Effective dynamics of soft non-abelian gauge fields at finite temperature

Abstract

We consider time dependent correlation functions of non-abelian gauge fields at finite temperature. An effective theory for the soft ($p\sim g^2 T$) field modes is derived by integrating out the field modes with momenta of order $T$ and of order $g T$ in a leading logarithmic approximation. In this effective theory the time evolution of the soft fields is determined by a local Langevin-type equation. As an application, the rate for hot electroweak baryon number violation is estimated as $Γ\sim g^2 \log(1/g) (g^2 T)^4$. Furthermore, possible consequences for non-perturbative lattice computations of unequal time correlation functions are discussed.

Figures (3)

• Figure 1: Sub-leading contributions to the effective theory for the soft ($p\sim g^2T$) gauge fields. The loop momenta are semi-hard ($k\sim gT$). The small dots are "bare" (non hard thermal loop) vertices. The full lines denote hard thermal loop resummed propagators, the dashed lines represent ghost propagators.
• Figure 2: Leading contributions to the effective theory for the soft ($p\sim g^2T$) gauge fields. The loop momenta are semi-hard ($k\sim gT$). The full lines denote hard thermal loop resummed propagators and the heavy dots are hard thermal loop vertices.
• Figure 3: Contribution to the effective theory for the soft ($p\sim g^2T$) gauge fields involving hard thermal loop $n$-point vertices. The notation is the same as in Fig. \ref{['htlvertex']}.