# Analysis 2019

This analysis became the first measurement of neutrino oscillation parameters using neutrinos and antineutrinos.

The best-fit point is found for the normal hierarchy and the upper $\theta_{23}$ octant:

$\Delta m_{32}^2 = +2.48^{=0.11}_{-0.06} \times 10^{-3} eV^2/c^4$

$sin^2 \theta_{23} = 0.56^{+0.04}_{-0.03}$

$\delta_{CP} = 0.0^{+1.3}_{-0.4} \pi$

The data prefer the normal hierarchy with a significance of $1.9 \sigma$ and the upper $\theta_{23}$ octant with a significance of $1.6 \sigma$. These results exclude $\delta_{CP}$ values in the inverted mass hierarchy from $- 0.04$ to $0.97\pi$ in the lower $\theta_{23}$ octant and $0.04$ to $0.91\pi$ in the upper octant by more than $3\sigma$.

Other results:

 NO, LO IH, UO IH, LO $\Delta m_{32}^2/ (10^{-3} eV^2/c^4)$ $+2.47$ $-2.54$ $-2.53$ $sin^2 \theta_{23}$ $0.48$ $0.56$ $0.47$ $\delta_{CP}/ \pi$ $1.9$ $1.5$ $1.4$ $+1.6\sigma$ $+1.8\sigma$ $+2.0\sigma$

# Analysis 2017

The results utilize significant improvements in both the simulations and analysis of the data. A joint fit to the data for $\nu_{\mu}$ disappearance and $\nu_{e}$ appearance gives the best-fit point as normal mass hierarchy,

$\Delta m^{2}_{32} = 2.44 \times 10^{-3} eV^{2}/c^{4}$,

$\sin^{2} \theta_{23} = 0.56$,

$\delta_{CP} = 1.21 \pi$.

The 68.3% confidence intervals in the normal mass hierarchy are

$\Delta m^{2}_{32} \in [2.37, 2.52] \times 10^{-3} eV^{2}/c^{4}$,

$\sin^{2} \theta_{23} \in [0.43, 0.51] \cup [0.52, 0.60]$,

$\delta_{CP} \in [0, 0.12\pi] \cup [0.91\pi, 2\pi]$.

The inverted mass hierarchy is disfavored at the 95% confidence level for all choices of the other oscillation parameters.

# Second Analysis (2016)

The results of the second analysis were published in 2017. This analysis used an exposure equivalent to $6.05 \times 10^{20} POT$ from the Fermilab NuMI beam.

## Muon neutino disappearance results

The best fit in the normal hierarchy gives:

$\Delta m_{32}^2 = (2.67 \pm 0.11 ) \times 10^{-3} eV^2$

$sin^2 \theta_{23} = 0.404^{+0.030}_{-0.022} \ (0.624^{+0.022}_{-0.030})$

The best fit in the inverted hierarchy gives:

$\Delta m_{32}^2 = (-2.72 \pm 0.11 ) \times 10^{-3} eV^2$

$sin^2 \theta_{23} = 0.398^{+0.030}_{-0.022} (0.618^{+0.022}_{-0.030})$

Maximal mixing, where $sin^2 \theta_{23} = 0.5$, was disfavored at $2.6 \sigma$.

## Electron neutrino appearance results

$33 \ \nu_{e}$ candidates were observed with a background of $8.2 \pm 0.8 \ (syst.)$.

The hypothesis of inverted mass hierarchy with $\theta_{23}$ in the lower octant is disfavored at greater than 93% C.L. for all values of $\delta_{CP}$.

## Sterile neutrinos

Sterile analysis used data collected from February 2014 to May 2016.

With an exposure of $6.05 \times 10^{20}$ POT-equivalent, 95 NC-like events were observe in the FD, compared with an expectation of $83.5 \pm 9.7(stat.) \pm 9.4(syst.)$. This result is consistent with three-flavor mixing within 1.03 σ. No evidence for depletion of NC events is observed in the FD at a distance of 810 km from the neutrino source and NOvA sees no evidence for active-sterile neutrino mixing.

NOvA set limits of $\theta_{24} < 20.8^{\circ}$ and $\theta_{34} < 31.2^{\circ}$ in a 3+1 model scenario.

# First Analysis (2015)

The results of the first analysis were published in 2016. This analysis used a 14 kton-equivalent exposure of $2.74 \times 10^{20} POT$ from the Fermilab NuMI beam.

## Muon-neutrino disappearance results

Assuming the normal hierarchy, the measurements have a next view:

$\Delta m^{2}_{32} = 2.52^{+0.20}_{-0.18} \times 10^{-3} eV^2$

and $sin^2 \theta_{23}$ in the 68% CL range $[0.38, 0.65]$, with two statistically degenerate best-fit values:

$sin^2 \theta_{23} = 0.43 \ (0.60)$

Assuming the inverted hierarchy, the measurements have a next view:

$\Delta m^{2}_{32} = -2.56 \pm 0.19 \times 10^{-3} eV^2$

and $sin^2 \theta_{23}$ in the 68% CL range $[0.37, 0.64]$, with two statistically degenerate best-fit values:

$sin^2 \theta_{23} = 0.44 \ (0.59)$

## Electron neutrino appearance results

NOvA had observed $6 \ \nu_{e}$-like events in the FD, with a background prediction of $0.99 \pm 0.11 \ (syst.)$

The range of $0.1 \pi < \delta_{CP} < 0.5\pi$ in the IH is disfavored at the 90% C.L. The range of $0.25 \pi < \delta_{CP} < 0.95 \pi$ in the NH is disfavored at the 90% C.L.