Comment on SU(16) grand unification

In a recent paper on SU(16) grand unification, because of the presence of intermediate-energy gauge groups containing products of U(1) factors which are not orthogonal among themselves, the renormalization-group treatment has a few small errors. I correct it. I emphasize that one should not switch gauge couplings at the various thresholds. It is easier, and it avoids errors, to use throughout the gauge couplings of the standard model, and compute at each threshold, in the usual way, the extra contributions to the beta functions from the extra non-decoupled fields. I also point out that the SU(16) grand unification theory, due to the large number of scalars present in it, is not asymptotically free. It becomes a strong-coupling theory at energies only slightly larger than the unification scale.Comment: 5 latex pages, 2 tables, no figure

Constrained analytical interrelations in neutrino mixing

Hermitian squared mass matrices of charged leptons and light neutrinos in the flavor basis are studied under general additive lowest order perturbations away from the tribimaximal (TBM) limit in which a weak basis with mass diagonal charged leptons is chosen. Simple analytical expressions are found for the three measurable TBM-deviants in terms of perturbation parameters appearing in the neutrino and charged lepton eigenstates in the flavor basis. Taking unnatural cancellations to be absent and charged lepton perturbation parameters to be small, interrelations are derived among masses, mixing angles and the amount of CP-violation.Comment: To be published in the Springer Proceedings in the Physics Series under the heading of the XXI DAE-BRNS Symposium (Guwahati, India

Asymmetric neutrino Yukawa matrices and neutrino mixing

We study leptonic CKM mixing matrices when the neutrino Yukawa matrices are antisymmetric which gives rise to mass patterns suitable to explain solar, atmospheric and LSND neutrino oscillation experiments. Taking diagonal leptonic matrices which can give rise to hierarchical lepton masses, we compute the leptonic CKM matrix.Comment: version to appear in Phys. Rev.

Proton Decay and Related Processes in Unified Models with Gauged Baryon Number:

In unification models based on SU(15) or SU(16), baryon number is part of the gauge symmetry, broken spontaneously. In such models, we discuss various scenarios of important baryon number violating processes like proton decay and neutron-antineutron oscillation. Our analysis depends on the effective operator method, and covers many variations of symmetry breaking, including different intermediate groups and different Higgs boson content. We discuss processes mediated by gauge bosons and Higgs bosons parallely. We show how accidental global or discrete symmetries present in the full gauge invariant Lagrangian restrict baryon number violating processes in these models. In all cases, we find that baryon number violating interactions are sufficiently suppressed to allow grand unification at energies much lower than the usual $10^{16}$ GeV.Comment: (32 pages LATEX) [DOE-ER\,40757-022, CPP-93-22] {Small changes made and two references added. This version will appear in Phys. Rev. D

Left-Right Symmetry and Supersymmetric Unification

The existence of an SU(3) X SU(2)_L X SU(2)_R X U(1) gauge symmetry with g_L = g_R at the TeV energy scale is shown to be consistent with supersymmetric SO(10) grand unification at around 1O^{16} GeV if certain new particles are assumed. The additional imposition of a discrete Z_2 symmetry leads to a generalized definition of R parity as well as highly suppressed Majorana neutrino masses. Another model based on SO(10) X SO(10) is also discussed.Comment: 11 pages, 2 figures not included, UCRHEP-T124, Apr 199

Infrared Quasi Fixed Point Structure in Extended Yukawa Sectors and Application to R-parity Violation

We investigate one-loop renormalization group evolutions of extended sectors of Yukawa type couplings. It is shown that Landau Poles which usually provide necessary low energy upper bounds that saturate quickly with increasing initial value conditions, lead in some cases to the opposite behaviour: some of the low energy couplings decrease and become vanishingly small for increasingly large initial conditions. We write down the general criteria for this to happen in typical situations, highlighting a concept of {\sl repulsive} quasi-fixed points, and illustrate the case both within a two-Yukawa toy model as well as in the minimal supersymmetric standard model with R-parity violation. In the latter case we consider the theoretical upper bounds on the various couplings, identifying regimes where $\lambda_{kl3}, \lambda'_{kkk}, \lambda''_{3kl}$ are dynamically suppressed due to the Landau Pole. We stress the importance of considering a large number of couplings simultaneously. This leads altogether to a phenomenologically interesting seesaw effect in the magnitudes of the various R-parity violating couplings, complementing and in some cases improving the existing limits.Comment: Latex, 33 pages, 6 figure

Effects of 126 dimensional Higgs scalar on Bottom-Tau unification and quasi-infrared fixed point

In the presence of ${\bf 126 + \bar{126}}$ Higgs multiplets in a SO(10) theory, the fermion masses get contributions from an induced vacuum expectation value (VEV) of a $SU(2)_L$ doublet residing in ${\bf 126}$ which differentiates between quarks and leptons by a relative sign leading to a significant correction to the prediction of the mass ratio of the bottom quark and the tau lepton for ranges of the mass of this extra doublet. We perform a two-loop renormalization group analysis of the minimal version of the one-step supersymmetric SO(10) model to display this and re-calculate the corrections to the top quark mass in the presence of such an induced VEV. We show that these effects make the infra-red fixed point scenario consistent with experimental results.Comment: revised version with same conclusions. To appear in Phys. Rev.

B-physics constraints on baryon number violating couplings: grand unification or R-parity violation

We investigate the role that baryon number violating interactions may play in $B$ phenomenology. Present in various grand unified theories, supersymmetric theories with R-parity violation and composite models, a diquark state could be quite light. Using the data on B decays as well as $B - {\bar B}$ mixing, we find strong constraints on the couplings that such a light diquark state may have with the Standard Model quarks.Comment: 19 pages, latex, no figures, 13 tables include

Infrared Fixed Point Structure in Minimal Supersymmetric Standard Model with Baryon and Lepton Number Violation

We study in detail the renomalization group evolution of Yukawa couplings and soft supersymmetry breaking trilinear couplings in the minimal supersymmetric standard model with baryon and lepton number violation. We obtain the exact solutions of these equations in a closed form, and then depict the infrared fixed point structure of the third generation Yukawa couplings and the highest generation baryon and lepton number violating couplings. Approximate analytical solutions for these Yukawa couplings and baryon and lepton number violating couplings, and the soft supersymmetry breaking couplings are obtained in terms of their initial values at the unification scale. We then numerically study the infrared fixed surfaces of the model, and illustrate the approach to the fixed points.Comment: 16 pages REVTeX, figures embedded as epsfigs, replaced with version to appear in Physical Review D, minor typographical errors eliminated and references reordered, figures correcte

Can the SO(10) Model with Two Higgs Doublets Reproduce the Observed Fermion Masses?

It is usually considered that the SO(10) model with one 10 and one 126 Higgs scalars cannot reproduce the observed quark and charged lepton masses. Against this conventional conjecture, we find solutions of the parameters which can give the observed fermion mass spectra. The SO(10) model with one 10 and one 120 Higgs scalars is also discussed.Comment: 7 pages, 1 figure, REVTe