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Properties of Vector Mesons in Matter - Theory and Phenomenology

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. 1.) Introduction: Basic Questions. E.M. Correlation Function:.

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Properties of Vector Mesons in Matter - Theory and Phenomenology

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  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 E.M. Correlation Function: rI =1 ImPem ~ [ImDr+ImDw /10+ImDf /5] 4p+... pp • Vector-meson propagators • Broader Impact: • Are r, w and f alike? • cold vs. hot matter • in-medium hadrons + equation of state • phase transitions (condensates, fp, susceptibilities, …) r+w +f _ KK qq • Phenomenology: • production mechanism (elementary: p-A, g-A, thermal: A-A) • competing sources (centrality, pT, √s, …)

  3. Outline 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

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

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

  6. 3.) Medium Effects I: Hadronic Interactions > rB /r0 0 0.1 0.7 2.6 > rMeson “Melting” Switch off Baryons [RR,Wambach etal ’99] [Chanfray etal, Herrmann etal, RR etal, Koch etal, Weise etal, Mosel etal, Eletsky etal, Oset etal, Lutz etal …] DV(M,q;mB ,T) = [M 2 - mV2 -SVP-SVB -SVM ] -1 V-Propagator: B*,a1,K1... Sp V V SVB,VM= Selfenergies: SVP = N,p,K… Sp Constraints: decays: B,M→ VN, Vp, ... , scattering:gN/A,pN→VN, …

  7. [Eletsky etal ’01] [RR+Wambach ’99] 3.2Spectral Functions from Free V-N/-p Scattering • ImSV ~ ImTVNrN + ImTVprp ~ sVN,Vp+ dispersion relation forReTV [Eletsky etal ’01] r-Meson w-Meson • fair model agreement (~ compatible with QCDSR) • w-broadening somewhat less pronounced

  8. 3.2 Medium Effects II: Dropping Mass • Hidden Local Symmetry: r-mass ↔ “Higgs” mechanism • Vector Manifestation of Chiral Symmetry: rL↔p • In-Medium: thermal p-loops, mr(0), gr→0 (renormalization group) •  - dropping r-mass • - vector dominance violated: a = 2 → 1 [Harada+ Yamawaki ‘01] p EM Formfactor p g 0.85Tc p ~(a-2) ~a vac • Open Issues: • - “flash temperature” Tf ~0.7Tc (c symm.!) • - extrapolation to Tc • - no resonances, baryons [Sasaki+Harada ’06: P81]

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

  10. [van Hees+ RR ‘06] • absolute norm., meltingr • M>0.9GeV: “4p”→mm; wandf ?! • baryon effects essential 4.) Dilepton Spectra in Heavy-Ion Collisions Thermal Emission: m+ m- • evolve over thermal fireball, isentropic QGP-Mix-HG • central In-In: T0-fo=195→120MeV, Tc=175MeV, tFB=7fm

  11. 4.2 Chiral Virial Approachvs. NA60 • low-density expansion + chiral reduction • also: compare fireball vs. hydrodynamics [Dusling,Teaney+Zahed ’06] [van Hees+RR ‘06] • good agreement fireball - hydro (pT-spectra!) • lack of broadening

  12. 4.3 NA60pT-Spectra vs. Hadronic Many-Body • improved freezeout-r (g-factor!) + Drell-Yan (pT>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 [R. Averbeck, PHENIX] [Toia etal. ’06] [RR ’01] QGP • low mass: thermal! (mostly in-medium r) • connection to Chiral Restoration: a1 (1260)→ pg ,3p • intermed. mass:QGP vs.cc → e+e-X (softening?) -

  15. 5.) Conclusions • Hot+Dense Hadronic Matter: • r-broadening matured (melting at ~Tc→ hadronic liquid!?) • Differences between r and w (critical point)?! • NA45, NA60: - support “quark-hadron duality” • - (anti-)baryon-induced medium effects • Chiral Restoration: • - direct (exp.): measure axialvector (pg) • - 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.]) Looking forward to further exciting developments …

  16. [van Hees+RR ‘06] 4.2.3 Intermediate-Mass Region • “4p“ states dominate the vacuum • e.m. correlator above M ≈ 1.1GeV • lower estimate: • use vacuum4p correlator • upper estimate: • O(T2) medium effect → • “chiral V-A mixing”: • with 4p 2p [Eletsky+Ioffe ‘90]

  17. 0.2% 1% [Leupold ’98, Ruppert etal ’05] 4-quark condensate! 3.1.3 QCD Sum Rules + r(770) in Nuclear Matter dispersion relation for correlator: [Shifman,Vainshtein +Zakharov ’79] • lhs: OPE (spacelike Q2): • rhs: hadronic model (s>0):

  18. 3.1.2 r(770) Spectral Function in Nuclear Matter In-med p-cloud + r-N → B* resonances Relativist.r-N → B* (low-density approx) In-med p-cloud + r-N → N(1520) [Urban etal ’98] [Post etal ’02] [Cabrera etal ’02] rN=0.5r0 rN=r0 rN=r0 p N →r NPWA Constraints: g N ,g A • good agreement: strong broadening + small mass-shift up • constraints from (vacuum) data important quantitatively

  19. 3.) Medium Effects and Thermal Dileptons 3.1 Lattice QCD (QGP) Dilepton Rate ~ ImP(w,q=0)/w2 EM Correlator ImP(w,q)/w2 T=1.5Tc [Bielefeld Group ’02, ‘05] • lQCD << pQCD at low mass (finite volume?) • currently no thermal photons from lQCD • vanishing electric conductivity!? but: [Gavai ’04]

  20. 4.6 Dropping-Mass Scenarios vs. NA60 [Brown+Rho ’91, Hatsuda+Lee ’92,…, Harada+Yamawaki ‘01] • thermal fireball with absolute normalization HLS: [Sasaki+Harada ‘06] (Tflash=122MeV) • dropping mass disfavored? • free r decays at freezeout? • flash temperature? baryons? • p chem. potentials? extrapolation to Tc?

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

  22. WA98 “Low-qt Anomaly” • addt’l meson-Bremsstrahlung • pp→ ppgpK→pKg • substantial at low qt [Liu+ RR’05] 5.) Electromagnetic Probes 5.1.1 Thermal Photons I : SPS Expanding Fireball + pQCD • pQCD+Cronin at qt >1.6GeV •  T0=205MeV suff., HG dom. [Turbide,RR+Gale’04]

  23. 4.2.2 In-In at SPS: Theory vs. NA60 • predictions based on r-spectral function of [RR+Wambach ’99] • uncertainty in fireball lifetime (±25% norm.); or: infer tFB≈7fm/c ! • relative strength of thermal sources fix • good agreement with r melting, including pt dependence [van Hees +RR ‘06]

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