Dynamical zeros in neutrino-electron elastic scattering at leading order

We show the existence of dynamical zeros in the helicity amplitudes for neutrino-electron elastic scattering at lowest order in the standard theory. In particular, the $\lambda =1\mathrm{/}2$ non-flip electron helicity amplitude in the electron antineutrino process vanishes for an incident neutrino energy $E_{\nu }=m_e\mathrm{/}(4si{n}^2{\theta }_W)$ and forward electrons (maximum recoil energy). The rest of helicity amplitudes show kinematical zeros in this configuration and therefore the cross section vanishes. Prospects to search for neutrino magnetic moment are discussed.