The intermediate weak boson and weak interactions at high energy

The high-energy pire-leptonic weak interaction is investigated based on the assumption of the existence of a charged vector boson which mediates the weak processes. With the aid of the fixed-t dispersion relation the following relation is obtained: The weak boson mass m_W should satisfy $\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{? G}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, with G the Fermi coupling constant, if the asymptotic value of the cross section becomes of the order of the strong interaction in the energy region observable in cosmic rays, etc.The scattering processes $\text{e}\text{+ν→}\text{e}\text{+ν}\text{and}\text{e}\text{+}\text{ν}\text{→}\text{e}\text{+}\text{ν}$ are examined by the aid of the N/D method. For a large vector-boson mass $\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{?100}\text{GeV}$, an S-wave resonance should exist for the process e+ν→e+ν while for $\text{e}\text{+}\text{ν}\text{→}\text{e}\text{+}\text{ν}$ there should exist a P-wave resonance which corresponds to the intermediate weak boson. The neutral current is then estimated. It is shown that the neutral current produced as a higher-order effect is not inconsistent with the present experiments on the pure-leptonic weak interaction if m_W?1 TeV.