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Theory of Thermal Dilepton Emission

Theory of Thermal Dilepton Emission. Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, Texas USA International School for High-Energy Nuclear Collisions Wuhan (China), Oct. 31- Nov. 05, 2011.

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Theory of Thermal Dilepton Emission

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  1. Theory of Thermal Dilepton Emission Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, Texas USA International School for High-Energy Nuclear Collisions Wuhan (China), Oct. 31- Nov. 05, 2011

  2. 1.) Intro-I:Probing Strongly Interacting Matter • Bulk Properties: • Equation of State • Phase Transitions: • (Pseudo-) Order Parameters • Microscopic Properties: • -Degrees of Freedom • - Spectral Functions • Would like to extract from Observables: • temperature + transport properties of the matter • signatures of deconfinement + chiral symmetry restoration • in-medium modifications of excitations (spectral functions)

  3. 1.2 Dileptons in Heavy-Ion Collisions e+ e- r • Sources of Dilepton Emission: • “primordial” qq annihilation (Drell-Yan): NN→e+e-X - • 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. qq 1.3 Schematic Dilepton Spectrum in HICs • Characteristic regimes in invariant • e+e- mass, M2 = (pe++ pe- )2 • Drell-Yan: primordial, • power law ~ M- n • thermal radiation: • - entire evolution • - Boltzmann ~ exp(-M/T) ImΠem(M,q;mB,T) Thermal rate: q0≈ 0.5GeV  Tmax ≈ 0.17GeV , q0≈ 1.5GeV  Tmax ≈ 0.5GeV

  5. 1.4 EM Spectral Function + QCD Phase Structure e+e-→ hadrons ~ ImPem/ M2 • Electromagn. spectral function • -√s ≤ 1 GeV: non-perturbative • -√s > 1.5 GeV: pertubative (“dual”) • Modifications of resonances • ↔ phase structure: • - hadron gas → Quark-Gluon Plasma • - realization of transition? √s = M • Thermal e+e- emission rate from • hot/dense matter (lem >>Rnucleus ) • Temperature? Degrees of freedom? • Deconfinement? Chiral Restoration? ImΠem(M,q;mB,T)

  6. 1.5 Low-Mass Dileptons at CERN-SPS CERES/NA45 e+e-[2000] NA60 m+m- [2005] Mee [GeV] • strong excess around M ≈ 0.5GeV , M > 1GeV • little excess in r, w, f region

  7. Outline 2.) Chiral Symmetry in QCD - Nonperturbative QCD, Chiral Breaking + Hadron Spectrum 3.) Thermal Electromagnetic Emission Rates - EM Spectral Function: Hadronic vs. Partonic Regimes 4.) Vector Mesons in Medium - Many-Body Theory, Spectral Functions + Chiral Partners (r-a1) 5.) Quark-Gluon Plasma Emission - Perturbative vs. Lattice-QCD Rates, “Quark-Hadron-Duality” 6.) Dilepton + Photon Spectra in Heavy-Ion Collisions - Space-Time Evolution, Phenomenology + Interpretation 7.) Summary and Conclusions

  8. Q2≤ 1GeV2 → transition to “strong” QCD: • effective d.o.f. = hadrons (Confinement) • massive “constituent quarks” • mq* ≈ 350 MeV ≈ ⅓ Mp(Chiral Symmetry • ~ ‹0|qq|0› condensate! Breaking) ↕⅔fm 2.1 Nonperturbative QCD • well tested at high energies, Q2>1GeV2: • perturbation theory (as = g2/4π<< 1) • degrees of freedom = quarks + gluons (mu ≈ md ≈ 5 MeV) _

  9. qR qL > > > > - - qL qR 2.2 Chiral Symmetry + QCD Vacuum : flavor + “chiral” (left/right) invariant • “Higgs” Mechanism in Strong Interactions: • qq attraction  condensate fills QCD vacuum! • Spontaneous Chiral Symmetry Breaking - • Profound Consequences: • effective quark mass: • ↔ mass generation! • near-massless Goldstone bosons p0,± • “chiral partners” split, DM ≈ 0.5GeV JP=0±1± 1/2±

  10. 2.2.2 Dynamics of Chiral Symmetry Breaking Axial-/Vector Correlators Constituent Quark Mass “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] pQCD cont. • Weinberg Sum Rule(s) ● chiral breaking:|q2| ≤ 1 GeV2

  11. 2.3 Phase Transition(s) in Lattice QCD - - ≈ qq / qq “Tcchiral”~150MeV “Tcconf” ~170MeV • different “transition” temperatures?! • extended transition regions • partial chiral restoration in “hadronic • phase” ?! (low-mass dileptons!) • leading-order hadron gas

