Theoretical Review of Dileptons from Heavy Ion Collisions

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1 Theoretical Review of Dileptons from Heavy Ion Collisions Hendrik van Hees Texas A&M University February 8, 28 Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 1 / 22

2 Outline 1 QCD, Chiral Symmetry, and Dileptons 2 Hadronic Models in Medium 3 Models vs. Experiments 4 Sensitivities to QCD Matter 5 Conclusions Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 2 / 22

3 Dileptons and in-medium em. current correlation function q γ l q l + M,q t 1.5 GeV π,... ρ/ω γ l M,q t 1.5 GeV l + Dilepton emission rate [McLerran, Toimela 85] dn e + e d 4 xd 4 q = gµν α2 em 3q 2 Im Π(em) π3 µν (q) f B (q ) q 2 =M 2 e + e [ ] Π (em) µν (q) = d 4 x exp(iq x)θ(x ) j µ (em) (x), j ν (em) () T l + l spectra in-medium em. current-current correlator Vector dominance in-medium modifications of vector mesons! Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 3 / 22

4 Chiral Symmetry Restoration light-quark sector of QCD: chiral symmetry spontaneously broken in vacuum ( qq ) high temperature/density: restoration of chiral symmetry Lattice QCD: Tc χ Tc deconf Im Π V,A /(πs) [dim. less] V [τ > 2nπ ν τ ] A [τ > (2n+1)π ν τ ] ρ(77) + cont. a 1 (126) + cont..2 "ρ" pert. QCD "a 1 " s [GeV 2 Mass ] Mechanism of chiral restoration? dropping masses : m had ψψ melting resonances : broadening of spectra through medium effects Spectral Function Spectral Function "ρ" Dropping Masses? "a 1 " pert. QCD Melting Resonances? Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 4 / 22

5 Weinberg sum rules ds M n = π sn [Im Π V (s) Im Π A (s)] M 2 = 1 3 f π 2 r 2 π FA, M 1 = fπ 2 M =, M 1 = cα s ( qq) 2 [Weinberg 67; Das et al 67; Kapusta, Shuryak 93] theory connection of chiral symm. restoration with dileptons in HICs Π V, Π A from chiral hadronic model at finite T, µ B compare M n (T, µ B ) to lqcd chiral order parameters at finite T compare Π V from hadronic model to dileptons from HICs also QCD sum rules relate current correlators to condensates VMD vector-meson spectral functions width in GeV ρ N = ρ κ = 2.36 S. Leupold, W. Peters, U. Mosel Nucl. Phys. A 628, 311 (1998) mass in GeV Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 5 / 22

6 Hadronic many-body theory pion-cloud modifications and baryonic/mesonic excitations [Chanfray et al, Herrmann et al, Ko et al, Rapp et al, Klingl et al, Post et al, Friman et al,...] ρ π B *, a 1, K 1,... ρ ρ ρ -Im D ρ (GeV -2 ) ρ(77) SPS vacuum T=12 MeV, ρ B =.1 ρ T=15 MeV, ρ B =.7 ρ T=175 MeV, ρ B =2.6 ρ M (GeV) π Im D ρ [GeV -2 ] N, K, π,... RHIC vacuum T=12MeV,ρ eff =.21ρ T=15MeV,ρ eff =.41ρ T=18MeV,ρ eff =.68ρ q=.3gev ρ(77) M [GeV] substantial broadening of vector mesons with little mass shift! baryon effects prevalent (ρ B + ρ B, not ρ B ρ B, relevant!) different approaches consistent if constrained by data (γn, γa, πn ρn) Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 6 / 22

7 Hadronic models vs. lattice QCD (dn ee /dm) / (dn ch /dy) [GeV -1 ] Dilepton Excitation Function in Central Au-Au (N part =33) QGP Isovector Susceptibility e 17 GeV (N ch =355) y e <.5, p t >.2GeV 4 4 GeV (N ch =415) µ q /T=1. 8 GeV (N ch =525) χ I /T 2 µ q /T=.8 2 GeV (N ch =735) µ q /T=.6 3 µ q /T=.4 µ q /T=.2 µ q /T=. Hadronic Matter M ee [GeV] χ q,i = T/T p µ q,i, µ q = µ u + µ d, µ I = µ u µ d excitation function from top SPS to top RHIC energies: little change in hadronic contribution [Rapp 2] lqcd: Smooth behavior of susceptibilities in I = 1 channel [Allton et al 4] consistent with no mass shift in I = 1 channel NB: χ q (I = ) shows peak at T T c : signature of phase transition! Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 7 / 22

