Standard Weinberg-Salam Model Research Articles

Parity-Violating Asymmetry in Electron- Polarized Deuteron Scattering

5in the electron (or muon) scattering angles from 0 to 35 for a given energy of 1 Ge V in the Weinberg-Salam model. It has been of particular interest to determine the relevant structure of electron-( muon-) quark sector weak neutral-current couplings. ' ) The determination, however, has been rather difficult to study experimentally, because electron (or muon) is coupled with quarks by the electromagnetic and weak interaction, so that one must look for effects that are characteristic of the weak interaction, and for a parity-violation. Parity-violation in longitudinally polarized electrons from unpolarized deuterons has been observed at SLAC. 2 ) That in atomic physics has also been studied, while the experimental situations for bismuth are still confusing. 3 ) So, we need some other experiments to determine the weak neutral-current couplings of electron­ (muon-) quark sector and to discuss the reliability of some gauge models on weak and electro­ magnetic interactions. The neutral current effects in the lepton elastic scattering by polarized proton target have been investigated by Bilen'kii et al. ' ) They have defined the longitudinal asymmetry and have estimated at very high energy of a few handred GeV. They also have defined the transverse asymmetry and have only referred to be small which is the proton part of our parity-violating asymmetry and is suggested to be important in this letter. Because of the high energy of incident leptons, the cross sections discussed by them are quite small and they are far from performing the experiment. Then, when we consider similar reactions, the in­ termediate energy less than a few Ge V is one of the essential parts on feasibility. In this letter, we discuss the parity-violating asymmetry in the process e+ d i ..... e' + d or (p, n) and give the numerical estimates using the standard Weinberg-Salam model 4 ) at the incident electron (or muon) energy of 1 GeV. The relevant Feynman diagrams and the kine­ matical configuration are shown in Figs. 1 and 2. The calculation has been made in the impulse approximation and we have neglected the nuclear corrections such as the final state interaction between proton and neutron which are expected to be smaller contributions to our results. In the impulse approximation, it is well known that the matrix elements of the electro­ magnetic and the weak hadronic currents are given in terms of the Sachs form factors 5 ) when

Front-Back and Charge Asymmetries of Leptons from Hadronic Productions of W± and Z0-Bosons

Using the QCD perturbation theory up to O (α s ) and the standard Weinberg-Salam model we carry out numerical evaluation for the frontback asymmetry and the charge asymmetry of the leptons from the decay of the W ± - and Z 0 -bosons produced in the reactions p p , \bar p p → W ± +anything → l ± + ν l +anything and p p , \bar p p →(γ, Z 0 )+anything → l + + l - +anything. For the scale violating parton distribution we employ the Glück-Owens-Reya parametrization. We show that these asymmetries are fairly large under certain kinematical conditions.

Renormalization Effects on the Weak Mixing Angle in the Standard Weinberg-Salam Model

Higher order corrections to neutral current amplitudes modify the relative strength of the electromagnetic to isovector couplings from the lowest order value sin 2θW. This modification effect is studied in the neutrino-quark scattering νq →νq in the Weinberg-Salam model. The relative strength is smaller by 0.004 for √-q2∼0.25 GeV but approaches sin 2 θW for larger √-q2, where q is the momentum transfer.

Mixing angles andCPviolation in anSU(2)L×U(1)gauge model

Expressions for the mixing parameters are obtained in terms of mass ratios in the standard Weinberg-Salam model with permutation symmetry S/sub 3/ for six quarks. The CP-violating phase delta is taken into account and there are no arbitrary parameters except for the quark masses. In the lowest order, the angles defined by Kobayashi and Maskawa are sintheta/sub 1/ approx. = (m/sub d//(m/sub d/+m/sub s/))/sup 1/2/, sintheta/sub 2/ approx. = -((m/sub s//m/sub b/)/sup 2/-(m/sub c//m/sub t/)/sup 2/)/sup 1/2/, and sintheta/sub 3/=(m-italic/sub s//m/sub b/)/sup 2//costheta/sub 1/. The model can be consistent with the observed magnitude of CP violation. The b quarks decay predominantly into c quarks with lifetime of tau/sub b/ approx. = 10/sup -11/ sec.

Full quark-lepton correspondence within a multigenerationSU(2)L×U(1)-based model

A full quark-lepton correspondence is established without upsetting (a) the standard Weinberg-Salam model, (b) the cosmological limits on the number of neutrino flavors, and (c) the neutrino masslessness property to all orders of perturbation theory. All this is within a minimal multigeneration tight scheme which is anomaly-free, conserves lepton numbers, and gives rise to a proper Cabibbo structure. A natural fermionic mass hierarchy accompanies the suppression of the horizontal gauge interactions through an absolute minimum of a symmetric Higgs potential. The model predicts ${m}_{t}=14.7$ GeV, and suggests a smaller current-algebra mass for the charmed quark without contradicting the measured ${K}_{L}\ensuremath{-}{K}_{S}$ mass difference.

