We study the scattering of neutrinos on polarized and unpolarized free nucleons, and also the polarization of recoil particles in these scatters. In contrast to electromagnetic processes, the parity-violating weak interaction gives rise to large spin asymmetries at leading order. Future polarization measurements could provide independent access to the proton axial structure and allow the first extraction of the pseudoscalar form factor from neutrino data without the conventional partially conserved axial current (PCAC) ansatz and assumptions about the pion-pole dominance. The pseudoscalar form factor can be accessed with precise measurements with muon (anti)neutrinos of a few hundreds $mathrm{MeV}$ of energy or with tau (anti)neutrinos. The axial form factor can be extracted from scattering measurements using accelerator neutrinos of all energies.
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