QCD thermodynamics Effects due to non-zero width Implications

Hard Gluon damping in hot Hard Gluon damping in hot QCD QCD hep-ph/hep-ph/04032250403225

André Peshier André Peshier **

Institut for Theoretical Physics, Giessen UniversityInstitut for Theoretical Physics, Giessen University

QCD thermodynamics Effects due to non-zero width Implications

* * supported by BMBF

A. Peshier, Hard gluon damping in hot QCDA. Peshier, Hard gluon damping in hot QCD 22

[Pisarski, …]

1-particle & many-particle 1-particle & many-particle propertiesproperties

bulk properties (pressure,

entropy, density …) transport properties (viscosities, conductivities) …

weak coupling QCD,

dispersion relation damping rate = width

• thermal massesthermal masses

• expectation expectation quasiparticlesquasiparticles

• : (HTL) : (HTL) resummationresummation required already at leading order! required already at leading order!

IR divergence;generic sensitivity to non-perturbative sector

entropy

strong coupling QCD, near

… large width ??

lattice QCD: ???

self-consistent resummation: non-trivial gauge invariancegauge invariance non-perturbative renormalizationnon-perturbative renormalization


perturbation theory

„diverges“ for large coupling

[Arnold et al.]

lattice QCD

phase transition at

QCD QCD (here:(here: quenched)quenched) thermodynamicsthermodynamics

[Boyd et al., CPPACS]


Divergent series, toy modelDivergent series, toy model

‘partition function’

asymptotic seriescut in complex plane ~ # diagrams

i) truncatei) truncate at at low orderlow order

ii) resumii) resum

+ + …


propagator

thermodynamic potential

Resummation in theoryResummation in theory

[Luttinger, Ward, …]


‘large coupling resum leading-loop order’ NB: resummation necessary for thermodynamic consistency

cf. screend perturbation theory [Karsch et al.]

-derivable (sc) approximations-derivable (sc) approximations

truncate

& calc. selfconst’ly

non-perturbative renormalization!


phenomenological QP modelsinteracting gluons massive QP

[Peshier et al.]

Interlude: QCD quasiparticle Interlude: QCD quasiparticle modelsmodels

based on appropriate approximations of propagators

HTL QP models

HTL entropy: [Blaizot et al.] HTL pressure: [Peshier]

HTL pT: [Braaten et al.]


Relevance of widthRelevance of width

near Tc: small entropy

entropy (~ population of phase space)

large coupling large width?? & widthaffected by mass

large qp mass


Dynamical quasiparticle entropyDynamical quasiparticle entropy

Luttinger-Ward formalism

consider entropy

leading-loop resummation for large coupling

contribs. from graphs with more than 2 vertices

quasiparticles withdispersion rel.

effect offinite width


Width increases entropy,Width increases entropy,

i) properties of propagator & spectral function

retarded propagator:



ii) two typical cases for propagator

`regular´ `singular´

common: `dispersion relation´ determined by real part of self-energy


iii) integrand of


`rather symmetric´exp. decreasing

under rather general assumptions:

(more rigorously: hep-ph/0403225)


Lorentz spectral functionLorentz spectral function

introduce width

parameterize`dispersion relation´ by mass


Entropy for Lorentz spectral Entropy for Lorentz spectral functionfunction

cf. phenomeno-logical QP models

in QCD: can be large near ?in QCD: can be large near ?


Momentum dependence of andMomentum dependence of and

quantify: bulk properties are determined by hard momenta

negligiblesensitivityon small


Sensitivity on shape of spectral Sensitivity on shape of spectral function?function?example: `quartic´ spectral function

NB: chose same dispersion relation to compare to Lorentzian


Spectral function in Fourier spaceSpectral function in Fourier space

model peaked at

damping (need not be exponential)

(from sum rule)

typical attenuation time

`forward´ Fourier transform


Non-exponential time behaviorNon-exponential time behavior

damping models with their Fourier transform


Polynomial modelsPolynomial models

expectation: sensitivity on long-time behavior, insensitive to short-time behavior

width has strong effect on entropy except for singular spectral functionswidth has strong effect on entropy except for singular spectral functions


QCDQCD

approximately self-consistent scheme

entropy dominated by transverse modes (longitudinal excitations: collective, give small contribution to HTL entropy)

gaugeinvar.!

parameterized by and (gauge inv.)


QCDQCD : `quasiparticles´ with : `quasiparticles´ with widthwidth

a phenomenological parametrization

[Pisarski, …]

NB: is not just a 3rd fit parameter,functional form fixed!

assumptions

• • soft gluons: HTL, hard gluons: • magn. mass IR regulator, pole struct.


QCDQCD : quasiparticles?: quasiparticles?

width ~ mass• small for ,

• result robust (cf. hep-ph/…) QP!

• fulfilled …


ImplicationsImplications

estimate magnetic mass:

[Nakamura et al.]



empirical observation for Debye mass:

[Nakamura et al.]


again at : characteristic changes in observables again at : characteristic changes in observables


radiative energy loss ~ missing jet quenching at SPS– parton in (quark-) gluon plasma of extent Lparton in (quark-) gluon plasma of extent L

– several independent scatterings ( ): LPM regimeseveral independent scatterings ( ): LPM regime

– for for [Baier et al.]


ResuméResumé

width has significant effect on thermodyn. bulk properties (unless for exotic spectral functions)

for QCD at : broad exciations

for : heavy narrow modes (quasiparticles)

charact. (universal?) temp. could be observable

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QCD thermodynamics Effects due to non-zero width Implications

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