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This is a review article on recent developments, of researches on the parity nonconserving nuclear interactions in connection with the weak neutral currents. Properties of the weak neutral currents clarified by high energy neutrino reactions are presented. Problems of the parity violating nucleon-meson vertices and of the parity nonconserving nuclear potentials are discussed. Dependences on inner parts of strong interaction potentials are argued. Parity nonconserving quantities are explicitly given in terms of the parity nonconserving weak interactions and discussed in details.

Weak neutral currents give a significant contribution to parity violation in nuclear transitions. Many calculations have been presented on this effect. These depend strongly on the evaluation of the strength of the weak nucleon-pion coupling, on the treatment of the nuclear wave functions and on the choice of models of the weak neutral currents and others. In this note first we present an estimation of the weak nucleon-pion coupling constant and comment on previous evaluation of this quantity. Secondly, taking into account the modified factorization approach proposed by Donoghue and adopting previous evaluation of nuclear matrix elements in the literature, we calculate the parity violating quantities in various transitions. The recently claimed discrepancy between a theoretical prediction and an experimental result of the Pasadena-Los Angeles-Seattle group on the circular polarization of γ rays in the transitions of 18F disappears in our treatment.

The violation of the |ΔI|=1/2 rule in K →3 π decays is discussed on the assumption that the weak-interaction Hamiltonian has the pure |ΔI|=1/2 property and that the violation of the |ΔI|=1/2 rule is caused by the electromagnetic interaction. The assumptions of chiral SU3 ×SU3 algebra, P. C. A. C. and soft pion approximation are also used. The results are in good agreement with experiments.

The parity-nonconserving-nuclear force is discussed in the process n + p →d + γ. Formulae for the circular polarization (Pγ) and the asymmetry (α) of the emitted γ rays are given for various nucleon-nucleon potentials. Dependence of the Pγ and α on nucleon-nucleon potential is investigated.

We make analyses of the parity-violating asymmetries of electron-deuteron and electron-proton deep inelastic scatterings including sea quark contribution and adopting three different kinds of parton distribution functions. Both results from electron-deuteron and from electron-proton scatterings coincide with the prediction of the Weinberg-Salam model. Our results are found to be insensitive to the difference among the three kinds of parton distribution functions. We also study the x-, y- and si 2θw-dependences of A/Q2 in the Weinberg-Salam model. Experiments at higher y values will be useful for more precise determination of the Weinberg angle θw.

A model-independent analysis of new data provides, for the first time, a unique determination of the weak neutral-current couplings of the electron, if we disregard the parity violation in atomicf transitions and the neutrino electron scattering reported by the Gargamelle collaboration at CERN-SPS. The recent result at SLAC for inelastic scattering of longitudinally polarized electrons from deuterium is a crucial new input in this analysis. The solution is consistent with the Weinberg-Salam model, but disagrees with the vectorlike gauge model of the electron.

The matrix elements of the D→Kπ decays are evaluated on the basis of the effective Hamiltonian in the Kobayashi-Maskawa model and compared with the data. The possibility of the excess of the D→πeν decays is shown from the phenomenological analysis.

The effective nonleptonic weak interaction Hamiltonian for the |ΔC|=1 processes is calculated by using the quantum chromodynamics with the color octet massless gluons and the renormalization group equations, in the Kobayashi-Maskawa model. The “penguin” diagram contributes to the effective Hamiltonian by the division of the range of virtual momenta integration. The U-spin operators are taken as the operator bases.

A parity nonconserving asymmetry in proton-proton scattering is studied. We calculate the longitudinal analyzing power for the momentum of incident proton up to PL∼6GeV/c. For the weak matrix element, we adopt one-boson-exchange interactions coming from vector mesons (ρ0 and ω) as well as Z-boson, which are unitarized by the strong initial and final state interactions. The result is consistent with the experimental data at low energy, but, significantly smaller at high energy.

We calculate the QCD corrections for parity-violating ΔS = ΔC = 0 nonleptonic weak interactions in the Kobayashi-Maskawa model. The effective Hamiltonians are evaluated for its isospin ΔI = 0, 1 and 2 parts.

In view of possible existence of the nucleonic second-class current, the weak charged urbaryonic and leptonic V-A currents are generalized so as to contain derivative currents by assuming two-component neutrino theory and baryon-lepton correspondence. Values of parameters associated with the derivative currents of lepton are determined from µ-, π- and K-decays. The generalized currents can explain ξ parameter of the µ-decay.

Using the QCD-corrected effective Hamiltonian of the parity-violating ΔS = ΔC =0 nonleptonic interaction in the Kobayashi-Maskawa model, we calculate the parity-violating coupling constants of the NNπ, NNρ and NNω interactions. The comparison with the experiments is made.