Coupling the Supersymmetric 210 Vector Multiplet to Matter in SO(10)

An analysis of the couplings of the 210 dimensional SO(10) vector multiplet to matter is given. Specifically we give an $SU(5)\times U(1)$ decomposition of the vector couplings $\bar{16}_{\pm}-16_{\pm}-210$, where $16_{\pm}$ is the semispinor of SO(10) chirality ${\pm}$, using a recently derived basic theorem. The analysis is carried out using the Wess-Zumino gauge. However, we also consider the more general situation where all components of the vector multiplet enter in the couplings with the chiral fields. Here elimination of the auxiliary fields leads to a sigma model type nonlinear Lagrangian. Interactions of the type analysed here may find applications in effective theories with the 210 vector arising as a condensate. The analysis presented here completes the explicit computation of all lowest order couplings involving the $16_{\pm}$ of spinors with Higgs and vectors multiplets using the basic theorem.Comment: 33 pages, Latex. To appear in Nuclear Physics

Complete Cubic and Quartic Couplings of 16 and 16ˉ\bar {16} in SO(10) Unification

A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving $16_{\pm}$ semispinors of SO(10) chirality $\pm$ and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and $\bar{126}$ tensor representations we compute here couplings involving the 1, 45 and 210 dimensional tensor representations, i.e., we compute the $\bar{16}_{\mp}16_{\pm}1$,$\bar{16}_{\mp}16_{\pm}45$ and $\bar{16}_{\mp}16_{\pm}210$ Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1, 45 and 210 dimensional representations is also given. The vector couplings $\bar{16}_{\pm}16_{\pm}1$, $\bar{16}_{\pm}16_{\pm}45$ and $\bar{16}_{\pm}16_{\pm}210$ are also analyzed. The role of large tensor representations and the possible application of results derived here in model building are discussed.Comment: 21 pages, Latex. Revised version to appear in Nuclear Physics

An apprach to generate large and small leptonic mixing angles

We take up the point of view that Yukawa couplings can be either 0 or 1, and the mass patterns of fermions are generated purely from the structure of the Yukawa matrices. We utilize such neutrino as well as charged leptonic textures which lead to (maximal) mixing angles of $\pi/4$ in each sector for relevant transitions. The combined leptonic CKM mixing angles are $\pi/4 \pm \pi/4$ which lead to very small $\sin^2 2 \Theta$ relevant to solar neutrino and LSND experiments. We propose that on the other hand the absence of the charged leptonic partner of the sterile neutrino maintains the angle $\pi/4$ from the neutrino sector for the transition $\nu_\mu \leftrightarrow \nu_s$ and hence atmospheric neutrino anomaly is explained through maximal mixing

SU(3) Mixing for Excited Mesons

The SU(3)-flavor symmetry breaking and the quark-antiquark annihilation mechanism are taken into account for describing the singlet-octet mixing for several nonets assigned by Particle Data Group(PDG). This task is approached with the mass matrix formalism

Analysis of Couplings with Large Tensor Representations in SO(2N) and Proton Decay

We develop techniques for the analysis of SO(2N) invariant couplings which allow a full exhibition of the SU(N) invariant content of the spinor and tensor representations. The technique utilizes a basis consisting of a specific set of reducible SU(N) tensors in terms of which the SO(2N) invariant couplings have a simple expansion. The technique is specially useful for couplings involving large tensor representations. We exhibit the technique by performing a complete determination of the trilinear couplings in the superpotential for the case of SO(10) involving the 16 plet of matter, i.e., we give a full determination of the ${16-16-10_s}$, ${16-16-120_a}$ and ${16-16-\bar{126}_s}$ couplings. The possible role of large tensor representations in the generation of quark lepton textures is discussed. It is shown that the couplings involving $\bar{126}$ dimensional representation generate extra zeros in the Higgs triplet textures which can lead to an enhancement of the proton decay lifetime by a factor of $10^3$. These results also have implications for neutrino mass textures.Comment: 14 pages, Latex: With the corrections of an Erratum included in the text of pape

New Supersymmetric Contributions to t−>cVt->cV

We calculate the electroweak-like one-loop supersymmetric contributions to the rare and flavor-violating decay of the top quark into a charm quark and a gauge boson: $t->c V$, with $V=\gamma,Z,g$. We consider loops of both charginos and down-like squarks (where we identify and correct an error in the literature) and neutralinos and up-like squarks (which have not been calculated before). We also account for left-right and generational squark mixing. Our numerical results indicate that supersymmetric contributions to $t->cV$ can be upto 5 orders of magnitude larger than their Standard Model counterparts. However, they still fall short of the sensitivity expected at the next-generation top-quark factories.Comment: 13 pages, LaTex, 1 figure included. Final version to appear in Physical Review D. Chargino contribution dealt with in greater detail. Minor revisions in tex

The Effects of Fourth Generation on the double Lepton Polarization in B \rar K \ell^+ \ell^- decay

This study investigates the influence of the fourth generation quarks on the double lepton polarizations in B \rar K \ell^+ \ell^- decay. Taking |V_{t's}V_{t'b}|\sim \{0.01-0.03\} with phase about 100^\circ, which is consistent with the b\to s\ell^+\ell^- rate and the B_s mixing parameter Delta m_{B_s}$, we obtain that the double lepton(muon and tau) polarizations are quite sensitive to the existence of fourth generation. It can serve as a good tool to search for new physics effects, precisely, to indirect search for the fourth generation quarks(t', b').Comment: 30 pages, 27 figure

The Comparative Osteology of the Petrotympanic Complex (Ear Region) of Extant Baleen Whales (Cetacea: Mysticeti)

Anatomical comparisons of the ear region of baleen whales (Mysticeti) are provided through detailed osteological descriptions and high-resolution photographs of the petrotympanic complex (tympanic bulla and petrosal bone) of all extant species of mysticete cetaceans. Salient morphological features are illustrated and identified, including overall shape of the bulla, size of the conical process of the bulla, morphology of the promontorium, and the size and shape of the anterior process of the petrosal. We place our comparative osteological observations into a phylogenetic context in order to initiate an exploration into petrotympanic evolution within Mysticeti.The morphology of the petrotympanic complex is diagnostic for individual species of baleen whale (e.g., sigmoid and conical processes positioned at midline of bulla in Balaenoptera musculus; confluence of fenestra cochleae and perilymphatic foramen in Eschrichtius robustus), and several mysticete clades are united by derived characteristics. Balaenids and neobalaenids share derived features of the bulla, such as a rhomboid shape and a reduced anterior lobe (swelling) in ventral aspect, and eschrichtiids share derived morphologies of the petrosal with balaenopterids, including loss of a medial promontory groove and dorsomedial elongation of the promontorium. Monophyly of Balaenoidea (Balaenidae and Neobalaenidae) and Balaenopteroidea (Balaenopteridae and Eschrichtiidae) was recovered in phylogenetic analyses utilizing data exclusively from the petrotympanic complex.This study fills a major gap in our knowledge of the complex structures of the mysticete petrotympanic complex, which is an important anatomical region for the interpretation of the evolutionary history of mammals. In addition, we introduce a novel body of phylogenetically informative characters from the ear region of mysticetes. Our detailed anatomical descriptions, illustrations, and comparisons provide valuable data for current and future studies on the phylogenetic relationships, evolution, and auditory physiology of mysticetes and other cetaceans throughout Earth's history