  We determine the effective theory of neutrino-electron and neutrino-quark
scattering and provide the most precise up-to-date prediction for
neutrino-electron scattering cross sections quantifying errors for the first
time to be of order $0.2-0.4~\%$. Radiative corrections in the theory with
electron and neutrinos only involve three effective couplings. One is the Fermi
constant which is known with sub-ppm accuracy. Another one has a small error of
order $0.02~\%$. The uncertainty of the third one is limited by the knowledge
of hadronic contributions to charge-isospin vector-vector correlation function.
