Measurement of the Muon Neutrino Charged Current Single Positive Pion Production Cross Section on Water in the ND280 Near Detector

T2K is a long-baseline neutrino oscillation experiment, situated in Japan, which measures the oscillation probability of muon neutrinos produced at the J-PARC accelerator complex and detected at the water Cherenkov far detector, Super-Kamiokande. Essential to measur- ing neutrino oscillation probabilities is the understanding of the underlying neutrino-nucleus interaction cross section, which is currently a leading systematic uncertainty in oscillation measurements. It is therefore crucial to reduce this uncertainty, particularly as neutrino physics moves towards next generation experiments, where measurements will no longer be statistically limited.
This thesis presents a measurement of the muon neutrino charged current single positive pion cross section on both water and hydrocarbon targets, made using data taken by the T2K near detector ND280, with a simultaneous extraction using log-likelihood minimisation. Although such measurements exist, this is the first of its kind to be performed in the form of a double differential cross section as a function of the outgoing pion kinematics, which are sensitive to both the underlying nuclear ground state model and the neutrino interaction model. The initial unblinding to data shows a reasonable level of tension with the nominal Monte Carlo model used, with a χ2/Ndf value of 4.31. In addition to this measurement, an attempt is made to measure the 4-dimensional differential cross section, in terms of both muon and pion kinematics simultaneously. Whilst successful, this measurement is seen to be statistically limited. Both measurements also feature a novel method for reconstructing the kinematics of pions detected through their decay to muons and subsequently Michel electrons, providing access to a region of pion kinematics previously unmeasured by T2K.