Nonequilibrium dilepton production from hot hadronic matter Björn Schenke and Carsten Greiner 22nd Winter Workshop on Nuclear Dynamics La Jolla Phys.Rev.C (in print) hep-ph/

2 Motivation: NA60 + off-shell transport Realtime formalism for dilepton production in nonequilibrium Vector mesons in the medium Timescales for medium modifications Fireball model and resulting yields Brown-Rho-scaling Outline RESULTS

3 Motivation: CERES, NA60 Fig.1 : J.P.Wessels et al. Nucl.Phys. A715, (2003)

4 medium modifications Motivation: off-shell transport thermal equilibrium: (adiabaticity hypothesis) Time evolution (memory effects) of the spectral function? Do the full dynamics affect the yields? We ask:

5 Example: ρ-meson´s vacuum spectral function Mass: m=770 MeV Width: Γ=150 MeV Green´s functions and spectral function spectral function:

6 Realtime formalism – Kadanoff-Baym equations  Evaluation along Schwinger-Keldysh time contour  nonequilibrium Dyson-Schwinger equation  Kadanoff-Baym equations are non-local in time → memory - effects with

7 Principal understanding  Wigner transformation → phase space distribution: → quantum transport, Boltzmann equation…  spectral information: noninteracting, homogeneous situation: interacting, homogeneous equilibrium situation:

8 From the KB-eq. follows the Fluct. Dissip. Rel.: Nonequilibrium dilepton rate The retarded / advanced propagators follow surface term → initial conditions This memory integral contains the dynamic infomation

9 What we do… → → (VMD) → → temperature enters here follows eqm. put in by hand (FDR) (KMS)

10 We use a Breit-Wigner to investigate mass-shifts and broadening: And for coupling to resonance-hole pairs: M. Post et al. In-medium self energy Σ Spectral function for the coupling to the N(1520) resonance: k=0 (no broadening)

11 Contribution to rate for fixed energy at different relative times: From what times in the past do the contributions come? History of the rate…

12 At this point compare e.g. from these differences we retrieve a timescale… Introduce time dependence like Fourier transformation leads to (set and (causal choice)) Time evolution - timescales We find a proportionality of the timescale like, with c≈2-3.5 ρ-meson: retardation of about 3 fm/c The behavior of the ρ becomes adiabatic on timescales significantly larger than 3 fm/c

13 Oscillations and negative rates occur when changing the self energy quickly compared to the introduced timescale For slow and small changes the spectral function moves rather smoothly into its new shape Interferences occur But yield stays positive Quantum effects

14 Dilepton yields – mass shifts Fireball model: expanding volume, entropy conservation → temperature T=175 MeV → 120 MeV Δτ =7.5 fm/c ≈2x Δτ=7.5 fm/c m = 400 MeV m = 770 MeV

15 Dilepton yields - resonances T=175 MeV → 120 MeV Δτ =7.2 fm/c coupling on no coupling Fireball model: expanding volume, entropy conservation → temperature

16 Dropping mass scenario – Brown Rho scaling T=Tc → 120 MeV Δτ =6.4 fm/c ≈3x  Expanding “Firecylinder” model for NA60 scenario  Brown-Rho scaling using:  Yield integrated over momentum  Modified coupling B. Schenke and C. Greiner – in preparation

17 NA60 data m → 0 MeV m = 770 MeV

18 The ω-meson T=175 MeV → 120 MeV Δτ =7.5 fm/c m = 682 MeV Γ = 40 MeV m = 782 MeV Γ = 8.49 MeV

19 Timescales of retardation are ≈ with c=2-3.5 Quantum mechanical interference-effects, yields stay positive Differences between yields calculated with full quantum transport and those calculated assuming adiabatic behavior. Memory effects play a crucial role for the exact treatment of in-medium effects Summary and Conclusions