The Tokai to Kamioka (T2K) is a long-baseline neutrino oscillation experiment in Japan producing precise measurements of neutrino oscillations and neutrino interactions with nuclear targets. T2K utilizes a muon (anti-)neutrino beam produced at the J-PARC proton accelerator facility which is measured at a suite of near detectors, ND280 and INGRID, and the far detector, Super-Kamiokande. One of the dominant systematic uncertainties for the oscillation analysis is from the uncertainty in neutrino interaction modeling with complex nuclei, which will eventually become the limiting uncertainty for the next generation of neutrino oscillation experiments. Therefore measurements of neutrino cross sections on nuclear targets is essential for understanding how to model these complicated nuclear interactions. This thesis presents a novel neutrino cross section measurement utilizing both of the T2K near detectors, ND280 and INGRID, in a joint statistical fit. Because the T2K near detectors are exposed to neutrinos from the same beamline, the uncertainties in the neutrino flux prediction will be correlated. This fact combined with the different neutrino energy spectra seen at each detector will allow for some separation of flux and cross section effects, and presents an opportunity to study the neutrino cross section as a function of energy using the same neutrino beam. This analysis is the first cross section measurement on T2K to use samples from multiple detectors in the same beamline. This thesis presents a description of the statistical analysis framework, the event selection, the treatment of systematic uncertainties, and the extracted muon neutrino CC0pi double differential cross section in bins of muon kinematics for ND280 and INGRID, including the correlations between the detectors.
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