chapter  9
6 Pages

Theory Of Quark Mixing

The idea of mixing between quarks as an effect of symmetry breaking was introduced by Cabibbo in 1963 [28], in the context of a quark theory with three flavours: up, down and strange. In this picture, it is natural to classify the left-handed fields up and down as an electroweak doublet, and the other fields as singlets, according to the scheme:(

u d

) L

; uR; dR; sL; sR. (9.1)

Cabibbo observed that symmetry breaking can give rise to a mixing between dL and sL, giving an expression for the weak current of the form:

J1µ + iJ 2 µ = u¯Lγµ (cos θdL + sin θsL) . (9.2)

With a single electroweak parameter, the Cabibbo angle θ, and a few phenomenological parameters related to strong interactions, excellent agreement for β decays of baryons and mesons, with and without strangeness, is obtained.