Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

An SO(10) supersymmetric grand unified theory

A realistic supersymmetric SO(10) grand unified theory is explicitly constructed. The neutrino masses turn out to be 10^?5 eV or less. It is also found that the proton life time can be longer than 10³¹ yr.     

Explicit SO(10) supersymmetric grand unified model for the higgs and yukawa sectors

A complete set of fermion and Higgs superfields is introduced with well-defined SO(10) properties and U(1)xZ2xZ2 family charges from which the Higgs and Yukawa superpotentials are constructed. The structures derived for the four Dirac fermion and right-handed Majorana neutrino mass matrices coincide with those previously obtained from an effective operator approach. Ten mass matrix input parameters accurately yield the twenty masses and mixings of the quarks and leptons with the bimaximal atmospheric and solar neutrino vacuum solutions favored in this simplest version.     

Suppressing proton decay in the minimal SO(10) model

We show that in a class of minimal supersymmetric SO(10) models which have been found to be quite successful in predicting neutrino mixings, all proton decay modes can be suppressed by a particular choice of Yukawa textures. The required texture not only fits all lepton and quark masses as well as Cabibbo-Kobayashi-Maskawa parameters, but it also predicts neutrino mixing parameter U(e3) and Dirac CP phase sin(/delta(MNS)/ to be 0.07-0.09 and 0.3-0.7, respectively.     

A unified treatment of the groups SO(4) and SO(3,1)

The irreducible representations of the group SO(4) in which the SO(3) subgroup is reduced are studied by an explicit construction of the operators and the basis in the spinor representation. The basis function which is formally identical with that for the coupling of two angular momentaj ₁ andj ₂ is expressible in terms of a hypergeometric function and strongly resembles the one for the irreducible representations of the groups SO(3,1). For the Lorentz group, the bases for the unitary representations which require unphysical values ofj ₁ andj ₂ are found to be analytic continuation of those for SO(4). The realization of the unitary irreducible representations of the group SO(4) in the Hilbert space of these functions leads, for appropriate unphysical values ofj ₁,j ₂, to the Gelfand-Naimark formula for the principal and complementary series of the representations of SO(3;1). The matrix elements for finite transformations of SO(4) and SO(3,1) can be evaluated, in this approach, in a unified manner by using standard properties of the hypergeometric function. These turn out to be a finite sum of₃ F ₂-functions which, as expected, are polynomials for SO(4) and infinite series for SO(3,1). A number of special matrix elements are calculated from the general formula and these agree with the results obtained previously.The authors are deeply indebted to Professor S.Dutta Majumdar fo many important suggestions and clarifications.     

Bimaximal mixing in an SO(10) minimal Higgs model

An SO(10) SUSY GUT model was previously presented based on a minimal set of Higgs fields. The quark and lepton mass matrices derived fitted the data extremely well and led to large ν_μ−ν_τ mixing in agreement with the atmospheric neutrino data and to the small-angle MSW solution for the solar neutrinos. Here we show how a slight modification leading to a non-zero up quark mass can result in bimaximal mixing for the atmospheric and solar neutrinos. The “just-so” vacuum solution is slightly favored over the large-angle MSW solution on the basis of the hierarchy required for the right-handed Majorana matrix and the more nearly-maximal mixing angles obtained.     

Flipped SO(10)

We constract an N = 1 supersymmetric SO(10) GUT broken down to SU(3)_c×SU(2)_L×U(1)_Y with an intermediate flipped SU(5)×U(1)_X gauge symmetry. A solution to the triplet-doublet mass-splitting problem is proposed in terms of a non-minimal missing-partner mechanism.     

On the SO(7) symmetry of the SO(8) monopole and quadrupole pairing model

The SO(7) D-pairing symmetry of the SO(8) monopole and quadrupole pairing model is shown to be unusual in that there is no corresponding group generated only by number-conserving operators. Rather, the SO(7) symmetry is manifested in terms of number-conserving operators only by taking a particular combination of the Casimir operators appropriate for the other subgroup chains.     

An SO(10) model with 54 + 126 + 10 higgs

We find an absolute minimum of an SO(10) symmetric potential with SU(3) × U(1) invariance. By fixing the higher scales M_R(〈126〉) ? M_x(〈54〉), the model is consistent with the experimental knowledge about matter stability and the value of sin²θ_w. We determine the spectrum of scalar particles and show that their tree-diagram contributions to nucleon decay amplitudes are proportional to 1/M_x².     

Neutrino mass in the SO(10) grand unified gauge model

The problem of neutrino mass generation by a large Majorana mass term in the SO(10) grand unified gauge model is discussed. In particular, it is pointed out that the left-hand Majorana mass induced by the radiative corrections does not exceed that obtained by diagonalization of the mass matrix.     

SO(10) v ×SO(10) H grand unified-extended technicolour models

We discuss a recently proposedSO(10) _v ×SO(10) _H grand unified-extended technicolour model. Because proton decay is probably too fast in this model, we study the other possible models based onSO(10) _v ×SO(10) _H . As a result of this analysis only a few of these models could possibly be realistic, they would be slight modifications of that previously proposed. None of them predicts the expected value forΛ _TC, it must be adjusted by introducing another mass scale. In these models ordinary fermion masses tend to be too small.     

Third generation Yukawa couplings unification in supersymmetric SO(10) model

In the minimal supersymmetric standard model (MSSM) contained in SUSY SO(10), top-- Yukawa unification is achieved at the intermediate mass scale GeV using the recent world average experimental value of the top-quark mass, GeV, which has been directly established by CDF and D0 experiments at the Tevatron Collider. It is also observed that the Yukawa couplings unification scale can be further decreased by taking lower input values of the top-quark mass. This trend indicates the possible existence of an intermediate symmetry breaking scale in SUSY SO(10). The present finding does not agree with the earlier notion that the third generation Yukawa couplings unification should occur at the GUT scale . Received: 22 September 1997 / Revised version: 22 January 1998 / Published online: 24 March 1998