Invariant amplitudes, unpolarized cross sections, and polarization asymmetries in (anti)neutrino-nucleon elastic scattering

At leading order in weak and electromagnetic couplings, cross sections for (anti)neutrino-nucleon elastic scattering are determined by four nucleon form factors that depend on the momentum transfer $Q^2$. Including radiative corrections in the Standard Model and potential new physics contributions beyond the Standard Model, eight invariant amplitudes are possible, depending on both $Q^2$ and the (anti)neutrino energy $E_\nu$. We review the definition of these amplitudes and use them to compute both unpolarized and polarized observables including radiative corrections. We show that unpolarized accelerator neutrino cross-section measurements can probe new physics parameter space within the constraints inferred from precision beta decay measurements.