A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

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, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

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The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

Nonlocal theory of the electromagnetic and weak interactions with W-boson

The perturbation theory of the electromagnetic and weak interactions is considered in the framework of nonlocal theory. A hypothesis is proposed that the photon and neutrino fields are connected with the charged local fields of the electrons, muons, and W bosons in the nonlocal way.The definite intermediate regularization procedure is introduced that the S matrix is finite, unitary, causal, gauge invariant in perturbation theory when regularization is moved off. The interaction Lagrangian contains no infinite counter terms and the S matrix is finite without any infinite renormalizations.     

μ decay and neutrino-neutrino interactions in a non-local theory of weak interactions

The contributions of the ordinary current-current weak interaction and a pure νν interaction to the spectrum of μ decay to second order are analysed in the framework of a non-local theory of weak interactions. Comparison of the obtained results with experimental data allows an upper bound on the coupling constant of the νν interaction to be established.     

The weak pion-nucleon vertex revisited

We evaluate the parity-violating weak pion-nucleon vertex in the framework of a chiral soliton model including pions and the vector mesons ρ and ω. The weak πN coupling constant >G_π is enhanced by a factor of 13.3 for the standard electro-weak model as compared to the Cabbibo model, with its absolute value given by G_π ≈ 2.7 · 10⁻⁸. We compare our results to available data and other theoretical determinations. In particular, we predict the γ-asymmetry in ¹⁸F to be |P(¹⁸F)|= 1.2 · 10⁻⁴. We also discuss calculational differences to standard quark model estimates.     

Non-renormalization of the weak vertex in gauge theories with integrally charged quarks

We give current algebra arguments to show that toO(α) the colour octet vertices do not renormalize the effective weak vertex between colour singlet hadrons in models with broken colour symmetry. The result does not depend on the details of the mixing between colour gluons and electro-weak bosons.     

A gauge theory of weak and electromagnetic interactions with spontaneous parity breaking

We present a unified gauge theory of weak and electromagnetic interactions in which parity is spontaneously broken together with gauge invariance, by the Higgs mechanism. The gauge group is SU(2) × U(1), and a heavy neutrino is associated with every charged lepton. After the breaking of the original parity-conserving theory, both a purely vector electromagnetic current and the usual V-A charged currents are obtained. Z is coupled to a vector electron current, and the model predicts equal $\text{ν}{}_{\mathrm{\mu }}\text{e}\text{and}\text{ν}{}_{\mathrm{\mu }}\text{e}$ cross sections. Extension to hadrons is made by introducing three charmed quarks p′, n′ and λ′ of the same charges as p, n and λ. All the experimental results $\text{(ν}{}_{\mathrm{\mu }}\text{e}\text{,}\text{ν}{}_{\mathrm{\mu }}\text{e}\text{,}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}\text{e}$, ν_μ and $\text{ν}{}_{\mathrm{\mu }}$ hadron scatterings) are compatible with a value of sin²θ_W of order 0.4.     

Universal theory of weak interactions in the paracharge scheme and quark-lepton analogy

A universal theory of weak interaction is constructed by exploiting an analogy inherent between the four leptons and the four quarks of the paracharge scheme proposed recently to deal with theψ-particles. The leptons (ν _e,ν _μ,e _L,μ _L) are assigned to the representation (1/2, 1/2) and the quarks (p, n _W)_L and (χ,λ _W)_L to the representations (1/2, 0) and (0, 1/2), respectively, of the groupO ₄ (L stands for the left-handed projections and W for the Cabibbo rotated orthogonal combinations ofn andλ). Universality is ensured by embedding the above (weak)O ₄ into thesimple groupO ₅ and gauging the latter. In the final effective weak interaction, besides the conventionalV-A charged-current part, a (V-A)neutral current interaction (consistent with the present data) is naturally present. The neutral current has a \(\bar \nu _\mu \nu _\mu \) term but no \(\bar \nu _e \nu _e \) term, thus providing a crucial test of the theory.     

Pseudo-Cabibbo structure in a gauge theory of weak interactions and electromagnetism

We present an alternative to the Cabibbo theory in the context of a renormalizable gauge model of weak and electromagnetic interactions. The strangeness-changing hadronic weak current is assumed to be V+A.     

Unified theory of weak and electromagnetic interactions with ΔI = 12 rule

An SU(2) ? U (1) gauge theory of weak and electromagnetic interactions satisfying the $\text{ΔI =}\text{1}\text{2}$ rule is proposed, which has the following characteristic: (i) A neutral boson Z, coupling to the neutral strangeness-changing current is used in addition to the usual charged ones, to give the $\text{ΔI =}\text{1}\text{2}$ rule in the standard fashion. Couplings are chosen such that the Z decouples from the observed leptons, in order to agree with experiment. (ii) It is assumed that the |ΔY| = 2 transitions due to neutral vector-boson exchange cancel the |ΔY| = 2 contributions due to charged vector-boson exchange. This constraints the Cabibbo angle in a manner consistent with experiment.     

Fourth-order contributions to μμ elastic scattering in the gauge theory of weak interactions

The fourth-order contributions of WW, Z? and ZZ intermediate states to the S-matrix elements of μμ elastic scattering have been calculated by dispersion theoretic techniques in the U-gauge. It is shown that the contributions are finite and very small compared to the low-order contributions. It is also shown that the main part of these finite contributions comes from the WW intermediate state.     

Perturbative quantum gravity in analogy with Fermi theory of weak interactions using bosonic tensor fields

In this paper we work in perturbative quantum gravity and we introduce a new effective model for gravity. Expanding the Einstein–Hilbert Lagrangian in graviton field powers we have an infinite number of terms. In this paper we study the possibility of an interpretation of more than three graviton interacting vertices as effective vertices of a most fundamental theory that contain tensor fields. Here we introduce a Lagrangian model named I.T.B. (intermediate-tensor-boson) where four gravitational pseudo-currents that contain two gravitons couple to three massive tensorial fields of ranks one, three and five, respectively. We show that the exchange of those massive particles reproduces, at low energy, the interacting vertices for four or more gravitons. In a particular version, the model contains a dimensionless coupling constant g and the mass M of the intermediate bosons as free parameters. The universal gravitational constant G_N is shown to be proportional to the inverse of mass squared of mediator fields, particularly . A foresighting choice of the dimensionless coupling constant could lower the energy scale where quantum gravity aspects show up.     

Purely hadronic weak interactions in unified field theories of the weak and electromagnetic interactions

Non-leptonic weak interactions are investigated in unified gauge theories. A large enhancement of parity violation in nuclei relative to conventional Cabibbo theory is indicated.     

Unified theory of weak,strong, electromagnetic,and gravitational interactions

This study will attempt to construct a unified theory of weak, strong, electromagnetic, and gravitational interactions, based on a generalization of Weinberg-Salam theory [1] and a theory proposed previously by the present author [2, 3].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 25–30, January, 1985.     

Loop vertex expansion for higher-order interactions

This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail the example of the \((\bar{\phi } \phi )^p\) field theory in zero dimension. We find that the important feature to extend the loop vertex expansion is not to use an intermediate field representation, but rather to force integration of exactly one particular field per vertex of the initial action.     

Higher-order effects in Fermi-type charged current theory of weak interactions: Semi-leptonic neutral currents

In a convergent field theory rescattering graphs lead to neutral-current effects of the observed magnitude if the effective cut-off momentum is $\text{～G}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{≈ 300}\text{GeV}$. A perturbation expansion is justified owing to the value f=0.18 of the resulting expansion parameter.