Minimal anomaly-free electroweak model for several generations

A horizontal U'(1) gauge symmetry is invoked to distinguish several fermion generations which have one and the same Weinberg-Salam (WS) structure. It is assumed that both weak hypercharges associated with the WS U(1) and the new U'(1) factorize, i. e., they are of the form lambda/sub i/y and lambda'/sub i/y', where the scales lambda/sub i/, lambda'/sub i/ are the so-called seriality numbers of the ith generation. The motivation for such an assumption comes from the standard WS model. The generation structure is extended to the Higgs system as well, i.e., associated with the ith generation, there is an ith Higgs doublet whose U' (1) hypercharge is lambda'/sub i/h, where h is a number. We study as a prototype the simplest but the fundamental two-generation scheme in detail and show how, when the above assumptions are combined with (a) anomaly-free conditions, (b) conservation of lepton numbers, and (c) the emergence of a proper Cabibbo structure, we are led to a unique choice for Y' which can be expressed as Y' = -+(Y/3 + 2(B - L)/3) with the (-+) signs being the seriality numbers for the two generations, respectively. A hierarchy in the vacuum expectation values (VEV's) of the Higgs doubletsmore » produces the desired hierarchy in the fermion masses, and correlates the smallness of m/sub e/ with the smallness of m/sub u/, m/sub d/, and theta/sub C/. The gauge boson associated with U'(1) produces of course the undesirable flavor-changing neutral currents and the violation of e-..mu.. universality. However, an additional Higgs singlet with zero Y and with a large VEV suffices to make the mass of Z' heavy enough to suppress the unwanted features to any desirable degree. From the K/sub L/-K/sub S/ mass difference we estimate M (Z') > (1/..cap alpha..) M(Z). We investigate briefly a three-generation scheme. The existence of a third generation suggests the existence of a fourth one as well.« less

Minimal gauge model for the leptonic interactions with fixed Weinberg angle of 30°

A gauge model for leptons is proposed, based on the groupSU3. It establishes a minimal extension of the standard Weinberg-Salam model fixing the angle toθw = 30°. An investigation of μ-decay and elastic νμe scattering data shows that the masses of the additionally appearing bosons can be as small as about 250 GeV. They do not introduce new processes among leptons.

Neutral currents and quark mass ratiomumd=msmcin an SU(2)×U(1)×U(1) model

It is proposed that the relationship $\frac{{m}_{u}}{{m}_{d}}=\frac{{m}_{s}}{{m}_{c}}$ is a zeroth-order relationship of the spontaneously broken Lagrangian. This relationship is achieved by a symmetry which exchanges fields of different charges, and SU(2)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{}U(1) is the smallest extension of SU(2)\ifmmode\times\else\texttimes\fi{}U(1) by which one can implement such an exchange symmetry. Extended to leptons, the scheme achieves $\frac{{m}_{e}}{{m}_{\ensuremath{\mu}}}\ensuremath{\sim}\frac{{m}_{d}}{{m}_{c}}=\frac{{m}_{u}}{{m}_{s}}$ in a natural way. Limited to light quarks and leptons and the Higgs particles to which they couple, the model considered has identical neutral-current parametrization to the standard Weinberg-Salam model. When heavy quarks and leptons are introduced, and an extra Higgs field is added to provide their masses, the neutral-current parametrization is modified. The limit to the Weinberg-Salam case is discussed. Various sets of parameter values can be chosen which provide an adequate description of neutrino scattering data, polarized electron scattering from deuterium, and any one of the results of the different atomic parity violation experiments in bismuth.

Remarks on the parity-violating effects in the decayΣ0→Λ+e++e−

The correlation expected between the ..sigma.. spin and the positron momentum in the decay ..sigma../sup 0/ ..-->.. ..lambda.. + e/sup +/ + e/sup -/ is presented for three distinct gauge models. We show that a measurement of this correlation effect may help to distinguish between the standard Weinberg-Salam model and models in which the electron's neutral-current coupling is pure vector or in which parity is conserved by all neutral currents in lowest order.