8 ρ meson in hot hadronic matter -Im D ρ (GeV -2 ) RW vacuum EBEK vacuum RW, ρ N =ρ /2 EBEK, ρ N =ρ /2 RW, ρ N =ρ EBEK, ρ N =ρ T=1 MeV, p=35 MeV -Im D ρ (GeV -2 ) RW vacuum EBEK vacuum RW, ρ N =ρ /2 EBEK, ρ N =ρ /2 RW, ρ N =ρ EBEK, ρ N =ρ T=15 MeV, p=35 MeV M (GeV) M (GeV) EBEK: [Eletsky, Belkacem, Ellis, Kapusta 1] empirical ρ + B/M scattering amplitudes + Pomeron/Regge background T ρ approximation for finite-t effects RW: Hadronic many-body theory [Rapp, Wambach 99] Somewhat different results more broadening and level repulsion: in-med modifications of pion-cloud + ρbn interactions Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 8 / 22

9 Chiral approaches Chiral reduction formalism [Steele et al 96] leading order in π and N density + chiral reduction formulas in-medium current correlators in terms of vacuum correlators no Dyson resummation! Hidden local symmetry [Bando et al 85; Harada, Yamawaki 1,...] Vector manifestation of chiral symmetry: ρ long chiral partner of π dropping ρ mass + violation of vector dominance (T > T flash =.7T c ) b T.6TC dn ds GeV 2 s GeV d T.8TC dn ds GeV 2 s GeV e dn ds GeV 2 T.85TC s GeV dilepton rates similar to more simple dropping mass models [Harada, Sasaki 7] Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 9 / 22

10 Elementary reactions (γ + A, p + A) left: JLaB γ + A e + + e [CLAS Collab. 7] Theory: Boltzmann Uehling Uhlenbeck (BUU) transport [Effenberger et al ] good agreement: no mass shift, broadening of the ρ: Γ ρ 22 MeV right: KEK p+a e + + e [E325 Collaboration 7] fit to dropping-mass ansatz: m /m = (1 Cϱ/ϱ ) C =.92 ±.2, no broadening Contradiction with JLab ρ/ω ratio small; yield for M >.85 GeV? Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 1 / 22

11 1-2 AGeV A-A: HADES and DLS M ee [GeV/c 2 ] HADES confirms DLS Theory: transport model (HSD); coll. broadening + dropping mass [Bratkovskaya, Cassing 7] moderate sensitivity to vector-meson medium effects! solution of DLS puzzle improved e + e Bremsstrahlung [de Jong, Mosel 97; Kaptari, Kämpfer 6] updated η- and -Dalitz contributions Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

12 CERES vs. Hadronic many-body theory Dilepton emission from thermal source thermal fireball evolution (isentropic QGP/MIX + hadron gas) dnll therm d dm d 4 3 q x Im Π (em) (q, q)f B (q )Acc Mq FB (dn ee /dm) / <N ch > [1 MeV/c 2 ] Pb(158 AGeV)+Au (7% central) <N ch >=335 CERES in-med ρ+ω+φ 4π mix QGP DY total total (no bar ρ) p t >.2GeV 2.1<η<2.65 Θ ee >35mrad M ee [GeV] baryon effects essential! many-body effects very low-mass excess [HvH, R. Rapp 7] Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

13 NA6 vs. Hadronic many-body theory + HR fireball dn µµ /dm (counts) ρ, ω, φ multi-π, QGP, freeze-out+primordial ρ, Drell-Yan semicentral In-In all q T T c =T ch =175 MeV NA6 in-med ρ QGP+DD FO + prim ρ 4π mix DY sum dn µµ /dm (counts) semicentral In-In q T <.5 GeV T c =T ch =175 MeV NA6 in-med ρ QGP+DD FO + prim ρ 4π mix DY sum dn µµ /dm (counts) semicentral In-In q T >1. GeV T c =T ch =175 MeV NA6 in-med ρ QGP+DD FO + prim ρ 4π mix DY sum /q T dn µµ /(dq T dy) (counts) M (GeV) T c =T ch =175 MeV semicentral In-In.4 GeV<M<.6 GeV m T -M (GeV) NA6 NA6 incl. total in-med ρ DY FO+prim ρ 1/q T dn µµ /(dq T dy) (counts) M (GeV) T c =T ch =175 MeV semicentral In-In.6 GeV<M<.9 GeV m T -M (GeV) NA6 NA6 incl. total in-med ρ DY FO+prim ρ 1/q T dn µµ /(dq T dy) (counts) M (GeV) T c =T ch =175 MeV semicentral In-In 1. GeV<M<1.4 GeV M spectra [HvH, Rapp 7] consistent with predicted broadening of ρ meson M < 1GeV: thermal ρ; M > 1 GeV: thermal multi-pion processes m t spectra q t < 1 GeV: thermal radiation q t > 1 GeV: freeze-out + hard primordial ρ, Drell-Yan Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22 m T -M (GeV) NA6 NA6 incl. total 4π mix DY FO+prim ρ

