Electromagnetic probes: Messengers from the hot and dense fireball

Transcription

1 Electromagnetic probes: Messengers from the hot and dense fireball Hendrik van Hees Goethe University Frankfurt November 5, 2014 Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

2 Outline 1 Electromagnetic probes and hadron resonances Em. current correlation function and electromagnetic probes Sources of dilepton emission in heavy-ion collisions Thermal (effective hadronic) QFT approach Kinetic theory (transport) approach 2 Dileptons in pp, pn, pa, AA in pure transport (GiBUU with J. Weil) GiBUU Dalitz decays of hadron resonances Baryon-resonance model at SIS energies Dielectrons (SIS/HADES) 3 Dileptons at SPS and RHIC (with Ralf Rapp) 4 Conclusions Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

3 Em. current correlator in-medium approaches l + l and γ rates Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

4 Em. current correlation function and electromagnetic Probes photon and dilepton thermal emission rates given by same electromagnetic-current-correlation function (J µ = f Q f ψ f γ µ ψ f ) [MT85, Wel90, GK91] q 0 Π < µν(q) = d 4 xexp(iq x) J µ (0)J ν (x) T = 2f B(q u)imπ (ret) µν (q) dn γ d 4 xd 3 q = α 2π 2 gµν Im Π (ret) µν (q) f B(q u) q0 = q dn e + e d 4 xd 4 q = α 2 gµν 3q 2 π 3 ImΠ(ret) µν (q) f B (q u) q 2 =M 2 e + e u: four-velocity of the fluid cell; p u = p hb 0 to lowest order in α: e 2 Π µν Σ (γ) µν vector-meson dominance model: Σ γ µν = energy in heat-bath frame G ρ Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

5 Sources of dilepton emission in heavy-ion collisions 1 initial hard processes: Drell Yan 2 core emission from thermal source 1 dn (thermal) = q T dmdq T d 4 x dy Mdϕ dn(thermal) d 4 xd 4 q 3 corona emission from primordial mesons (jet-quenching) 4 after thermal freeze-out emission from freeze-out mesons [CF74] [HR08, HR06] d N (fo) 3 q = q 0 q µ dσ µ f B (u µ q µ /T) Γ meson l + l Γ meson Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

6 Hadronic many-body theory HMBT for vector mesons [Ko et al, Chanfray et al, Herrmann et al, Rapp et al,...] ππ interactions and baryonic excitations ρ π B *, a 1, K 1,... ρ ρ ρ π N, K, π,... +corresponding vertex corrections gauge invariance Baryon (resonances) important, even at RHIC with low net baryon density n B n B reason: n B +n B relevant (CP inv. of strong interactions) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

7 Rapp-Wambach model pion cloud: dressing with baryon resonance excitations [RW00] direct ρ-n/ interactions [RW00] direct ρ-heavy-meson interactions [GR99] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

8 Photoabsorption on nucleons and nuclei important: fit of model parameters to data particle-data book: decay widths, branching rations,... photo-absorption on nucleons and nuclei [RW00] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

9 Meson contributions to ρ-selfenergy 70 Im Σ ρ /m ρ [MeV] T=150MeV q=0.3gev ω sum a 1 10 K 1 h 1 π 0 f 1 30 sum Re Σ ρ /m ρ [MeV] ω K 1 a 1 20 [GR99, RW00] M [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

10 In-medium spectral functions and baryon effects ρ(770) T=0 T=120 MeV T=150 MeV T=175 MeV -Im D ρ (GeV -2 ) [GR99, RW00] M (GeV) baryon effects important large contribution to broadening of the peak responsible for most of the strength at small M Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

11 In-medium spectral functions and baryon effects ω(782) T=0 T=120 MeV T=150 MeV T=175 MeV -Im D ω (GeV -2 ) 10 5 [GR99, RW00] M (GeV) baryon effects important large contribution to broadening of the peak responsible for most of the strength at small M Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

