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The MINOS (Main Injector Neutrino Oscillation Search) experiment has observed muon neutrino disappearance consistent with the oscillation hypothesis tested by Super-Kamiokande and K2K. The survival probability for {nu}{sub {mu}} is given approximately by 1 - sin{sup 2}2{theta}{sub 23}sin{sup 2}(1.27{Delta}m{sup 2}{sub 32}L/E), where{theta}{sub 23} and {Delta}m{sup 2}{sub 32} are the mixing angle and difference in mass squared in eV{sup 2}/c{sup 4} between the mass eigenstates {nu}{sub 3} and {nu}{sub 2}, L is the distance traveled in km, and E is the neutrino energy in GeV. In the Near Detector at Fermilab, a measurement of the energy spectrum of the NuMI neutrino beam is made 1 km from the beam target. The neutrinos travel to the Far Detector in the Soudan Underground Laboratory, where another measurement of the energy spectrum is made 735 km from the target. MINOS measures |{Delta}m{sub 32}{sup 2}| and sin{sup 2}2{theta}{sub 23} by comparing the ND and FD neutrino energy spectra. In this dissertation, a n alternate method is presented that utilizes rock muons, a class of events that occur when a {nu}{sub {mu}} interaction takes place in the rock surrounding the FD. Many muons that result from these interactions penetrate the rock and reach the detector. Muon events from {nu}{sub {mu}} interactions in the non-fiducial volume of the FD are also used in this analysis. The distribution of reconstructed muon momentum and direction relative to the beam is predicted by Monte Carlo simulation, normalized by the measured {nu}{sub {mu}} energy spectrum at the ND. In the first year of NuMI running (an exposure of 1.27x10{sup 20} protons on target) 117 selected events are observed below 3.0 GeV/c, where 150.2{+-}16.1 events are expected. When a fit is performed to events below 10.0 GeV/c, the null (no disappearance) hypothesis is ruled out at significance level {alpha} = 4.2 x 10{sup -3}. The data are consistent with the oscillation hypothesis given parameter values |{Delta}m{sup 2}{sub 32}| = 2.32 {+-}{sup 1.06}{sub 0.75} x 10{sup -3} eV{sup 2}/c{sup 4} (stat+sys) and sin{sup 2}2{theta}{sub 23} &gt; 0.48 (68% CL) which is in agreement with the published MINOS result |{Delta}m{sup 2}{sub 32}| = 2.74 {+-}{sup 0.44}{sub 0.26} x 10{sup -3} eV{sup 2}/c{sup 4} (stat+sys) and sin{sup 2}2{theta}{sub 23} &gt; 0.87 (68% CL)

Observation of deficit in NuMI neutrino-induced rock and non-fiducial muons in MINOS Far Detector and measurement of neutrino oscillation parameters