Nonequilibrium dilepton production from hot hadronic matter

Björn Schenke and Carsten Greiner

22nd Winter Workshop on Nuclear DynamicsLa Jolla

Phys.Rev.C (in print) hep-ph/0509026

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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

RE

SU

LTS

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Motivation: CERES, NA60

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

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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:

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Example:ρ-meson´s vacuumspectral function

Mass: m=770 MeVWidth: Γ=150 MeV

Green´s functions and spectral function

spectral function:

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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

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Principal understanding

Wigner transformation → phase space distribution:

→ quantum transport, Boltzmann equation…

spectral information:

• noninteracting, homogeneous situation:

• interacting, homogeneous equilibrium situation:

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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

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What we do…

→

→

(VMD)→

→

temperatureenters here

follows e

qm.

put in by hand

(FDR)

(FDR)

(KMS)

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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)

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Contribution to rate for fixed energy at different relative times:

From what times in the past do the contributions come?

History of the rate…

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At this point compare

e.g. from thesedifferenceswe 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

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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

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Dilepton yields – mass shiftsFireball model: expanding volume, entropy conservation → temperature

T=175 MeV → 120 MeVΔτ =7.5 fm/c

≈2x

Δτ=

7.5

fm/c

m = 400 MeV

m = 770 MeV

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Dilepton yields - resonances

T=175 MeV → 120 MeVΔτ =7.2 fm/c

Δτ=

7.2

fm/c

coupling on

no coupling

Fireball model: expanding volume, entropy conservation → temperature

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Dropping mass scenario – Brown Rho scaling

T=Tc → 120 MeVΔτ =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

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NA60 datam → 0 MeV

m = 770 MeV

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The ω-meson

T=175 MeV → 120 MeVΔτ =7.5 fm/c

Δτ=

7.5

fm/c

m = 682 MeVΓ = 40 MeV

m = 782 MeVΓ = 8.49 MeV

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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