12 In-medium spectral functions and baryon effects -Im D φ (GeV -2 ) T=0 T=120 MeV T=150 MeV T=175 MeV φ(1020) [GR99, RW00] M (GeV) baryon effects important large contribution to broadening of the peak responsible for most of the strength at small M Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

13 Intermediate masses: hadronic 4π contributions e.m. current-current correlator τ 2nπ -Im Π V,A /(π M 2 ) V [τ 2n π ν τ ] V [τ 2 π ν τ ] ρ + cont. 2π (ρ) 4π (fit) -Im Π V,A /(π M 2 ) A [τ (2n+1) π ν τ ] A [τ 3 π ν τ ] a 1 + cont. 3π (a 1 ) 5π (fit) M 2 (GeV 2 ) M 2 (GeV 2 ) 4π contributions : π + ω,a 1 µ + + µ leading-order virial expansion for four-pion piece additional strength through chiral mixing [HR08, HR06] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

14 Dileptons from thermal QGP in QGP phase: q q annihilation HTL improved electromagnetic current correlator q γ iπ em,qgp = γ or em. current correlator from the lattice [DFK + 11] (extrapolated to finite q) quark-hadron duality around T c q [Rap13] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

15 Dilepton rates: Hadron gas QGP in-medium hadron gas matches with QGP similar results also for γ rates quark-hadron duality? [Rap13] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

16 Kinetic theory (transport) approach cross sections in collision terms: same physics as in QFT approaches Fermi s golden rule: S-matrix amplitudes Mji 2 self-energy diagrams other way around: cut self-energy diagrams S-matrix amplitudes p/n N/ ρ p/n p/n N/ ρ π... [FHK + 11] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

17 Dileptons in pp, pn, pa, AA pure transport: GiBUU (with Janus Weil) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

18 The GiBUU Model Boltzmann-Uehling-Uhlenbeck (BUU) framework for hadronic transport reaction types: pa, πa, γa, ea, νa, AA open-source modular Fortran 95/2003 code version control via Subversion publicly available realeases: Review on hadronic transport (GiBUU): [BGG + 12] all calculations for dileptons: J. Weil Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

19 Resonance Model reactions dominated by resonance scattering: ab R cd Breit-Wigner cross-section formula 2s R + 1 4π σ ab R cd = (2s a + 1)(2s b + 1) p 2 lab sγ ab R Γ R cd (s m 2 R )2 + sγ 2 tot applicable for low-energy nuclear reactions E kin 1.1 GeV example: σ π p π p [Teis (PhD thesis 1996), data: Baldini et al, Landolt-Börnstein 12 (1987)] σ (mb) Daten total (1232) N(1440) N(1535) p lab (GeV/c) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

20 GiBUU: Resonance Model further cross sections Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

21 GiBUU: Extension to HADES energies [WHM12, WM13] keep same resonances (parameters from Manley analysis) production channels in Teis: NN N, NN NN,N, NN extension to NN N,, NN NNπ, NN NNρ,NNω,NNπω,NNφ, NN BYK (B = N,, Y = Λ,Σ) [WHM12, WM13] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

22 GiBUU Extension to HADES energies good description of total pp, pn (inelastic) cross section dilepton sources Dalitz decays: π 0,η γl + l ; ω π 0 l + l, Nl + l ρ,ω,φ l + l : invariant mass l + l spectra spectral properties of vector mesons for details, see [WHM12] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

23 Exclusive pion production: p+p (3.5 GeV) (SIS/HADES) exclusive p + p p + n + π + left: M pπ + spectrum; right: M nπ + spectrum model 1: GiBUU; model 2: UrQMD chance to refine resonance models further! Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

24 GiBUU: ρ meson in pp production through hadron resonances NN NR NNρ, NN N NNπρ ρ -line shape modified already in elementary hadronic reactions due to production mechanism via resonances Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

