Elementary Particles and Spin Representations

We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation degrees of freedoms in terms of a single chiral spin representation of one of the groups SO(13,1), SO(9,5), SO(7,7) or SO(3,11). The realization of these groups as higher dimensional space-time symmetries produces unification of all fundamental fermions is a single space-time spinor.Comment: 4 page

Neutrino masses and mixings

We propose a novel theoretical understanding of neutrino masses and mixings, which is attributed to the intrinsic vector-like feature of the regularized Standard Model at short distances. We try to explain the smallness of Dirac neutrino masses and the decoupling of the right-handed neutrino as a free particle. Neutrino masses and mixing angles are completely related to each other in the Schwinger-Dyson equations for their self-energy functions. The solutions to these equations and a possible pattern of masses and mixings are discussed.Comment: LaTex 11 page

Dark matter from SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on SU(4) and SU(2)xSU(2) groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the 4-th generation of fermions are the same as that of the ordinary-matter fermions in first three generations except for the family charge of the SU(4)_F group: F=(1/3,1/3,1/3,-1), where F=1/3 for fermions of ordinary matter and F=-1 for the 4-th generation. The difference in F does not allow the mixing between ordinary and fourth-generation fermions. Because of the conservation of the F charge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the 4-th generation. As a result the excess n_B of baryons over antibaryons leads to the excess n_{\nu 4}=N-\bar N=n_B of neutrinos over antineutrinos in the 4-th generation. This massive fourth-generation neutrino may form the non-baryonic dark matter. In principle their mass density n_{\nu 4}m_N in the Universe can give the main contribution to the dark matter, since the lower bound on neutrino mass m_N from the data on decay of the Z-bosons is m_N > m_Z/2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude bigger than allowed by observations. This inconsistency may be avoided by non-conservation of the F-charge.Comment: 9 pages, 2 figures, version accepted in JETP Letters, corrected after referee reports, references are adde

General impossible operations in quantum information

We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal superposition of the original and its complement state. Surprisingly, we find that Hadamard transformations exist for an unknown qubit chosen either from the polar or equatorial great circles. Also, we show that for an unknown qubit one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement state. We discuss why it is impossible to design a controlled-NOT gate for two unknown qubits and discuss the implications of these limitations.Comment: 15 pages, no figures, Discussion about personal quantum computer remove

Unification of SU(2)xU(1) Using a Generalized Covariant Derivative and U(3)

A generalization of the Yang-Mills covariant derivative, that uses both vector and scalar fields and transforms as a 4-vector contracted with Dirac matrices, is used to simplify and unify the Glashow-Weinberg-Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.Comment: 12 pages, no figures. To be published in Int. J. Mod. Phys.

Neutrinoless double beta decay in SO(10) inspired seesaw models

By requiring the lower limit for the lightest right-handed neutrino mass, obtained in the baryogenesis from leptogenesis scenario, and a Dirac neutrino mass matrix similar to the up-quark mass matrix we predict small values for the $\nu_e$ mass and for the matrix element $m_{ee}$ responsible of the neutrinoless double beta decay, $m_{\nu_e}$ around $5\cdot10^{-3}$ eV and $m_{ee}$ smaller than $10^{-3}$ eV, respectively. The allowed range for the mass of the heaviest right-handed neutrino is centered around the value of the scale of B - L breaking in the SO(10) gauge theory with Pati-Salam intermediate symmetry.Comment: 9 pages, RevTex4. Revised, title change

Non-universal gaugino masses from non-singlet F-terms in non-minimal unified models

In phenomenological studies of low-energy supersymmetry, running gaugino masses are often taken to be equal near the scale of apparent gauge coupling unification. However, many known mechanisms can avoid this universality, even in models with unified gauge interactions. One example is an F-term vacuum expectation value that is a singlet under the Standard Model gauge group but transforms non-trivially in the symmetric product of two adjoint representations of a group that contains the Standard Model gauge group. Here, I compute the ratios of gaugino masses that follow from F-terms in non-singlet representations of SO(10) and E_6 and their sub-groups, extending well-known results for SU(5). The SO(10) results correct some long-standing errors in the literature.Comment: 13 page

Maximally Symmetric Minimal Unification Model SO(32) with Three Families in Ten Dimensional Space-time

Based on a maximally symmetric minimal unification hypothesis and a quantum charge-dimension correspondence principle, it is demonstrated that each family of quarks and leptons belongs to the Majorana-Weyl spinor representation of 14-dimensions that relate to quantum spin-isospin-color charges. Families of quarks and leptons attribute to a spinor structure of extra 6-dimensions that relate to quantum family charges. Of particular, it is shown that 10-dimensions relating to quantum spin-family charges form a motional 10-dimensional quantum space-time with a generalized Lorentz symmetry SO(1,9), and 10-dimensions relating to quantum isospin-color charges become a motionless 10-dimensional quantum intrinsic space. Its corresponding 32-component fermions in the spinor representation possess a maximal gauge symmetry SO(32). As a consequence, a maximally symmetric minimal unification model SO(32) containing three families in ten dimensional quantum space-time is naturally obtained by choosing a suitable Majorana-Weyl spinor structure into which quarks and leptons are directly embedded. Both resulting symmetry and dimensions coincide with the ones of type I string and heterotic string SO(32) in string theory.Comment: 17 pages, RevTex, published version with minor typos correcte

Non SUSY Unification in Left-Right Models

We explore in a model independent way the possibility of achieving the non supersymmetric gauge coupling unification within left-right symmetric models, with the minimal particle content at the left-right mass scale which could be as low as 1 TeV in a variety of models, and with a unification scale M in the range $10^5$ GeV $< M< 10^{17.7}$ GeV.Comment: 18 pages, Latex file, uses epsf style, four figures. Submitted for publication to Phys. Rev. D on Oct. 13, 199