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Theory of Thermal Electromagnetic Radiation

Theory of Thermal Electromagnetic Radiation

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Theory of Thermal Electromagnetic Radiation

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  1. Theory of Thermal Electromagnetic Radiation Ralf Rapp Cyclotron Institute + Dept. of Physics & Astronomy Texas A&M University College Station, Texas USA JET Summer School The Ohio State University (Columbus, OH) June 12-14, 2013

  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: • hadronic matter → Quark-Gluon Plasma? √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 • quantitative description?

  7. 1.6 Phase Transition(s) in Lattice QCD - - ≈ qq / qq Tpcchiral~150MeV Tpcconf ~170MeV [Fodor et al ’10] • different “transition” temperatures?! • extended transition regions • partial chiral restoration in “hadronic • phase”! (low-mass dileptons!) • leading-order hadron gas

  8. 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

  9. 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) _

  10. 2.2 Chiral Symmetry in QCD Lagrangian g qL (bare quark masses: mu ≈ md ≈ 5-10MeV ) qL ChiralSU(2)V × SU(2)A transformation: Up to O(mq),LQCDinvariant under Rewrite LQCDusing left- and right-handed quark fields qL,R=(1±g5)/2 q : Invariance under isospin and “handedness”

  11. qR qL > > > > - - qR qL 2.3 Spontaneous Breaking of Chiral Symmetry - strong qq attraction  Chiral Condensate fills QCD vacuum: [cf. Superconductor: ‹ee›≠0 , Magnet ‹M› ≠ 0 , … ] Simple Effective Model: • assume “mean-field” , expand: • linearize: • free energy: • ground • state: Gap Equation

  12. JP=0±1± 1/2± 2.3.2 (Observable) Consequences of SBCS • mass gap , not observable! • but: hadronic excitations reflect SBCS • “massless” Goldstone bosons p 0,± • (explicit breaking: fp2 mp2= mq ‹qq›) • “chiral partners” split:DM ≈ 0.5GeV! • chiral trafo: , • Vector mesons r and w: - -ieijktk chiral singlet

  13. 2.3.3 Manifestation 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. ● chiral breaking:|q2| ≤ 1 GeV2 • quantify chiral breaking?

  14. 2.4 Chiral (Weinberg) Sum Rules • Quantify chiral symmetry breaking via observable spectral functions • Vector (r) - Axialvector (a1) spectral splitting [Weinberg ’67, Das et al ’67] t→(2n+1)p t→(2n)p [ALEPH ‘98, OPAL ‘99] pQCD pQCD • Key features of updated “fit”: [Hohler+RR ‘12] • r+a1 resonance, excited states (r’+a1’), universal continuum (pQCD!)

  15. 2.4.2 Evaluation of Chiral Sum Rules in Vacuum • pion decay • constants • chiral quark • condensates • vector-axialvector splitting (one of the) cleanest observable of • spontaneous chiral symmetry breaking • promising (best?) starting point to search for chiral restoration

  16. 2.5 QCD Sum Rules: r and a1 in Vacuum • dispersion relation: [Shifman,Vainshtein+Zakharov ’79] • lhs: hadronic spectral fct. • rhs: operator product expansion • 4-quark + gluon condensate dominant

  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. 3.1 EM Correlator + Thermal Dilepton Rate g*(q) e+ e- (T,mB) [McLerran+Toimela ’85] Im Πem(M,q;T,mB) • EM Correlation Fct.: • Quark basis: • Hadron basis: → 9 : 1 : 2

  19. 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

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

  21. 3.4 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 = lim(q0→0) [ -ImΠem(q0,q=0)/2q0 ]

  22. 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

  23. |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

  24. 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

  25. 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

  26. gN gA p-ex 4.3.2 r Spectral Function in Nucl. Photo-Absorption On the Nucleon On Nuclei • fixes coupling constants and • formfactor cutoffs for rNB • 2.+3. resonances melt • (selfconsistent N(1520)→Nr) [Urban,Buballa,RR+Wambach ’98]

  27. 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

  28. Hot Meson Gas rB/r0 0 0.1 0.7 2.6 [RR+Gale ’99] 4.5r-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

  29. 4.6 Light Vector Mesons “at RHIC + LHC” • baryon effects remain important at rB,net = 0: • sensitive to rB,tot= rB + rB(r-N = r-N, CP-invariant) • w also melts, f more robust ↔ OZI - - [RR ’01]

  30. = = 4.7 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”)

  31. p Sp Sp Sp r Sr Sr Sr 4.8 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:

