Heavy-Quark Diffusion in the Primordial Quark-Gluon Liquid Vector Mesons in Medium and Dileptons in Heavy-Ion Collisions Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA Strong Interaction Seminar TU München,

1.) Intro-I: Probing Strongly Interacting Matter Electromagnetic Probes: penetrating: EM >> R nuc Equilibrium: EM spectral function Im  EM (q 0,q;  B,T)  Information via EM Spectral Function: degrees of freedom (parton vs. hadron) transport properties (EM conductivity, susceptibility) relation to order parameters (chiral symmetry) measure of temperature

1.2) Intro-IIa: Low-Mass Dileptons at CERN-SPS CERES/NA45 [2000] m ee [GeV] strong excess around M ≈ 0.5GeV (and M > 1GeV ) little excess in  region NA60 [2005]

1.2) Intro-IIb: Low-Mass Dileptons SIS + RHIC HADES [2008] awaiting larger system sizes … PHENIX [2008] m ee [GeV] very large low-mass excess awaiting HBD results (run-10) …

1.) Introduction 2.) Chiral Symmetry + Vector Mesons  EM Emission and Vector Mesons  Chiral Symmetry Breaking   and a 1 Meson in Medium 3.) Dilepton Spectra in A-A and  -A  Thermal Emission and NA60 (SPS)  Photoproduction and CLAS (JLab) 4.) Conclusions Outline

2.1 Thermal Electromagnetic Emission EM Current-Current Correlation Function: e+ e-e+ e- γ Im Π em (M,q) Im Π em (q 0 =q) Thermal Dilepton and Photon Production Rates: Im  em ~ [ImD  + ImD  /10 + ImD  /5] Low Mass:   -meson dominated

But: “Higgs” Mechanism in Strong Interactions: qq attraction  “Bose” condensate fills QCD vacuum Spontaneous Chiral Symmetry Breaking 2.2 Chiral Symmetry + QCD Vacuum : isospin + “chiral” (left/right-handed) invariant > > > > qLqL qRqR qLqL - qRqR - - Profound Consequences: effective quark-mass: ↔ mass generation massless Goldstone bosons  0,±, pion pole-strength f  = 93MeV “chiral partners” split,  M ≈ 0.5GeV: J P =0 ± 1 ± 1/2 ±

Weinberg Sum Rule(s) 2.3 Hadron Spectra + Chiral Symm. Breaking Axial-/Vector Correlators pQCD cont. “Data”: lattice [Bowman et al ‘02] Theory: Instanton Model [Diakonov+Petrov; Shuryak ‘85] Constituent Quark Mass chiral breaking: |q 2 | ≤ 1 GeV 2 Gellmann Oakes Renner: m  2 f  2 = m q ‹0|qq|0› -

2.4 Sum Rules and Order Parameters [Weinberg ’67, Das et al ’67, Kapusta+Shuryak ‘93] QCD-SRs [Hatsuda+Lee ’91, Asakawa+Ko ’92, Klingl et al ’97, Leupold et al ’98, Kämpfer et al ‘03, Ruppert et al ’05, Kwon et al ‘08]  Promising synergy of lQCD and effective models Weinberg-SRs: moments Vector  Axialvector

> >    B *,a 1,K 1... N, ,K … 2.5  -Meson in Medium: Hadronic Interactions D  (M,q;  B,T) = [M 2 - m  2 -   -   B -   M ] -1  -Propagator: [Chanfray et al, Herrmann et al, RR et al, Koch et al, Klingl et al, Mosel et al, Eletsky et al, Oset et al, Sasaki et al …]   =   B,  M  = Selfenergies:  Constraints: decays: B,M→  N,  scattering:  N →  N,  A, …  B /  [RR,Wambach et al ’99]  Meson “Melting” Switch off Baryons

2.6 Axialvector in Medium: Dynamical a 1 (1260) =           Vacuum: a 1 resonance In Medium: in-medium  +  propagators substantial broadening of  -  scattering amplitude consequences for chiral restoration to be elaborated [Cabrera,Jido,Roca+RR ’09 in preparation]

