1. 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

2. A. Peshier, Hard gluon damping in hot QCD2 [Pisarski, …] 1-particle & many-particle properties  bulk properties (pressure, entropy, density …) transport properties (viscosities, conductivities) …  weak coupling QCD, dispersion relation damping rate = width thermal masses thermal masses expectation  quasiparticles expectation  quasiparticles : (HTL) resummation required already at leading order! : (HTL) resummation 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 invariance gauge invariance non-perturbative renormalization non-perturbative renormalization

3. A. Peshier, Hard gluon damping in hot QCD3  perturbation theory „diverges“ for large coupling [Arnold et al.] lattice QCD phase transition at QCD (here: quenched) thermodynamics [Boyd et al., CPPACS]

4. A. Peshier, Hard gluon damping in hot QCD4 Divergent series, toy model ‘partition function’ asymptotic series cut in complex plane ~ # diagrams low order i) truncate at low order ii) resum ++ …

5. A. Peshier, Hard gluon damping in hot QCD5 propagator thermodynamic potential Resummation in theory [Luttinger, Ward, …]

6. A. Peshier, Hard gluon damping in hot QCD6 ‘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!

7. A. Peshier, Hard gluon damping in hot QCD7 phenomenological QP models interacting gluons massive QP [Peshier et al.] Interlude: QCD quasiparticle models based on appropriate approximations of propagators  HTL QP models HTL entropy: [Blaizot et al.] HTL pressure : [Peshier]  HTL pT: [Braaten et al.]

8. A. Peshier, Hard gluon damping in hot QCD8 Relevance of width near Tc: small entropy entropy (~ population of phase space)  large coupling  large width?? & widthaffected by mass large qp mass 

9. A. Peshier, Hard gluon damping in hot QCD9 Dynamical quasiparticle entropy Luttinger-Ward formalism consider entropy leading-loop resummation for large coupling contribs. from graphs with more than 2 vertices quasiparticles with dispersion rel. effect of finite width

10. A. Peshier, Hard gluon damping in hot QCD10 Width increases entropy, i) properties of propagator & spectral function retarded propagator:

11. A. Peshier, Hard gluon damping in hot QCD11 Width increases entropy, ii) two typical cases for propagator `regular´ `singular´ common: `dispersion relation´ determined by real part of self-energy

12. A. Peshier, Hard gluon damping in hot QCD12 iii) integrand of Width increases entropy, ` rather symmetric ´ exp. decreasing under rather general assumptions: (more rigorously: hep-ph/0403225)

13. A. Peshier, Hard gluon damping in hot QCD13 Lorentz spectral function introduce width parameterize `dispersion relation´ by mass

14. A. Peshier, Hard gluon damping in hot QCD14 Entropy for Lorentz spectral function cf. phenomeno- logical QP models in QCD: can be large near ?

15. A. Peshier, Hard gluon damping in hot QCD15 Momentum dependence of and quantify: bulk properties are determined by hard momenta negligible sensitivity on small

16. A. Peshier, Hard gluon damping in hot QCD16 Sensitivity on shape of spectral function? example: `quartic´ spectral function NB: chose same dispersion relation to compare to Lorentzian

17. A. Peshier, Hard gluon damping in hot QCD17 Spectral function in Fourier space model peaked at damping (need not be exponential) (from sum rule) typical attenuation time `forward´ Fourier transform

18. A. Peshier, Hard gluon damping in hot QCD18 Non-exponential time behavior damping models with their Fourier transform

19. A. Peshier, Hard gluon damping in hot QCD19 Polynomial models expectation: sensitivity on long-time behavior, insensitive to short-time behavior width has strong effect on entropy except for singular spectral functions

20. A. Peshier, Hard gluon damping in hot QCD20 QCD approximately self-consistent scheme entropy dominated by transverse modes (longitudinal excitations: collective, give small contribution to HTL entropy) gauge invar.! parameterized by and (gauge inv.)

21. A. Peshier, Hard gluon damping in hot QCD21 QCD: `quasiparticles´ with width 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.

22. A. Peshier, Hard gluon damping in hot QCD22 QCD: quasiparticles? width ~ mass small for, result robust (cf. hep-ph/…) QP! fulfilled …

23. A. Peshier, Hard gluon damping in hot QCD23 Implications estimate magnetic mass: [Nakamura et al.]

24. A. Peshier, Hard gluon damping in hot QCD24 Implications empirical observation for Debye mass: [Nakamura et al.]

25. A. Peshier, Hard gluon damping in hot QCD25 again at : characteristic changes in observables 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.]

26. A. Peshier, Hard gluon damping in hot QCD26 Resumé 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