Neutrino (antineutrino) scattering off $^{12}$C is one of various important key reactions for $ u$-process in the nucleosysnthesis of light nuclei. Most of neutrino-nucleus scattering are considered through indirect processes within the energy range from a few to tens of MeV. Target nuclei are excited by incident neutrino (antineutrino) through various transitions, and subsequently decay into other nuclei with emitting particles. But, direct processes are also feasible, in which incident neutrino (antineutrino) strips directly one nucleon from target nuclei. Consequently, direct processes may affect abundances of $^{11}$C and $^{11}$B additionally to indirect processes. We investigate direct neutrino (antineutrino) quasi-elastic scattering off $^{12}$C around the energy region liberating one nucleon and discuss implications of direct processes in the nucleosynthesis. The direct processes might be comparable to the indirect processes if the final state interaction is taken into account.
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