GRADED DIFFERENTIAL LIE ALGEBRAS AND SU(5)×U(1)-GRAND UNIFICATION

1998 ◽  
Vol 13 (15) ◽  
pp. 2627-2692 ◽  
Author(s):  
RAIMAR WULKENHAAR
Keyword(s):  
Mass Matrix ◽  
Algebraic Approach ◽  
Higgs Field ◽  
Higgs Bosons ◽  
Tree Level ◽  
The Matrix ◽  
The Masses ◽  
The Given ◽  
Higgs Fields ◽  
General Gauge

We formulate the flipped SU(5)×U(1)-GUT within a Lie-algebraic approach to non-commutative geometry. It suffices to take the matrix Lie algebra su(5) as the input; the u(1)-part with its representation on the fermions is an algebraic consequence. The occurring Higgs multiplets (24, 5, 45, 50-representations of su(5)) are uniquely determined by the fermionic mass matrix and the spontaneous symmetry breaking pattern to SU(3)C×U(1)EM. We find the most general gauge invariant Higgs potential that is compatible with the given Higgs vacuum. Our formalism yields tree-level predictions for the masses of all gauge and Higgs bosons. It turns out that the low-energy sector is identical with the standard model. In particular, there exists precisely one light Higgs field, whose upper bound for the mass is 1.45 mt. All remaining 207 Higgs fields are extremely heavy.

QUASI SUPERSYMMETRY WITHIN THE STANDARD MODEL AND HIGGS MASS

1999 ◽  
Vol 14 (35) ◽  
pp. 2447-2452
Author(s):  
B. B. DEO ◽  
L. P. SINGH
Keyword(s):  
Standard Model ◽  
Top Quark ◽  
Degrees Of Freedom ◽  
Higgs Mass ◽  
Higgs Bosons ◽  
Tree Level ◽  
Mass Relation ◽  
The Standard Model ◽  
A Charge ◽  
Higgs Fields

The 12 bosonic degrees of freedom of the standard model (SM) are exactly matched by fermionic degrees of freedom of a single colored quark, e.g. top. Indeed, we construct a charge involving top-quark, gauge and Higgs fields which satisfy usual supersymmetry algebra. The colored quark states behave like the superpartners of gauge and Higgs bosons and vice versa. When this SUSY is broken, a mass relation must be satisfied at the tree level from which the mass of the Higgs is predicted to be 300.5±11 GeV.

scholarly journals R-symmetric flipped SU(5)

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Koichi Hamaguchi ◽  
Shihwen Hor ◽  
Natsumi Nagata
Keyword(s):  
Scale Up ◽  
Higgs Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Large Mass ◽  
Proton Decay ◽  
Decay Modes ◽  
Splitting Problem ◽  
The Masses ◽  
Higgs Fields

Abstract We construct a supersymmetric flipped SU(5) grand unified model that possesses an R symmetry. This R symmetry forbids dangerous non-renormalizable operators suppressed by a cut-off scale up to sufficiently large mass dimensions so that the SU(5)-breaking Higgs field develops a vacuum expectation value of the order of the unification scale along the F- and D-flat directions, with the help of the supersymmetry-breaking effect. The mass terms of the Higgs fields are also forbidden by the R symmetry, with which the doublet-triplet splitting problem is solved with the missing partner mechanism. The masses of right-handed neutrinos are generated by non-renormalizable operators, which then yield a light neutrino mass spectrum and mixing through the seesaw mechanism that are consistent with neutrino oscillation data. This model predicts one of the color-triplet Higgs multiplets to lie at an intermediate scale, and its mass is found to be constrained by proton decay experiments to be ≳ 5 × 1011 GeV. If it is ≲ 1012 GeV, future proton decay experiments at Hyper-Kamiokande can test our model in the p → π0μ+ and p → K0μ+ decay modes, in contrast to ordinary grand unified models where p → π0e+ or p → $$ {K}^{+}\overline{\nu} $$ K + ν ¯ is the dominant decay mode. This characteristic prediction for the proton decay branches enables us to distinguish our model from other scenarios.

scholarly journals COSMOLOGICAL MODEL WITH BORN–INFELD TYPE SCALAR FIELD

2007 ◽  
Vol 04 (02) ◽  
pp. 249-275 ◽  
Author(s):  
A. TROISI ◽  
E. SÉRIÉ ◽  
R. KERNER
Keyword(s):  
Scalar Field ◽  
Order Term ◽  
Higgs Field ◽  
Natural Generalization ◽  
Relative Strength ◽  
First Approximation ◽  
The Matrix ◽  
Primordial Inflation ◽  
Double Well Potential ◽  
Higgs Fields

The non-abelian generalization of the Born–Infeld non-linear lagrangian is extended to the non-commutative geometry of matrices on a manifold. In this case, not only do the usual SU(n) gauge fields appear, but also a natural generalization of the multiplet of scalar Higgs fields, with the double-well potential as a first approximation. The matrix realization of non-commutative geometry provides a natural framework in which the notion of a determinant can be easily generalized and used as the lowest-order term in a gravitational lagrangian of a new kind. As a result, we obtain a Born–Infeld-like lagrangian as a root of sufficiently high order of a combination of metric, gauge potentials and the scalar field interactions. We then analyze the behavior of cosmological models based on this lagrangian. It leads to primordial inflation with varying speed, with possibility of early deceleration ruled by the relative strength of the Higgs field.

scholarly journals Restrictions on the parameters of the Minimal Supersymmetric Standard Model with CP-violation

