Sphaleron
A sphaleron (Greek: σφαλερός "slippery") 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 numbers. Such processes cannot be represented by perturbative methods such as Feynman diagrams, and are therefore called non-perturbative. Geometrically, a sphaleron is simply a saddle point of the electroweak potential (in infinite-dimensional field space), much like the saddle point of the surface z(x,y)=x2−y2 in three-dimensional analytic geometry.
In the Standard Model, the anomaly violating baryon number can convert three baryons to three antileptons, and related processes, with a change in baryon number of 3. This violates conservation of baryon number and lepton number, but the difference B−L is conserved. A sphaleron may convert three baryons to anti-leptons and three anti-leptons to baryons, in multiples of 3.
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.
Since a sphaleron may convert baryons to antileptons and antibaryons to leptons, if the density of sphalerons was at some stage high enough, they would wipe out any net excess of baryons or anti-baryons. This has two important implications in any theory of baryogenesis within the Standard Model:
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