  12. Outline 2.) Chiral Symmetry in QCD - Nonperturbative QCD, Chiral Breaking + Hadron Spectrum 3.) Thermal Electromagnetic Emission Rates - EM Spectral Function: Hadronic vs. Partonic Regimes 4.) Vector Mesons in Medium - Many-Body Theory, Spectral Functions + Chiral Partners (r-a1) 5.) Quark-Gluon Plasma Emission - Perturbative vs. Lattice-QCD Rates, “Quark-Hadron-Duality” 6.) Dilepton + Photon Spectra in Heavy-Ion Collisions - Space-Time Evolution, Phenomenology + Interpretation 7.) Summary and Conclusions

  13. 3.1 EM Correlator + Thermal Dilepton Rate g*(q) e+ e- (T,mB) Im Πem(M,q;T,mB) EM Correlation Fct.: quark basis: hadron basis: → 9 : 1 : 2

  14. 3.1.2 Versatility of EM Correlation Function • Photon Emission Rate γ Im Πem(q0=q) ~O(αs ) e+ e- Im Πem(M,q) ~ O(1) g* same correlator! • EM Susceptibility ( → charge fluctuations): • Q2 -Q 2 =χem = Πem(q0=0,q→0) • EM Conductivity: • sem = q0→0 [-ImΠem(q0,q=0)/2q0]

  15. 3.2 EM Correlator in Vacuum: e+e-→ hadrons e+ e- p - p + rI =1 r pp 4p+6p+... e+ e- h1 h2 r+w+f KK q q _ qq … _ s ≥ sdual ~ (1.5GeV)2 pQCD continuum s < sdual Vector-Meson Dominance

  16. T > Tc: Chiral Restoration 3.3 Low-Mass Dileptons + Chiral Symmetry Vacuum • How is the degeneration realized? • “measure” vector withe+e- , axialvector?

  17. Outline 2.) Chiral Symmetry in QCD - Nonperturbative QCD, Chiral Breaking + Hadron Spectrum 3.) Thermal Electromagnetic Emission Rates - EM Spectral Function: Hadronic vs. Partonic Regimes 4.) Vector Mesons in Medium - Many-Body Theory, Spectral Functions + Chiral Partners (r-a1) 5.) Quark-Gluon Plasma Emission - Perturbative vs. Lattice-QCD Rates, “Quark-Hadron-Duality” 6.) Dilepton + Photon Spectra in Heavy-Ion Collisions - Space-Time Evolution, Phenomenology + Interpretation 7.) Summary and Conclusions

  18. |Fp|2 dpp 4.1 Axial/Vector Mesons in Vacuum Introduce r, a1 as gauge bosons into free p +r +a1 Lagrangian p p r r -propagator: p EM formfactor pp scattering phase shift • 3 parameters: mr(0), g, Lr

  19. 4.2 r-Meson in Matter: Many-Body Theory r Sp > Sp > Sp interactions with hadrons from heat bath  In-Medium r-Propagator r Dr(M,q;mB,T) = [M2 – (mr(0))2 - Srpp- SrB- SrM]-1 • In-Medium • Pion Cloud Srpp = + [Chanfray et al, Herrmann et al, Urban et al, Weise et al, Koch et al, …] R=D, N(1520), a1, K1... r • Direct r-Hadron • Scattering SrB,M = h=N, p, K … [Haglin, Friman et al, RR et al, Post et al, …] • estimate coupling constants fromR→ r + h, • more comprehensive constraints desirable

  20. Sp r > Sp > g N → B* direct resonance! g N → p N,D meson exchange! 4.3 Constraints I: Nuclear Photo-Absorption total nuclear g -absorption in-mediumr-spectral cross section function at photon point D,N*,D* r N-1

  21. gN gA p-ex r Spectral Function in Nuclear Photo-Absorption On the Nucleon On Nuclei • fixes coupling constants and • formfactor cutoffs for rNB • 2.+3. resonances melt • (selfconsistent N(1520)→Nr) [Peters,Mosel et al ’98] [Urban,Buballa,RR+Wambach ’98]

  22. 4.4 r-Meson Spectral Function in Nuclear Matter r+N→B* resonances (low-density approx.) In-med. p-cloud + r+N→B* resonances In-med. p-cloud + r+N → N(1520) [Urban et al ’98] [Post et al ’02] [Cabrera et al ’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

  23. 0.2% 1% 4.5 Constraints II: QCD Sum Rules in Medium dispersion relation for correlator: [Shifman,Vainshtein +Zakharov ’79] • lhs: OPE (spacelike Q2): • rhs: hadronic model (s>0): Nonpert. Wilson coeffs. (condensates) [Hatsuda+Lee’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05]

