Unified Gauge Theories Research Articles

Double gauge theory of stresses and defects

Elasticity and plasticity can both be formulated in a geometric language. In linear approximation, there are two gauge theories. We exhibit the dual relationship between the two and present a coupled unified double gauge theory of both stresses and defects.

Systematic analysis of lepton family number violating processes in the framework of local gauge theories

General unified electroweak gauge theories with neutral lepton mixing are reexamined with regard to processes that change lepton family numbers L f. The most general allowed mass sectors of models based on SU(2) × U(1) and SU(2) L × SU(2) R × U(1) are studied and the consequences for L f changing processes such as μ → e γ, ν f′ → ν f + γ are worked out. We discuss models that break individual lepton family numbers but still conserve total lepton number L, as well as models in which L is broken too.

The Lorentz structure of leptonic charged weak interactions

We analyze all available data on leptonic, charge changing, weak interactions in terms of more general Lorentz structures than V-A. For this purpose we construct classes of models which follow the pattern of unified gauge theories but which are general enough so as to make use of the nearly complete experimental information. In a first class of models we assume the interactions to be mediated by the exchange of charged bosons whose couplings to leptons fulfill either strict universality or modified universality (for spin-zero exchanges). In a second class of models we investigate to which extent the data admit or require unconventional couplings in addition to V-A. A χ 2 analysis is presented for nine typical cases and limits on non-canonical couplings are given. As expected the data admit relatively large deviations from V-A. A few per mill measurement of the parameter ξ in μ decay as well as an absolute measurement of the muon neutrino helicity from pion decay would help to remedy this unsatisfactory situation.

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.

Unified Gauge Theories and Galaxy Formation

Grand Unified strings may provide us with the primordial density fluctuations needed for galaxy formation. The properties and the cosmological evolution of such strings are discussed. A Grand Unified Theory with strings is constructed.

A unified gauge and gravity theory with only matter fields

We propose a purely fermionic action with gauge and general relativistic invariances. This implies a unified treatment of gravity and gauge theories without elementary metric tensor and gauge boson fields. At the quantum level this scale-invariant theory generates, as vacuum properties, both a metric and a scale Λ which becomes related to the Planck mass. The analysis of the spectrum displays, besides the original fermions, massless composite vierbein and gauge bosons, as well as a set of states with masses of order Λ. In a low-energy regime in which these heavy modes are not excited, the light sector is shown to be governed by a phenomenological action which coincides with the conventional gravity-gauge-matter theory without cosmological term and with a Newton constant and gauge couplings determined by Λ. For increasing energies, the gauge interactions are predicted to grow towards their merging with gra Λ, the theory differs substantially from the conventional one, not even allowing a definition of a space-time metric and providing hints for a milder ultraviolet behaviour.

Equivalence principle and multidimensional unified gauge theories

Equations of motion for point-like test masses subjected to Yang-Mills-Lorentz and gravitational forces are derived from geodesic motion in the multidimensional space of a non-Abelian Kaluza-Klein theory with vanishing cosmological constant.

Walls bounded by strings

Extended structures consisting of walls bounded by strings appear in some unified gauge theories. The Spin(10) grand-unified-theory model provides the simplest example, provided the symmetry breaking proceeds via SU(4)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(2). It is shown that the presence of such structures may cause conflict with standard cosmology.

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.

Renormalization group constraints on unified gauge theories

Renormalization group constraints on the behavior of Yukawa and scalar quartic couplings in unified gauge theories are examined. Yukawa couplings are generally asymptotically free whenever the gauge couplings are, but scalar quartic couplings can be asymptotically free only for simple scalar multiplets in large groups with large fermion content. The infrared behavior of Yukawa and scalar quartic couplings implied by the renormalization group equations has interesting and phenomenologically useful consequences: infrared fixed points (or quasifixed points) lead to bounds on masses of fermions and scalars, while scalar quartic couplings can be driven out of the domain of positivity of the classical potential, with possible implications for patterns of symmetry breaking.

SO(10) and the invisible axion

We study the Dine, Fischler, and Srednicki mechanism for solving the strong CP problem in the context of the SO(10) unified gauge theory. We find that this mechanism can be implemented in a minimally extended SO(10) model, where the SO(10) symmetry breaks down to SU(3) x SU(2) x U(1) via SU(5). The resulting theory is consistent with the standard hot-big-bang cosmology and with present phenomenology. We also show that, in other minimally extended SO(10) models, where SO(10) breaks down to SU(3) x SU(2) x U(1) either directly or via SU(4) x SU(2) x SU(2), the Dine, Fischler, and Srednicki mechanism cannot be implemented.

Superheavy Magnetic Monopoles

The basic principles of magnetism and the history of thought on the existence of magnetic monopoles are reviewed. The properties of magnetic monopoles as predicted by Dirac, time reversal arguments and unified gauge theories are discussed. Gauge theory predictions of the mass and flux of monopoles suggest why efforts to detect them have not yet been successful and point to promising directions for future experiments. Proposals for experiments are described.

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.

Conformal invariance and the Higgs boson mass in the Weinberg-Salam theory with gravitational mechanism of instability

The assumption that the Higgs scalar field equation is conformally invariant leads to new features of the unified gauge theories including classical gravitation. Both the self-consistent approach and the external curved space-time method are discussed here. The purpose is to compute the upper and lower bounds on the mass of the stable Higgs particle. Also an attempt to obtain a discrete mass spectrum at classical level was made.

Geodesic motion in multidimensional unified gauge theories

We briefly review a recently proposed version of the multidimensional (generalized non-Abelian Kaluza-Klein) gauge theory. A generalized equivalence principle is discussed and used to derive the equations of motion for pointlike test masses with nonvanishing Yang-Mills charges. A curious consequence of causality is noted: these classical point charges cannot be massless.

Unified gauge theories and bilinear invariant forms

Gauge theories based on a simple Lie algebra orU(1) have only one coupling constant. It is shown that there are no other Lie algebras with this property.

Massive neutrinos ?

Various aspects of the subject of neutrino masses and their implications are outlined: Dirac and Majorana masses, suggestions from unified gauge theories, limits and hints from cosmology, galactic neutrinos and their detectability, experiments involving weak decays. The main voluntary lacunae are oscillations and double beta decay.

CP violation in particle physics and cosmology: Is there any connection?

We discuss, in the framework of unified gauge theories, the possible connection between the CP-violating phase(s) ( δ B) responsible for matter-antimatter asymmetry and those phase(s) ( δ K responsible for low-energy CP-violating observables, like ϵ and ϵ′ in the kaon system and the electric dipole moment of the neutron. We conclude, from the study of a variety of models with either intrinsic or spontaneous breaking of CP symmetry, that due to the existence of the SU(2) L × U(1) phase transition in general δ B and δ K bear no relation to each other, although they are both expressible in terms of the parameters characterizing the effective lagrangian of the theory.

Experimental test of electroweak effects at PETRA energies

The differential cross sections for Bhabha scattering and μ pair production, and the total τ pair cross section as measured by the PLUTO detector at PETRA, have been analyzed to extract information on the weak interaction of leptons. The data are compared with unified gauge theories. Since the observed electroweak effects are still consistent with zero (within errors) we can set experimental limits on neutral current parameters atQ2 values of 950 GeV2. In the framework of the standard SU(2)×U(1) model we find sin2Θ w <0.52(95% c.l.). In the context of general singleZo models we can excludeZo masses of less than 40 GeV.

Radial and Regge excitations in unified, grand unified and subconstituent models

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin 3 2 quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.