# SU(3) sphaleron: Numerical solution

## TL;DR

This paper numerically constructs and analyzes the properties of an $SU(3)$ sphaleron solution in Yang-Mills-Higgs theory, exploring its energy and potential relevance to nonperturbative QCD dynamics.

## Contribution

It provides the first numerical solution of the $SU(3)$ sphaleron in a single Higgs triplet model and discusses its implications in extended theories resembling QCD.

## Key findings

- The $SU(3)$ sphaleron energy is comparable to the embedded $SU(2) imes U(1)$ sphaleron.
- Numerical solutions for the sphaleron are obtained in the single Higgs triplet model.
- Extended $SU(3)$ models suggest a role for sphalerons in nonperturbative QCD.

## Abstract

We complete the construction of the sphaleron $\widehat{S}$ in $SU(3)$ Yang-Mills-Higgs theory with a single Higgs triplet by solving the reduced field equations numerically. The energy of the $SU(3)$ sphaleron $\widehat{S}$ is found to be of the same order as the energy of a previously known solution, the embedded $SU(2)\times U(1)$ sphaleron $S$. In addition, we discuss $\widehat{S}$ in an extended $SU(3)$ Yang-Mills-Higgs theory with three Higgs triplets, where all eight gauge bosons get an equal mass in the vacuum. This extended $SU(3)$ Yang-Mills-Higgs theory may be considered as a toy model of quantum chromodynamics without quark fields and we conjecture that the $\widehat{S}$ gauge fields play a significant role in the nonperturbative dynamics of quantum chromodynamics (which does not have fundamental scalar fields but gets a mass scale from quantum effects).