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

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


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

Motivation: CERES, NA60

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


Nonequilibrium dilepton production from hot hadronic matter

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:


Nonequilibrium dilepton production from hot hadronic matter

Green´s functions and spectral function

spectral function:

Example:

ρ-meson´s vacuum

spectral function

Mass: m=770 MeV

Width: Γ=150 MeV


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

Principal understanding

  • Wigner transformation → phase space distribution:

→ quantum transport, Boltzmann equation…

  • spectral information:

  • noninteracting, homogeneous situation:

  • interacting, homogeneous equilibrium situation:


Nonequilibrium dilepton production from hot hadronic matter

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

What we do…

(KMS)

follows eqm.

temperature

enters here

(FDR)

(VMD)

(FDR)

put in by hand


Nonequilibrium dilepton production from hot hadronic matter

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)


Nonequilibrium dilepton production from hot hadronic matter

History of the rate…

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

    From what times in the past do the contributions come?


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

NA60 data

m → 0 MeV

m = 770 MeV


Nonequilibrium dilepton production from hot hadronic matter

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


Nonequilibrium dilepton production from hot hadronic matter

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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