25 GiBUU: meson in VMD model so far: -Dalitz decay treated separately from other resonances now: treating as all other resonances via VMD model model for em. transition form factor Γ [GeV] πn Manley πn Moniz πn Bass (ρn) P Manley + ρn m [GeV] [WEH + 14] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

26 GiBUU: meson in VMD model so far: -Dalitz decay treated separately from other resonances now: treating as all other resonances via VMD model model for em. transition form factor 10 0 πn Manley πn Moniz πn Bass Manley + ρn A [GeV -2 ] m [GeV] [WEH + 14] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

27 GiBUU: meson in VMD model so far: -Dalitz decay treated separately from other resonances now: treating as all other resonances via VMD model model for em. transition form factor p + p at 1.25 GeV dσ/dm ee [µb/gev] data GiBUU total π 0 e + e - γ QED VMD N* VMD Brems. OBE dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

28 GiBUU: meson in VMD model so far: -Dalitz decay treated separately from other resonances now: treating as all other resonances via VMD model model for em. transition form factor d + p at 1.25 GeV dσ/dm ee [µb/gev] data GiBUU total π 0 e + e - γ η e + e - γ QED VMD N* VMD Brems. OBE dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

29 GiBUU: meson in VMD model so far: -Dalitz decay treated separately from other resonances now: treating as all other resonances via VMD model model for em. transition form factor p + p at 2.2 GeV dσ/dm ee [µb/gev] data GiBUU total ω e + e - ω π 0 e + e - π 0 e + e - γ η e + e - γ QED VMD N* VMD * VMD Brems. OBE dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

30 GiBUU: meson in VMD model so far: -Dalitz decay treated separately from other resonances now: treating as all other resonances via VMD model model for em. transition form factor p + p at 3.5 GeV dσ/dm ee [µb/gev] data GiBUU total ω e + e - φ e + e - ω π 0 e + e - π 0 e + e - γ η e + e - γ QED VMD N* VMD * VMD Brems. OBE dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

31 GiBUU: p+nb (3.5 GeV) (SIS/HADES) with vacuum spectral functions: p + Nb at 3.5 GeV dσ/dm ee [µb/gev] preliminary data GiBUU total ρ e + e - ω e + e - φ e + e - ω π 0 e + e - π 0 e + e - γ η e + e - γ Ne + e dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

32 GiBUU: p+nb (3.5 GeV) (SIS/HADES) with medium modified spectral functions: p + Nb at 3.5 GeV dσ/dm ee [µb/gev] prelim. data vac CB CB+shift shift ρ dilepton mass m ee [GeV] ω no definite hint for medium modifications in p Nb Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

33 GiBUU: p+nb (3.5 GeV) (SIS/HADES) medium effects built in transport model binding effects, Fermi smearing, Pauli blocking final-state interactions production from secondary collisions sensitivity on medium effects of vector-meson spectral functions? p + Nb at 3.5 GeV dσ/dm ee [µb/gev] prelim. data vac CB CB+shift shift ρ dilepton mass m ee [GeV] ω Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

34 GiBUU: Ar+KCl (1.76AGeV) (SIS/HADES) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

35 GiBUU: Ar+KCl (1.76AGeV) (SIS/HADES) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

36 GiBUU (NEW!): Au+Au (1.23 AGeV) (SIS/HADES) Au GeV 1/N π 0 dn/dm ee acceptance from pp@ GeV < p lep < 1.1 GeV θ ee > 9 GiBUU total Res VMD ππ ω e + e - φ e + e - ω π 0 e + e - π 0 e + e - γ η e + e - γ QED VMD pn Brems. pp Brems. πn Brems dilepton mass m ee [GeV] caveat: pp/np acceptance filter with single-e cut, p t < 100 MeV correct filter urgently needed! comparison to preliminary HADES data [Gal14] room for medium modifications (data points not shown here on request of the HADES collaboration) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

37 GiBUU (NEW!): π+p (566 MeV) (SIS/HADES) dσ/dm ee [µb/gev] π - + p, E kin = GeV GiBUU total π 0 e + e - γ η e + e - γ πn Brems. N* VMD D 13 (1520) S 11 (1535) QED VMD * VMD dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

