Weinberg Model Research Articles

Conserved Currents, Their Commutators, and the Symmetry Structure of Renormalizable Theories of Electromagnetic, Weak, and Strong Interactions

This paper discusses the role played by conserved currents in fixing the structure of currently popular renormalizable theories of strong, electromagnetic, and weak interactions. The major objective of this work is to show that these theories correspond to another kind of symmetry --which we call a Higga-type asymmetry--and to clarify the relation of this scheme to the already familiar normal and Goldstone aymmetries. In order to do this, we introduce a language which makes no reference to any specific Lagangian formalism and so avoids questions of whether or not hadrons are composite and whether or not the Goldstone bosons (massless particles of these theories) necessarily have massive partners. For pedagogical reasons, we discuss the original Weinberg model of leptons and a model coupling leptons and hadrons from the current-algebra point of view. (auth)

Deep inelastic electroproduction and Weinberg's model of weak and electromagnetic interactions

Deep inelastic electroproduction and Weinberg's model of weak and electromagnetic interactions

On some generalizations of the Weinberg model

A generalization of the Weinberg model of leptons is proposed which introduces additional gauge fields. Experimental consequences for the amplitude of νe scattering the W-boson masses are discussed.

Comments on Dispersion Theoretic Calculations of Muon Anomalous Magnetic Moment in Weinberg's Model

Comments on Dispersion Theoretic Calculations of Muon Anomalous Magnetic Moment in Weinberg's Model

Neutral weak currents and the proton-neutron mass difference

The logarithmically divergent contributions to the proton-neutron mass difference arising from the exchange of intermediate vector bosons are investigated. Within the framework of Weinberg's model we find a divergent contribution of opposite sign to the electromagnetic divergence which is, however, insufficient to cancel it completely.

Weinberg's gauge model for weak and electromagnetic interactions with Han-Nambu quarks

A version of the Weinberg model is constructed using Han-Nambu quarks, in order to obtain the conventional classification of hadrons. The use of Han-Nambu quarks leads to a suppression of neutrinos coupled to the ΔS = 0 hadronic current, while the coupling to neutral leptonic currents remains as in Weinberg's theory.

Renormalization of Gauge Theories,WDecay, andμDecay

We present a renormalization program for spontaneously broken gauge theories in the unitary formalism. It is compared with the renormalization program for renormalizable gauges and necessary constraints are discussed. We then explicitly formulate this program for the Weinberg SU(2)\ifmmode\times\else\texttimes\fi{}U(1) theory of leptons and show how it provides the basis for the dispersive calculations of higher-order corrections to $\ensuremath{\mu}$ decay reported in a previous paper. As we pointed out there, certain symmetry-breaking effects are finite and calculable. In this paper, we calculate the breaking of $\ensuremath{\mu}\ensuremath{-}e$ universality in order $\ensuremath{\alpha}$. We also explicitly verify the consistency of our renormalization procedure on the one-loop level. There are certain subtleties in the treatment of infrared divergences in gauge models, particularly in dispersive calculations. We give a method for handling this problem, calculate the rate for $W$ decay, and complete the calculation of the photonic contributions to $\ensuremath{\mu}$ decay in the Weinberg SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model. Our predictions for the decay rate and the electron energy spectrum in $\ensuremath{\mu}$ decay for the Weinberg model are experimentally indistinguishable from those of the old current-current theory of weak interactions. Finally we make some comments about other gauge models and other physical processes.

A Comment on the Anomalous Magnetic Moment of the Muon in Weinberg's Model

It is pointed out that the difference between the n-dimensional method and the dispersion relation approach for evaluating the W boson contribution to the anomalous magnetic moment of the muon in Weinberg's model consists in the order of integration. (LBS)

Divergence Cancellations in Spontaneously Broken Gauge Theories

An extremely simple method is presented to calculate unambiguously higher-order corrections in the unitary ($U$) gauge of theories with spontaneously broken gauge symmetries. Manipulating Feynman integrals in coordinate space, the spurious nonrenormalizable infinities of this gauge are isolated in the form of (contracted) Feynman graphs. Without making reference to any specific global regularization scheme, the complete cancellation of these graphs is demonstrated in the cases of fermion-fermion scattering to fourth order in the Abelian model considered by Appelquist and Quinn and for the similar neutrino scattering in Weinberg's ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}Y$ model. The reason for such complete cancellation is seen to be a consequence of the algebraic structure of the equal-time commutators among currents, their divergences, and various fields. This structure, of course, is dictated by the original gauge symmetry. As a check on our methods, the weak muon anomaly in Weinberg's model is calculated, and agreement is found with the (gauge-invariant) results of other authors.

CP-Violation in the Renormalizable Theory of Weak Interaction

In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed. When we apply the renormalizable theory of weak interaction1l to the hadron system, we have some limitations on the hadron model. It is well known that there exists, in the case of the triplet model, a difficulty of the strangeness chang­ ing neutral current and that the quartet model is free from this difficulty. Fur­ thermore, Maki and one of the present authors (T.M.) have shown2l that, in the latter case, the strong interaction must be chiral SU ( 4) X SU ( 4) invariant as precisely as the conservation of the third component of the iso-spin 13 • In addi­ tion to these arguments, for the theory to be realistic, CP-violating interactions should be incorporated in a gauge invariant way. This requirement will impose further limitations on the hadron model and the CP-violating interaction itself. The purpose of the present paper is to investigate this problem. In the following, it will be shown that in the case of the above-mentioned quartet model, we cannot make a CP-violating interaction without introducing any other new fields when we require the following conditions: a) The mass of the fourth member of the quartet, which we will call (, is sufficiently large, b) the model should be con­ sistent with our well-established knowledge of the semi-leptonic processes. After that some possible ways of bringing CP-violation into the theory will be discussed. We consider the quartet model with a charge assignment of Q, Q -1, Q -1 and Q for p, n, A. and (, respectively, and we take the same underlying gauge group SUweak (2) X SU(1) and the scalar doublet field cp as those of Weinberg's original model.1l Then, hadronic parts of the Lagrangian can be devided in the following way:

