Xing, ZZ (reprint author), Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China.
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) x U(1)(Y) gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p + q) x (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-l seesaw relation between the effective p x p light Majorana neutrino mass matrix M, and the q x q heavy Majorana neutrino mass matrix M-R. In other words, the numbers of massive left- and right-handed neutrinos axe 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.