Fine-tuning problem in a left-right symmetric model and Sogami's generalized covariant derivative method

We study Sogami's generalized covariant derivative method for an 5(7(2)_L, x SU(2)_R x U(1)_B-L x SU(3)_c model that contains bi-doublet and triplet Higgs bosons. In particular, a detailed study is made on the minimization conditions of the Higgs potential. It is known that a minimization condition and certain phenomenology for an extra gauge boson mass yield a restriction on potential parameters, which require fine-tuning. We show that the restriction can be reduced to a condition of Yukawa coupling constants, giving a heavy mass of the right-handed tau neutrino in our model. We also discuss the consistency among parameter restrictions of our model by taking the phenomenology of the Higgs boson masses into account.