Past exam of the nuclear and particle physics course of the University of Oxford / 2022 / 2 / f / iii

Both $t$-channel Z boson exchange and $s$-channel annihilation $e^{-}{\bar{\nu }}_e\to W^{-\ast }\to e^{-}{\bar{\nu }}_e$ occur. Replacing the incident neutrino by an antineutrino interchanges the two chiral angular weights. In the same contact-interaction regime,At $x=0.231$ the factor is $0.2315$, between parts (i) and (ii). The comparison is energy dependent outside this regime: near $s=m_W^2$, the annihilation channel has a W boson resonance, and the low-energy formula is inapplicable.