The classical baryon current is anomalous under $SU(2)_L$:
$$
\partial_\mu J_B^\mu
\propto g^2W_{\mu\nu}^a\widetilde W^{a\mu\nu}.
$$
An electroweak instanton or <electroweak sphaleron> changes the topological charge and produces
$$
\Delta B=\Delta L=3,
\qquad
\Delta(B-L)=0
$$
for three generations. At zero temperature, instanton-induced baryon violation is exponentially tiny and irrelevant to proton decay. Above the electroweak scale, thermal sphaleron transitions are rapid; they can erase a pre-existing $B+L$ asymmetry or convert a $B-L$ asymmetry into the observed baryon asymmetry, making the anomaly central to <baryogenesis>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 305 / 4 / iii / Solution

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Baryogenesis is the dynamical production of the cosmic excess of baryons over antibaryons. It requires baryon-number violation, C and CP violation, and departure from thermal equilibrium, or an appropriate generalization of these Sakharov conditions.


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 Incoming links: Baryogenesis