1 / 23

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:.

glenys
Download Presentation

Properties of Vector Mesons in Matter - Theory and Phenomenology

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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]

More Related