A theoretical and experimental review of the weak neutral current: a determination of its structure and limits on deviations from the minimalSU(2)L×U(1)electroweak theory

Abstract

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 ${{sin}^{2}\ensuremath{\theta}}_{w}$ 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, $\ensuremath{\nu}$ 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)\ifmmode\times\else\texttimes\fi{}U(1) models we find the following limits on mixing between right-handed singlets and doublets: ${sin}^{2}{\ensuremath{\alpha}}_{u}\ensuremath{\le}0.103$, ${sin}^{2}{\ensuremath{\alpha}}_{d}\ensuremath{\le}0.348$, and ${sin}^{2}{\ensuremath{\alpha}}_{e}\ensuremath{\le}0.064$. Assuming these mixing angles to be zero, a fit to the most accurate data (deep-inelastic and the polarized $\mathrm{eD}$ asymmetry) yields $\ensuremath{\rho}=0.992\ifmmode\pm\else\textpm\fi{}0.017(\ifmmode\pm\else\textpm\fi{}0.011)$ and ${{sin}^{2}\ensuremath{\theta}}_{w}=0.224\ifmmode\pm\else\textpm\fi{}0.015(\ifmmode\pm\else\textpm\fi{}0.012)$, where $\ensuremath{\rho}=\frac{{M}_{W}^{2}}{{M}_{Z}^{2}}{{cos}^{2}\ensuremath{\theta}}_{w}$ and the numbers in parentheses are the theoretical uncertainties. The value of $\ensuremath{\rho}$ 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 $\ensuremath{\rho}$ implies ${m}_{L}\ensuremath{\le}500$ GeV, where ${m}_{L}$ is the mass of any heavy lepton with a massless partner. In addition, for $\ensuremath{\rho}=1.0$, the authors determine ${{sin}^{2}\ensuremath{\theta}}_{w}=0.229\ifmmode\pm\else\textpm\fi{}0.009(\ifmmode\pm\else\textpm\fi{}0.005)$. Fits which also include the semi-inclusive, elastic, and leptonic data yield very similar results. A two-parameter fit gives $\ensuremath{\rho}=1.002\ifmmode\pm\else\textpm\fi{}0.015(\ifmmode\pm\else\textpm\fi{}0.011)$ and ${{sin}^{2}\ensuremath{\theta}}_{w}=0.234\ifmmode\pm\else\textpm\fi{}0.013(\ifmmode\pm\else\textpm\fi{}0.009)$, while a one-parameter fit to ${{sin}^{2}\ensuremath{\theta}}_{w}$ gives ${{sin}^{2}\ensuremath{\theta}}_{w}=0.233\ifmmode\pm\else\textpm\fi{}0.009(\ifmmode\pm\else\textpm\fi{}0.005)$. 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 $\frac{{M}_{{Z}_{2}}}{{M}_{{Z}_{1}}}g1.61 \mathrm{and} 3.44$ 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.