We propose a new mechanism for generating small neutrino masses which predicts the relation m ν ∼ v 4 /M 3 , where v is the electroweak scale, rather than the conventional seesaw formula m ν ∼ v 2 /M . Such a mass relation is obtained via effective dimension seven operators LLHH(H † H)/M 3 , which arise when an isospin 3/2 Higgs multiplet Φ is introduced along with iso-triplet leptons. The masses of these particles are naturally in the TeV scale. The neutral member of Φ acquires an induced vacuum expectation value and generates neutrino masses, while its triply charged partner provides the smoking gun signal of this scenario. These triply charged bosons can be pair produced at the LHC and the Tevatron, with Φ +++ decaying into W + ℓ + ℓ + or W + W + W + , possibly with displaced vertices. The leptonic decays of Φ +++ will help discriminate between normal and inverted hierarchies of neutrino masses. This scenario also allows for raising the standard Higgs boson mass to values in excess of 500 GeV.

By supplementing minimal supersymmetric SU (5) (MSSU(5)) with a flavor U (1) symmetry and two pairs of 15+15 'matter' supermultiplets, we present an improved model which explains the charged fermion mass hierarchies and the magnitudes of the CKM matrix elements, while avoiding the undesirable asymptotic mass relations m s = m µ , m d ms = me mµ . The strong coupling α s (M Z ) is predicted to be approximately 0.115, and the proton lifetime is estimated to be about five times larger than the MSSU(5) value. The atmospheric and solar neutrino puzzles are respectively resolved via maximal ν µ − ν τ and small mixing angle ν e − ν s MSW oscillations, where ν s denotes a sterile neutrino. The U (1) symmetry ensures not only a light ν s but also automatic 'matter' parity.

We present a class of realistic unified models based on supersymmetric SO(10) wherein issues related to natural doublet-triplet (DT) splitting are fully resolved. Using a minimal set of low dimensional Higgs fields which includes a single adjoint, we show that the Dimopoulos-Wilzcek mechanism for DT splitting can be made stable in the presence of all higher order operators without having pseudo-Goldstone bosons and flat directions. The µ term of order TeV is found to be naturally induced. A Z 2 -assisted anomalous U(1) A gauge symmetry plays a crucial role in achieving these results. The threshold corrections to α 3 (M Z ), somewhat surprisingly, are found to be controlled by only a few effective parameters. This leads to a very predictive scenario for proton decay. As a novel feature, we find an interesting correlation between the d = 6 (p → e + π 0 ) and d = 5 (p → νK + ) decay amplitudes which allows us to derive a constrained upper limit on the inverse rate of the e + π 0 mode. Our results show that both modes should be observed with an improvement in the current sensitivity by about a factor of five to ten.

We present the supersymmetric SU (5) models which provide a simple "all order" solution to the doublet-triplet splitting problem through the missing doublet mechanism. The crucial role is played by the anomalous U (1) A gauge symmetry and no additional discrete or global symmetries are needed. Remarkably, such models can be realized even if the 75-plet Higgs is replaced by the standard 24-plet. The same U (1) A symmetry can also guarantee an exact or approximate conservation of R parity, by suppressing the B and L violating operators to the needed level. The neutrino masses and the proton decay via d = 5 operators are also examined. We also extend the model by incorporating U (1) A as a horizontal symmetry for explaining the fermion mass and mixing hierarchy. Interestingly, in this scheme the necessary mild violation of the troublesome SU (5) degeneracy between the down quark and the charged lepton masses can be induced by certain R-parity violating operators.

The group E6 for grand unification is combined with the generation symmetry group SO(3)g. The coupling matrices in the Yukawa interaction are identified with the vacuum expectation values of scalar fields which are representations of the generation symmetry. These values determine the hierarchy of the fermions as well as their mixings and CP-violation. This generation mixing appears in conjunction with the mixing of the standard model fermions with the heavy fermions present in the lowest representation of E6. A close connection between charged and neutral fermions is observed relating for instance the CKM mixings with the mass splittings of the light neutrinos. Numerical fits with only few parameters reproduce quantitatively all known fermion properties. The model predicts an inverted neutrino hierarchy and gives rather strict values for the light and heavy neutrino masses as well as for the 0ν2β decay parameter. It also predicts that the masses of the two lightest of six 'right handed' neutrinos lie in the low TeV region.