Neutrino-pair bremsstrahlung with generation change of the charged lepton

The ratio $R_{\nu \overline{\nu }}\equiv \frac{\sigma (l{}_{}{}^A{}_{}{}^{}Z\to l{}_{}{}^A{}_{}{}^{}Z\Sigma {\nu }^{}\nu \overline{\nu })}{\sigma (l{}_{}{}^A{}_{}{}^{}Z\to l^{\prime }{}_{}{}^A{}_{}{}^{}Z{\nu }_l{\overline{\nu }}_{l^{\prime }})}$, where $l$ and $l^{\prime }$ are distinct charged leptons, is evaluated in the framework of the standard theory. The dependences on the number of generations, the helicity of the incoming lepton, and the lepton masses are analyzed. It is shown that in spite of the high energies considered lepton-mass effects are important, modifying the $R_{\nu \overline{\nu }}$ estimate for vanishing lepton masses by a factor of about three.