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Introduction to Dileptons and in-Medium Vector Mesons

Introduction to Dileptons and in-Medium Vector Mesons. Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, Texas USA 2 Lectures at ECT* EM-Probes Workshop T rento , 04. + 06.06.05.

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Introduction to Dileptons and in-Medium Vector Mesons

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  1. Introduction to Dileptons and in-Medium Vector Mesons Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, Texas USA 2 Lectures at ECT* EM-Probes Workshop Trento, 04. + 06.06.05

  2. 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 (GRBs?!) • - heavy-ion collisions: [SPS, RHIC, LHC, FAIR] • g (q2=0) ,e+e- (q2>0) What is the electromagnetic spectrum of QCD matter?

  3. 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

  4. 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?

  5. - ‹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!

  6. qq 1.4.1 Schematic Dilepton Spectrum in HICs • Characteristic regimes in invariant e+e- mass, M2=(pe++ pe- )2 : • Drell-Yan: power law ~ Mn ↔ high mass • thermal ~ exp(-M/T): - QGP (highest T) ↔ intermediate mass • - HG (moderate T) ↔ low mass

  7. 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

  8. Outline 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 - Hadronic Many-Body Approach - Dropping Mass, Chiral Restoration?! 5. QGP Emission 6. Thermal Photons 7. Dilepton Spectra in Heavy-Ion Collisions - Space-Time Evolution; Comparison to SPS and RHIC Data 8. Summary and Conclusions

  9. = O(1) = O(αs ) e+ e- γ 2.) Electromagnetic Emission Rates E.M. Correlation Function: Im Πem(M,q) Im Πem(q0=q) also: e.m susceptibility (charge fluct.):χ = Πem(q0=0,q→0) • In URHICs: • source strength:dependence onT, mB, mp , medium effects, … • system evolution:V(t), T(t), mB(t), transverse expansion, … • nonthermal sources: Drell-Yan, open-charm, hadron decays, … • consistency!

  10. 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

  11. 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?!

  12. 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

  13. 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”

  14. qR qL JP=0±1± 1/2± > > > > - - qL qR 3.1.2 Spontaneous Breaking of Chiral Symmetry - • strongqqattraction  Chiral Condensate • fillsQCD vacuum: [cf. Superconductor: ‹ee›≠0 , Magnet ‹M› ≠ 0 , … ] • mass generation , not observables! • but:hadronic excitations reflect SBCS: • “massless” Goldstone bosonsp0,± • (explicit breaking: fp2 mp2= mq ‹qq› ) • “chiral partners” split:DM ≈ 0.5GeV! • vector mesons r and w: - chiral singlet !

  15. 3.2.2 Hadron Spectra and SBCS in Vacuum Axial-/Vector Correlators Constituent Quark Mass “Data”: lattice [Bowman etal ‘02] Curve: Instanton Model [Diakonov+Petrov ’85, Shuryak] pQCD cont. ●chiral breaking:|q2| ≤ 1 GeV2 ●quark condensate: nvac≈ (2Nf ) fm-3! • entire spectral shape matters • Weinberg Sum Rule(s)

  16. 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?

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

  18. Upshot of Chapters 2 + 3 E.M. Emission Rates: ● proportional to e.m. correlator (photon selfenergy) ●vacuum: separation in perturbative (qq) -- nonpert.(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  mass generation! Mq* ~ ‹qq› ≠ 0 (low q2) ● hadronic spectrum: chiral partners split (p-s, r-a1, …) ● excite vacuum → condensate melts → chiral restoration → chiral partners degenerate - -

  19. 4.) Vector Mesons in Medium 4.1 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 4.2 Vector Meson in URHICs: Hot+Dense Matter 4.3 Dropping r-Mass; Vector Manifestation of CS 4.4 Chiral Restoration?!

  20. |Fp|2 dpp 4.1 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

  21. 4.1.2 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

  22. > > (2) Direct r-Hadron Interactions: r + h → R Decay Phase Space (ii) r-Baryon Interactions (h = N, D, …) D(1700) • S-wave:r + N → N(1520), D(1700) → r + N, etc. • Coupling constant → free decay: N(1520) e.g.:G(N(1520)→Nr) ≈ 25MeV, G(D(1700)→Nr) ≈ 130MeV R r h (i) Meson Gas (h = p, K, r) p G e.g. r + p → w(770) , a1(1260) → r + p fix coupling G via decay widthG(a1→rp) a1 r Generic features: real parts cancel, imaginary parts add

  23. Sp r > Sp > g N → B* direct resonance! g N → p N,D meson exchange! 4.1.3 Constraints I: Nuclear Photo-Absorption total nuclear g-absorption in-mediumr–spectral cross section function at photon point D,N*,D* N-1

  24. 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]

  25. 4.1.4 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

  26. 4-quark condensate! 4.1.5 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:

  27. 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]

  28. 4.2 Vector-Meson Spectral Functions in High-Energy Heavy-Ion Collisions: Hot and Dense Matter

  29. rB/r0 0 0.1 0.7 2.6 Model Comparison [Eletsky etal ’01] [RR+Wambach ’99] 4.2.1 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

