On tunneling at finite energies and temperatures

Abstract

The rate of vacuum transitions for a system at finite temperature has contributions from both classical thermal fluctuations and quantum tunneling. The first is given in terms of the free energy of a sphaleron configuration by Γ β ≈exp(− βF sphaleron), while the latter, Γ ħ, is a complicated function of finite energy tunneling rates. It is usually assumed that Γ ħ is always negligible at temperatures greater than the order of the mass of the lowest excitation. We show that models exist in which, even at large temperatures, Γ h ̵ ⪢Γ β . We examine the issue in the (1 + 1) abelian Higgs model, as well as in the case of electroweak ( B + L) violating processes. We show how the persistence of the cosmological baryon asymmetry yields a bound on the inclusive two particle cross section σ 2→all( E) as a function of center of mass energy.