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Dileptons in Heavy-Ion Reactions and (Light) Vector Mesons in Medium

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  1. Dileptons in Heavy-Ion Reactionsand (Light) Vector Mesons in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, Texas USA International School on QGP and HICs Torino, 14.+16.05.05

  2. Outline 1. Introduction 2. Thermal Electromagnetic Emission Rates - Vacuum: Quarks vs. Hadrons, Vector Mesons 3. Chiral Symmetry in QCD - Spontaneous Breaking, Hadronic Spectrum, Restoration 4. (Light) Vector Mesons in Medium - Chiral Expansion, Hadronic Many-Body Approach - QCD Sum Rules, Lattice QCD, Chiral Restoration?! 5. QGP Emission 6. Dilepton Spectra in Heavy-Ion Collisions - Space-Time Evolution - Phenomenology: BEVALAC/SIS, SPS and RHIC 7. Summary and Conclusions

  3. 1.) Introduction 1.1 Electromagnetic Probes in Strong Interactions • g-ray spectroscopy of atomic nuclei: collective phenomena, … • DIS off the nucleon: - parton model, PDF’s (high q2< 0) • - nonpert. structure of nucleon [JLAB] • Drell-Yan: pp → eeX (q2> 0: symmetry, nucl. shadowing) • thermal emission: - compact stars (?!) • - heavy-ion collisions: [SPS, RHIC, LHC, FAIR] • g (q2=0) ,e+e- (q2>0) What is the electromagnetic spectrum of QCD matter?

  4. Creating Strong-Interaction Matter in the Laboratory e+ e- r • Sources of Dilepton Emission: • “primordial” (Drell-Yan) qq annihilation: NN→e+e-X - • emission from equilibrated matter (thermal radiation) • - Quark-Gluon Plasma: qq → e+e-, … • - Hot+Dense Hadron Gas: p+p- → e+e-, … - _ • final-state hadron decays: p0,h → ge+e- , D,D → e+e-X, … Au + Au NN-coll. Hadron Gas “Freeze-Out” QGP

  5. 1.2 Objective:Use Dileptons to Probe the Nature of Strongly Interacting Matter • Bulk Properties: • Equation of State • Microscopic Properties: • -Degrees of Freedom • - Spectral Functions • Phase Transitions: • (Pseudo-) Order Parameters •  (some)Key Questions:Can we • infer the temperature of the matter? • establish in-medium modifications of r , w , f → e+e- ? • extract signatures of chiral symmetry restoration?

  6. - ‹qq› • QCD Order Parameters and Hadronic Modes • condensate:‹qq› = ∂W / ∂mq • suscept.:cs=∂2W / ∂mq2 =Ps (q=0) = ls2 Ds (q=0) • ~ (ms )-2 • pdecay const:fp2= - ∫ ds/s (Im PV- Im PA ) • lr2 ImDr lattice QCD cs - 1.0 T/Tc [Weinberg ’67, Kapusta+Shuryak ’94] 1.3 Intro-III: EoS and Hadronic Modes • All information encoded in free energy: • EoS: , , • correlation functions: : “hadronic” current ↔ iso/scalarpppairs! ↔dileptons,photons!

  7. qq 1.4.1 A Schematic Dilepton Spectrum in HICs • Characteristic regimes in invariant • e+e- mass, M2=(pe++ pe- )2 : • uncertainty principle: • - high masses ↔ early in time • - low masses ↔ late in time • more quantitative: • - Drell-Yan: power law ~ Mn • - thermal radiation ~ exp(-M/T) Thermal rate: q0≈ 0.5GeV  Tmax≈ 0.17GeV , q0≈ 1.5GeV  Tmax≈ 0.5GeV

  8. Intermediate Mass:NA50 Central Pb-Pb 158 AGeV open charm (DD) Drell- Yan Mmm [GeV] Mee [GeV] • final-state hadron decays • saturate yield in p-A collisions • strong excess around M≈0.5GeV • little excess in r,w,f region • factor ~2 excess • open charm? thermal? … 1.4.2 Dilepton Data at CERN-SPS Low Mass:CERES/NA45