38 GiBUU (NEW!): π+p (566 MeV) (SIS/HADES) transverse momentum p T [GeV] dσ/dp T [µb/gev] dσ/dp T [µb/gev] m < 140 MeV 140 MeV < m < 280 MeV 280 MeV < m dσ/dy [µb] GiBUU total N* VMD * VMD π 0 e + e - γ η e + e - γ πn Brems. QED VMD dσ/dy [µb] rapidity y Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

39 GiBUU (NEW!): π+c (566 MeV) (SIS/HADES) dσ/dm ee [µb/gev] π - + C, E kin = GeV GiBUU total π 0 e + e - γ η e + e - γ πn Brems. pn Brems. N* VMD D 13 (1520) S 11 (1535) QED VMD * VMD dilepton mass m ee [GeV] Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

40 GiBUU (NEW!): π+c (566 MeV) at (SIS/HADES) transverse momentum p T [GeV] dσ/dp T [µb/gev] dσ/dp T [µb/gev] dσ/dy [µb] m < 140 MeV 140 MeV < m < 280 MeV 280 MeV < m GiBUU total π 0 e + e - γ η e + e - γ πn Brems. pn Brems. N* VMD D 13 (1520) S 11 (1535) QED VMD * VMD dσ/dy [µb] rapidity y Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

41 Dileptons at SPS and RHIC thermal fireball model (with Ralf Rapp) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

42 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm all q T NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

43 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 0<q t <0.2 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

44 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 0.2 GeV<q t <0.4 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

45 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 0.4 GeV<q t <0.6 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

46 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 0.6 GeV<q t <0.8 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

47 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 0.8 GeV<q t <1.0 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

48 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 1.0 GeV<q t <1.2 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

49 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 2.0 GeV<q t <2.2 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

50 M spectra (in p T slices) NA60 experiment: dimuon measurement (In-In collisions at top SPS energy) (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) T c =T ch =175 MeV, a t =0.1 c 2 /fm 2.2 GeV<q t <2.4 GeV NA60 in-med ρ QGP prim ρ FO ρ 4π mix DY ω-t ex ωφ total +ω-t ex [HR06, HR08] M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

51 Importance of baryon effects baryonic interactions important! in-medium broadening low-mass tail! (1/N ch ) d 2 N µµ /(dm dη) (20 MeV) NA60 no baryons full model all q T T c =T ch =175 MeV, a t =0.1 c 2 /fm M (GeV) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

52 Update: Using lattice equation of state use equation of state from lattice calculations (cross over!) use QGP rates adapted to recent lattice results IMR slope: true (average) temperature of source (no blue shift as in q T spectra!): T MeV (above T c 160 MeV!) Dimuon Yield dn µµ /dm µµ [(20 MeV) -1 ] T c =170 MeV, T ch =160 MeV, EoS-L all q T total 4π mix QGP NA Dimuon Invariant Mass M µµ (GeV/c 2 ) compatible with coarse-grained UrQMD calculation (see Stephan Endres s talk!) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

53 RHIC beam-energy scan (STAR) dielectron spectra Au+Au collisions ( s NN = 200 GeV) at RHIC/STAR same model as before successful over wide range of beam energies [Rap13] NB: together with CG UrQMD also at SIS energies! (see S. Endres s talk) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

54 RHIC beam-energy scan (STAR) dielectron spectra Au+Au collisions at RHIC same model as before successful over wide range of beam energies [Rap13] NB: together with CG UrQMD also at SIS energies! (see S. Endres s talk) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

55 RHIC beam-energy scan (STAR) N l + l /Nch fireball model lifetime, dilepton excess, temperature as fct. of s NN indications of phase transition??? HGvac HGmed QGP HGvac+QGP HGmed+QGP τfb 0.3GeV < M < 0.7GeV τfb(fm/c) T (GeV) Fit range: 1.5GeV < M < 2.5GeV snn (GeV) snn GeV Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

