays at freezeout? flash temperature? baryons?  chem. potentials? extrapolation to T c ? [Brown+Rho ’91, Hatsuda+Lee ’92,…, Harada+Yamawaki ‘01] HLS: [Sasaki+Harada ‘06] (T flash =122MeV)

21. 4.2.5 Chiral Virial Approach vs. NA60 (central) [Steele,Yamagishi +Zahed ’99] [implementation van Hees+RR ’05]

22. 5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS Expanding Fireball + pQCD pQCD+Cronin at q t >1.6GeV  T 0 =205MeV suff., HG dom. addt’l meson-Bremsstrahlung  →   K→  K  substantial at low q t [Liu+ RR’05] WA98 “Low-q t Anomaly” [Turbide,RR+Gale’04]

23. 4.2.2 In-In at SPS: Theory vs. NA60 predictions based on  -spectral function of [RR+Wambach ’99] uncertainty in fireball lifetime (±25% norm.); or: infer  FB ≈ 7fm/c ! relative strength of thermal sources fix good agreement with  melting, including p t dependence [van Hees +RR ‘06]