 Solution

Only $t$-channel Z boson exchange contributes at leading order. A W boson would connect ${\nu }_{\mu }$ to ${\mu }^{-}$, rather than to $e^{-}$, and therefore does not supply this elastic channel. With the assumptions and normalization of part (i),For the illustrative value $x=0.231$, the dimensionless factors in parts (i) and (ii) are $0.5521$ and $0.09015$. The electron-flavor reaction is therefore about $6.1$ times as large in this limit. This uses the weak flavour selection in neutrino-electron scattering, not a hypothetical flavor-changing neutral vertex.