Gauge Theory Of Interactions Research Articles

Effects of heavy Higgs scalars at low energies

Working within the left-right-symmetric ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory of weak and electromagnetic interactions we find that contrary to the usual belief heavy Higgs scalars do not decouple in low-energy phenomena.

Low energy neutrino elastic scattering and supernova explosions

COLGATE AND WHITE1 have proposed that neutrinos could transport energy outwards during the gravitational collapse of a star, thus initiating a supernova explosion. Detailed calculations by Wilson2 seemed to rule out this possibility, but Freedman3 pointed out in the context of unified gauge theories of weak and electromagnetic interactions that there could be both a large neutrino–neutron elastic scattering cross section and a very large coherent neutrino–heavy nucleus cross section. Wilson4 has recently recalculated the collapse of an iron core formed at the end of a stellar evolution from massive stars and shown that the calculations do simulate an explosion, and that a stronger explosion results from smaller coherent scattering off heavy nuclei. This surprising result arises because a smaller cross section allows more neutrinos to escape, lowering the pressure and thereby letting the neutron core reach a higher density before the outward shock wave is formed. We have calculated neutrino–nucleon and neutrino–heavy nucleus neutral current cross sections in weak SU(2)×U(1) and compared with those of the standard unified theory. Important differences are found which could make simulated supernova explosions easier to obtain. Possible experiments to test the two theories are outlined here.

A generalized non-Riemannian super-gauge formalism

One of the most fruitful approaches to theoretical physics is to postulate a group of symmetries and ask which physical meaningful structures it leaves invariant . In the present state of the physics of fundamental interactions, three different kinds of symmetries are of particular interest: The general group of space-time co-ordinate transformations associated with gravitation, internal local gauge symmetries associated with gauge theories of electromagnetic, weak and strong interactions, and supersymmetry (Fermi-Bose symmetry) which opens up the possibility of treating bosons and fermions on equal footing. I t is accordingly of great interest to investigate whether these symmetries in a natural manner can be regarded as parts of a single symmetry group, and if so, to find the corresponding invar iant physical theory. As it is well known, this question has been considered within the framework of superficial theory (~), and ~NATlt, ARNOWITT and ZUMINO (2.4) in particular, have suggested interesting geometrical models. In the following we shall consider a generalized non-Riemannian formalism which differs from the models proposed by these authors, and discuss its possible physical significance. We consider an 8-dimensional superspace J labelled by co-ordinates Z ~ = (x~, 0~), where p, r . . . . 0, ..., 3 label the space-time co-ordinates x (commuting Bose-co-ordinates) and a, fl . . . . l, ..., 4 label the ant icommuting Fermi-co-ordinates 0. Such a space forms a Grassmann algebra with even elements x and odd elements 0, generated by three ant icommuting variables w~, w2, w a. Consider an arbitrary contravariant vector field V A transforming under a co-ordinate transformation Z-~ Z like

New gravitational instantons and universal spin structures

An infinite class of new gravitational instantons for the axial anomaly is found. It consists entirely of algebraic spin- manifolds. In theories that allow manifolds without ordinary spin structure we find the presence of spinorial matter fields to require the existence of a “universal” gauged SU(2) or higher internal symmetry (e.g., SU(2) × SU(2) × G) and of an “internal-spin” -statistics connection. The possible relation of this to the gauge theory of weak and electromagnetic interactions is explored.

Conformal relativity, a theory of mass. I: Survey of Theoretical Results

In a series of papers it will be explained how a kinematic theory of mass follows from adopting the conformal groupC as basic space-time symmetry group. As an aspect of the group, kinematic masses are bare masses; physical masses are to be calculated from these and interactions. The particle solutions are of two kinds: massless, or massive families consisting of theC plus an infinite set of discrete excited mass states. An unexpected consequence of conformal symmetry is the extrapolation of the space-time origin of (some at least) internal symmetries. In particular,C provide isospin labels and the free Lagrangians, pure conformal group constructs, possess isospinSU2 invariance as an accidental («dynamical») symmetry. New possibilities for gauge theories of interactions are also implied. The new way of handling mass allows gauge bosons of nonzero bare mass (as well as massless ones) without violating gauge invariance. Thus Higgs fields and vacuum broken symmetries are no longer necessary in gauge theory.

Unified SU(3) ⊗ U(1) Gauge Theory with Different Muon and Electron Neutral Currents

We propose a gauge theory of weak and electromagnetic interactions based on SU(3) \ensuremath{\bigotimes} U(1). The muonic and electronic doublets are classified differently. As a consequence, we get the same predictions of the Weinberg-Salam SU(2) \ensuremath{\bigotimes} U(1) theory for the ${\ensuremath{\nu}}_{{\ensuremath{\mu}}^{\ensuremath{-}}}({\overline{\ensuremath{\nu}}}_{{\ensuremath{\mu}}^{\ensuremath{-}}})$ initiated processes and parity conservation in atoms. The muon number is exactly conserved. Predictions are made that will be tested in the future high-energy colliding-beam experiments.

