We use the NOvA near detector and the NuMI beam at Fermilab to study the neutrino-electron elastic scattering and the muon neutrino magnetic process beyond the Standard Model physics. The particle identifications of neutrino on electron elastic scattering are trained by using the multi-layer neural networks. This thesis provides a general discussion of this technique and shows a good agreement between data and MC for the neutrino-electron elastic weak scattering. By using 3.62e20 POT dataset in the NOvA near detector, we find 1.58e-9 Bohr magneton as the 90% C.L. upper limit. We also find a sensitivity of 8e-10 Bohr magneton at the 90% C.L. for 1.8e21 POT
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