  32. 4.9 QCD + Weinberg Sum Rules in Medium [Hatsuda+Lee’91, Asakawa+Ko ’93, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05] [Weinberg ’67, Das et al ’67; Kapusta+Shuryak ‘94] T [GeV] rV,A/s Vacuum T=140MeV T=170MeV s [GeV2] [Hohler et al ‘12] • melting scenario quantitatively compatible with chiral restoration • microscopic calculation of in-medium axialvector to be done

  33. 4.10 Chiral Condensate + r-Meson Broadening > Sp effective hadronic theory > - • h = mq h|qq|h > 0 contains quark core + pion cloud • = Shcore + Shcloud ~ ++ • matches spectral medium effects: resonances + pion cloud • resonances + chiral mixing drive r-SF toward chiral restoration Sp r - - qq / qq0

  34. 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

  35. e+ e- q q _ Sq 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 dRee/d4q 1.45Tc q=0 • marked low-mass enhancement • comparable to recent lattice-QCD • computations [Ding et al ’10]

  36. 5.2 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 …

  37. 5.2.2 Back to Spectral Function -Im Pem /(C T q0) • suggestive for approach to chiral restoration and deconfinement

  38. 5.3 Summary of Dilepton Rates: HG vs. QGPdRee /dM2 ~ ∫d3q f B(q0;T) ImPem • Lattice-QCD rate somwhat below Hard-Thermal Loop • hadronic→QGP toward Tpc: resonance melting + chiral mixing • Quark-Hadron Duality at all Mee?! (QGP rates chirally restored!)

  39. 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

  40. 6.1 Space-Time Evolution + Equation of State • Evolve rates over • fireball expansion: • 1.order → lattice EoS: • - enhances temperature above Tc • - increases “QGP” emission • - decreases “hadronic” emission • initial conditions affect lifetime • simplified: parameterize space-time • evolution by expanding fireball • benchmark bulk-hadron observables Au-Au (200GeV) [He et al ’12]

  41. 6.1.2 Bulk Hadron Observables: Fireball Model [van Hees et al ’11] • Mulit-strange hadrons freeze-put at Tpc • Bulk-v2 saturates at ~Tpc

  42. 6.2 Di-Electron Spectra from SPS to RHIC Pb-Au(8.8GeV) Au-Au (20-200GeV) QM12 Pb-Au(17.3GeV) • consistent excess emission source • suggests “universal” medium effect around Tpc • FAIR, LHC? [cf. also Bratkovskaya et al, Alam et al, Bleicher et al, Wang et al …]

  43. + full acceptance correction… 6.3 In-In at SPS: Dimuons from NA60 • excellent mass resolution and statistics • for the first time, dilepton excessspectra could be extracted! [Damjanovic et al ’06]

  44. 6.3.2 NA60 Multi-Meter: Accept.-Corrected Spectra Spectrometer Emp. scatt. ampl. + T-r approximation Hadronic many-body Chiral virial expansion Chronometer Thermometer [CERN Courier Nov. 2009] • Thermal source! • Low-mass: good sensitivity to medium effects, T~130-170MeV • Intermediate-mass: T ~ 170-200 MeV > Tpc • Fireball lifetime tFB = (6.5±1) fm/c

  45. 6.3.3 Spectrometer m+m- Excess Spectra In-In(17.3AGeV) [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!

  46. 6.4 Conclusions from Dilepton “Excess” Spectra • thermal source (T~120-230MeV) • in-medium r meson spectral function • - avg. Gr(T~150MeV)~350-400MeV • Gr (T~Tpc) ≈ 600 MeV → mr • - “divergent” width ↔ Deconfinement?! • M > 1.5 GeV: QGP radiation • 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]

  47. 6.5 The RHIC-200 Puzzle in Central Au-Au • PHENIX, STAR and theory: • - consistent in non-central collisions • - tension in central collisions

  48. 6.6 Direct Photons at RHIC Spectra Elliptic Flow ← excess radiation • Teffexcess = (220±30) MeV • QGP radiation? • radial flow? • v2g,dir as large as for pions!? • underpredcited by QGP-dominated • emission [Holopainen et al ’11, Dion et al ‘11]

  49. 6.6.2 Thermal Photon Radiation thermal + prim. g [van Hees, Gale+RR ’11] • flow blue-shift: Teff ~ T √(1+b)/(1-b) , b~0.3: T ~ 220/1.35 ~160 MeV • “small” slope + large v2 suggest main emission around Tpc • other explanations…? [Skokov et al ‘12; McLerran et al ‘12]

  50. 6.7 Direct Photons at LHC Spectra Elliptic Flow ● ALICE [van Hees et al in prep] • similar to RHIC (not quite enough v2) • non-perturbative photon emission rates around Tpc?