  24. Hot Meson Gas rB/r0 0 0.1 0.7 2.6 [RR+Gale ’99] 4.6r-Meson Spectral Functions “at SPS” Hot + Dense Matter mB =330MeV [RR+Wambach ’99] • r-meson “melts” in hot/dense matter • baryon density rB more important than temperature

  25. 4.6.2 Light Vector Mesons at RHIC + LHC • baryon effects remain important at rB,net = 0 : • sensitive to rB,tot= rB + rB(r-N = r-NCP-invariant) • w also melts, f more robust ↔ OZI - -

  26. p Sp Sp Sp r Sr Sr Sr 4.7 Axialvector in Medium: Dynamical a1(1260) p a1 resonance + + . . . = Vacuum: r In Medium: + + . . . [Cabrera,Jido, Roca+RR ’09] • in-medium p + r propagators • broadening ofp-rscatt. Amplitude • pion decay constant in medium:

  27. Upshot of Chapters 2 - 4 Chiral Symmetry: ● spontaneously broken in vacuum, Mq* ~ ‹qq› ≠ 0 (low q2) ● hadronic spectrum: chiral partners split (p-s, r-a1, …) ● excite vacuum → condensate melts → chiral restoration → chiral partners degenerate EM Emission Rates + Medium Effects: ● determined by EM spectral function (correlator) ●perturbative (qq) - nonpert.(r, w, f); duality scale√sdual ~1.5GeV ● in-med radiation: low-mass ↔ r-meson, high-mass ↔ QGP ● many-body theory: eff. Lagrangian + constraints; broadening! - -

  28. Outline 2.) Chiral Symmetry in QCD - Nonperturbative QCD, Chiral Breaking + Hadron Spectrum 3.) Thermal Electromagnetic Emission Rates - EM Spectral Function: Hadronic vs. Partonic Regimes 4.) Vector Mesons in Medium - Many-Body Theory, Spectral Functions + Chiral Partners (r-a1) 5.) Quark-Gluon Plasma Emission - Perturbative vs. Lattice-QCD Rates, “Quark-Hadron-Duality” 6.) Dilepton + Photon Spectra in Heavy-Ion Collisions - Space-Time Evolution, Phenomenology + Interpretation 7.) Summary and Conclusions

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

  30. 5.2 Updated Dilepton Rate from Lattice QCD [Ding et al ’10] dRee/d4q 1.45Tc(quenched) q=0 • low-mass enhancement in lattice rate! • similar to hard-thermal-loop resummed perturbation theory [Braaten,Pisarski+Yuan ‘90]

  31. 5.2.2 Euclidean Correlators: Lattice vs. Hadronic • Euclidean Correlation fct. Lattice (quenched) [Ding et al‘10] Hadronic Many-Body [RR ‘02] • “Parton-Hadron Duality” of lattice and in-medium hadronic?!

  32. 5.2.3 Back to Spectral Function -ImPem /(C T q0) • suggestive for approach to chiral restoration and deconfinement

  33. = = 5.3 Intermediate Mass: “Chiral Mixing” [Dey, Eletsky +Ioffe ’90] • low-energy pion interactions fixed by chiral symmetry 0 0 0 0 • mixing parameter • degeneracy with perturbative • spectral fct. down to M~1GeV • physical processes at M ≥ 1GeV: • pa1→ e+e-etc. (“4pannihilation”)

  34. e+ e- q q _ - - [qq→ee] [qq+HTL] 5.4 Summary of Dilepton Rates: HG vs. QGPdRee /dM2 ~ ∫d3q f B(q0;T) ImPem • Hard-Thermal-Loop • ~ lattice-QCD rate • “matching” HG - QGP at ~Tc: • resonance melting + chiral mixing • Quark-Hadron Duality at all Mee?! • (N.B.: perturbative QGP rate • chirally restored!)

