Dalitz Decays and Bremsstrahlung from in-Medium EM Spectral Functions Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA ExtreMe Matter Institute Workshop on Virtual Bremsstrahlung and HADES Frankfurt University,

Thermal electromagnetic radiation ↔ EM correlation function 1.) Introduction e+ e-e+ e- γ Im Π em (M>0,q;  B,T) Im Π em (M=0,q,  B,T)  B e+e-e+e- γ  Leading orders annihilation Dalitz, scattering Bremsstrahlung ~ O , M>2m   ~ g s 2, soft ~ g s 4, super-soft

1.2 Electric Conductivity pion gas (chiral pert. theory)  EM / T ~ 0.01 for T ~ MeV [Fernandez-Fraile+Gomez-Nicola ’07] quenched lattice QCD  EM / T ~ 0.35 for T = (1.5-3) T c [Gupta ’04] soft-photon limit of thermal emission rate

1.) Introduction 2.) Phenomenology at SPS  Low-Mass Dileptons  Low-Energy Photons and  Bremsstrahlung 3.) EM Emission Rates  In-Medium  Spectral Function  Process Decomposition: SPS vs. HADES   -Dalitz 4.) Conclusions Outline

2.1 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]

2.2 Direct Photons at SPS: WA98 [Turbide,RR +Gale’04] Thermal Radiation + pQCD pQCD+Cronin at q t > 1.5 GeV Add  →  Bremsstrahlung [Liu+RR’06]

1.) Introduction 2.) Phenomenology at SPS  Low-Mass Dileptons  Low-Energy Photons and  Bremsstrahlung 3.) EM Emission Rates  In-Medium  Spectral Function  Process Decomposition: SPS vs. HADES   -Dalitz 4.) Conclusions Outline

> >    B *,a 1,K 1... N, ,K … 3.1 In-Medium  Spectral Function : Im D  ~ Im  EM D  (M,q;  B,T) = [M 2 - m  2 -   -   B -   M ] -1  -Propagator:   =   B,  M  = Selfenergies:  Constraints: decays: B,M→  N,  scattering:  N →  N,  A, …  B /   Meson “Melting” Switch off Baryons

3.2 Production Processes from  Spectral Function ↔ Cuts (imag. parts) of Selfenergy Diagrams:   N -1 >        N →  N,   N →  →  N meson-exchange scattering resonance Dalitz decays  → a 1  →  Bremsstrahlung  N →  NN,  N    

3.2.2 Decomposition of Emission Rates ”SPS” “SIS” in-medium  annihilation leading at SPS ( ~ N ch 1.3 !?) baryon resonance “Dalitz decays” at SIS ( ~ N  !?) interference toward m 

3.3 Dileptons at DLS/HADES Transport Simulations (HSD) importance of: - NN Bremsstrahlung (non-thermal) -  Dalitz (long tail) - in-medium  (1-  threshold) [Bratkovskaya+Cassing ’08]

3.3.2  Selfenergy and  Dalitz Decay production phase space ~   ! dilepton rate > >  N   N = 

3.3.3  Dalitz at SIS appreciable only below M < 0.3GeV  –  crossing at ~ 0.4 GeV

4.) Conclusions Bremsstrahlung, Dalitz decays ↔ in-medium EM SF (  SF) nontrivial excitation function consistency with transport models to be quantified

2.3  –Meson 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]

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

Light-like  -Spectral Function, D  (q 0 =q), and Nuclear Photo-Absorption NANA  -ex [Urban,Buballa,RR+Wambach ’98] On the Nucleon On Nuclei resonance melt (parameter) (selfconsistent N(1520)→N  ) [Post,Mosel et al ’98] fixes coupling constants and formfactor cutoffs for  NB

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

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]

2.6 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]  Promising synergy of lQCD and effective models Weinberg-SRs: moments Vector  Axialvector

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 ’08 in progress]

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