We discuss the sensitivity reach of a neutrino factory measurement to non-standard neutrino interactions (NSI), which may exist as a low-energy manifestation of physics beyond the Standard Model. We use the muon appearance mode u_e --> u_mu and consider two detectors, one at 3000 km and the other at 7000 km. Assuming the effects of NSI at the production and the detection are negligible, we discuss the sensitivities to NSI and the simultaneous determination of theta_{13} and delta by examining the effects in the neutrino propagation of various systems in which two NSI parameters epsilon_{alpha beta} are switched on. The sensitivities to off-diagonal epsilons are found to be excellent up to small values of theta_{13}. We demonstrate that the two-detector setting is powerful enough to resolve the theta_{13}-NSI confusion problem. We believe that the results obtained in this paper open the door to the possibility of using neutrino factory as a discovery machine for NSI while keeping its primary function of performing precision measurements of the lepton mixing parameters.
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