Generalized Seesaw Mechanism of Neutrino and Bose-Einstein Condensation in the Modified O'Raifeartaigh Model

Abstract

The modified O'Raifeartaigh model from the context of the generalized seesaw mechanism of neutrino mass is investigated. In our evaluation of effective potentials of the theory, both the component field and the superspace formalisms to approach the problem are presented. In the component field formalism, we take into account the Bose-Einstein condensates in the scalar sector by the method of many-boson theory, i.e. we consider both the condensates and the Hartree-Fock-Bogoliubov-type self-energies of quantum fluctuations. The diagonalization of the mass matrix of the fermion sector gives the same functional forms of the mass eigenvalues in the generalized seesaw mechanism. The stability condition in the vicinity of the classical vacuum which shows the generalized seesaw situation is obtained by the examination of the mass eigenvalues of the scalar sector of the model. The superspace formalism will be devoted to a comparison between its result with that of the component field formalism.