From hard thermal loops to Langevin dynamics - INSPIRE

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From hard thermal loops to Langevin dynamics

Dietrich Bodeker
(
- Bohr Inst.
)

May, 1999

45 pages

Published in:

Nucl.Phys.B 559 (1999) 502-538

e-Print:

hep-ph/9905239 [hep-ph]

DOI:

10.1016/S0550-3213(99)00435-6

Report number:

NBI-HE-99-13

View in:

ADS Abstract Service

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Abstract:

In hot non-Abelian gauge theories, processes characterized by the momentum scale

g^2 T

(such as electroweak baryon number violation in the very early universe) are non-perturbative. An effective theory for the soft (

|\vec{p}|\sim g^2 T

) field modes is obtained by integrating out momenta larger than

g^2 T

. Starting from the hard thermal loop effective theory, which is the result of integrating out the scale

T

, it is shown how to integrate out the scale

gT

in an expansion in the gauge coupling

g

. At leading order in

g

, one obtains Vlasov-Boltzmann equations for the soft field modes, which contain a Gaussian noise and a collision term. The 2-point function of the noise and the collision term are explicitly calculated in a leading logarithmic approximation. In this approximation the Boltzmann equation is solved. The resulting effective theory for the soft field modes is described by a Langevin equation. It determines the parametric form of the hot baryon number violation rate as

\Gamma = \kappa g^{10} \log(1/g) T^4

, and it allows for a calculation of

\kappa

on the lattice.

Note:

42 pages, 2 figures, uses elsart.sty; explanatory paragraph added to the introduction, 4 references added, a few quotations added; to appear in Nucl. Phys. B Report-no: NBI-HE-99-13

11.10.Wx
11.15.Kc
11.30.Fs
Finite temperature
Gauge theory
Non-Abelian
Real time
Non-perturbative
Hot sphaleron rate
Lattice

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