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Description
Sphalerons are processes which are able to violate individually the conservation of the $B+L$ number. Consequently, in the presence of a source, like a chemical potential, the sphalerons can produce a baryon number. This is the case of the traditional electroweak baryogenesis scenario where a chiral asymmetry produced by the bubble wall biases the sphalerons in the symmetric phase. If the wall is too fast or too thin, this mechanism fails. However sphalerons can still be biased if the thin higgs wall contain a axion profile coupled to the $SU(2)$ sector. In the regime in which the bubble wall is thinner than the size of the sphalerons, the effect of the wall on the sphalerons is non-adiabatic. In this paper, we study this source of baryon number.