  9. 2. Thermal Electromagnetic Emission Rates 2.1 Electromagnetic Correlator 2.2 Vacuum: Quark vs. Hadronic Degrees of Freedom 2.3 Role of Light Vector Mesons(r ,w ,f )

  10. 2.1 E.M. Correlator + Thermal Dilepton Emission g*(q) e+ e- (T,mB) photon selfenergy Im Πem(M,q;T,mB) E.M. Correlation Fct.: quark basis: hadron basis:

  11. 2.1.2 Side Note: Versatility of the E.M. Correlation Function • Photon Emission Rate γ Im Πem(q0=q) ~O(αs ) e+ e- Im Πem(M,q) ~ O(1) g* same correlator! • E.M. Susceptibility (charge fluctuations): • <Q2> - <Q>2 =χem = Πem(q0=0,q→0)

  12. 2.2 E.M. Correlator in Vacuum: s(e+e-→hadrons) e+ e- p - p + rI =1 r 2p+4p+... pp e+ e- h1 h2 r+w+f KK q q _ qq … _ s ≥ sdual~(1.5GeV)2: pQCD continuum s < sdual : Vector-Meson Dominance

  13. thermal emission tFB ~ 10fm/c after freezeout tV ~ 1/GVtot 2.3 The Role of Light Vector Mesons in HICs Contribution to invariant mass-spectrum: Gee [keV] Gtot [MeV] (Nee )thermal (Nee )cocktail ratio r(770) 6.7 150 (1.3fm/c) 1 0.13 7.7 w(782) 0.6 8.6 (23fm/c) 0.09 0.21 0.43 f(1020) 1.3 4.4 (44fm/c) 0.07 0.31 0.23  In-medium radiation dominated by r -meson! Connection to chiral symmetry restoration?!

  14. 3.) Chiral Symmetry in QCD 3.1 Chiral Symmetry and its Breaking in Vacuum 3.2 Consequences for the Hadronic Spectrum 3.3 Vector-Axialvector Correlation Functions and Chiral Restoration

  15. 3.1.1 Chiral Symmetry in QCD:Vacuum current quark masses: mu ≈ md ≈ 5-10MeV Chiral SU(2)V × SU(2)A transformation: Up to O(mq ), LQCD invariant under Rewrite LQCD using qL,R=(1±g5)/2 q : Invariance under isospin and “handedness”

  16. qR qL > > > > - - qR qL 3.1.2 Spontaneous Breaking of Chiral Symmetry - strongqqattraction  Chiral Condensate fillsQCD vacuum: [cf. Superconductor: ‹ee›≠0 , Magnet ‹M› ≠ 0 , … ] Simple (NJL) Model: • assume “mean-field” , expand: • linearize: • free energy: • ground • state: Gap Equation

  17. Constituent Quark Mass in the QCD Vacuum “Data”: lattice [Bowman etal ‘02] Curve: Instanton Model [Diakonov+Petrov ’85, Shuryak] (spacelike, q2<0): • , chiral breaking:|q2| ≤ 1 GeV2 • constituent-quark “size” ≈rinstanton≈ (0.6GeV)-1 ≈ 1/3 fm • quark condensate , nvac≈ (2Nf ) fm-3!

  18. JP=0±1± 1/2± 3.2 (Observable) Consequences of SBCS • mass gap , not observables! • but:hadronic excitations reflect SBCS: • “massless” Goldstone bosonsp0,± • (explicit breaking: fp2 mp2= mq ‹qq› ) • “chiral partners” split:DM ≈ 0.5GeV! • chiral trafo: , • vector mesons r and w: - -ieijktk chiral singlet !