56 Conclusions General ideas em. probes in-medium em. current-correlation function effective QFT models for hadronic interactions and l + l (and γ!) production HTL improved or lattice QGP l + l (and γ) rates dual rates around T c (compatible with χ symmetry restoration) medium modifications of ρ, ω, φ importance of hadron-resonance interactions baryon resonances prevalent for medium effects reliable input on resonance physics in elementary reactions crucial! need to fix masses, couplings, form factors (including em. transition FFs) Application to dileptons in HICs thermal fireball, (ideal) hydrodynamics, (coarse-grained) transport, hybrid... equation of state compatibility with QFT/transport models!?! use of thermal-qft spectral VM functions successful description at HADES, SPS, and RHIC (STAR) consistent description of M and m T spectra! not too sensitive to details of medium evolution beam-energy scan at RHIC and FAIR signature of phase transition? sensitivity to equation of state? signature of cross-over vs. 1st order (or even critical endpoint)? effective slope of M spectra in higher IMR (1.5 GeV < M < M J/ψ ) provides T Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

57 Bibliography I [BGG + 12] O. Buss, et al., Transport-theoretical Description of Nuclear Reactions, Phys. Rept. 512 (2012) 1. [CF74] [DFK + 11] [FHK + 11] F. Cooper, G. Frye, Single-particle distribution in the hydrodynamic and statistical thermodynamics models of multiparticle production, Phys. Rev. D 10 (1974) H.-T. Ding, et al., Thermal dilepton rate and electrical conductivity: An analysis of vector current correlation functions in quenched lattice QCD, Phys. Rev. D 83 (2011) B. Friman, et al. (eds.), The CBM Physics Book, vol. 814 of Lecture Notes in Physics, Springer-Verlag, Berlin, Heidelberg (2011). PhysicsBook.html Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

58 Bibliography II [Gal14] [GK91] [GR99] [HR06] [HR08] T. Galatyuk, HADES overview, Nucl. Phys. A (2014), published online; DOI: /j.nuclphysa C. Gale, J. I. Kapusta, Vector Dominance Model at Finite Temperature, Nucl. Phys. B 357 (1991) C. Gale, R. Rapp, Rho Properties in a hot Gas: Dynamics of Meson-Resonances, Phys. Rev. C 60 (1999) H. van Hees, R. Rapp, Comprehensive interpretation of thermal dileptons at the SPS, Phys. Rev. Lett. 97 (2006) H. van Hees, R. Rapp, Dilepton Radiation at the CERN Super Proton Synchrotron, Nucl. Phys. A 806 (2008) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

59 Bibliography III [MT85] [Rap13] [RW00] L. D. McLerran, T. Toimela, Photon and dilepton emission from the quark-gluon plasma: some general considerations, Phys. Rev. D 31 (1985) R. Rapp, Dilepton Spectroscopy of QCD Matter at Collider Energies, Adv. High Energy Phys (2013) R. Rapp, J. Wambach, Chiral symmetry restoration and dileptons in relativistic heavy-ion collisions, Adv. Nucl. Phys. 25 (2000) 1. [WEH + 14] J. Weil, S. Endres, H. van Hees, M. Bleicher, U. Mosel, Dilepton Production in Transport-based Approaches (2014). [Wel90] H. A. Weldon, Reformulation of finite temperature dilepton production, Phys. Rev. D 42 (1990) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45

60 Bibliography IV [WHM12] [WM13] J. Weil, H. van Hees, U. Mosel, Dilepton production in proton-induced reactions at SIS energies with the GiBUU transport model, Eur. Phys. J. A 48 (2012) epja/i J. Weil, U. Mosel, Dilepton production at SIS energies with the GiBUU transport model, J. Phys. Conf. Ser. 426 (2013) Hendrik van Hees (GU Frankfurt) Electromagnetic probes November 5, / 45