Nonequilibrium dilepton production from hot hadronic matter

1. 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/0509026

2. Outline • 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 RESULTS

3. Motivation: CERES, NA60 Fig.1 : J.P.Wessels et al. Nucl.Phys. A715, 262-271 (2003)

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

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

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

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

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

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

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

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

12. Time evolution - timescales • Introduce time dependence like • Fourier transformation leads to (set and(causal choice)) e.g. from these differences we retrieve a timescale… At this point compare 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. Quantum effects • 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

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

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

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

17. NA60 data m → 0 MeV m = 770 MeV

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

19. Summary and Conclusions • 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