# The electroweak sphaleron on the lattice

## TL;DR

This paper investigates the properties of the electroweak sphaleron on a finite lattice using a cooling algorithm, finding good agreement with variational methods and small lattice artifacts near the physical mass ratio.

## Contribution

It introduces a lattice-based method to study the electroweak sphaleron and compares results with variational approaches, demonstrating the effectiveness of the cooling algorithm.

## Key findings

- Good agreement with variational results
- Small lattice artifacts near physical mass ratio
- Effective use of cooling algorithm for saddle points

## 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 $M_W\approx M_H$.