Flipped SU(5), see-saw scale physics and degenerate vacua

We investigate the requirement of the existence of two degenerate vacua of the effective potential as a function of the Weinberg-Salam Higgs scalar field norm, as suggested by the multiple point principle, in an extension of the Standard Model including see-saw scale physics. Results are presented from an investigation of an extension of the Standard Model to the gauge symmetry group SU(3)_C\times SU(2)_L\times U(1)'\times \tilde U(1), where two groups U(1)' and \tilde U(1) originate at the see-saw scale M_{SS}, when heavy (right-handed) neutrinos appear. The consequent unification of the group SU(3)_C\times SU(2)_L\times U(1)' into the flipped SU(5) at the GUT scale leads to the group SU(5)\times \tilde U(1). We assume the position of the second minimum of the effective potential coincides with the fundamental scale, here taken to be the GUT scale. We solve the renormalization group equations in the one-loop approximation and obtain a top-quark mass of 171\pm 3 GeV and a Higgs mass of 129\pm 4 GeV, in the case when the Yukawa couplings of the neutrinos are less than half that of the top quark at the GUT scale.