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
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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
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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)
Time evolution (memory effects) of the spectral
function? Do the full dynamics affect the yields?
We ask
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Greens functions and spectral function
spectral function
Example ?-mesons vacuum spectral function
Mass m770 MeV Width G150 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
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In-medium self energy S

• 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

k0
(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 c2-3.5
?-meson retardation of about 3 fm/c
The behavior of the ? becomes adiabatic on
timescales significantly larger than 3 fm/c
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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

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Dilepton yields mass shifts
Fireball model expanding volume, entropy
conservation ? temperature
m 400 MeV
2x
?t7.5 fm/c
m 770 MeV
T175 MeV ? 120 MeV ?t 7.5 fm/c
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Dilepton yields - resonances
Fireball model expanding volume, entropy
conservation ? temperature
coupling on
?t7.2 fm/c
no coupling
T175 MeV ? 120 MeV ?t 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

TTc ? 120 MeV ?t 6.4 fm/c
3x
B. Schenke and C. Greiner in preparation
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NA60 data
m ? 0 MeV
m 770 MeV
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The ?-meson
m 682 MeV G 40 MeV
?t7.5 fm/c
m 782 MeV G 8.49 MeV
T175 MeV ? 120 MeV ?t 7.5 fm/c
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Summary and Conclusions

• Timescales of retardation are with
  c2-3.5
• 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