The electroweak sphaleron on the lattice

Abstract

We study the properties of the electroweak sphaleron on a finite lattice. The cooling algorithm for saddle points is used to obtain the static classical solutions of the SU(2)-Higgs field theory. Results are presented for $M_H=\infty ,M_W,0.75M_W$. After performing finite size scaling we find good agreement with the results obtained from variational approaches. Of relevance for numerical determinations of the transition rate is that the lattice artefacts are surprisingly small for $M_W\approx M_H$.

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