  30. 4.2.2 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 - -

  31. 1- MEM 0- extracted [Laermann, Karsch ’04] 4.2.3 Lattice Studies of Medium Effects calculated on lattice

  32. calculate integrate More direct! Proof of principle, not yet meaningful (need unquenched) 4.2.4 Comparison of Hadronic Models to LGT

  33. (3) Vector Manfestation of Chiral Symmetry (a) Vacuum: effective Lpr with rL≡p (“VM”) (b) Finite Temperature: thermal p- and r -loop expansion → fp(T) , mr(T) QCD-matchingrequires “intrinsic” T-dependence of bare mr(0), gr  dropping r -mass [Harada+Yamawaki, ’01] 4.3 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]

  34. - - [qq→ee] [qq+O(as)-HTL] 4.4 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?

  35. > D,N(1900)… Sp a1 Sp + + . . . > N(1520)… Sr > > Exp: - HADES(pA): a1→(p+p-)p - URHICs (A-A) : a1→pg 4.4.2 Current Status of a1(1260)

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

  37. 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

  38. 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

  39. r Sp Hot and Dense Hadron Gas Emission Rates Low energy: vector dominance Sp q  Im Πem(q0=q) ~ Im Dr(q0=q) g q γ p p,a1,w High energy: meson exchange r p Total HG ≈ in-med QGP ! to be understood… [Kapusta,Lichard+Seibert ’91, … , Turbide,RR+Gale’04] 6.) Thermal Photon Emission Rates Quark-Gluon Plasma “Naïve” LO: q + q (g) → g (q) +γ But: other contributions inO(αs) collinear enhanced Dg=(t-mD2)-1~1/αs Bremsstrahlung Pair-ann.+scatt. + ladder resummation (LPM) [Aurenche etal ’00, Arnold,Moore+Yaffe ’01]

  40. 7.) Dilepton Spectra in Relativistic Heavy-Ion Collisions 7.1 Space-Time Evolution of URHIC’s - Formation and Freezeouts - Trajectories in the QCD Phase Diagram 7.2 Comparison to Data - Dileptons at SPS (√s = 17, 8 GeV) - Photons at SPS (√s = 17 GeV) - RHIC (√s = 200 GeV)

  41. 7.1.1 Hadron Production in Heavy-Ion Collisions → well described by hadron gas in thermal+chemical equilibrium: [Braun-Munzinger etal ‘03] • SPS / RHIC: “chemical freezeout” close to phase boundary •  need to construct “evolution” • before: up to earliest “formation” time t0↔ T0 > Tchem • after: down to thermal freezeout tf↔ Tfo < Tchem

  42. Thermal Dilepton Emission Spectrum 7.1.2 Trajectories in the Phase Diagram • Basic assumption: entropy (+baryon-number) conservation •  fixes T(mB) in the phase diagram • Time scale: hydrodynamics, e.g.VFB(t)=(z0+vzt) p (R┴0+ 0.5a┴t2)2 Caveat: conserve hadron ratios after chem. f.o.  chemical potentials for p ,K,N,…: mp,K,N > 0 for T < Tchem mN [GeV] t [fm/c]

  43. Lower SPS Energy • enhancement increases! • confirms importance of • baryonic effects (predicted) 7.2.1 Low-Mass Dileptons at SPS Top SPS Energy • QGP contribution small • medium effects! • drop. mass or broadening?!

  44. Hydrodynamics (chem-eq) Thermal Fireball (chem-off-eq) Ti≈300MeV, more QGP contr. Ti≈210MeV, HG-dominated [RR+Shuryak ’99] [Kvasnikowa,Gale+Srivastava ’02] 7.2.2 Intermediate-Mass Dileptons at SPS: NA50 e.m. corr. continuum-like: Im Πem~M2(1 + as/p +…) QGP + HG!

  45. Expanding Fireball + pQCD [Turbide,RR+Gale’04] • pQCD+Cronin at qt >1.5GeV •  T0=205MeV suff., HG dom. 7.2.3 Photon Spectra at the SPS: WA98 Hydrodynamics: QGP + HG [Huovinen,Ruuskanen+Räsänen ’02] • T0≈260MeV, QGP-dominated • still true if pp→gX included

  46. MinBias Au-Au (200AGeV) [R. Averbeck, PHENIX] [RR ’01] thermal run-4 results eagerly awaited … • low mass: thermal dominant • int. mass:cc e+X , rescatt.? • e-X - 7.3 Dilepton Spectrum at RHIC

  47. 8.) Conclusions • Thermal E.M. Radiation from QCD matter • - Low-mass dileptons: in-med r (w, f) ↔Chiral Restoration!? • - Intermediate mass: qq annihilation ↔ QGP Radiation!? • - similar for photons but M=0 - • extrapolations into phase transition region •  in-med HG and QGP shine equally bright (“duality”) • deeper reason? lattice calculations? axialvector mode? • phenomenology for URHICs so far promising • - importance of model constraints • - precision data+theory needed for definite conclusions • much excitement ahead: PHENIX, NA60, CERES, HADES, • ALICE, … and theory!

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