Transcript Dilepton Production from hot hadronic matter in nonequilibrium

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
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RESULTS
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Motivation: CERES, NA60
Fig.1 : J.P.Wessels et al. Nucl.Phys. A715, 262-271 (2003)
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Motivation: off-shell transport
medium modifications
thermal equilibrium:
(adiabaticity hypothesis)
We ask:
Time evolution (memory effects) of the spectral function?
Do the full dynamics affect the yields?
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Green´s functions and spectral function
spectral function:
Example:
ρ-meson´s vacuum
spectral function
Mass: m=770 MeV
Width: Γ=150 MeV
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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
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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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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
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What we do…
→
→
(FDR)
→
(VMD)
→
(FDR) put in by hand
(KMS)
temperature
enters here
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In-medium self energy Σ

We use a Breit-Wigner to investigate mass-shifts and broadening:

And for coupling to resonance-hole pairs:
M. Post et al.
 Spectral function for the
coupling to the N(1520) resonance:
k=0
(no broadening)
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History of the rate…

Contribution to rate for fixed energy at different relative times:
From what times in the past do the contributions come?
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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 12
Quantum effects

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
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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
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Dilepton yields – mass shifts
Fireball model: expanding volume, entropy conservation → temperature
≈2x
Δτ=7.5 fm/c
m = 400 MeV
m = 770 MeV
T=175 MeV → 120 MeV
Δτ =7.5 fm/c
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Dilepton yields - resonances
Fireball model: expanding volume, entropy conservation → temperature
Δτ=7.2 fm/c
coupling on
no coupling
T=175 MeV → 120 MeV
Δτ =7.2 fm/c
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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
B. Schenke and C. Greiner – in preparation
≈3x
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NA60 data
m → 0 MeV
m = 770 MeV
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The ω-meson
Δτ=7.5 fm/c
m = 682 MeV
Γ = 40 MeV
m = 782 MeV
Γ = 8.49 MeV
T=175 MeV → 120 MeV
Δτ =7.5 fm/c
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Summary and Conclusions

Timescales of retardation are ≈

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
with c=2-3.5
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