Weak inelastic production and leptonic decays of heavy leptons

We examine here reactions of the type $\left\{\nu \right(\overline{\nu })N\to L^{\pm }+``\mathrm{a}\mathrm{n}\mathrm{y}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{g}\text{'}\text{'}\mathrm{a}\mathrm{n}\mathrm{d}{l}^{\pm }N\to L^0({\overline{L}}^0)+``\mathrm{a}\mathrm{n}\mathrm{y}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{g}\text{'}\text{'}\}\left\{\searrow \searrow \right\}\left\{ \nu \right(\overline{\nu })+l^{\pm }+{\nu }_{l^{\mp }} l^{\pm }+l^{\prime \mp }+{\nu }_{l^{\prime \pm }}\}$ where $L$ is a lepton heavier than the muon, and derive expressions for the inclusive cross sections of the outgoing charged leptons. The phase-space integration is simplified by neglecting the electron and muon masses, and the differential cross sections, with respect to the transverse momentum of the charged leptons in the final state, are calculated. Using a simple parameterization for the hadronic structure functions, results are presented for several incident lepton energies, between 50 and 500 GeV in the lab frame, and, for heavy-lepton masses ranging from 2 to 11 GeV, assuming the coupling constant of the heavy lepton to be identical to that of the muon. A simple relation between the differential cross section of the outgoing charged leptons along the beam axis and the total cross section is obtained. Throughout these calculations the effects produced on the spectrum of the final charged lepton by the polarization of the heavy lepton are fully incorporated.