  19. Baryons chiral breaking: Q2 < (1.5-2GeV)2 , J± < 5/2 (?!) 3.2.2 Hadron Spectra and SBCS in Vacuum Axial-/Vector Correlators pQCD cont. • entire spectral shape matters • Weinberg Sum Rule(s)

  20. lattice QCD - cm ‹qq› 1.0 T/Tc cPTmany-bodydegrees of freedom?QGP (2 ↔ 2)(3-body,...) (resonances?) consistentextrapolatepQCD 0 0.05 0.3 0.75 e[GeVfm-3] 120, 0.5r0 150-160, 2r0 175, 5r0 T[MeV], rhad 3.3.1 “Melting” the Chiral Condensate • Excite vacuum (hot+dense matter) • quarks “percolate” / liberated •  Deconfinement • ‹qq›condensate “melts”, ciral Symm. • chiral partners degenerateRestoration • (p-s, r-a1, … medium effects → precursor!) - How?

  21. At Tc: Chiral Restoration 3.3.2 Low-Mass Dileptons + Chiral Symmetry Vacuum • How is the degeneration realized ? • “measure” vector withe+e-, but axialvector?

  22. Dileptons in Heavy-Ion Reactionsand (Light) Vector Mesons in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, Texas USA International School on QGP and HICs Torino, 14.+16.05.05

  23. Outline 1. Introduction 2. Thermal Electromagnetic Emission Rates - Vacuum: Quarks vs. Hadrons, Vector Mesons 3. Chiral Symmetry in QCD - Spontaneous Breaking, Hadronic Spectrum, Restoration 4. (Light) Vector Mesons in Medium - Chiral Expansion, Hadronic Many-Body Approach - QCD Sum Rules, Lattice QCD, Chiral Restoration?! 5. QGP Emission 6. Dilepton Spectra in Heavy-Ion Collisions - Space-Time Evolution - Phenomenology: BEVALAC/SIS, SPS and RHIC 7. Summary and Conclusions

  24. Upshot of Chapters 2 + 3 E.M. Emission Rates: ● directly prop. to (imag.) e.m. correlator (photon selfenergy) ●separation in perturbative (qq) - nonperturbative(r, w, f) at “duality scale” sdual ~ (1.5GeV)2 ●in-med radiation: low-mass ↔ r-meson, high-mass ↔ QGP Chiral Symmetry: ●spontaneously broken in the vacuum, Mq* ~ ‹qq› ≠ 0 (low q2) ● hadronic spectrum: chiral partners split (p-s, r-a1, …) ● excite vacuum → condensate melts → chiral restoration → chiral partners degenerate - -

  25. 4.) Vector Mesons in Medium 4.1 Chiral Expansion Approach - Low-Density Pion Gas 4.2 Hadronic Many-Body Theory for Vector Mesons - r-Meson in Vacuum - r-Selfenergies and Spectral Functions - Constraints and Consistency: Photo-Absorption, QCD Sum Rules, Lattice QCD - w- and f-Mesons 4.3 Dropping r-Mass; Vector Manifestation CS 4.4 Chiral Restoration?!

  26. = = 4.1 Low-Temp. Expansion: “Chiral Mixing” [Dey, Eletsky + Ioffe ’90] Correction due to Thermal 1-Pion Contribution: Use: pion reduction formula and current algebra to find: 0 0 0 0 (chiral limit) “Mixing parameter”:

  27. Effect on Rate • mixing fills “hole” at ~1.2GeV • “duality scale” reduced from • √sdual ≈ 1.5GeV → 1GeV “Chiral Mixing” and Dilepton Rate Vacuum V- and A-Correlators • extrapolate to “full” mixing: • e=1/2 ↔ Tc=√3fp≈160MeV, • mp=140MeV ↔ Tc≈225MeV

  28. |Fp|2 dpp 4.2 Many-Body Approach: r-Meson in Vacuum Introduce r as gauge boson into free p +r Lagrangian p p r r -propagator: p e.m. formfactor pp scattering phase shift

