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The dynamical generation of Dirac mass in the supersymmetricNambu$-$Jona-Lasinio (SNJL) model with the seesaw mechanism of neutrino isinvestigeted. The right and left handed Majorana mass parameters are introducedinto the SNJL model; we regard them as external model parameters. The questionon the origin of these Majorana masses are set aside, and we concentrate on theexamination of the effect of the Majorana mass parameters on the dynamicalgeneration of Dirac mass. The effective potential of the model and the gapequation for the self-consistent determination of Dirac mass are derived andsolved. We use both the four-dimensional covariant and three-dimensionalnon-covariant cutoff schemes for the regularizations of the effectivepotential. We find there are cases of the first and second order phasetransitions with respect to variation of the coupling constant of theNambu$-$Jona-Lasinio-type four-body interaction of the SNJL model. In the caseof second-order phase transition, the dynamically generated Dirac mass$|\phi_{S}|$ can arbitrarily be small compared with the right-handed Majoranamass parameter $|M|$ and thus the seesaw condition $0<|\phi_{S}|\ll|M|$ can besatisfied by a fine tuning of the coupling constant, while at the first-ordercase it seems very difficult and/or "unnatural" to satisfy the condition. Thenumerical results do not depend on the difference of the cutoff schemesqualitatively.

Dynamical Dirac Mass Generation in the Supersymmetric Nambu--Jona-Lasinio Model with the Seesaw Mechanism of Neutrinos