Chiral Anomaly - An Example: Baryonic Charge Non-conservation

An Example: Baryonic Charge Non-conservation

The Standard Model of electroweak interactions has all the necessary ingredients for successful baryogenesis. Beyond the violation of charge conjugation and CP violation (charge+parity), baryonic charge violation appears through the Adler-Bell-Jackiw anomaly of the group.

Baryons are not conserved by the usual electroweak interactions due to quantum chiral anomaly. The classic electroweak Lagrangian conserves baryonic charge. Quarks always enter in bilinear combinations, so that a quark can disappear only in collision with an antiquark. In other words, the classical baryonic current is conserved:

However, quantum corrections destroy this conservation law and instead of zero in the right hand side of this equation, one gets

where is a numerical constant,

and the gauge field strength is given by the expression

An important fact is that the anomalous current non-conservation is proportional to the total derivative of a vector operator, (this is non-vanishing due to instanton configurations of the gauge field, which are pure gauge at the infinity), where the anomalous current is:

which is the Hodge dual of the Chern-Simons 3-form.