Hard Gluon damping in hot QCD
hep-ph/0403225
André Peshier *
Institut for Theoretical Physics, Giessen University
 QCD thermodynamics
 Effects due to non-zero width
 Implications
*
supported by BMBF
1-particle & many-particle properties


dispersion relation
damping rate = width
weak coupling
 strong
couplingQCD,
QCD,
• thermal masses
• expectation
•

bulk properties (pressure,
entropy density …)
entropy,
transport properties
(viscosities, conductivities)
…
near
…
large
width ??
quasiparticles
: (HTL) resummation required already at leading order!
lattice QCD: ???
self-consistent resummation: non-trivial
IR divergence;
gauge invariance
generic sensitivity to
non-perturbative renormalization
non-perturbative sector
[Pisarski, …]
A. Peshier, Hard gluon damping in hot QCD
2
QCD (here: quenched) thermodynamics

lattice QCD
phase transition at
[Boyd et al., CPPACS]
A. Peshier, Hard gluon damping in hot QCD
 perturbation theory
„diverges“ for large coupling
[Arnold et al.]
3
Divergent series, toy model

‘partition function’

asymptotic series
cut in complex  plane ~ # diagrams
i) truncate at low order
ii) resum
+
A. Peshier, Hard gluon damping in hot QCD
+…
4
Resummation in

propagator

thermodynamic potential
theory
[Luttinger, Ward, …]
A. Peshier, Hard gluon damping in hot QCD
5
-derivable (sc) approximations

‘large coupling
resum leading-loop order’
NB: resummation necessary for thermodynamic consistency
truncate
& calc. selfconst’ly
non-perturbative
renormalization!

cf. screend perturbation theory [Karsch et al.]
A. Peshier, Hard gluon damping in hot QCD
6
Interlude: QCD quasiparticle models
based on appropriate approximations of propagators

phenomenological QP models
interacting gluons massive QP
[Peshier et al.]
 HTL QP models
HTL entropy: [Blaizot et al.]
HTL pressure: [Peshier]
 HTL pT: [Braaten et al.]
A. Peshier, Hard gluon damping in hot QCD
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
near Tc: small entropy

Relevance of width
large qp mass

large coupling

large width??

entropy (~ population of phase space) affected by mass & width
A. Peshier, Hard gluon damping in hot QCD
8
Dynamical quasiparticle entropy

Luttinger-Ward formalism

consider entropy
contribs. from graphs
with more than 2 vertices

leading-loop resummation for large coupling
quasiparticles with
dispersion rel.
effect of
finite width
A. Peshier, Hard gluon damping in hot QCD
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Width increases entropy,
i) properties of propagator & spectral function
retarded propagator:
A. Peshier, Hard gluon damping in hot QCD
10
Width increases entropy,
ii) two typical cases for propagator
`regular´
`singular´
common: `dispersion relation´ determined by real part of self-energy
A. Peshier, Hard gluon damping in hot QCD
11
Width increases entropy,
iii) integrand of
exp. decreasing
`rather symmetric´
(more rigorously:
hep-ph/0403225)
under rather general assumptions:
A. Peshier, Hard gluon damping in hot QCD
12
Lorentz spectral function
introduce width
parameterize
`dispersion relation´
by mass
A. Peshier, Hard gluon damping in hot QCD
13
Entropy for Lorentz spectral function
cf. phenomenological QP models
in QCD: can
be large near
A. Peshier, Hard gluon damping in hot QCD
?
14
Momentum dependence of

and
quantify: bulk properties are determined by hard momenta
negligible
sensitivity
on small
A. Peshier, Hard gluon damping in hot QCD
15
Sensitivity on shape of spectral function?
example: `quartic´ spectral function
NB: chose same dispersion relation to compare to Lorentzian
A. Peshier, Hard gluon damping in hot QCD
16
Spectral function in Fourier space


model
peaked at
damping (need not be exponential)
(from sum rule)
typical attenuation time
`forward´ Fourier transform
A. Peshier, Hard gluon damping in hot QCD
17
Non-exponential time behavior

damping models with their Fourier transform
A. Peshier, Hard gluon damping in hot QCD
18
Polynomial models
expectation: sensitivity on long-time behavior,
insensitive to short-time behavior
width has strong effect on entropy except for singular spectral functions
A. Peshier, Hard gluon damping in hot QCD
19
QCD

approximately self-consistent scheme
gauge
invar.!

entropy dominated by transverse modes
(longitudinal excitations: collective, give small contribution to HTL entropy)
parameterized by and
(gauge inv.)
A. Peshier, Hard gluon damping in hot QCD
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QCD: `quasiparticles´ with width

a phenomenological parametrization
NB: is not just a
3rd fit parameter,
functional form fixed!
assumptions
[Pisarski, …]
A. Peshier, Hard gluon damping in hot QCD
•
• soft gluons: HTL,
hard gluons:
• magn. mass
IR regulator, pole struct.
21
QCD: quasiparticles?
•
small for
,
• result robust (cf. hep-ph/…)
•
A. Peshier, Hard gluon damping in hot QCD
width ~ mass
QP!
fulfilled …
22
Implications

estimate magnetic mass:
[Nakamura et al.]
A. Peshier, Hard gluon damping in hot QCD
23
Implications

empirical observation for Debye mass:
[Nakamura et al.]
A. Peshier, Hard gluon damping in hot QCD
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Implications

radiative energy loss ~ missing jet quenching at SPS
– parton in (quark-) gluon plasma of extent L
– several independent scatterings (
): LPM regime
– for
[Baier et al.]
again at
A. Peshier, Hard gluon damping in hot QCD
: characteristic changes in observables
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Resumé


width has significant effect on thermodyn. bulk properties
(unless for exotic spectral functions)
for QCD at
for

: broad exciations
: heavy narrow modes (quasiparticles)
charact. (universal?) temp.
A. Peshier, Hard gluon damping in hot QCD
could be observable
26