Constraints on the reaction νμ(νμ) + Z → νμ(νμ) + μ− + μ+ + Z in theories with neutral currents

In the presence of neutral lepton currents, the characteristics of the reaction $\text{ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) +}\text{Z}\text{→ ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) + μ}{}^{\mathrm{?}}\text{+ μ}{}^{\mathrm{+}}\text{+}\text{Z}$ are modified from those expected in the conventional V-A theory. We show that in a very general class of intermediate boson theories, the modification produced can be specified entirely in terms of the cross sections for $\text{ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) +}\text{e}{}^{\mathrm{?}}\text{→ ν}{}_{\mathrm{\mu }}\text{(}\text{ν}{}_{\mathrm{\mu }}\text{) +}\text{e}{}^{\mathrm{?}}$. Such a constraint does not necessarily exist in models with four-fermion interaction.