Fermion masses in SO(10)

Abstract

Yukawa-coupling-constant unification together with the known fermion masses is used to constrain SO(10) models. We consider the case of one (heavy) generation, with the tree-level relation m b = m ,, calculating the limits on the intermediate scales due to the known limits on fermion masses. This analysis extends previous analyses which addressed only the simplest symmetry-breaking schemes. In the case where the low-energy model is the standard model with one Higgs doublet, there are very strong constraints due to the known limits on the top-quark mass and the r-neutrino mass. The two-Higgs-doublet case is less constrained, though we can make progress in constraining this model also. We identify those parameters to which the viability of the model is most sensitive. We also discuss the "triviality" bounds on m, obtained from the analysis of the Yukawa renormalization-group equations. Finally we address the role of a speculative constraint on the T-neutrino mass, arising from the cosmological implications of anomalous B + L violation in the early Universe. PACS numberk): 12.10.Dm, 12.15.Ff 4004 0 1 9 9 2 The American Physical Society

Cosmological consequences of spontaneous lepton number violation in SO(10) grand unification

“…This implies, by a triviality bound discussed in Ref. [6], that the heaviest righthanded neutrino must be less than approximately 1.5M…”

“…Note that we can derive an upper bound on the right-handed neutrino masses by a "triviality" argument, as discussed in Ref. [6]; |f ij | < ∼ 1.5, so that the heaviest right-handed neutrino should satisfy M N < ∼ 1.5v R , implying 1/R < ∼ 3 × 10 14 .…”

“…In Ref. [6] it was pointed out that, when the radiative corrections are taken into account, this constraint is reduced to a level that is consistent with gauge coupling unification. These are the issues which we set out to understand with the present work.…”

“…Constraints on the intermediate scales arising from gauge coupling unification and Yukawa coupling unification are analysed in Ref. [6].…”

On the renormalization-group analysis of gauge groups containing U(1) ⊗ U(1) factors

“…Using then the first of Eqs. (9), we get he numerical difference between the two procedures may however slightly affect analyses which use the gauge group SU(3), @ SU(2), 8 U(1), @ U(l)* as part of a three-step breaking chain of SO(10)[5,6].…”