Minimal SUSY SO(10) and Yukawa Unification

The minimal supersymmetric (SUSY) SO(10) model, where only two Higgs multiplets {10 circle plus(126) over bar} are utilized for Yukawa couplings with matter fields, can nicely fit the neutrino oscillation parameters as well as charged fermion masses and mixing angles. In the fitting of the fermion mass matrix data, the largest element in the Yukawa coupling with the (126) over bar -plet Higgs (Y-126) is found to be of order one, so that the right see-saw scale should be provided by Higgs vacuum expectation values (VEVs) of O(10(14)GeV). This fact causes a serious problem, namely, the gauge coupling unification is spoiled because of the presence of many exotic Higgs multiples emerging at the see-saw scale. In order to solve this problem, we consider a unification between bottom-quark and tau Yukawa couplings (b - tau Yukawa coupling unification) at the grand unified theory (GUT) scale, due to threshold corrections of superpartners to the Yukawa couplings at the 1 TeV scale. When the b - tau Yukawa coupling unification is very accurate, the largest element in Y-126 can become O(0.01), so that the right see-saw scale is realized by the GUT scale VEV and the usual gauge coupling unification is maintained. Since the b - tau Yukawa unification alters the Yukawa coupling data at the GUT scale, we re-analyze the fitting of the fermion mass matrix data by taking all the relevant free parameters into account. Unfortunately, we find that no parameter region shows up to give a nice fit for the current neutrino oscillation data and therefore, the usual picture of the gauge coupling unification cannot accommodate the fermion mass matrix data fitting in our procedure.