Deep-inelastic contribution for the neutral current

Abstract

The effective coupling constants are calculated for the processes $\ensuremath{\nu}p\ensuremath{\rightarrow}\ensuremath{\nu}p$ and ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ by taking account of the deep-inelastic contribution. The formal light-cone analysis is applied to get the momentum dependence of the structure functions. It is shown that the lowest-order perturbation is small and that the deep-inelastic contribution for the coupling constant is arranged in the form of sum rules which are derived from U(6) \ifmmode\times\else\texttimes\fi{} U(6) quark algebra for the process $\ensuremath{\nu}p\ensuremath{\rightarrow}\ensuremath{\nu}p$. Sum rules are also obtained for the decay process ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ by using SU(3) symmetry where the ${K}^{+}$ and ${\ensuremath{\pi}}^{+}$ meson mass difference is neglected. By comparing with the experimental upper bound for the neutral current the following results are obtained: The weak boson mass should be less than $11 \frac{\mathrm{GeV}}{{c}^{2}}$ and the local theory of the weak interaction is valid up to 50 GeV.