2019 ◽  
Vol 222 ◽  
pp. 04005
Author(s):  
Albina Gurskaya ◽  
Mikhail Dolgopolov ◽  
Elza Rykova
Keyword(s):  
Cp Violation ◽  
Standard Model ◽  
Higgs Bosons ◽  
Boson Mass ◽  
Supersymmetric Particle ◽  
Model Parameters ◽  
Mixing Angle ◽  
The Standard Model ◽  
The Masses ◽  
Higgs Fields

The minimal supersymmetric extension of the standard model with CP-violation is considered in this paper. The main area of the model parameters, which is attractive for researchers, corresponds to small values of the tangent mixing angle of two doublets Higgs fields (tanβ). The authors discuss the possibilities of the model in correlation with the data on the search for the lightest stable supersymmetric particle. The masses of neutral Higgs bosons in the basis of CP-violationwas calculated.The results are presented as dependencies neutral CP-odd Higgs boson mass mA on tanβ. At small values tgβ the mass of the lightest stable particle must be more than ∼ 250 GeV.

GAUGED SU(2)L×SU(2)R/SU(2)L+Rσ MODEL IN THE FRAMEWORK OF NONCOMMUTATIVE GEOMETRY

1994 ◽  
Vol 09 (31) ◽  
pp. 5531-5539 ◽  
Author(s):  
DAE SUNG HWANG ◽  
TAEHOON LEE
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Axial Vector ◽  
Scalar Fields ◽  
Gauge Fields ◽  
The Matrix ◽  
Vector Gauge ◽  
The Masses ◽  
Higgs Fields ◽  
Matrix Derivative

We study the gauged SU(2) L× SU(2) Rσ model in the SU(2|2) superalgebra formalism. The superconnection is taken to have one-form vector fields as its even part and zero-form scalar fields as its odd part. Incorporating the matrix derivative of noncommutative geometry proposed by Connes and Coquereaux et al., we naturally obtain the spontaneously symmetry broken SU(2) L× SU(2) Rσ model. The masses of the axial vector gauge fields and the Higgs fields are obtained.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

GAUGE BOSON MASSES FROM FERMION MASSES?

1992 ◽  
Vol 07 (22) ◽  
pp. 1991-1996 ◽  
Author(s):  
R. FOOT ◽  
S. TITARD
Keyword(s):  
Gauge Boson ◽  
Z Boson ◽  
Heavy Fermions ◽  
Mass Matrix ◽  
Gauge Bosons ◽  
Fermion Masses ◽  
The Masses

We examine the possibility that the masses of the W and Z gauge bosons are induced radiatively from the masses of heavy fermions. From experiment we know that [Formula: see text][Formula: see text]. We point out that this relation can be naturally obtained if the W and Z boson masses are radiatively generated from heavy fermions which arise from a mass matrix which has large electroweak violating masses as well as very large electroweak invariant masses. Two examples of this are considered: The usual see-saw neutrino model and the SU(5)c/quark-lepton symmetric models.

scholarly journals Integrated Recycling Process of Matrices of Organic Moulding Sands

2013 ◽  
Vol 58 (3) ◽  
pp. 809-812 ◽  
Author(s):  
R. Dańko
Keyword(s):  
Recycling Process ◽  
Conceptual Approach ◽  
Assessment Index ◽  
Experimental Stand ◽  
Synthetic Resins ◽  
The Matrix ◽  
Ignition Loss ◽  
On Line ◽  
The Given ◽  
Reclamation Process

Abstract The idea and experimental verification of assumptions of the integrated recycling process of matrices of uniform self-hardening moulding sands with synthetic resins, leading to obtaining moulding sands matrix of expected quality - is presented in the hereby paper. The basis of the presented process constitutes a combination of the method of forecasting averaged ignition losses of moulding sands after casting and defining the range of necessary matrix reclamation treatments in order to obtain its full recycling. Simultaneously, the empirically determined dependence of dusts amounts emitted during the reclamation process of the matrix from the given spent sand on the ignition loss values (which is the most proper assessment index of the obtained reclaimed material quality) was taken into account. The special experimental stand for investigations of the matrix recycling process was one of the elements of the conceptual approach and verification of its assumptions. The stand was equipped with the system of current on-line control of the purification degree of matrix grains from organic binder remains. The results of own investigations, allowing to combine ignition loss values of spent moulding sands after casting knocking out with amounts of dusts generated during the mechanical reclamation treatment of such sands, were utilized in the system.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

scholarly journals HIDING THE EXISTENCE OF A FAMILY SYMMETRY IN THE STANDARD MODEL

2005 ◽  
Vol 20 (36) ◽  
pp. 2767-2774 ◽  
Author(s):  
ERNEST MA
Keyword(s):  
Standard Model ◽  
Neutrino Mass ◽  
Mass Matrix ◽  
Higgs Sector ◽  
Higgs Doublet ◽  
Neutrino Mass Matrix ◽  
Tree Level ◽  
Family Symmetry ◽  
The Standard Model

If a family symmetry exists for the quarks and leptons, the Higgs sector is expected to be enlarged to be able to support the transformation properties of this symmetry. There are, however, three possible generic ways (at tree level) of hiding this symmetry in the context of the Standard Model with just one Higgs doublet. All three mechanisms have their natural realizations in the unification symmetry E6 and one in SO (10). An interesting example based on SO (10)×A4 for the neutrino mass matrix is discussed.

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