Signatures of neutral currents and heavy leptons in weak inelastic processes

The signatures of various neutrino-induced inelastic reactions are theoretically analyzed. With the aim of differentiating "muonless" reactions which proceed via neutral currents from those via an intermediate heavy lepton, we derive the expressions for their differential cross sections, including all polarization effects due to the heavy lepton. Similarly, reactions involving charged leptons in the final state are also discussed. A simple parameterization for the hadronic structure functions is used for a numerical comparison of various differential spectra. For the hadronic decay channels of the heavy lepton the vertex is phenomenologically related to $e^{+}{e}^{-}\to \mathrm{hadrons}$ and the observed constancy of the cross section for the latter process is incorporated. Finally, expressions for the differential spectra in the limit of vanishing transverse momenta of the final lepton or hadron state are related to the total production cross section of heavy leptons, and characteristic difference in such spectra for reactions with and without heavy leptons is pointed out and explained on the basis of a simple theorem on the decay of polarized spin-½ particles via a general ($aV+bA$) leptonic current.