14 NA 6 vs. Chiral reduction formalism + hydrodynamics dn/dm per 2 MeV In-In Central all p T <dn ch /dη> 3.8 =19 excess data Total w/ pqgp Total w/ npqgp Hadronic pqgp npqgp DD dn/dm per 2 MeV In-In SemiCentral all p T <dn ch /dη> 3.8 =14 excess data Total w/ pqgp Total w/ npqgp Hadronic pqgp npqgp DD M (GeV) M (GeV) 1 9 In-In SemiCentral.4 < M (GeV) <.6 Data Had QGP FO Total 1 9 In-In SemiCentral.6 < M (GeV) <.9 Data Had QGP FO Total 1 9 In-In SemiCentral 1. < M (GeV) < 1.4 Data Had QGP FO Total /q T dn/dq T (arb units) 1 7 1/q T dn/dq T (arb units) 1 7 1/q T dn/dq T (arb units) q T (GeV) q T (GeV) low-mass + IMR spectrum described ρ: lack of broadening (due to low-density approximation) q T spectra: only thermal + freezeout, no primordial ρ q T (GeV) [Dusling, Teaney, Zahed 7] Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

15 NA6 vs. empirical spectral functions + RR fireball q T > 1GeV all q T 1/p T dn/dp T [a.u.] GeV < Mc 2 <.6 GeV.6 GeV < Mc 2 <.9 GeV 1. GeV < Mc 2 < 1.4 GeV p T [GeV] only thermal + freeze-out large QGP contribution sensitivity of spectral functions to data?! [Ruppert et al 7] Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

16 Sensitivity I: Fireball models vs. hydrodynamics dn/dp T (a.u.) HR prim+fo fo prim NA6 π - (prel.) [Damjanovic 6] [HvH, Rapp 7] p T (GeV) HR fireball [HvH, Rapp 6, 7] thermal dileptons: agrees with hydro pions: need primordial hard comp. low p T : resonance decays consistent with measured R (π) AA RR fireball [Ruppert, Renk 7] dileptons: harder than hydro pions: thermal only RR [Ruppert, Renk 7] Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

17 Sensitivity II: Intermed. mass region QGP vs. hadron gas dn µµ /dm (counts) semicentral In-In all p T QGP (EoS-B) QGP (EoS-C) 4π (EoS-B) 4π (EoS-C) dn µµ /dm (counts) NA6 total EoS-C total EoS-B total EoS-A M (GeV) M (GeV) EoS-B: T c = T chem = 16 MeV (large QGP part) EoS-C: T c = 19 MeV, T chem = 16 MeV (small QGP part) volume T : emission dominated by temperatures around T c (QGP vs. high-density hadronic phase) description of spectra comparable for different EoS [HvH, Rapp 7] Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

18 Sensitivity III: Critical temperature and freeze-out dn µµ /dm (counts) semicentral In-In all q T NA6 total EoS-A total EoS-B total EoS-C M (GeV) EoS-A: T c = T chem = 175 MeV; EoS-B: T c = T chem = 16 MeV EoS-C: T c = 19 MeV, T chem = 16 MeV norm depends on t fireball (kept fixed here)! description of spectra comparable reason for insensitivity to EoS and hadro-chemistry [HvH, Rapp 7]: hadronic and partonic radiation dual for T T c (pqcd: Π V Π A compatible with chiral symmetry restoration!) Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

19 PHENIX e + e -mass spectrum min. bias 2AGeV Au+Au dn/dm [GeV -1 ] Minimum Bias Au-Au Cocktail + Yield Data M [GeV] chiral reduction formalism hadronic many-body theory [Rapp 1, 2] (for N part = 125) [Dusling, Zahed 7] (central scaled by N part ) LMR enhancement cannot be described! Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

20 Predictions: e + e -q T spectra at RHIC 1/q T dn ee /(dq T dy) (GeV -2 ) central Au-Au 2 AGeV.5 GeV < M < 1. GeV thermal HG vacuum HG QGP q T (GeV) theory: thermal [Rapp 8 (unpublished)]; hard contributions [Turbide et al 6] hard contributions (jet-thermal) take over for q T 3 GeV Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, 28 2 / 22

21 Conclusions and Outlook Models for vector (ρ) mesons in medium hadronic many-body theory broadening, small mass shifts of spectra (baryon effects prevalent) hadron-parton duality of dilepton rates (QGP portion depends on T c) chiral reduction formalism low-density approximation, no broadening HLS+Vector Manifestation dropping mass, no vector dominance near T c Theory vs. Experiment Elementary reactions JLAB: BUU transport with broadening (with no mass shift) KEK: Dropping-mass ansatz Heavy-ion collisions HADES (DLS): HSD transport; improved Bremsstrahlung and Dalitz CERES, NA6: Hadronic many-body theory robust due to duality involved mix of contributions at high q T PHENIX: Low-mass enhancement can not be described! Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22

22 Conclusions and Outlook Not covered in this talk: Thermal Photons Same em. correlator as for dileptons! Hadronic many body theory: improvement in description of WA98 data [Liu, Rapp 6] Possibility to measure T initial : dn ll /dq T dn γ /dq T [Alam et al 7] Connection between chiral symmetry restoration and dilepton data hadronic chiral model at finite T Π V and Π A confront Π V with dilepton data check moments of Π V Π A with lqcd via Weinberg sum rules Hendrik van Hees (Texas A&M University) Theoretical Dilepton Review February 8, / 22