A theory of flavor mixing

Abstract

We investigate the origin of the Cabibbo angle and other flavor-mixing angles in an ambidextrous SU(2) L × SU(2) R × U(1) gauge theory of weak and electromagnetic interactions involving 2 n quark flavors. We show how a discrete symmetry of the Lagrangian leads to flavor-diagonal weak currents where all flavor-mixing angles vanish. Each quark is assigned a position on the “clock of flavor” and the charged-current weak interactions are identified as nearest-flavor couplings. Soft breakdown of the discrete symmetry leads to a one-parameter family of flavor-mixing angles in the charged weak currents. All angles are expressed in terms of this parameter and quark mass ratios. The neutral currents remain flavor diagonal. Upper and lower bounds on 2 n, the number of flavors, are obtained by constraining the theory to fit what is known from experiment. Departures from Cabibbo universality become intolerable if 2 n < 8. It is impossible to obtain enough CP violation if 2 n > 12. We conclude that the number of flavors must be 8, 10, or 12. We construct a more ambitious theory in which the Cabibbo angle and its analogs are O( α) calculable radiative corrections. For reasonable values of the quark mass ratios, we fail to obtain a Cabibbo angle of the right order of magnitude. Our theory involves an equal number of lepton flavors and quark flavors. A large number of flavors is required if neutrinos are to be sufficiently light. We explore the case of 2 n = 12, and find a novel mechanism for the neutrino induction of trimuon events.