Reorganization of Perturbation Theory for Thermal QCD

Eric Braaten
The Ohio State University

{Problem: Weak-coupling expansiontex2html_wrap_inline262 appears to diverge!

The series appears to converge only for such extremely small values of tex2html_wrap_inline267
that T is approaching the grand unification scale.

tex2html_wrap_inline265 Arnold and Zhai, Phys. Rev. D50, 7603 (1994) hep-ph/9408276;
Phys. Rev. D51, 1906 (1995) [hep-ph/9410360].
Kastening and Zhai, Phys. Rev. D52, 7232 (1995) [hep-ph/9507380].
Braaten and Nieto, Phys. Rev. Lett. 76, 1417 (1995) [hep-ph/9508406];
Phys. Rev. D53, 3421 (1995) [hep-ph/9510408].

Solution: Reorganization of perturbation theory?


tex2html_wrap_inline281 should give a sequence of approximations with successively smaller errors
tex2html_wrap_inline281 should reduce to the weak-coupling expansion in the limit tex2html_wrap_inline285
tex2html_wrap_inline281 should match on to lattice gauge theory results (equation of state, etc.)
for intermediate values of tex2html_wrap_inline267

Possible approaches

  1. Pade approximationtex2html_wrap_inline298
  2. Screened perturbation theorytex2html_wrap_inline300
    and its generalization to gauge theories, HTL perturbation theorytex2html_wrap_inline304
  3. Luttinger-Ward or tex2html_wrap_inline307-derivable approachtex2html_wrap_inline308
    and HTL-inspired approximations to ittex2html_wrap_inline312

tex2html_wrap_inline265 Hatsuda, Phys. Rev. D56, 8111 (1997) [hep-ph/9708257];
Kastening, Phys. Rev. D56, 8107 (1997) [hep-ph/9708219].

tex2html_wrap_inline301 Karsch, Patkos, and Petreczky, Phys. Lett. B401, 69 (1997) [hep-ph/9702376].

tex2html_wrap_inline305 Andersen, Braaten, and Strickland, Phys. Rev. Lett. 83, 2139 (1999)
[hep-ph/9902327]; [hep-ph/9905337]; [hep-ph/9908323].

tex2html_wrap_inline309 Vanderheyden and Baym, J. Stat. Phys. 93, 843 (1998) [hep-ph/9803300];
Peshier, Kampfer, Pavlenko, and Soff, Europhys. Lett. 43, 381 (1998)

tex2html_wrap_inline313 Blaizot, Iancu, and Rebhan, Phys. Rev. Lett. 83, 2906 (1999)
[hep-ph/9906340]; [hep-ph/9910309].
Peshier, [hep-ph/9910451].

Advantages and Disadvantages

HTL Perturbation Theory

(Andersen, Braaten, and Strickland)

tex2html_wrap_inline281 exact gauge invariance: tex2html_wrap_inline339
tex2html_wrap_inline281 approximate thermodynamic consistency: tex2html_wrap_inline343 higher order in tex2html_wrap_inline267
tex2html_wrap_inline281 running of tex2html_wrap_inline267 via renormalization group
tex2html_wrap_inline281 tractable at order tex2html_wrap_inline267 (calculation in progress)
tex2html_wrap_inline281 can be generalized to order tex2html_wrap_inline357, but magnetic mass problem at order tex2html_wrap_inline359

tex2html_wrap_inline307-derivable approach

(Vanderheyden and Baym)

tex2html_wrap_inline281 approximate gauge invariance: tex2html_wrap_inline365 higher order in tex2html_wrap_inline267
tex2html_wrap_inline281 exact thermodynamic consistency: tex2html_wrap_inline371
tex2html_wrap_inline281 incorrect running of tex2html_wrap_inline267
tex2html_wrap_inline281 intractable (requires solving integral equation for gluon propagator)

HTL approximation to tex2html_wrap_inline307-derivable entropy

(Blaizot, Iancu, and Rebhan)

tex2html_wrap_inline281 gauge invariant by neglecting gauge-dependent terms
tex2html_wrap_inline281 approximate thermodynamic consistency
tex2html_wrap_inline281 running of tex2html_wrap_inline267 via simple substitution
tex2html_wrap_inline281 tractable
tex2html_wrap_inline281 no obvious generalization to higher order in tex2html_wrap_inline267

Laurence Yaffe
Thu Dec 23 14:25:14 PST 1999