A theoretical and experimental review of the weak neutral current: a determination of its structure and limits on deviations from the minimal $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ electroweak theory

A detailed analysis of existing neutral-current data has been performed in order (a) to determine as fully as possible the structure of the hadronic and leptonic neutral currents without recourse to a specific weak-interaction model; (b) to search for the effects of small deviations from the Weinberg-Salam (WS-GIM) model; and (c) to determine the value of ${{sin}^2\theta }_w$ as accurately as possible. The authors attempt to incorporate the best possible theoretical expressions in the treatment of each of the reactions. For deep-inelastic scattering, for example, the effects of quantum chromodynamics, including the contributions of the $s$ and $c$ quarks, have been included. The sensitivity of the results both to systematic uncertainties in the data and to theoretical uncertainties in the treatment of deep-inelastic scattering, semi-inclusive pion production, $\nu$ elastic scattering from protons, and the asymmetry in polarized $\mathrm{eD}$ scattering have been considered; the systematic errors are generally found to be smaller than the statistical uncertainties. In the model-independent analyses the authors find that the hadronic neutral-current parameters are uniquely determined to lie within a small domain consistent with the WS-GIM model. The leptonic couplings are determined to within a twofold ambiguity; one solution, the axial-vector-dominant, is consistent with the WS-GIM model. If factorization is assumed then the axial-dominant solution is uniquely determined and null atomic parity violation experiments are inconsistent with other neutral-current experiments. Within generalized SU(2)×U(1) models we find the following limits on mixing between right-handed singlets and doublets: ${sin}^2{\alpha }_u\le 0.103$, ${sin}^2{\alpha }_d\le 0.348$, and ${sin}^2{\alpha }_e\le 0.064$. Assuming these mixing angles to be zero, a fit to the most accurate data (deep-inelastic and the polarized $\mathrm{eD}$ asymmetry) yields $\rho =0.992\mathrm{}\pm 0.017(\pm 0.011)$ and ${{sin}^2\theta }_w=0.224\mathrm{}\pm 0.015(\pm 0.012)$, where $\rho =\frac{M_W^2}{M_Z^2}{{cos}^2\theta }_w$ and the numbers in parentheses are the theoretical uncertainties. The value of $\rho$ is remarkably close to 1.0 and strongly suggests that the Higgs mesons occur only as doublets and singlets. If one makes this assumption, then the limit on $\rho$ implies $m_L\le 500$ GeV, where $m_L$ is the mass of any heavy lepton with a massless partner. In addition, for $\rho =1.0\mathrm{}$, the authors determine ${{sin}^2\theta }_w=0.229\mathrm{}\pm 0.009(\pm 0.005)$. Fits which also include the semi-inclusive, elastic, and leptonic data yield very similar results. A two-parameter fit gives $\rho =1.002\mathrm{}\pm 0.015(\pm 0.011)$ and ${{sin}^2\theta }_w=0.234\mathrm{}\pm 0.013(\pm 0.009)$, while a one-parameter fit to ${{sin}^2\theta }_w$ gives ${{sin}^2\theta }_w=0.233\mathrm{}\pm 0.009(\pm 0.005)$. Finally, the authors have found no evidence for a violation of factorization or for the existence of additional $Z$ bosons. Fits to two explicit two-boson models yield the lower limits $\frac{M_{Z_2}}{M_{Z_1}}>1.61\mathrm{} \mathrm{and} 3.44$ for the mass of the second $Z$ boson. The desirability of a complete analysis of radiative and higher-order weak corrections, which have not been included in the authors' theoretical uncertainties, is emphasized.