Narrow Results

The renormalization group equations (RGEs) of the mass matrices of quarks and leptons in an SO(10) model with two-Higgs scalars in the Yukawa coupling are studied. This model is the minimal model of SUSY and non-SUSY SO(10) GUT which can reproduce all the experimental data. Non-SUSY SO(10) GUT model has the intermediate energy phase, Pati–Salam phase, and passes through the symmetry breaking pattern, SO(10) → SU(2)_L × SU(2)_R × SU(4)_C → SU(2)_L × U(1)_Y × SU(3)_C. Though minimal, it has, after the Pati–Salam phase, four Higgs doublets in Yukawa interactions. We consider the RGEs of the Yukawa coupling constants of quarks and charged leptons and of the coupling constants of the dimension-five operators of neutrinos corresponding to the above symmetry breaking pattern. The scalar quartic interactions are also incorporated.

We show that superheavy threshold corrections in the New Minimal Supersymmetric GUT based on the SO(10) Higgs system can comfortably correct the prediction for the value of α₃(M_Z) from the relatively large value predicted by the two-loop RG equations to the central value determined by the current world average. The unification scale is raised above the one-loop value over almost all of the viable parameter space.

Alternative renormalizable minimal non-SUSY SO(10) GUT model is proposed. Instead of a 126-dimensional Higgs field, a 120-dimensional Higgs filed is introduced in addition to a 10-dimensional Higgs field and plays a crucial role to reproduce the realistic charged fermion mass matrices. With contributions of 120 Higgs field, the original Witten’s scenario of inducing the right-handed Majorana neutrino mass through 2-loop diagrams becomes phenomenologically viable. This model inherits the nice features of the conventional renormalizable minimal SO(10) GUT model with $10+\overline{126}$ Higgs fields, while supplemented with a low scale seesaw mechanism due to the 2-loop induced right-handed Majorana neutrino mass.

To facilitate explicit analysis of SO(10) GUT's we present rules for rewriting SO(10) tensor and spinor invariants in terms of invariants of its "Pati–Salam" maximal subgroup (SU(4)×SU(2)_L×SU(2)_R) supplemented by the discrete symmetry called D parity. Explicit decompositions of quadratic and cubic invariants relevant to GUT model building are presented and the role of D parity in organizing the terms explained. Our rules provide a complete and explicit method for obtaining the "Clebsch–Gordon" coefficients for SO(10)↔SU(4)×SU(2)_L×SU(2)_R in a notation appropriate for field theory models. We illustrate the usefulness our methods by calculating previously unavailable mass matrices and couplings of the SU(2)_L doublets and SU(3)_c triplets in the minimal SUSY SO(10) GUT which are essential to specify the phenomenology of this model. We also present the bare effective potential for baryon number violation in this model and show that it receives novel contributions from exchange of triplet Higgsinos contained the in "neutrino mass" Higgs submultiplets . This further tightens the emerging connection between neutrino mass and proton decay.

We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent generation of nonuniversal supersymmetry breaking scalar mass terms. We derive squark and slepton mass relations, taking into account these nonuniversal contributions to the sfermion masses, which can help distinguish between the different chains through which the SO(10) gauge group breaks to the Standard Model gauge group. We then study some implications of these nonuniversal supersymmetry breaking scalar masses for the low energy phenomenology.

We carry out a detailed analysis of sparticle mass spectrum in supersymmetric grand unified theories. We consider the spectroscopy of the squarks and sleptons in SU(5) and SO(10) grand unified theories, and show how the underlying supersymmetry breaking parameters of these theories can be determined from a measurement of different sparticle masses. This analysis is done analytically by integrating the one-loop renormalization group equations with appropriate boundary conditions implied by the underlying grand unified gauge group. We also consider the impact of nonuniversal gaugino masses on the sparticle spectrum, especially the neutralino and chargino masses which arise in supersymmetric grand unified theories with nonminimal gauge kinetic function. In particular, we study the interrelationships between the squark and slepton masses which arise in grand unified theories at the one-loop level, which can be used to distinguish between the different underlying gauge groups and their breaking pattern to the Standard Model gauge group. We also comment on the corrections that can affect these one-loop results.

The problem of understanding quark mass and mixing hierarchies has been an outstanding problem of particle physics for a long time. The discovery of neutrino masses in the past decade, exhibiting mixing and mass patterns so very different from the quark sector has added an extra dimension to this puzzle. This is specially difficult to understand within the framework of conventional grand unified theories which are supposed to unify the quarks and leptons at short distance scales. In the paper, I discuss a recent proposal by Dutta, Mimura and this author that appears to provide a promising way to resolve this puzzle. After stating the ansatz, we show how it can be realized within a SO(10) grand unification framework. Just as Gell-Mann's suggestion of SU(3) symmetry as a way to understand the hadronic flavor puzzle of the sixties led to the foundation of modern particle physics, one could hope that a satisfactory resolution of the current quark-lepton flavor problem would provide fundamental insight into the nature of physics beyond the standard model.

Supersymmetric GUT's are the most natural extension of the Standard Model unifying electroweak and strong forces. Despite their indubitable virtues, among these the gauge coupling unification and the quantization of the electric charge, one of their shortcomings is the large number of parameters used to describe the high energy thresholds, which are hard to handle. We present a new method according to which the effects of the high energy thresholds, in any GUT model, can be described by fewer parameters that are randomly produced from the original set of the parameters of the model. In this way, regions favored by the experimental data are easier to locate, avoiding a detailed and time-consuming exploration of the parameter space, which is multidimensional even in the most economic unifying schemes. To check the efficiency of this method, we directly apply it to a SUSY SO(10) GUT model in which the doublet–triplet splitting is realized through the Dimopoulos–Wilczek mechanism. We show that the demand of gauge coupling unification, in conjunction with precision data, locates regions of the parameter space in which values of the strong coupling α_strong are within the experimental limits, along with a suppressed nucleon decay, mediated by a higgsino driven dimension five operators, yielding lifetimes that are comfortably above the current experimental bounds. These regions open up for values of the SUSY breaking parameters m₀, M_1/2 < 1 TeV being therefore accessible to LHC.