Neutrino-pair bremsstrahlung and the number of lepton generations

Neutrino pair creation in bremsstrahlung processes of the type \(l \to l{\text{ }}v{\text{ }}\bar v\) contains vital information on the number of lepton generations, and is catalyzed by the coherent nuclear Coulomb effect or other forms of intense fields. Of particular interest is the ratio \(R_{v\bar v} = \sigma 1\mathop \to \limits_A l(v\bar v)]/\sigma 1\mathop \to \limits_A l'(v\bar v)]\) (wherel, l′ are distinct charged leptons). It is sensitive to the number of neurino types and their couplings in the same way that the ratio \(R_{q\bar q} = \sigma e^ + e^ - \to {\text{hadrons}}]/\sigma e^ + e^ - \to \mu ^ + \mu ^ - ]\) is to those of quarks. In the Weinberg-Salam model withN lepton generations, the ratio \(R_{v\bar v}\) is approximately given by \((N + 4) + 4(1 - 4\sin ^2 \theta _W )]/8\) .