摘要
The observation of neutrino oscillations requires new physics beyond the standard model （SM）. A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU（2）L × U（1）Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric （p＋q） × （p＋q） matrix. Given p 〉 q, the rank of M is in general equal to 2q, corresponding to 2q non-zero mass eigenvalues. The existence of （p-q） massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix Mv and the q × q heavy Majorana neutrino mass matrix MR. In other words, the numbers of massive left- and right-handed neutrinos are fairly matched. A good example to illustrate this ＂seesaw fair play rule＂ is the minimal seesaw model with p = 3 and q = 2, in which one massless neutrino sits on the unbalanced seesaw.
The observation of neutrino oscillations requires new physics beyond the standard model （SM）. A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU（2）L × U（1）Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric （p＋q） × （p＋q） matrix. Given p 〉 q, the rank of M is in general equal to 2q, corresponding to 2q non-zero mass eigenvalues. The existence of （p-q） massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix Mv and the q × q heavy Majorana neutrino mass matrix MR. In other words, the numbers of massive left- and right-handed neutrinos are fairly matched. A good example to illustrate this ＂seesaw fair play rule＂ is the minimal seesaw model with p = 3 and q = 2, in which one massless neutrino sits on the unbalanced seesaw.
基金
Supported by National Natural Science Foundation of China (10425522)