Semisimple unified gauge theories of strong, weak, and electromagnetic interactions

Unified theories of strong, weak, and electromagnetic interactions, which are based on simple groups, require large unification energies on the order of 10/sup 9/ to 10/sup 1/7 GeV. This paper describes a new type of semisimple model in which the unification occurs at energies as low as 10/sup 3/ GeV. Most gauge models for a group C x F have two coupling constants which cannot be related without destroying renormalizability. In this work a computer is used to look at millions of different models for various C x F and fermion representations. The machine picks out those models which are compatible with the existence of any renormalizable coupling-constant relation at the two-loop level. A small number of such theories is found. In every case the coupling-constant relation is linear and fixes the strengths of the C and F interactions so that they are inversely proportional to the size of the respective groups. Therefore, a semisimple model, which is constructed from a small C group and a large F group, will have a natural hierarchy of interaction strengths. If we embed color SU(3) in C and SU(2) x U(1) in F, this group-theoretical effect can account for much of the observedmore » difference between strong and weak interactions. Because the remaining difference can be explained by a relatively small renormalization effect, the unification energy can be small. We exhibit an SU(3) x O(11) model of this sort, in which the unification energy is 10/sup 3/ or 10/sup 4/ GeV. The theory is in agreement with the usual low-energy phenomenology and particle spectra. As the energy approaches the unification energy from below, many new leptons and O(11) gauge bosons will be produced suddenly. In this model the great strength of the strong interactions can be attributed to the fact that color SU(3) is one of the smallest Lie groups.« less

SU(3) ⊗ U(1) gauge theory of weak and electromagnetic interactions

We describe an SU(3) \ensuremath{\bigotimes} U(1) gauge theory of weak and electromagnetic interactions and study its experimental implications. In this theory all nonsinglet fermions are assigned to triplet representations of SU(3). The theory satisfactorily accounts for the trimuon events recently observed in neutrino reactions. Furthermore, the model naturally ensures quark-lepton and $e\ensuremath{-}\ensuremath{\mu}$ universality, absence of right-handed currents in $\ensuremath{\beta}$ and $\ensuremath{\mu}$ decay, and absence of $s\ensuremath{-}d$ neutral currents to order ${G}_{F}\ensuremath{\alpha}$. Various discrete symmetries play an important role in maintaining these properties. The model allows for $\ensuremath{\mu}$- and $e$-type lepton-number nonconservation at a naturally strongly suppressed level. The weak contributions to the anomalous magnetic moments of the electron and muon are calculated and shown to be in accord with experimental bounds. The predictions of the model for most neutral-current reactions are in good agreement with the data on these processes. Other features of the theory include the prediction of an absolutely stable massive neutral lepton, the absence of a sizable high-$y$ anomaly in antineutrino charged-current reactions, and the absence of large parity violation in heavy atoms.

Implications of theϒ(9.5)for gauge theories of weak interactions

We analyze the implications of the discovery of the $\ensuremath{\Upsilon}(9.5)$, assumed to be a heavy-quark-antiquark bound state, for gauge theories of weak interactions and especially for neutrino reactions. Taking into account all present experimental constraints, we study the consequences of particular multiplet assignments of the new heavy quark in models based on the group SU(2) \ensuremath{\bigotimes} U(1) and higher gauge groups, in particular SU(3) \ensuremath{\bigotimes} U(1). In neutrino and antineutrino reactions in which this new quark is produced, its semileptonic decays will provide a key signal for its discovery. We specialize to the SU(3) \ensuremath{\bigotimes} U(1) model and give a careful analysis of multimuon events arising from the production of this heavy quark and the concomitant heavy lepton.

Polarized-electron-nucleon scattering in gauge theories of weak and electromagnetic interactions

The asymmetry in the scattering of longitudinally po1arize.d electrons by nucleons is considered in the context of gauge theories of the weak and electromagnetic interactions. The predictions of a variety of gauge groups and assignments of fermion representations of present interest are given for deep inelastic scattering, elastic scattering, and A electroproduction. It is shown that a combination of the three experiments carried out to a few parts in lo5 at Q2 - 1Gev2/c2, can distinguish between various SU(2) x U(1) models and between various classes of models based on larger gauge groups.

Gauge theory of weak and electromagnetic interactions with an SU(3)×U(1) symmetry

A gauge-theory model of weak and electromagnetic interactions is proposed. The symmetry group is SU(3)\ifmmode\times\else\texttimes\fi{}U(1) and the fermions are all placed in triplets (or antitriplets) and singlets. The theory is vectorlike and hence anomaly-free. Discrete symmetries are imposed to avoid unwanted mixings and to appropriately restrict the Higgs potential. The details of fermion and boson mass generation are given. The couplings and masses of the two massive neutral flavor-preserving gauge bosons are determined by fitting the neutral-current data; agreement is excellent. We also analyze the predictions for multimuon production in neutrino scattering as a function of lepton and hadron masses. Finally we examine the limits on such processes as ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$, etc.

Problem of StrongPandTInvariance in the Presence of Instantons

The requirement that P and T be approximately conserved in the color gauge theory of strong interactions without arbitrary adjustment of parameters is analyzed. Several possibilities are identified, including one which would give a remarkable new kind of very light, long-lived pseudoscalar boson.

