Latest Results from MINOS and MINOS+

The MINOS and MINOS+ experiments collected accelerator beam neutrino and antineutrino data for 11 years corresponding to peak energies of 3 GeV and 6 GeV, respectively, over a baseline of 735 km. These proceedings report on new limits and constraints set by MINOS and MINOS+ in and beyond the standard three-flavor paradigm. The atmospheric neutrino mass splitting in the three-flavor model is measured to be (2.42 ± 0.09) × 10−3 eV2 for normal mass ordering and − ( 2.48 − 0.11 + 0.09 ) × 10 − 3 eV 2 for inverted mass ordering. Constraints are set on sterile neutrinos and antineutrinos in the four-flavor model by looking for sterile-driven νμ and ν ¯ μ disappearance and sterile-driven νe and ν ¯ e appearance. A combination of the MINOS four-flavor νμ disappearance search and the Daya Bay and Bugey-3 four-flavor ν ¯ e disappearance searches excludes the parameter space allowed by LSND and MiniBooNE for Δ m 41 2 < 0.8 eV 2 at 90% C.L. The size of large extra dimensions is constrained to be smaller than 0.17 μm at 90% C.L. in the limit of a vanishing lightest active neutrino mass. Finally, a search for non-standard νe and ν ¯ e appearance in MINOS is presented.


Introduction
MINOS and MINOS+ are long baseline neutrino oscillation experiments that ran from 2005 through 2012 and 2013 through 2016, respectively. Charged Current (CC) and Neutral Current (NC) interactions of accelerator beam muon neutrinos from the Neutrinos at the Main Injector (NuMI) beam [1] at Fermilab are measured by two functionally identical detectors located on the NuMI beamline axis. Both detectors are magnetized tracking-sampling calorimeters built of iron plates interleaved with scintillator planes, the latter being read out using wavelengthshifting fibers coupled to multi-anode photomultiplier tubes. The Near Detector (ND) is located 1.04 km downstream of the NuMI target at Fermilab and has a 23.7 t fiducial (980 t total) mass. The Far Detector (FD) is located 735 km downstream of the NuMI target in Soudan, Minnesota and has a 4.2 kt fiducial (5.4 kt total) mass [2].
The magnetic horns in NuMI allow to operate the beam in either ν µ or ν µ mode. During the MINOS era, NuMI provided a beam with a peak neutrino energy of 3 GeV corresponding to an exposure of 10.71 × 10 20 protons-on-target (POT) when operating in ν µ mode and 3.36 × 10 20 POT in ν µ mode. The peak neutrino energy increased to 6 GeV for MINOS+, with NuMI providing an exposure of 5.80 × 10 20 POT in ν µ mode during the first two years of running. The analysis of the final year of MINOS+ beam data is ongoing.
MINOS was originally designed to perform precision measurements of the atmospheric neutrino oscillation parameters in the standard three-flavor model, ∆m 2 32 and θ 23 , by observing muon neutrino disappearance occurring along the FD baseline.

Standard Three-Flavor Oscillation
In the three-flavor oscillation paradigm, MINOS and MINOS+ employ CC ν µ beam and atmospheric events to search for ν µ disappearance in the FD, and CC ν e beam events to search for ν e appearance in the FD. An update to the MINOS result [3] was performed by adding the first two years of MINOS+ beam exposure and an extra year of atmospheric events to the MINOS dataset [4]. The FD reconstructed beam ν µ energy spectrum is shown in Fig. 1a  The 68% (red line) and 90% (blue line) C.L. contours resulting from a fit to 48.67 kt-yrs of atmospheric data combined with disappearance and appearance data from the MINOS beam and disappearance data from the MINOS+ beam during the first two years of operation. The combined MINOS and MINOS+ contours are compared with the 90% C.L. limits of NOνA [5], T2K [6], and IceCube DeepCore [7] presented at Neutrino 2016.

Sterile Neutrinos in the Four-Flavor Model
As precision experiments, MINOS and MINOS+ employ their data to look for discrepancies from the three-flavor paradigm that could be accounted for by small modifications to the standard three-flavor model. One such scenario adds one sterile neutrino state that can mix with the three active neutrino states. This minimal extension to the three-flavor model requires three additional mixing angles, θ 14 , θ 24 , and θ 34 , one additional independent mass splitting, ∆m 2 41 , and two additional CP-violating phases, δ 14 and δ 24 .

Sterile Neutrino Search through Disappearance
MINOS and MINOS+ are sensitive to θ 24 by searching for CC ν µ disappearance and sterile neutrino appearance, the latter showing itself as a deficit of NC ν i (i = e,µ,τ) events compared to the three-flavor expectation. Unlike in the three-flavor model, significant oscillation along the ND baseline is possible. To account for this, the ratio of the measured FD and ND neutrino energy spectra, the Far-over-Near ratio, is compared to the four-flavor predictions. The Far-over-Near ratio for MINOS and MINOS+ selected CC events is shown in Fig. 2a.
MINOS and MINOS+ put constraints on θ 24 over many orders of magnitude of ∆m 2 41 . No evidence for a sterile neutrino has been found [4,8]. The combined MINOS and MINOS+ 90% and 95% C.L. Feldman-Cousins corrected contours are compared to results from other experiments in Fig. 2b.

Sterile Antineutrino Search through Disappearance
The ND and FD are magnetized, allowing separation of neutrinos and antineutrinos on an eventby-event basis. CC ν µ events are selected from the MINOS beam data acquired during both ν µ and ν µ operations. Figure 3b compares the MINOS 90% C.L contour to results from other experiments. MINOS provides the strongest disappearance constraints for ∆m 2 41 < 0.5 eV 2 . The regions excluded at 90% C.L. by KARMEN2 [19] and NOMAD [20] are also shown. (b) The MINOS 90% C.L. Feldman-Cousins corrected contour in the (sin 2 θ 24 , ∆m 2 41 ) plane using ν µ disappearance.

Large Extra Dimensions
MINOS and MINOS+ also search for extra dimensions. In the Large Extra Dimension (LED) model of [22,23,24,25], sterile neutrinos arise as Kaluza-Klein states in a large extra dimension compactified on a circle with radius R. These sterile neutrino states mix with the active neutrino states and thereby modify the neutrino oscillation probabilities. The effects of the large extra dimension are governed by R and the lightest active neutrino mass m 0 .
Following the Far-over-Near ratio approach of the four-flavor search and in the limit of a vanishing m 0 , MINOS beam data constrains R to be smaller than 0.45 µm [26], while adding MINOS+ beam data tightens the constraint to R < 0.17 µm at 90% C.L. [4]. Figure 4a shows the 90% C.L. contours based on MINOS beam data and combined MINOS and MINOS+ beam data.

Non-Standard Interactions
The oscillation probability observed in the FD would also be modified if neutrinos undergo non-standard interactions with matter when traveling from Fermilab to Minnesota. Such nonstandard interactions would induce an additional term in the interaction Hamiltonian which can be parameterized by the coupling coefficients αβ (α, β = e, µ, τ), where G F is the Fermi coupling constant and N e is the electron density of the matter through which the neutrinos travel. The oscillation probabilities furthermore depend on three additional phases, δ eµ , δ eτ , and δ µτ [27,28,29,30]. Employing ν e and ν e appearance events in the FD, MINOS has set constraints on | eτ | as a function of (δ CP + δ eτ ) [31], as shown in Fig. 4b.