Mass Differences in a Unified Theory of Weak and Electromagnetic Interactions

The soft-pion and soft-kaon mass differences are calculated in the Weinberg model of weak and electromagnetic interactions. Both are found to be finite without using the second spectral-function sum rule. In addition several comments are made about mass differences of massive hadrons.

Weak corrections to the muon magnetic moment in a renormalizable gauge

Abstract A renormalizable gauge calculation of the weak corrections to the muon magnetic moment in Weinberg's model is presented. The calculation is performed in the context of the recently developed theory of non-Abelian gauge fields.

Higher-order corrections in muon decay

In this paper the second-order weak and electromagnetic corrections to the decay rate of the muon are calculated from Weinberg's model of leptons. The calculation is performed in a manifestly renormalisable gauge.

Effects of a Neutral Weak Current in the Processe+e−→μ+μ−

The effects of a weak neutral current or a heavy neutral intermediate vector boson on the reaction ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are studied. Particular attention is paid to weak-electromagnetic interference effects which may be observable even for large (> 50 BeV) boson mass. The colliding beams of electrons and positrons are taken to be polarized normal to the plane of the storage ring as a result of the emission of synchrotron radiation. The helicities and angular distributions of the muons are calculated, with emphasis on those features which indicate unambiguous parity violation. The results are then specialized to Weinberg's model of leptons, where effects of order 1% are expected.

Macroscopic consequences of the Weinberg model

Consequences of the Weinberg model are discussed in application to a large system of thermodynamically equilibrium weakly interacting particles. It is shown that at a temperature higher than about 10 3 GeV the symmetry broken at lower temperature is re-established, the masses of the intermediate bosons vanish and weak interaction becomes a long-range one. The conditions are pointed out providing the appearance of anomalously great repulsion forces between the particles of the system. Some applications to the “hot” Universe model are considered.

Higher-Order Contributions toμDecay in a Spontaneously Broken Gauge Model

The one-loop contributions to $\ensuremath{\mu}$ decay are calculated in Weinberg's model of the weak and electromagnetic interactions of leptons. The higher-order weak contributions are shown to be finite in this model, despite the high order of divergence of individual Feynman graphs. Thus this calculation is practical evidence in favor of the renormalizability of spontaneously broken gauge theories. The electromagnetic corrections to $\ensuremath{\mu}$ decay are finite after in the Weinberg model. The renormalized higher-order weak corrections do not affect the shape of the final electron spectrum. The effect on the $\ensuremath{\mu}$ decay rate is of the same order of magnitude as the electromagnetic correction, \ensuremath{\sim}\textonehalf{}%. Since this is effectively just a small renormalization of the weak coupling constant, it appears to be impossible to detect this effect experimentally unless other weak processes can be calculated and measured with comparable precision. The calculation is done by evaluating Feynman graphs dispersively. This calculational technique may be of interest in further work with spontaneously broken gauge theories.

Gauge Theory of Strong, Weak, and Electromagnetic Interactions

Starting from the recent U(3) $\ensuremath{\bigotimes}$ U(3) gauge model of strong interactions, we discuss the very natural synthesis with Weinberg's model of leptons. As a result of the interplay of the two models (a) neutral $\ensuremath{\Delta}S=1$ currents are eliminated without enlarging the number of quarks, and (b) a natural $(3,\overline{3})\ensuremath{\bigoplus}(3,\overline{3})$ symmetry breaking emerges for the hadrons. Incorporation of alternative lepton theories is mentioned.

Static quantities in Weinberg's model of weak and electromagnetic interactions

Within Weinberg's model of weak and electromagnetic interactions, we calculate the static quantities of the charged intermediate bosons. We also prove that the neutrino charge remains zero in second order, and discuss its charge radius. Finally, an unambiguous calculation of the muon g-2 is presented. All calculations are done using the n dimensional regularization procedure of 't Hooft and Veltman. Our results support the claim that Weinberg's model is renormalizable.

The process vμ+p → vμ+p+ π° in Weinberg's model of weak interactions

The ratio R = σ( v μ +p → v μ +p+ π°)/ σ( v μ +n → μ+p+ π°) in Weinberg's model of weak interactions is estimated on the basis of a static model for the neutrino production of the 3,3 resonance. For the Weinberg mixing angle α given by sin 2 α ⩽ 0.35 as deduced from the upper bound on σ( v e + e → v e + e) , it is concluded that R ≳ 0.4, which is not consistent with the experimental bound R ≲ 0.14 reported in the following paper.

The Drell-Hearn sum rule and the lepton magnetic moment in the Weinberg model of weak and electromagnetic interactions

We verify that the fourth-order Compton amplitude for the scattering of a photon off a charged lepton is finite in Weinberg's model of weak and electro-magnetic interactions, and obeys the Drell-Hearn sum rule. We also compute the second-order weak corrections to the anomalous magnetic moment of a charged lepton in the same model. For the case of the muon, we find the bounds: + 0.2 × 10 −8 ⩽ K ⩽ + 0.56 × 10 −8 .