Three-Flavor Neutrino Oscillations with MINOS+
This dissertation presents the analysis of the last two years of data from the MINOS+ long-baseline neutrino oscillation experiment. The analysis explores the data above the first oscillation maximum for neutrinos in the standard three-flavor neutrino oscillation model, adding significantly more neutrino events and constraining the model with increased precision. The analysis of the high-energy region of the MINOS+ data set, where previously there has been limited study, can help constrain alternative models or possibly show evidence of new phenomena. The predecessor to MINOS+, the MINOS experiment, measured $\nu_\mu$ disappearance and $\nu_{e}$ appearance using Fermilab's NuMI $\nu_\mu$ beam from 2005 to 2012. During this period the neutrino beam's energy spectrum was focused to peak near the first oscillation maximum. In addition to measuring accelerator beam neutrinos, the MINOS Far Detector collected a sample of atmospheric neutrinos from 2003 to 2011. With the se two samples, MINOS measured the atmospheric mass splitting, $\Delta{m}^2_{32}$, at the 5\% level and the value of $\sin^2\theta_{23}$ at the 15\% level. The data also constrained the CP violating parameter $\delta_{\rm CP}$. The MINOS+ experiment exposed the MINOS detectors to a neutrino beam peaked at energies above the oscillation maximum from 2013 to 2016. With this higher energy neutrino beam, MINOS+ measures the shape of the $\nu_\mu$ survival probability away from the oscillation maximum with unprecedented precision. Measuring the shape of the oscillation probability as a function of neutrino energy is an essential test of the three-flavor oscillation model. At these higher energies where the standard oscillation probability decreases, the neutrino energy spectrum is sensitive to potential perturbations from mixing with additional sterile neutrinos or non-standard neutrino interactions. This analysis of the complete data set from MINOS+ finds no significant deviatio ns from the three-flavor oscillation probability in the ener! gy region of 4 to 10\,GeV covered by the neutrino beam. This provides increased confidence in the three-flavor model in this region and provides new constraints of the atmospheric oscillation parameters, $\Delta{m}^2_{32}$ and $\sin^2\theta_{23}$, by combining the MINOS and MINOS+ data sets. The hierarchy of the neutrino masses is related to the sign of $\Delta{m}^2_{32}$. When $\Delta{m}^2_{32} > 0$, the mass hierarchy is classified as normal. When $\Delta{m}^2_{32} < 0$, the mass hierarchy is classified as inverted. This analysis cannot rule out either of the mass hierarchies. For the normal mass hierarchy, the combined analysis measures $\lvert{\Delta{m}^2_{32}}\rvert = 2.41\pm 0.09 \times 10^{-3}\,{\mathrm{eV}^2}$ at 68\% C.L. and $\sin^2\theta_{23} = 0.42_{-0.06}^{+0.23}$ at 90\% C.L. For the inverted mass hierarchy, this analysis measures $\lvert{\Delta{m}^2_{32}}\rvert = 2.47_{-0.10}^{+0.08} \times 10^{-3}\,{\mathrm{eV}^2}$ at 68\% C.L. and $\sin^2\theta_{23} = 0.42_{ -0.06}^{+0.23}$ at 90\% C.L. In addition to the analysis and measurement of the atmospheric oscillation parameters using MINOS+, this work updates the constraint on $\delta_{\rm CP}$ from MINOS and performs an exploratory combination using $\nu_\mu$ disappearance data from the NOvA experiment. The NOvA experiment uses the NuMI beam in an off-axis strategy that results in a narrow flux of muon neutrinos at the first oscillation maximum and allows precision measurements of the three-flavor parameters. Since NOvA and MINOS+ shared the same neutrino beam, their data can be combined taking advantage of common beam related uncertainties. Combined, the data from the MINOS, MINOS+, and NOvA experiments precisely map $\nu_\mu$ oscillation probabilities using the same neutrino beam in a way that could not be attempted before.