Charged- and neutral-current production ofΔ(1236)

Based on a quark-model approach previously developed by us which employs a ${q}^{2}$ continuation in terms of generalized meson-dominance form factors we study the weak production of the isobar $\ensuremath{\Delta}(1236)$. First we demonstrate that our model is in agreement with the Argonne data on charged-current production of the $\ensuremath{\Delta}$. We then study neutral-current $\ensuremath{\Delta}$ production using four different gauge models, namely, the standard Weinberg-Salam model, a vectorlike model with six quarks, a five-quark model due to Achiman, Koller, and Walsh, and a variant of the G\"ursey-Sikivie model. We fine that the results for the differential cross section in the forward region ($|{q}^{2}|\ensuremath{\lesssim}0.1$ Ge${\mathrm{V}}^{2}$) are very sensitive to the structure of the weak neutral current and suggest that measurements in this region constitute a stringent test of weak-interaction models. We also calculate the density-matrix elements measurable from decay correllations. The density-matrix elements are not so sensitive to the models containing some axial-vector contribution, whereas the vectorlike model shows a behavior quite distinct from the others.

Renormalization effects from superheavy Higgs particles

Using a modification of the standard Weinberg-Salam model, we compute renormalization corrections to the W and Z masses proportional to differences in the Higgs-particle mass squared. This contradicts the expectation that superheavy particles should be undetectable in low-energy phenomena.

Parity violation in atoms induced by radiative corrections

We discuss the radiative corrections that induce a parity-violating electron-nucleus interaction in gauge theories. These higher-order effects are shown to be much larger than one might anticipate in a wide class of models. In particular, for an SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge model in which the electron's neutral-current coupling is pure vector, they lead to an optical rotation in bismuth which is about 11% as large as that predicted by the standard Weinberg-Salam model and opposite in sign---an experimentally testable consequence. Similar results are also found for an ${\mathrm{SU}}_{L}(2)\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}}_{R}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ model in which parity-violating neutral currents are naturally absent in lowest order. General formulas for the dominant radiative corrections which are applicable to most models are presented. The relevance of our results for experiments on ordinary hydrogen and deuterium is also discussed.

Neutral-current effects in Bethe-Heitler pair production

We consider Bethe-Heitler pair production in which the exchanged photon is replaced with a neutral weak intermediate boson. The interference between this and the pure Bethe-Heitler amplitudes contributes to an asymmetry between the lepton pairs and, in addition, the leptons acquire a finite longitudinal polarization. Both effects are calculated and numerical examples are given in the standard Weinberg-Salam model.

Vector-like quark models and parity violating effects in nuclei

Parity violating effects in nuclei for a class of vector-like quark models with a right-handed u-b coupling are examined. Determination of the parity violating nucleon potential due to pion exchange in these models is shown to be free from some difficulties present in the standard Weinberg-Salam model. The long-standing discrepancy between theory and experiment in medium and heavy nuclei can be removed in these models.

V + A currents coupling old quarks to new

We study some consequences of the existence of new quark flavors. We do this in the framework of gauge models, with V + A couplings of old to new quarks and allowing for mixing of different SU(2) × U(1) representations. High-energy neutrino and e +e − experiments may suggest (and can prove) the existence of new flavors. Low-energy neutrino neutral current experiments are sensitive to the way new quarks and their currents are added to the standard Weinberg-Salam model. We show that if new quarks with weak couplings to old u, d quarks are needed at all, low-energy neutral current data may favor a new class of models having non-diagonal neutral currents. However, the special case of a maximal charm-changing neutral current appears to be excluded by high-energy experiments.

Analysis of a six-quark model with right-handed currents

A model for the weak interactions using the six-quark model of Harari, right-handed currents, and heavy leptons which was proposed previously by some of us is analyzed in considerable detail. The model is one of a class of “vector-like” theories that are free of gauge theory anomalies. The neutral current is pure vector, which leads to predictions for diffractive production of vector mesons by neutrinos that are different from the predictions of the standard Weinberg-Salam model; the A 1 uncouples and the fractions of ϱ and ω are enhanced. It is also predicted that relative production of I = 1 2 final states is larger than I = 3 2 final states in vN → vN π in contrast to the Weinberg-Salam model. The non-leptonic decays of hyperons and mesons and the restrictions imposed by chiral symmetry are discussed. The decays of the charmed mesons are shown to be very rich due to the presence of both V − A and V + A interactions. The y-anomalies in neutrino interactions are discussed and calculations of dσ dx and dσ dy for both neutrinos and antineutrinos using modified Kuti-Weisskopf distributions are presented. Cross sections and ratios of neutrino and a neutrino cross sections are shown along with available experimental data. The v-distribution of dimuon events is also presented and compared with experiment. It is concluded that the model is not inconsistent with the currently available data.