Dileptons in Heavy-Ion Collisions and Chiral Symmetry Hendrik van Hees Justus-Liebig Universit¨ at Gießen September 10, 2010 JUSTUS-LIEBIG- Institut für UNIVERSITÄT GIESSEN Theoretische Physik Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 1 / 20
Outline Electromagnetic probes in heavy-ion collisions 1 Dileptons at SIS energies 2 Dileptons at SPS and RHIC 3 Conclusions 4 Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 2 / 20
Electromagnetic probes in heavy-ion collisions γ, ℓ ± : no strong interactions π 0 , η Dalitz decays reflect whole “history” of collision: ρ/ω from pre-equilibrium phase Φ from thermalized medium QGP and hot hadron gas dN/(dy dm) from VM decays after thermal DD J/ Ψ freezeout ψ ’ Drell−Yan Low− Intermediate− High−Mass Region > 10 fm > 1 fm < 0.1 fm π , ... 0 1 2 3 4 5 ρ/ω γ ∗ e − M [GeV/c] Fig. by A. Drees e + Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 3 / 20
Vector Mesons and electromagnetic Probes ℓ + ℓ − thermal emission rates ⇔ em. current-correlation function, Π µν [L. McLerran, T. Toimela 85, H. A. Weldon 90, C. Gale, J.I. Kapusta 91] α 2 d N e + e − � d 4 x d 4 q = − g µν 3 q 2 π 3 Im Π (ret) µν ( q ) f B ( q 0 ) � � q 2 = M 2 e + e − vector-meson dominance model: G ρ Π µν = γ ∗ γ ∗ hadronic many-body theory for vector mesons * π B , a , K ,... 1 1 ρ ρ ρ ρ π N, K, π,... elementary processes ⇔ cut self-energy diagrams Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 4 / 20
Relation to the QCD-phase diagram at high temperature/density: restoration of chiral symmetry Lattice QCD: T χ c ≃ T deconf c Spectral Function Spectral Function " ρ " Dropping Masses? "a 1 " pert. QCD Melting Resonances? " ρ " pert. QCD "a 1 " Mass Mechanism of chiral restoration? Two main theoretical ideas � ¯ � “dropping masses”: m had ∝ ψψ “melting resonances”: broadening of spectra through medium effects More theoretical question: Realization of chiral symmetry in nature? Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 5 / 20
Dileptons at SIS energies dileptons from heavy-ion collisions at DLS at E = 1 A GeV [Porter et al, PRL 79 , 1229 (1997)] large enhancement at low invariant masses unexplained DLS puzzle [Fuchs et al (2003)] [Bratkovskaya et al (1999)] [Ernst et al (1998)] Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 6 / 20
Experimental solution DLS measurement confirmed by HADES at GSI [Sudol et al, EPJC 62 , 81 (2009)] Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 7 / 20
Theoretical “HADES Puzzle” one-boson-exchange model by Shyam/Mosel Bremsstrahlung in pp and pn collisions + e − e N γ * ∆ N* (a) π,ρ,σ,ω pp pn (b) (d) (c) + ρ − + ρ − ρ ρ , , Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 8 / 20
Recent update: π em. form factors 2 p + p 1.25 GeV 10 2 )] 0 decay 1 ρ d σ /dM [ µ b/(GeV/c 10 0 Dalitz decay π 0 10 Total QM (NEFF) Total QM (FF2) -1 10 Sum problems with the pn -2 10 bremsstrahlung contributions -3 10 importance of π formfactors for -4 10 2 10 radiation from the charged-meson quasi-free p + n 1.25 GeV 2 )] 1 10 d σ /dM [ µ b/(GeV/c exchange line 0 η Dalitz decay 10 -1 10 here form factors from -2 10 -3 [ G. E. Brown, M. Rho, and W. Weise, NPA 454 , 669 10 -4 10 (1986)] -5 10 -6 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 2 ) M (GeV/c [R. Shyam, U. Mosel, arXiv:1006.3873 [hep-ph] ] Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 9 / 20
GiBUU Gießen Boltzmann-Uehling-Uhlenbeck transport model describes pp data also here importance of em. form factors ∆ -Dalitz decay with form factors from [Q. Wan, F. Iachello, IJMPA 20 , 1846 (2005)] [J. Weil, private communication] Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 10 / 20
Dileptons at SPS and RHIC radiation from thermal sources: Hadronic many-body theory [R. Rapp, J. Wambach 99] baryon effects important n B + n ¯ B relevant quantity (not net-baryon density)! * π B , a , K ,... 1 1 ρ ρ ρ ρ π N, K, π,... Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 11 / 20
Dilepton rates: Hadron gas ↔ QGP in-medium hadron gas matches with QGP similar results also for γ rates “quark-hadron duality”!? consistent with chiral-symmetry restoration “resonance melting” rather than “dropping masses” Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 12 / 20
