1 / 55

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.

kennan
Télécharger la présentation

Theory of Thermal Dilepton Emission

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. 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]

More Related