Nonequilibrium dilepton production from hot hadronic matter
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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. Outline. Motivation: NA60 + off-shell transport

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Nonequilibrium dilepton production from hot hadronic matter

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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


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


Motivation: CERES, NA60

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


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:


Green´s functions and spectral function

spectral function:

Example:

ρ-meson´s vacuum

spectral function

Mass: m=770 MeV

Width: Γ=150 MeV


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


Principal understanding

  • Wigner transformation → phase space distribution:

→ quantum transport, Boltzmann equation…

  • spectral information:

  • noninteracting, homogeneous situation:

  • interacting, homogeneous equilibrium situation:


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


What we do…

(KMS)

follows eqm.

temperature

enters here

(FDR)

(VMD)

(FDR)

put in by hand


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)


History of the rate…

  • Contribution to rate for fixed energy at different relative times:

    From what times in the past do the contributions come?


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


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


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


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


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


NA60 data

m → 0 MeV

m = 770 MeV


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


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


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