Analysis of SO(2N) Couplings of Spinor and Tensor Representations in SU(N)×U(1)SU(N)\times U(1) Invariant Forms

A review is given of a recently developed technique for the analysis of SO(2N) invariant couplings which allows a full exhibition of the SU(N) invariant content of couplings involving the SO(2N) semi-spinors $|\Psi_{\pm}>$ with chiralilty $\pm$ and tensor representations. We discuss the Basic Theorem used in the analysis and then exhibit the technique by illustrative examples for the computation of the trilinear and quartic couplings for the SO(10) case involving three generations of 16 plets of matter.Comment: 8 pages Latex. Prepared for Proceedings of Pran Nath Fest in PASCOS04, August 17-22, 200

Yukawa Couplings and Quark and Lepton Masses in an SO(10) Model with a Unified Higgs Sector

An analytic computation is given of the generation of Yukawa couplings and of the quark, charged lepton and neutrino masses in the framework of an SO(10) model with a unified Higgs sector consisting of a single pair of vector-spinor $144 + \overline{144}$ of Higgs multiplets. This unified Higgs sector allows for a breaking of SO(10) to the gauge group $SU(3)\times SU(2)_L \times U(1)_Y$ and contains light Higgs doublets allowing for the breaking of the electroweak symmetry. Fermion mass generation in this model typically arises from quartic couplings $16\cdot 16\cdot 144\cdot 144$ and $16\cdot 16\cdot \overline{144}\cdot \overline{144}$. Extending a previous work it is shown that much larger third generation masses can arise for all the fermions from mixing with 45 and 120 matter multiplets via the cubic couplings $16\cdot45\cdot\overline{144}$ and $16\cdot120\cdot144$. Further it is found that values of $\tan\beta$ as low as 10 can allow for a $b-\tau-t$ unification consistent with current data. The quartic and cubic couplings naturally lead to Dirac as well as Majorana neutrino masses necessary for the generation of See Saw neutrino masses.Comment: 34 page, 1 figur