Perturbative contributions to the electroweak interface tension

Abstract

The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.

Non-perturbative contributions to the hot electroweak potential and the crossover

“…3-dimensional perturbation theory for the effective potential always predicts a first-order PT, mainly due to the −(ϕ 2 ) 3/2 term obtained from the simple gauge boson loop in a Higgs background ϕ 2 = 2φ + φ. It strongly deviates from lattice results for x ≥ 0.05 in particular for the interface tension of the critical bubble 6 and the latent heat.…”

On the gauge dependence of vacuum transitions at finite temperature

“…8. Some analytical details of this discussion are given in Appendix C. At this point, we would like to comment on [31] that compared the wall tension in the Landau and Feynman gauges for an effective three dimensional theory. There it was also found that including the Z factor does not lead to a systematic reduction of the gauge dependence.…”

SUSY variants of the electroweak phase transition

“…Here "integrate out" is understood in the sense of a matching procedure, matching a set of static 4-dimensional amplitudes containing the above modes in the loops to a 3-dimensional truncated Lagrangian [9] for the Higgs and transversal gauge zero modes: Figure 2: (from ref. [15]). The perturbatively calculated interface tension σ (including Z-factor effect and gauge variations) vs. x compared to lattice data from ref.…”