Trimuons in SU(3) gauge models

We discuss models of weak interactions which can account for the recently observed μ^?μ^?μ⁺ events in v_μ reactions by allowing for the production of a new heavy neutral lepton and a new quark. One model is based on an SU(3) × U(1) gauge theory in shich the left-handed leptons are classified in anti-triplets. The second model catagorizes the leptons in an octet in accord with the more restrictive SU(3) weak gauge theory.     

SU(2) ⊗ U(1) gauge theories of the generalized σ model for π0, η, η' → γγ decays

By embedding the chiral current-mixing gauge theories in the SU(2)_L ? SU(2)_R generalized σ model, it is shown that the correct sign and magnitude for π⁰ → γγ decay, as well as the SU(3) relation of π⁰, η, η' → γγ decays can be obtained within the framework of SU(2) ? U(1) gauge theories of weak and electromagnetic interactions.     

The price of natural flavour conservation in neutral weak interactions

The natural conservation of flavours to O(G_F²) in neutral weak interactions severely constrains choices of gauge groups as well as their fermion representations. In the absence of exactly conserved quantum numbers other than charge, and of |ΔQ| ? 2 charged currents, essentially the only weak and electromagnetic gauge groups whose neutral interactions naturally conserve all flavours are SU(2)_L ? U(1) and SU(2)_L ? [U(1)]². The plausible extensions of these gauge groups to grand unified models including the strong interactions are based on SU(5) and SO(10) respectively. Making the SU(5) model completely natural, including in the Higgs sector, gives the prediction $\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{/m}{}_{\mathrm{<mtext>e</mtext>}}\text{? m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{\mu }}\text{? m}{}_{\mathrm{<mtext>b</mtext>}}\text{/m}{}_{\mathrm{\tau }}\text{? 2605}$ where τ is the probable new heavy lepton and b is the conjectured third flavour of charge $\text{?1}\text{3}\text{quark}$. The SO(10) model contains a potential SU(2)_L ? SU(2)_R ? U(1) weak and electromagnetic gauge group, and has a complicated Higgs structure which does not naturally conserve quark flavours.     

Quarks and leptons

We review the physics of quarks and leptons within the framework of gauge theories for the weak and electromagnetic interactions. The Weinberg-Salam SU(2) × U(1) theory is used as a “reference point” but models based on larger gauge groups, especially SU(2)_L × SU(2)_R × U(1), are discussed. We distinguish among thre “generations” of fundamental fermions: The first generation (e^?, ν_e, u, d), the second generation (μ^?, ν_μ, c, s) and the third generation (τ^?, ν_τ, t, b). For each generation we discuss the classification of all fermions, the charged and neutral weak currents, possible right-handed currents, parity and CP-violation, fermion masses and Cabibbo-like angles and related problems. We review theoretical ideas as well as experimental evidence, emphasizing open theoretical problems and possible experimental tests. The possibility of unifying the weak, electromagnetic and strong interactions in a grand unification scheme is reviewed. The problems and their possible solutions are presented, generation by generation, but a brief subject-index (following the table of contents) enables the interested reader to follow any specific topic throughout the three generations.     

Gauge theoretical realization of the superweak model of CP violation

It is pointed out that the presence in a gauge theory of vector bosons or left-over Higgs bosons with a weak interaction strength of the order of10^?11G_E and which have CPviolating couplings to the strangeness-changing neutral current, will lead to the superweak model of CP violation. An example of such a theory, based on the gauge group SU (2) ?U(1), is given.     

Mixing of leptonic number in a general SU(2)L ⊗ U(1) ⊗ SU(2)R model

We discuss a general leptonic model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group and we present general results for the ? → ?′ γ and ν? → ν?′γ processes, which can be used for any model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group or on any of its subgroups. The predictions of the μ → eγ branching ratio and of the neutrino lifetime for various models discussed in the literature are reviewed. The main results are summarized in tables.     

Possible structures of the neutral current within a gauge theory framework

We examine a class of gauge theories based on U(1)×SU(2)×G allowing for an arbitrary number of gauge bosons, while retaining the lowq ² four fermion interaction of the standard model. Measurable consequences fore ⁺ e ^?→μ ⁺ μ ^? ande ⁺ e ^?→e ⁺ e ^? at presently available as well as LEP energies are presented. Implications of the recently determined QED cut-offΛ _? ? 100 GeV on gauge boson properties and the anomalous magnetic moment of the muon are pointed out.     

A gauge model without parity violation in heavy atoms

We address the question: “are weak right-handed non-singlet representations of quarks and leptons necessary?” An extension of the Weinberg-Salam model to SU(2) ? U(1) ? U(1) is found to adequately describe all existing weak interaction data including the lack of parity violation in atomic physics experiments. These data tightly constrain the additional parameters introduced by adding the second weak hypercharge. Although such a model may seem regressive when considered from the standpoint of “simple” unification schemes, we feel that it is aesthetics rather than experiment which leads to non-trivial right-handed multiplet structure. In contrast to most other models, ours predicts a substantial parity-violation effect in atomic experiments on hydrogen. We note that the second weak boson in our model is not constrained to be heavy by existing data and thus might already by accessable in pp → μ⁺μ^?X or possibly in the next generation of colliding beam facilities through e⁺e^? → μ⁺μ^?.     

Is there a new neutral lepton?

We discuss conservation laws of lepton flavors within the context of unified weak and electromagnetic gauge theories. We show that the present upper limit on the new (U) lepton-number violating processes U→3 charged leptons already requires the presence of a neutral lepton in the SU(2) ? U(1) theory. We discuss some of the possibilities and point out the constraints implied by lowering the bounds on μ→eγ and U→3 charged leptons.     

