QCD thermodynamics Effects due to non-zero width Implications

1. Hard Gluon damping in hot QCD hep-ph/0403225André Peshier *Institut for Theoretical Physics, Giessen University QCD thermodynamics Effects due to non-zero width Implications * supported by BMBF

2. 1-particle & many-particle properties • bulk properties (pressure, entropy, density …) • transport properties (viscosities, conductivities) • … entropy dispersion relation damping rate = width • weak coupling QCD, • strong coupling QCD, near • … large width ?? • lattice QCD: ??? self-consistent resummation:non-trivial • gauge invariance • non-perturbative renormalization • thermal masses • expectation quasiparticles • : (HTL) resummation required already at leading order! IR divergence; generic sensitivity to non-perturbative sector [Pisarski, …] A. Peshier, Hard gluon damping in hot QCD

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

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

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

6. -derivable (sc) approximations • ‘large coupling resum leading-loop order’ NB: resummation necessary for thermodynamic consistency • cf. screend perturbation theory [Karsch et al.] truncate & calc. selfconst’ly non-perturbative renormalization! A. Peshier, Hard gluon damping in hot QCD

7. 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.] A. Peshier, Hard gluon damping in hot QCD

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

9. 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 A. Peshier, Hard gluon damping in hot QCD

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

11. 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

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

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

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

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

16. 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

17. 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

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

19. 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

20. 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.) A. Peshier, Hard gluon damping in hot QCD

21. QCD : `quasiparticles´ with width • a phenomenological parametrization NB: is not just a 3rd fit parameter, functional form fixed! • assumptions • soft gluons: HTL, • hard gluons: • magn. mass • IR regulator, pole struct. [Pisarski, …] A. Peshier, Hard gluon damping in hot QCD

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

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

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

25. 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 : characteristic changes in observables A. Peshier, Hard gluon damping in hot QCD

26. 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 A. Peshier, Hard gluon damping in hot QCD