  35. Outline 2.) Chiral Symmetry in QCD - Nonperturbative QCD, Chiral Breaking + Hadron Spectrum 3.) Thermal Electromagnetic Emission Rates - EM Spectral Function: Hadronic vs. Partonic Regimes 4.) Vector Mesons in Medium - Many-Body Theory, Spectral Functions + Chiral Partners (r-a1) 5.) Quark-Gluon Plasma Emission - Perturbative vs. Lattice-QCD Rates, “Quark-Hadron-Duality” 6.) Dilepton + Photon Spectra in Heavy-Ion Collisions - Space-Time Evolution, Phenomenology + Interpretation 7.) Summary and Conclusions

  36. 6.1 Fireball Evolution in Heavy-Ion Collisions Thermal Dilepton Spectrum: Isentropic Trajectories in the Phase Diagram mN [GeV] t [fm/c] • “chemical” freezeout Tchem~ Tc ~170MeV, “thermal” freezeout Tfo ~ 120MeV • conserve entropy + baryon no.: Ti → Tchem → Tfo • time scale: hydrodynamics, fireball VFB(t ) = (z0+vz t ) p (r0 + 0.5a┴ t 2)2

  37. 6.2 Mass vs. Temperature Correlation • generic space-time argument: •  • Tmax ≈ M / 5.5 • (forImPem =const) • thermal photons: • Tmax≈ (q0/5) * (T/Teff)2 • → reduced by flow blue-shift! • Teff ~ T * √(1+b)/(1-b)

  38. Lower SPS Energy (Ti ~ 170MeV→ Tfo~100MeV) • enhancement increases!? • supports importance of • baryonic effects 6.3 Low-Mass Di-Electrons: CERES/NA45 Top SPS Energy (Ti ~ 200MeV → Tfo~110 MeV) [RR+Wambach ‘99] • QGP contribution small • medium effects! • drop. mass or broadening?!

  39. quantitative theory? 6.4 In-In at SPS: Dimuons from NA60 [Damjanovic et al. PRL ’06] • excellent mass resolution and statistics • for the first time, dilepton excessspectra could be extracted!

  40. 6.3.2 NA60 Data Before Acceptance Correction emp. ampl. + fireball hadr. many-body + fireball schem. broad./drop. + HSD transport chiral virial + hydro • Discrimination power of model calculations improved, but … • can compensate spectral “deficit” by larger flow: lift pairs into acceptance

  41. 6.3.3 NA60 II: Acceptance-Corrected Mass Spectra Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion [CERN Courier Nov. 2009] • Thermal source! • Low-mass: good sensitivitiy to medium effects, T~130-170MeV • Intermediate-mass: QGP vs. hadronic, T~160-210MeV

  42. 6.3.4 Spectrometer m+m- Excess Spectra In-In(158AGeV) [NA60 ‘09] Thermal m+m-Emission Rate Mmm [GeV] [van Hees+RR ’08] • in-med r + 4p + QGP • invariant-mass spectrum directly • reflects thermal emission rate!

  43. 6.3.5 Chronometer In-In Nch>30 • direct measurement of fireball lifetime: tFB≈ (6.5±1) fm/c • non-monotonous around critical point?

  44. 6.3.6 Intermediate-Mass Dileptons: Thermometer • QGP or Hadron Gas (HG) radiation? Emission rates “dual” … • vary critical temperature Tcin fireball evolution Tc=190MeV Tc=160MeV • HG emission: • r spectral fct. (2p) • + 4p→m+m- • (e.g. pa1 , pw → m+m-) • partition QGP vs. HG depends on “Tc” (spectral shape “dual”) • initial temperature Ti ~ 190-220 MeV at CERN-SPS

  45. 6.3.7 Dimuon pt-Spectra + Slopes: Barometer Effective Slopes Teff • slopes originally too soft • increase fireball acceleration, • e.g. a┴ = 0.085/fm → 0.1/fm • insensitive to Tc = 160-190 MeV

  46. 6.4 Summary of EM Probes at SPS In(158AGeV)+In Mmm [GeV] • calculated with same • EM spectral function!

  47. 6.4.2 Conclusions from Dilepton “Excess” Spectra • thermal source (T~120-210MeV) • M < 1GeV: in-medium r meson • - no significant mass shift • - avg. Gr(T~150MeV)~350-400MeV • Gr (T~Tc) ≈ 600 MeV → mr • - driven by baryons, good sensitivity • M > 1GeV: radiation around Tc • fireball lifetime “measurement”: • tFB ~ (6.5±1) fm/c (In-In) [van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ’08, Santini et al ‘10] Mmm [GeV]

  48. 6.5 Low-Mass e+e- at RHIC: PHENIX vs STAR • large enhancement not accounted • for by theory • cannot be QGP radiation … • enhancement closer to theory

  49. 6.6 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation • Teffexcess = (220±25) MeV • QGP radiation? • radial flow? • v2g,dir as large as for pions!? • underpredcited by QGP-dominated • emission [Holopainen et al ’11]

  50. 6.6.2 Thermal Photon Radiation thermal + prim. g • Empirical fireball constrained by • p, K, p and f spectra + v2 • same rate-model as for dileptons • both spectral slope and v2 point at • blue-shifted hadronic source… [van Hees,Gale+RR ’11]

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