A complex-angle rotation and geometric complementarity in fermion mixing

초록

The mixing among flavors in quarks or leptons in terms of a single rotation angle defined such that three flavor eigenvectors are transformed into three mass eigenvectors by a single rotation about a common axis. We propose that a geometric complement aritY condition exists between the complex angle of quarks and that of leptons in C2 space. The complementarity constraint has its rise in quark-lepton unification and is reduced to the correlation among 012,023,013 and the CP phase 6. The CP phase turns out to have a non-trivial dependence on all the other angles. We will show that further precise measurements in real angles can narrow down the allowed region of 6. In comparison with other complementarity schemes, this geometric one can avoid the problem of the 013 exception and cart naturally keep the lepton basis being independent of quark basis.

키워드