  29. 4.2.2 r-Selfenergies in Hot + Dense Matter r Sp Sp [Chanfray etal, Herrmann etal, RR etal, Weise etal, Oset etal, …] (1) Medium Modifications of Pion Cloud Sp In-med p-prop. Dp= [k02-wk2-Sp(k0 ,k)]-1 → mostly affected by (anti-) baryons modifications due to interactions with hadrons from heat bath  In-Medium r -Propagator r Dr (M,q;mB,T)=[M2-mr2-Srpp-SrB-SrM ]-1

  30. > > (2) Direct r-Hadron Interactions R r resonance-dominated: r+h → R, selfenergy: h (i) Meson Gas (h = p, K, r) e.g. , A=a1,h1 fix G viaG(a1→rp) ~ G2 v2 PS ≈ 0.4GeV, … • Generic features: • cancellations in real parts • imaginary parts strictly add up

  31. > > Sub-threshold Decay Phase Space D(1700) Coupling Constant → Free Decay: N(1520) (ii) Direct r-Baryon Interactions (h = N, D, …) S-waver + N → B3/2- : e.g.:G(N(1520)→Nr) ≈ 25MeV, G(D(1700)→Nr) ≈ 130MeV P-waver + N → B3/2+ : e.g.:G(D(1232)→Ng) ≈ 0.8MeV, G(N(1720)→Nr) ≈ 115MeV In-Medium Selfenergy: B* r N-1

  32. r Sp > Sp > g N → B* direct resonance! g N → p N,D meson exchange! 4.2.3 Constraints I: Nuclear Photo-Absorption • carry in-mediumr-spectral • function to the photon point: • constrain by nuclear g-absorption: D,N*,D* N-1

  33. gN gA p-ex Light-liker-Spectral Function, Dr(q0=q), and Nuclear Photo-Absorption On the Nucleon On Nuclei • fixes coupling constants and • formfactor cutoffs for rNB • 2.+3. resonance melt (parameter) • (selfconsistent N(1520)→Nr) [Post,Mosel etal ’98] [Urban,Buballa,RR+Wambach ’98]

  34. 4.2.4 r(770) Spectral Function in Nuclear Matter In-med p-cloud+ r-N → N(1520) In-med p-cloud + r-N→B* resonances r-N→B* resonances (low-density approx) [Urban etal ’98] [Post etal ’02] [Cabrera etal ’02] rN=0.5r0 rN=r0 rN=r0 pN →rNPWA Constraints: gN ,gA • Consensus: strong broadening + slight upward mass-shift • Constraints from (vacuum) data important quantitatively

  35. 4-quark condensate! 4.3 QCD Sum Rules + r(770) in Nuclear Matter General idea: dispersion relation for correlation function [Shifman,Vainshtein +Zakharov ’79] • lhs: operator product expansion • for large spacelike Q2: • rhs: model spectral function • at timelike s>0: • Resonance + • pQCD continuum Nonpert. Wilson coeffs (condensates) r -Meson:

  36. Vacuum: - Comparison to hadronic many-body models Nuclear Matter:<(qq)2> decreases  softening of r -propagator <(qq)2> = k <qq>2 - - 0.2% 1% • roughly consistent • sensitive to detailed shape • decreasing mass or • increasing width QCD Sum Rule Results: r(770)in Nuclear Matter [Leupold etal ’98]

  37. subtract • consistent with (some) hadronic • models based onwNscattering • dropping w-mass?! • (mw )med≈ 720MeV [Klingl etal ’97] 4.4 w-Meson in Nuclear Matter New Data for g A → w X→ p 0g X : [CBELSA-TAPS ‘05]

  38. 4.5 Vector-Meson Spectral Functions in High-Energy Heavy-Ion Collisions: Hot and Dense Matter

  39. rB/r0 0 0.1 0.7 2.6 Model Comparison [Eletsky etal ’01] [RR+Wambach ’99] 4.5.1 r-Meson Spectral Functions at SPS Hot+Dense Matter Hot Meson Gas [RR+Wambach ’99] [RR+Gale ’99] • r-meson “melts” in hot and dense matter • baryon density rB more important than temperature • reasonable agreement between models

