Non-standard neutrino-nucleon interaction is formulated and explored within the energy range of quasi-elastic scattering. In particular, the study focuses on the neutral-current elastic (anti)neutrino scattering off nucleons described by the exotic reactions $\nu_\alpha ({\bar \nu}\alpha) + n \rightarrow \nu\beta ({\bar \nu}\beta) + n \nu\alpha ({\bar \nu}\alpha) + p \rightarrow \nu\beta ({\bar \nu}_\beta) + p$, which provide corrections to the dominant Standard Model processes. In this context, it is shown that the required exotic nucleon form factors may have a significant impact on the relevant cross sections. Besides cross sections, the event rate is expected to be rather sensitive to the magnitude of the lepton-flavour violating parameters resulting in an excess of events. The overlap of non-standard interactions and strange quark contributions, in the region of few GeV neutrino energies, is also examined. The formalism is applied for the case of the relevant neutrino-nucleon scattering experiments (LSND, MiniBooNE, etc.) and motivates the notion that such facilities have high potential to probe NSI.

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