Radiative corrections to neutrino-induced neutral-current phenomena in theSU(2)L×U(1)theory

Abstract

Weak corrections of order $\ensuremath{\alpha}$ to $\ensuremath{\nu}$-induced neutral-current phenomena are studied in the $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ theory. Calculations are carried out using a simple renormalization framework in which ${cos\ensuremath{\theta}}_{W}=\frac{{m}_{W}}{{m}_{z}}$ exactly and amplitudes are expressed in terms of ${G}_{\ensuremath{\mu}}$, the universal constant of the weak interactions obtained from muon decay. To rigorously evaluate corrections to hadronic vertices, we employ the current-algebra formulation of radiative corrections. Our main emphasis is on large-momentum-transfer processes such as deep-inelastic scattering; however, we also discuss low-momentum transfers and $\ensuremath{\nu}$-lepton interactions. We find that the weak radiative corrections to $\ensuremath{\nu}$-hadron neutral-current scattering give rise to a universal renormalization factor ${\ensuremath{\rho}}_{\mathrm{Nc}}^{(\ensuremath{\nu};h)}$ multiplying the overall amplitude, a correction factor ${\ensuremath{\kappa}}^{(\ensuremath{\nu};h)}({q}^{2})$ multiplying ${{sin}^{2}\ensuremath{\theta}}_{W}$, and two new induced currents not present at the tree level. For nonexotic values of ${m}_{{\ensuremath{\varphi}}_{1}}$ (Higgs-scalar mass) and ${m}_{t}$ $t$-quark mass), the corrections ${\ensuremath{\rho}}_{\mathrm{Nc}}^{(\ensuremath{\nu};h)}$- 1 and ${\ensuremath{\kappa}}^{(\ensuremath{\nu};h)}({q}^{2})$- 1 turn out to be small over a wide range of momentum transfers. The smallness of these corrections is mainly due to the renormalization framework employed; but it is helped by a subtle partial cancellation between hadronic and bosonic contributions. Photonic corrections to the hadronic vertices are also briefly discussed in the leading-logarithm approximation of the quark-parton model. Detailed expressions for the $\mathrm{ZZ}$, $\mathrm{WW}$, $\ensuremath{\gamma}Z$, and $\ensuremath{\gamma}\ensuremath{\gamma}$ self-energies along with a discussion of the effect of large ${m}_{t}$ on these quantities are given. They play an important role in our renormalization scheme and are useful in the study of radiative corrections to many other processes of physical interest.