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The structure of effective potential surface of the Nambu$-$Jona-Lasinio(NJL) model with right-left asymmetric Majorana mass terms (corresponds to thesingle-flavor type-II seesaw situation of neutrino) is investigated. After thedynamical generation of Dirac mass, two collective modes appear similar to thecase of ordinary NJL model, and the phase mode (phason), which corresponds tomajoron or pion at vanishing Majorana mass parameter(s), has an excitationmass. The mechanism of generation of phason as a pseudo Nambu-Goldstone bosonis examined by a mathematical manner, summarized into a theorem  (claims as the generalized Nambu-Goldstone theorem). The mass of phason isalso evaluated in a supersymmetric version of the NJL-type model, and phasonmass takes the order of that of axion commonly accepted today. An$SU(2_{c})$-gauge model is constructed for the context of neutrino seesawmechanism, and the Schwinger-Dyson equation of dynamical mass functions isexamined. Several physical implications such as decay modes of phason, anon-linear sigma model for phason are given. It is proposed that themethod/result of this paper can be applied to an understanding on the origin ofthe Kobayashi-Maskawa matrix.

Dynamical Mass Generations and Collective Excitations in the  (Supersymmetric-)Nambu$-$Jona-Lasinio Model and a Gauge Theory with  Left-Right-Asymmetric Majorana Mass Terms