On-shell renormalization of the mixing matrices in Majorana neutrino theories
Abstract We generalize a recently proposed on-shell approach to renormalize the Cabibbo–Kobayashi–Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.
Renormalization of the Cabibbo–Kobayashi–Maskawa matrix at one-loop level
We have investigated the present renormalization prescriptions of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix. Based on one prescription which is formulated by comparing with the fictitious case of no mixing of quark generations, we propose a new prescription which can make the physical amplitude involving quark mixing gauge independent and ultraviolet finite. Compared with the previous prescriptions this prescription is very simple and suitable for actual calculations. Through analytical calculations we also give a strong proof for the important hypothesis that in order to keep the CKM matrix gauge independent the unitarity of the CKM matrix must be preserved.
Mixing between ordinary and exotic fermions.
The results of a comprehensive analysis of the limits on mixings between ordinary fermions and possible heavy fermions with exotic SU(2) x U(1) assignments (e.g., left-handed singlets and/or right-handed doublets) are presented. A general formalism for describing such mixings is given. It is shown that a variety of constraints, including the relation between the W and Z masses and the Fermi constant, charged-current universality, limits on induced right-handed charged currents, and flavor-diagonal neutral currents suffice to limit all directions in parameter space that are not excluded by the absence of flavor-changing neutral currents. Limits on s/sup 2/, the square of the mixing between ordinary and exotic fermions, are quite stringent for the ..nu../sub ..mu..//sub L/, ..mu../sub L//sup -/, u/sub L/, and d/sub L/ (s/sup 2/less than or equal to0.002--0.005) if only one particle is allowed to mix at a time, but are weaker by an order of magnitude if fine-tuned cancellations between different mixings are allowed. Similar statements apply to quark mixings with heavy sequential doublets. Limits on s/sup 2/ for the other light fermions (..nu../sub e//sub L/, e/sub L//sup -/,e/sub R//sup -/,..mu../sub R//sup -/, u/sub R/,d/sub R/) are in the range 0.02--0.06, while those for the s, c, b,more » ..nu../sub tau/, and tau/sup -/ are considerably weaker. Slightly stronger limits are found in specific models (e.g., E/sub 6/). Implications for the masses of the heavy exotic fermions are discussed.« less