Nonequilibrium dilepton production from hot hadronic matter Björn Schenke and Carsten Greiner 22nd...
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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