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

Weak corrections of order $\alpha$ to $\nu$-induced neutral-current phenomena are studied in the $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ theory. Calculations are carried out using a simple renormalization framework in which ${cos\theta }_W=\frac{m_W}{m_z}$ exactly and amplitudes are expressed in terms of $G_{\mu }$, 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 $\nu$-lepton interactions. We find that the weak radiative corrections to $\nu$-hadron neutral-current scattering give rise to a universal renormalization factor ${\rho }_{\mathrm{Nc}}^{(\nu ;h)}$ multiplying the overall amplitude, a correction factor ${\kappa }^{(\nu ;h)}\left(q^2\right)$ multiplying ${{sin}^2\theta }_W$, and two new induced currents not present at the tree level. For nonexotic values of $m_{{\phi }_1}$ (Higgs-scalar mass) and $m_t$ $t$-quark mass), the corrections ${\rho }_{\mathrm{Nc}}^{(\nu ;h)}$- 1 and ${\kappa }^{(\nu ;h)}\left(q^2\right)$- 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 $\mathrm{ZZ}$, $\mathrm{WW}$, $\gamma Z$, and $\gamma \gamma$ 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.