Mixing at 1-loop in a SU(2)_L gauge theory of weak interactions
Résumé
Flavor mixing is scrutinized at 1-loop in a SU(2)_L gauge theory of massive fermions. The main issue is to cope with kinetic-like, momentum (p^2) dependent effective interactions that arise at this order. They spoil the unitarity of the connection between flavor and mass states, which potentially alters the standard Cabibbo-Kobayashi-Maskawa (CKM) phenomenology by giving rise, in particular, to extra flavor changing neutral currents (FCNC). We explore the conservative requirement that these should be suppressed, which yields relations between the CKM angles, the fermion and $W$ masses, and a renormalization scale $\mu$. For two generations, two solutions arise: either the mixing angle of the fermion pair the closer to degeneracy is close to maximal while, inversely, the mass and flavor states of the other pair are quasi-aligned, or mixing angles in both sectors are very small. For three generations, all mixing angles of neutrinos are predicted to be large (theta_{23}, close to maximal, is the largest) and the smallness of their mass differences induces mass-flavor quasi-alignment for all charged leptons. The hadronic sector differs in that the top quark is twice as heavy as the W. The situation is, there, bleaker, as all angles come out too large, but, nevertheless, encouraging, because theta_{12} decreases as the top mass increases. Whether other super-heavy fermions could drag it down to realistic values stays an open issue, together with the role of higher order corrections. The same type of counterterms that turned off the 4th order static corrections to the quark electric dipole moment are, here too, needed, in particular to stabilize quantum corrections to mixing angles.
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