3.) Dilepton Spectra in A-A and  -A Thermal Dilepton Emission Rate: e+ e-e+ e- Im Π em (M,q;  B,T) Thermal Sources: Relevance: - Quark-Gluon Plasma: high mass + temp. qq → e + e , … M > 1.5 GeV, T >T c - Hot + Dense Hadron Gas: M ≤ 1 GeV       → e + e , … T ≤ T c - qqqq _ e+ee+e  e+ee+e   Im Π em ~ Im D 

3.1 Dilepton Rates: Hadronic vs. QGP dR ee /dM 2 ~ ∫d 3 q f B (q 0 ;T) Im  em Hard-Thermal-Loop [Braaten et al ’90] enhanced over Born rate Hadronic and QGP rates “degenerate” around ~T c Quark-Hadron Duality at all M ?! (  degenerate axialvector SF!) [qq→ee] [HTL] -

3.2 Dilepton “Excess” Spectra  at SPS “average”   (T~150MeV) ~ MeV    (T~T c ) ≈ 600 MeV → m  fireball lifetime:  FB ~ (6.5±1) fm/c [van Hees+RR ‘06, Dusling et al ’06, Ruppert et al ’07, Bratkovskaya et al ‘08] Thermal Emission Spectrum:

3.2.2 NA60 Data vs. In-Medium Dimuon Rates acceptance-corrected data directly reflect thermal rates! M  [GeV] [RR,Wambach et al ’99] [van Hees +RR ’07]

3.2.3 NA60 Dimuons: Sensitivity to QGP and T c vary critical and chemical-freezeout temperature (T fo ~ 130 MeV fix) overall shape of spectra robust: “duality” of dilepton rate around “T c ”! yields slightly larger for large T c (hadronic volume!), |  | < 1fm/c intermediate mass (M>1GeV): QGP vs. hadronic depends on T c Intermediate Mass Region “EoS-B” “EoS-C”

3.3 Low-Mass Dileptons at RHIC: PHENIX Successful approach at SPS fails at RHIC

3.4  Meson in Cold Nuclear Matter  + A → e + e  X  e+ ee+ e  Nuclear Photo-Production: [CLAS/JLab ‘08] [Riek et al ’08] Theoretical Approach: M ee  [GeV] Fe - Ti  N ≈ 0.5  0  N  elementary production amplitude in-medium  spectral function + M [GeV] E  =1.5-3 GeV

4.) Conclusions Electromagnetic Probes - study matter properties in nuclear reactions - low mass: in-medium vector mesons Chiral Symmetry Breaking (Restoration) - chiral partners:  - a 1 (degeneracy at T c ) Thermal Dilepton Rates - melting  toward T c (quark-hadron duality?) Dilepton Spectra - quantitative agreement at SPS - ok at TJNAF (  -A) - failure at RHIC thus far

4.5 EM Probes in Central Pb-Au/Pb at SPS updated fireball (a T =0.045→0.085/fm) very low-mass di-electrons ↔ (low-energy) photons [Srivastava et al ’05, Liu+RR ‘06] Di-Electrons [CERES/NA45] Photons [WA98] [van Hees+RR ‘07]

4.8 Axialvector in Medium: Explicit a 1 (1260)    > > > > N(1520) … ,N(1900) … a1a Exp: - HADES (  A): a 1 →(  +  - )  - URHICs (A-A) : a 1 →  N -1

2.5  Cold Nuclear Matter:  Photo-Production Fe -Ti  N ≈ 0.5  0  + A → e + e  X E  =1.5-3 GeV [Riek et al ’08] [CLAS/JLab +GiBUU ’08]

2.3.2 Acceptance-Corrected NA60 Spectra more involved at p T >1.5GeV: Drell-Yan, primordial/freezeout , … M  [GeV]

X.) Example for Comprehensive Analysis: NA60  thermal medium radiating from around T c with melted , well-bound J/  with large collectivity Dileptons Charmonium Flow Charmonium Production

2.4  Spectral Function at Lower Collision Energies largest sensitivity for M ≤ 0.4 GeV  soft modes! Critical point:  -  L mixing (q≠0) with m  → 0, but:  → e + e  signal (too) weak