  40. 4.5.2 Light Vector Mesons at RHIC • baryon effects important even at rB,tot= 0: • sensitive to rBtot= rB + rB (r-Nand r-N interactions identical) • w also melts, f more robust ↔ OZI - -

  41. 1- MEM 0- extracted [Laermann, Karsch ’04] 4.6 Lattice Studies of Medium Effects calculated on lattice

  42. calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched) 4.6.2 Comparison of Hadronic Models to LGT

  43. (3) Vector Manfestation of Chiral Symmetry (a) Vacuum: effective Lpr with rL≡p (“VM”) (also a1,L≡s) 1-loop expansionO(p/Lc , mr /Lc , g), Lc=4p fp≈1.2GeV (b) Finite Temperature: thermal p- and r -loop expansion → fp(T) , mr(T) matching of hadronic theory to OPE (Lmatch< Lc)requires “intrinsic” T-dependence of bare mr(0), gr dropping r -mass [Harada+Yamawaki, ’01] 4.7 Scenarios for Dropping r-Meson Mass (1)Naïve Quark Model:mr≈ 2Mq* → 0 at chiral restoration (problem: kinetic energy of bound state) (2) Scale Invariance of LQCD: implement into effective Lhad  universal scaling law [Brown+, Rho ’91]

  44. - - [qq→ee] [qq+O(as)-HTL] 4.8 Dilepton Rates and Chiral RestorationdRee /dM2 ~ f BImPem [Braaten,Pisarski+Yuan ’90] • Hard-Thermal-Loop result • much enhanced over Born rate • “matching” of HG and QGP • automatic! • Quark-Hadron Duality • at low mass ?! • Degenerate axialvector • correlator?

  45. > D,N(1900)… Sp a1 Sp + + . . . > N(1520)… Sr > > Exp: - HADES(pA): a1→(p+p-)p - URHICs (A-A) : a1→pg 4.8.2 Current Status of a1(1260)

  46. pS pS pS pS pS pP pP 4.8.3 Towards a Chiral + Resonance Scheme Options for resonance implementation: (i) generate dynamically from pion cloud [Kolomeitsev etal ‘03, …] (ii) genuine resonances on quark level → representations of chiral group [DeTar+Kunihiro ‘89, Jido etal ’00, …] e.g. p s N+ N(1535)- r a1D+ N(1520)- N(1900)+ D(1700)-(?) D(1920)+ rS (a1)S rS Importance of baryon spectroscopy to identify relevant decay modes!

  47. 5.) Dilepton Emission from the QGP 5.1 Pertubative vs. Lattice QCD 5.2 Emission from “Resonances”

  48. e+ e- q q _ • large enhancement at low M • not shared by lattice calculations: • threshold + resonance structures • (photon rate?!) Sq Sq [Bielefeld Group ‘02] 5.1 Perturbative vs. Lattice QCD But: small M → resummations finite-T perturbation theory (HTL) Baseline: [Braaten,Pisarski+Yuan ‘91] Im []= + + + … collinear enhancement: Dq,g=(t-mD2)-1 ~ 1/αs

  49. Dilepton Spectrum ratio to pert. qq rate _ Mee/mq 5.2 QGP Dileptons from Bound States → based on finite-T lattice potentials approach to “zero-binding line”  ~ stable-massr-resonance [Shuryak+Zahed ‘04] [Casalderrey+ Shuryak ‘04] • double-peak structure due to zero-binding line + mixed phase • factor 1.5-2 enhancement at M≈1.5GeV; depends on quark width

  50. 6.) Dilepton Spectra in Relativistic Heavy-Ion Collisions 6.1 Space-Time Evolution of URHIC’s - Formation and Freezeouts - Trajectories in the QCD Phase Diagram 6.2 Dilepton Spectra - SPS (√s = 17, 8 GeV) - RHIC (√s = 200 GeV)