SU(2) × U(l): A gauge theory of weak interactions?

We construct a gauge theory of weak interactions which fits all neutral current data, including the atomic physics experiments. It is shown that it is possible to include this theory in a unified theory of weak and electromagnetic interactions; the desirability of doing so is discussed.

Unified Gauge Theories of Weak Interactions

Unified Gauge Theories of Weak Interactions

Gauge theories of weak interactions with left-right symmetry and the structure of neutral currents

Failure to detect parity-violating effects in atomic transitions by Oxford and Washington groups would appear to rule out the Weinberg-Salam $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ model as well as any variation of it that respects natural conservation laws for charm and strangeness to order $\ensuremath{\alpha}$ ${G}_{F}$ (called "natural") and obeys quark-lepton symmetry. In this paper, a simple left-right-symmetric model based on the ${\mathrm{SU}(2)}_{L}\ensuremath{\bigotimes}{\mathrm{SU}(2)}_{R}\ensuremath{\bigotimes}\mathrm{U}(1)$ group with four and six quark flavors is analyzed and found to accomodate the results of the atomic experiments as well as the other features of neutral-current phenomena.

A theory of flavor mixing

We investigate the origin of the Cabibbo angle and other flavor-mixing angles in an ambidextrous SU(2) L × SU(2) R × U(1) gauge theory of weak and electromagnetic interactions involving 2 n quark flavors. We show how a discrete symmetry of the Lagrangian leads to flavor-diagonal weak currents where all flavor-mixing angles vanish. Each quark is assigned a position on the “clock of flavor” and the charged-current weak interactions are identified as nearest-flavor couplings. Soft breakdown of the discrete symmetry leads to a one-parameter family of flavor-mixing angles in the charged weak currents. All angles are expressed in terms of this parameter and quark mass ratios. The neutral currents remain flavor diagonal. Upper and lower bounds on 2 n, the number of flavors, are obtained by constraining the theory to fit what is known from experiment. Departures from Cabibbo universality become intolerable if 2 n < 8. It is impossible to obtain enough CP violation if 2 n > 12. We conclude that the number of flavors must be 8, 10, or 12. We construct a more ambitious theory in which the Cabibbo angle and its analogs are O( α) calculable radiative corrections. For reasonable values of the quark mass ratios, we fail to obtain a Cabibbo angle of the right order of magnitude. Our theory involves an equal number of lepton flavors and quark flavors. A large number of flavors is required if neutrinos are to be sufficiently light. We explore the case of 2 n = 12, and find a novel mechanism for the neutrino induction of trimuon events.

CURRENT PROBLEMS IN THE WEAK INTERACTIONS*

Some reasons are discussed showing why the recent SU(2) x U(1) gauge theory of weak and electromagnetic interactions is not a complete theory of these interactions, Lepton theory, charm, and the CP problem are considered. 60 references. (JFP)

Black holes are coloured

It is shown that a black hole may act as the source of Yang-Mills fields. This result is used to consider briefly the implications for black hole evaporation within the context of gauge theories of strong interactions.

U(1) ⊗ SU(4)L⊗ SU(4)R-Based Weak-Electromagnetic Synthesis with Manifest Left-Right Symmetry

We present a gauge theory of weak and electromagnetic interactions which is based on the group U(1) \ensuremath{\bigotimes} SU${(4)}_{\mathrm{L}}$ \ensuremath{\bigotimes} SU${(4)}_{\mathrm{R}}$ and which implements manifest left-right symmetry in a natural way. The theory is characterized by a rich lepton spectrum and is consistent with recent experimental results in atomic physics and weak trimuon production. Some novel predictions of the theory are discussed.

Local operator products in gauge theories. I

In this and a subsequent paper, we discuss the renormalization and gauge invariance of products of local gauge-invariant operators and their operator product expansions in gauge theories in detail. In this paper, we study in detail the following problem which when solved leads to the complete understanding of the operator product expansion of a product of two gauge-invariant operators. The problem is to consider the complete set of color singlet local functionals of gauge, matter, and ghost fields (F[A,c,c¯,η0]) in a non-Abelian unbroken gauge theory of strong interactions containing fermions and find what subset of these local operators have the property that all of their “physical matrix elements” are η-independent to all orders in the perturbation theory. (Note: All the phrases in quotes and the above statement are to be defined in the text by certain limiting procedures where-upon they become precise mathematical statements.) Here, η is a gauge parameter. We believe that the discussion given here can be extended to spontaneously broken gauge theories in a straightforward manner, where of course, the physical matrix elements exist in perturbation theory. The conclusion is that the only nontrivial operators that have this property to all orders are all the gauge-invariant operators and certain gauge variant operators which are a subset of the renormalization counterterms a gauge-invariant operator at zero momentum needs. However, these gauge-variant operators are not new physical entities in the sense that their “renormalized physical matrix elements” are not independent to the “S-matrix elements.” These results will be useful in understanding which operators appear in the operator product expansion of, say two currents, letting one use these methods with full understanding in gauge theories. As a by-product, certain technical discussions in this paper can be used to considerably shorten the proof of a theorem in the renormalization of gauge-invariant operators previously given.