New values of pion-nucleon scattering lengths and f2

From fixed t dispersion relations we have obtained more accurate values for the pion nucleon coupling constant and s-wave scattering lengths, using our recent low energy πN angular distribution and total cross section data. The results are: f² = 0.0790 ± 0.0010, a₁ ? a₃ = 0.262 ± 0.004μ^?1, a₁ + 2a₃ = ? 0.014 ± 0.005μ^?1.     

Gauge theories and “elastic” weak neutral currents

For the gauge group O(4) × U(1), the alternatives: left-handed leptons are (a) 4-spinors, (b) 4-vectors are shown to imply (a) possible presence, (b) absence of elastic ν_μ ? e and ν_μ ? nucleon amplitude to O(G). Some properties of the new spinor model are described. In contains a neutral current closely akin to the one in the Salam-Ward-Weinberg model.     

Neutral-current constraints on gauge models of weak and electromagnetic interactions

Sehgal and Hung and Sakurai have recently argued that neutrino-hadron neutral-current couplings must lie in one of two allowed regions in coupling-parameter space. We study this conjecture using realistic BNL ν_μ and ν&#x0304;_μ spectra in the elastic ν_μp (ν&#x0304;_μp) calculations and also study constraints imposed by theq²-distributions. On comparing to gauge models, we find that the Weinberg-Salam and SU(2)_L×SU(2)_R×U(1) models fall within one allowed region, while a vectorlike SU(3)×U(1) model and a hybrid SU(2)×U(1) model with a (u, b)_R doublet fall in the other region.     

On classical Yang-Mills equation with weak external sources

The method proposed by Jackiw, Jacobs and Rebbi for solving classical Yang-Mills equations with external color changes by an expansion of the solution in powers of the external color change is applied in order to find gauge potentials A_μ^a generated by the external color charge with Hopf index ±1. This topologically non-trivial charge turns out to support a non-abelian Coulomb type solution. We also propose a gauge invariant expression for the energy in the presence of external currents.     

Cabibbo angle,CP violation and quark masses

By adding suitable discrete flavor symmetries to SU(2)_L ? SU(2)_R ? U(1) left-right symmetric gauge models of weak and electromagnetic interactions, we are able to express all the mixing angles between the quark flavors (u, d, s,c) in terms of the quark masses. This enables us to compute the Cabibbo angle and the CP violating phases using plausible values for the quark masses. The CP violating K ar 2π decay amplitude η_+? (and η₀₀ in the model is then given purely in terms of the parity violating parameter of the model (m_WL⁺/m_WR⁺)².     

Bounds on the number and masses of quarks and leptons

We assume weak, electromagnetic and strong interactions to be asymptotically divergent, and to become strong at very large energies, of the order of the Plank mass. In this picture, the “low-energy” couplings (i.e. in the 10² GeV region) must be near the infrared stable point, and this allows us to put bounds on the number of elementary fermions (quarks and leptons). Similar assumptions on the Higgs couplings give bound on the fermion and on the Higgs boson masses. We consider the cases where weak and electromagnetic interactions are described by the gauge groups SU(2) ? U(1) or SU(2)_R ? U(1). The weak neutral current mixing angle is computed in both cases.     

On the possibility to determine weak hyperfine structure interaction constants by magnetic depolarization

A new method to measure weak hyperfine structure interaction constants (aτ ? 1) by magnetic depolarization, involving interaction between nuclear orientation and electronic alignment, was used on the 3 ¹P₁ level of ³He. It was found that a/Γ = 0.075 ± 0.010.     

Study of single weak boson production in electron-positron scattering

The studies of the week boson production in electron-positron scattering are reviewed. At the lowest order of the Weinberg-Salam gauge theory, the cross sections for the various processes of the single weak boson production are computed by paying an attention on the gauge invariance at the high energies, or by calculating all the relevant Feynman diagrams, some of which have been neglected in the studies so far. A formulation is presented to compute the cross sections for the various processes,e ⁺ e ^?→WUD, whereW is the weak boson,WUD stands for \(W^ + \bar U D\) , or \(W^ - U \bar D\) , andU(D) represents the up (down) state of theSU(2) _L doublet. Also the upper bound of the contributions from the single weak boson production via the two photon process is estimated by using the real photon approximation.     

A light neutral intermediate vector boson without large e+e−→ μ+μ− asymmetries

An effective SU(2)×U(1)×U(1)' electroweak theory is shown to permit the occurence of a pair of neutral intermediate vector bosons with masses 40 GeV?m_light?70 GeV, m^W.S._Z⁰<m_heavy?100 GeV. Neutrino neutral current interactions are shown to be the same as in the standard electroweak model, and e⁺e^?→μ⁺μ^? forward-backward asymmetries are within experimental bounds for m_light?40 GeV.     

Hard pions and axial meson exchange current effects in negative muon capture in deuterium

The contribution of the axial meson exchange current effects to the doublet transition rate in the reaction μ^? +d → 2n+ ν_μ is calculated by using the minimal, chiral and approximately gauge invariant Lagrangian model for the A₁ρπ system. The contribution from the ρ-π weak decay process current usually considered is found to be nearly cancelled by that from the A₁ pole graph which is prescribed by the underlying invariance principles. Correct treatment of the N¹ propagator in the N¹ excitation current of the pion range leads to ≈ 30 % suppression of the N¹ effect.     

Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

We study the light-front zero-mode contribution to the transition form factors (g, f, a _±, T _i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ?ν _? and rare P → V ? ⁺?^? decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ ^μ  = γ ^μ ? (2k ? P _V ) ^μ /D, the six form factors (g, f, a ₊, T ₁, T ₂, T ₃) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) ⁿ of the struck quark with the power n > 0. Although the form factor a _? is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ ^μ  = γ ^μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a _?.