Sources of dilepton emission in heavy-ion collisions 1 initial hard processes: Drell Yan 2 “core” ⇔ emission from thermal source [McLerran, Toimela 1985] d N ( thermal ) M d ϕ d N ( thermal ) 1 � � � d 4 x = d y Acc ( M, q T , y ) d 4 x d 4 q q T d M d q T use cylindrical thermal fireball with QGP, mixed and hadronic phase 3 “corona” ⇔ emission from “primordial” mesons (jet-quenching) 4 after thermal freeze-out ⇔ emission from “freeze-out” mesons [Cooper, Frye 1975] � d 3 q � q µ d σ µ f B ( u µ q µ /T )Γ meson → ℓ + ℓ − N ( fo ) = Acc q 0 Γ meson Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 13 / 20
CERES/NA45 dielectron spectra good agreement also for dielectron spectra in 158 GeV Pb-Au low-mass tail from baryon effects 35% Central Pb(158AGeV)+Au −6 ×10 -1 1.8 2 N ee /d η dM) / (dN ch /d η ) [100MeV] CERES ’00 Pb(158 AGeV)+Au <N ch >=250 CERES ’95+’96 -1 1.6 -5 in-med ρ+ω+φ 2 ] 10 (7% central) free ρ (dN ee /dM) / <N ch > [100 MeV/c 4 π mix 1.4 <N ch >=335 in-med ρ+ω+φ +QGP+4 π QGP 1.2 p t >0.2GeV DY -6 2.1< η <2.65 total 10 1.0 Θ ee >35mrad total (no bar ρ ) 0.8 p t >0.2GeV 0.6 -7 Cocktail 10 2.1< η <2.65 0.4 Θ ee >35mrad 4 π QGP 0.2 -8 10 (d 0 0.2 0.4 0.6 0.8 1 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M ee [GeV] M ee [GeV] Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 14 / 20
Hadron spectra NA60: Extracted hadronic p T spectra from µ + µ − “cocktail” analysis of “cocktail”: hadron- m T spectra comparison to fireball evolution ⇔ fixes radial acceleration “sequential freeze-out” due to different coupling strength prim+fo 10 6 fo prim (1/m T ) dN/dm T (a.u.) NA60 ρ 10 5 10 4 ρ (semicentral) (0.6 GeV<M<0.9 GeV) T c =T ch =175 MeV, a T =0.1 c 2 /fm 10 3 0 0.5 1 1.5 2 2.5 m T -M (GeV) Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 15 / 20
Hadron spectra NA60: Extracted hadronic p T spectra from µ + µ − “cocktail” analysis of “cocktail”: hadron- m T spectra comparison to fireball evolution ⇔ fixes radial acceleration “sequential freeze-out” due to different coupling strength 10 7 prim+fo fo prim (1/m T ) dN/dm T (a.u.) 10 6 NA60 ω 10 5 10 4 ω (semicentral) T c =T ch =175 MeV a T =0.1 c 2 /fm, t fo =5 fm 10 3 0 0.5 1 1.5 2 2.5 m T -M (GeV) Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 15 / 20
Hadron spectra NA60: Extracted hadronic p T spectra from µ + µ − “cocktail” analysis of “cocktail”: hadron- m T spectra comparison to fireball evolution ⇔ fixes radial acceleration “sequential freeze-out” due to different coupling strength 10 7 prim+fo fo prim (1/m T ) dN/dm T (a.u.) 10 6 NA60 φ 10 5 10 4 φ (semicentral) T c =T ch =175 MeV a T =0.1 c 2 /fm, t fo =4 fm 10 3 0 0.5 1 1.5 2 2.5 m T -M (GeV) Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 15 / 20
M spectra (in p T slices) norm corrected by ∼ 3% due to centrality correction (min-bias data: � N ch � = 120 , calculation N ch = 140 ) T c =T ch =175 MeV, a t =0.1 c 2 /fm NA60 10 -5 in-med ρ all q T QGP prim ρ (1/N ch ) d 2 N µµ /(dM d η ) (20 MeV) -1 FO ρ 10 -6 4 π mix DY φ ω 10 -7 ω -t ex total + ω -t ex 10 -8 10 -9 0.2 0.4 0.6 0.8 1 1.2 1.4 M (GeV) Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 16 / 20
M spectra (in p T slices) norm corrected by ∼ 3% due to centrality correction (min-bias data: � N ch � = 120 , calculation N ch = 140 ) T c =T ch =175 MeV, a t =0.1 c 2 /fm NA60 10 -5 in-med ρ 0<q t <0.2 GeV QGP prim ρ (1/N ch ) d 2 N µµ /(dM d η ) (20 MeV) -1 FO ρ 10 -6 4 π mix DY φ ω 10 -7 ω -t ex total + ω -t ex 10 -8 10 -9 0.2 0.4 0.6 0.8 1 1.2 1.4 M (GeV) Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 16 / 20
M spectra (in p T slices) norm corrected by ∼ 3% due to centrality correction (min-bias data: � N ch � = 120 , calculation N ch = 140 ) T c =T ch =175 MeV, a t =0.1 c 2 /fm NA60 10 -5 in-med ρ 0.2 GeV<q t <0.4 GeV QGP prim ρ (1/N ch ) d 2 N µµ /(dM d η ) (20 MeV) -1 FO ρ 10 -6 4 π mix DY φ ω 10 -7 ω -t ex total + ω -t ex 10 -8 10 -9 0.2 0.4 0.6 0.8 1 1.2 1.4 M (GeV) Hendrik van Hees (JLU Gießen) Dileptons in heavy-ion collisions September 10, 2010 16 / 20
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