Chiral anomaly: Encyclopedia II - Chiral anomaly - An example: baryonic charge non-conservation

Chiral anomaly - 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 C and CP violation CP, baryonic charge violation appears through the Adler-Bell-Jackiw anomaly [5] of the U(1) 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 C is a numerical constant,

and the gauge field strenth G_μν is given by the expression

An important fact is that the anomalous current nonconservation is proportional to the total derivative of a vector operator: where the anomalous current K_μ is

The last term in this expression is non-vanishing only for non-Abelian gauge theories because the antisymmetric product of three vector potentials A_ν can be nonzero due to different group indices (e.g. for the electroweak group it should contain the product of W ⁺ , W ⁻ and the isospin part of Z⁰).

Adapted from the Wikipedia article "An example: baryonic charge non-conservation", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki