Grand Unified Gauge Theories Research Articles

A magnetic-monopole-based mechanism to the formation of the Hot Big Bang modeled Universe

There are some particle physics theories that go beyond the so-called “standard cosmological model” to predict the existence of magnetic monopoles (MMs). The discovery of MMs would be an incredible breakthrough in high-energy physics. The existence of MMs in the early Universe has been speculated and anticipated from Grand Unified Theory. If MMs exist, the inverse powers of the unification mass will not suppress the baryon number violating effects of grand unified gauge theories. Therefore, MM catalyzing nucleon decay is a typical strong interaction. This phenomenon is due to the boundary conditions that must be imposed on the core of MM fermion fields. We present a possible mechanism to explain the formation of the Hot Big Bang Cosmology. The main ingredient in our model is nucleon decay catalyzed by MMs (i.e. the Rubakov–Callan effect). It is shown that Hot Big Bang developed naturally because the luminosity due to the Rubakov–Callan effect is much greater than the Eddington luminosity (i.e. [Formula: see text]).

Embedding A4 into SU(3) × U(1) flavor symmetry: large neutrino mixing and fermion mass hierarchy in the SO(10) GUT

We give an explanation of both the fermion mass hierarchy and the large lepton mixing angles in the context of a grand unified flavor and gauge theory (GUTF). Starting from an (SU(3) × U(1))F flavor symmetry and an SO(10) GUT, the main ingredient of our model is that two different breaking patterns of the flavor symmetry are at work. On the one hand, the dynamical breaking of (SU(3) × U(1))F flavor symmetry into (U(2) × Z3)F explains why one family is much heavier than the others. On the other hand, an explicit symmetry breaking of SU(3)F into a discrete flavor symmetry, A4, leads to the observed tri-bimaximal mixing for the leptons. Naturalness of the charged fermion mass hierarchy appears as a consequence of the continuous SU(3)F symmetry. Moreover, the same discrete SO(10) × A4 invariant operators are the root of the large lepton mixing, small Cabibbo angle and neutrino masses.

1020 eVcosmic-ray and particle physics with kilometer-scale neutrino telescopes

We show that a kilometer-scale neutrino observatory, though optimized for TeV to PeV energy, is sensitive to the neutrinos associated with super-EeV sources. These include super-heavy relics, neutrinos associated with the Greisen cutoff, and topological defects which are remnant cosmic structures associated with phase transitions in grand unified gauge theories. It is a misconception that new instruments optimized to EeV energy are required to do this important science, although this is not their primary goal. Because kilometer-scale neutrino telescopes can reject atmospheric backgrounds by establishing the very high energy of the signal events, they have sensitivity over the full solid angle, including the horizon where most of the signal is concentrated. This is important because up-going neutrino-induced muons, routinely considered in previous calculations, are absorbed by the Earth.

Naturally light Higgs doublets in grand unified gauge theories

A new mechanism (the use of the nonrenormalizable interactions for the suppression of the dangerous interactions of the Higgs triplets with quark) for the explanation of the fine-tuning problem is proposed. In the case of supersymmetric E 5 grand unified theories, which may arise as the low-energy limit of superstring theory, we predict nontrivial relations between Yukawa coupling constants of the low-energy superpotential.

Cosmological effects of superconducting strings

Superconducting cosmic strings are a plausible consequence of symmetry breaking in grand unified gauge theories. The luminosity in electromagnetic radiation of an oscillating current-carrying loop may substantially exceed the luminosity in gravitational radiation. In the typical case considered, the energy released electromagnetically is 10 49 erg s −1, or 10 66 erg in toto. Several consequences follow from this, the most interesting of which is the possibility that such loops may heat their surroundings, generating large, dense spherical shells of gas. Galaxies forming on these gravitationally unstable shells at moderate redshift will be seen at the present epoch to lie on bubbles having radii in the range 10–20 h −1 Mpc if the initial ratio of luminosity in electromagnetic waves to that in gravitational wavess is > 10 −3 for mass/length 10 22 g cm −1. The required primordial energy density in magnetic fields is > 3 × 10 −9 of the radiation energy density, if the charge carriers are bosons or superheavy fermions. Since these shells fill up space, the galaxies will have a distribution similar to that found in a recent survey of the northern sky. When the current saturates, a loop will emit particles copiously, and may be seen as an X-ray source at z ∼ 10–50. Such loops may also contribute significantly to the hard X-ray and γ-ray backgrounds and to 10 20 eV cosmic rays.

Ontological Economy and Grand Unified Gauge Theories

In his paper, “Grand Unified Gauge Theories and the Number of Elementary Particles,“ Robert Weingard (1984) suggests what he calls the Extended Redhead's Principle (ERP) for elementary particles: “Two particles for which there are conceivable circumstances in which one can be ‘rotated’ or reoriented into the other are the same (species of) particles” (p. 154). The philosophical soundness of such a principle is questionable.

Some remarks on the algebra of Eddington'sE numbers

This paper reviews the algebra of Eddington'sE numbers and identifies those points where Eddington anticipated results of current interest. He discovered the Majorana spinors, and was responsible for the standard γ 5 notation as well as the notion of chirality. Furthermore, Eddington defined Clifford algebras in eight and nine dimensions which are now appearing in grand unified gauge and supersymmetric theories. A point which Eddington cleared up, yet is still misunderstood, is that the Dirac algebra corresponds to afive-dimensional base space.

Grand Unified Gauge Theories and the Number of Elementary Particles

Recently, Michael Redhead has argued that the grouping of particles into multiplets by grand unified gauge theories (GUT's) does not, by itself, imply an ontological reduction in the number of elementary particles. While sympathetic to Redhead's argument, in this note I argue that under certain conditions involving Kaluza-Klein theories, GUT's would provide such an ontological reduction.

Thermodynamic potential of grand unified gauge theories

The thermodynamic potential for an arbitrary asymptotically free unified gauge theory is considered at higher temperatures. The calculations are performed up to O(g4 ln g). The results are further specialised in an SU(5) model and within this model the equation of state is derived for the matter in the very early universe.

Monopole catalysis of baryon decay

In the presence of magnetic monopoles, the baryon-number-violating effecs of grand unified gauge theories are not suppressed by inverse powers of the unification mass. As a result, monopoles catalyse proton decay at rates typical of the strong interactions. This phenomenon is caused by boundary conditions which must be imposed on fermion fields at the monopole core. They mix quarks and leptons and cause the monopole to have indefinite baryon number. We present a simplified account of these phenomena as well as their implications for proton decay and monopole search experiments.

Renormalizable asymptotically free quantum theory of gravity

We prove that higher derivative quantum gravity is asymptotically free in all essential coupling constants by the calculation of one-loop counterterms (correcting the previous result of Julve and Tonin) and the solution of the corresponding renormalization group (RG) equations. Strong arguments are presented in favour of the possibility that renormalizable asymptotically free gravity establishes asymptotic freedom for the effective mass parameters and non-gauge couplings in grand unified gauge theories. We also analyse the RG equations in the Einstein theory with Λ term and in the higher derivative conformal invariant theories. Among other topics discussed are the algorithm for the divergences of the determinant of the fourth-order differential operator, the consistent renormalization of the boundary terms in the action, the one-loop β-function in the fourth derivative vector gauge theory and the RG equations in the “gφ 4 + ηRφ 2” theory.

Primordial Irregularities in an Early Universe with Vacuum Phase Transitions

In an early universe with second-order or weakly first-order vacuum phase transitions which are associated with spontaneous symmetry breakdown in grand unified gauge theories, the evolution of primordial irregularities is considered. First the linear behavior of various perturbations in an isotropic and homogeneous model is treated and next the inhomogeneous models for an early universe are approximately derived and examined. It is shown that their evolution at this stage can be remarkably fast in the direction of homogenization and isotropi­ zation.

GRAND UNIFICATION AND POSSIBLE MATTER‐ANTIMATTER DOMAIN STRUCTURE IN THE UNIVERSE

The theory and basic concepts for the development of a matter-antimatter domain cosmology are outlined within the framework of the grand unified gauge theory paradigm. It is shown how spontaneous CP symmetry breaking leads to such a domain sturcture in the universe. Astrophysical data such as the cosmic gamma-ray background spectrum, cosmic-ray p flux measurements, and galaxy clustering are found to favor this point of view. Future tests of this form of big-bang cosmology are suggested and discussed, including tests using deep underwater cosmic ray neutrino detectors.

Renormalizable asymtotically free quantum theory of gravity

We prove that quantum gravity with a quadratic lagrangian of a general type is asymptotically free in all essential coupling constants (including the effective λ-term). One-loop counter terms are obtained and asymptotic freedom is established also in conformally-invariant theories. We discuss the possibility of a ultra-macroscopic radius of confinement of ghosts, the restoration of unitarity due to radiative corrections and propose also the interaction with gravity leads to asymptotic freedom for the effective masses and all coupling constants in grand unified gauge theories.

Inflation in the Universe

During the past 15 yr a small but remarkable collection of cosmological conundrums have been identified; each apparently independent, but probably all inter-related at a deeper level than existing theories have penetrated. The outstanding problems are of explaining the observed isotropy, homogeneity, flatness and specific entropy of the Universe1. Good explanations for the last of these have recently emerged2,3 from the study of C, CP and baryon nonconserving interactions which arise in grand unified gauge theories (GUTs) of the strong and electroweak interactions. Recently, Guth has discussed the inflationary Universe as a possible natural explanation for the observed large-scale homogeneity and near critical density (‘flatness’) of the Universal expansion4. We show that one cannot ignore the first conundrum—the isotropy; a Universe with a large amount of anisotropy will not undergo the inflationary phase. A Universe with only moderate anistropy will undergo inflation and will be rapidly isotropized. Other consequences of the inflationary Universe are discussed.

Fundamental fermion representations in generalisations of the SU(5) grand unified gauge theory

Generalisations of the SU(5) grand unified gauge theory are discussed. It is assumed that the gauge group is simple, and that the theory is both anomaly free and asymptotically free. All possible fundamental fermion representations are determined given that the fermions are massless at the unification level, but acquire mass at the level of the exact SU(3) × U(1) symmetry. No a priori restriction to standard colour SU(3) representations is made. It is found that E 6, SO(10) and SU( n) with n ⩾ 5 are the only acceptable gauge groups. Standard colour solutions are legion, but dull, incorporating at the SU(5) level, nothing other than p generations or copies of the familiar representation 10+ 5 . Exotic colour solutions are sparse, but interesting. Nine of these, all associated with SO(10), can accomodate those quarks and leptons currently thought to be fundamental, along with such things as colour sextets and octets, as well as doubly charged leptons.

The decay proton → e +γ in grand unified gauge theories

The rate for proton decay to the e +γ mode is calculated. Although its branching ratio is of order α, its ratio to observable e +π 0 correlated decays is 1 8 to 1 40 . Observable numbers of p → e + + γ decays can occur and would provide constraints on the proton wave function at the origin and grand unified parameters independent of hadron final state uncertainties.

Proton Decay Rate

The pionic two-body decay amplitude of the proton in the SU(5) grand unified gauge theory is computed by using the soft-pion method in the reference frame of the pion at rest. The normalization condition of the relativistic three-body Bethe-Salpeter wave function of the proton is used in the computation. It is shown that the partial decay rate of the process, proton \ensuremath{\rightarrow}${e}^{+}{\ensuremath{\pi}}^{0}$, is (${0.86\ifmmode\times\else\texttimes\fi{}{10}^{30}\mathrm{y}\mathrm{r})}^{\ensuremath{-}1}$ and (${1.4\ifmmode\times\else\texttimes\fi{}{10}^{31}\mathrm{y}\mathrm{r})}^{\ensuremath{-}1}$ for ${m}_{X}=4.0\ifmmode\times\else\texttimes\fi{}{10}^{14} \mathrm{GeV}\mathrm{and} 8.0\ifmmode\times\else\texttimes\fi{}{10}^{14} \mathrm{GeV}$, respectively. These values are on the boundary of the present experimental limit.

Remarks concerning the running coupling constants and the unifying mass scale of grand unified gauge theories

The prediction of sin2 theta w and the unifying mass scale of grand unified gauge theories are estimated up to the two-loop level. It is shown that the two-loop contributions alter the proton lifetime by a factor of order ten.

SU(8) grand unification

A grand unified gauge theory based on the group SU(8) is presented. The set of rules motivating the choice of SU(8) is given. The particle content of the theory suggests a natural embedding of a horizontal SU(3) symmetry in the SU(8) grand unified symmetry.