Abstracts Physics

From instantons to sphalerons: thermal baryon non-conservation in the weak interactions

by Keith Frost

The Weinberg-Salam theory of the weak interactions predicts that net baryon number can be altered by non-perturbative topological transitions of SU(2) gauge fields. These topological transitions are intimately related with the existence and properties of topologically non-trivial solutions of the classical field equations of four-dimensional SU(2)-Higgs theory. As is well known, in this theory there is a static solution, the sphaleron, which represents the top of an energy barrier separating bosonic vacua with different baryon number. There are also instanton configurations in Euclidean space, which approach minimal action as the instanton size goes to zero, and represent tunneling from one vacuum to another. We solved numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods, these solutions approach small instanton - anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. We discuss implications for the temperature dependence of the baryon number non-conservation rate in the standard model.