Sphaleron

From Wikipedia, the free encyclopedia

A sphaleron (σφαλερός, ά, όν: weak, or dangerous) is a static (time independent) solution to the electroweak field equations of the Standard Model of particle physics, and it is involved in processes that violate baryon and lepton number. Such processes cannot be represented by Feynman diagrams, and are therefore called non-perturbative. Geometrically, a sphaleron is simply a saddle point of the electroweak potential energy (in the infinite dimensional field space), much like the saddle point of the surface $z = x 2 - y 2$ in three dimensional analytic geometry.

In the standard model, baryon number violating processes convert three baryons to three antileptons, and related processes. This violates conservation of baryon number and lepton number, but the difference B−L is conserved. A sphaleron is similar to the midpoint ( $τ = 0$ ) of the instanton, so it is non-perturbative. This means that under normal conditions sphalerons are unobservably rare. However, they would have been more common at the higher temperatures of the early universe. In some theories of baryogenesis an imbalance of the number of leptons and antileptons is formed first by leptogenesis and sphaleron transitions then convert this to an imbalance in the numbers of baryons and antibaryons.