Neutrino mass ordering in light of recent data

We inspect recently updated neutrino oscillation data—specifically coming from the Tokai to Kamioka and NuMI Off-axis ${\nu }_e$ Appearance experiments—and how they are analyzed to determine whether the neutrino mass ordering is normal ($m_1<m_2<m_3$) or inverted ($m_3<m_1<m_2$). We show that, despite previous results giving a strong preference for the normal ordering, with the newest data from T2K and NOvA, this preference has all but vanished. Additionally, we highlight the importance of this result for nonoscillation probes of neutrinos, including neutrinoless double beta decay and cosmology. Future experiments, including JUNO, DUNE, and T2HK will provide valuable information and determine the mass ordering at a high confidence level.

Figure 1

Bi-probability plots of oscillation probabilities for neutrinos (x axes) and antineutrinos (y axes) at the $L$ and $E$ for NOvA (left panel) and T2K (right panel) while varying ${\delta }_{CP}$. Black (gray) crosses indicate measurements with statistical uncertainty only for the two experiments using their 2020 (pre-2020) results. Ellipses correspond to best-fit points according to NOvA (blue) and T2K (red) fits under the normal (solid) or inverted (dashed) mass ordering. Dots denote probabilities for ${\delta }_{CP}=0$, with arrows indicating increasing ${\delta }_{CP}$.

Figure 2

Sums (top) and differences (bottom) of oscillation probabilities at NOvA (x axes) and T2K (y axes) at fixed $L$ and $E$. Ellipses are generated by varying ${\delta }_{CP}$ while fixing the other oscillation parameters. Dots denote $\mathrm{\Sigma }{P}_{\mu e}$ (top) and $\mathrm{\Delta }{P}_{\mu e}$ (bottom) for ${\delta }_{CP}=0$, with arrows indicating increasing ${\delta }_{CP}$. Crosses display sums/differences of oscillation probabilities assuming statistically independent measurements at $\mathrm{NO}\text{vA}/\mathrm{T}2\mathrm{K}$ for current (black) and pre-2020 (gray) results.

Figure 3

Results of our fit of ${\delta }_{CP}$ and ${\sin }^2{\theta }_{23}$. Top: $\mathrm{\Delta }{\chi }^2$ as a function of ${\delta }_{CP}$ for fixed MO. Middle (bottom): ${\delta }_{CP}$ versus ${\sin }^2{\theta }_{23}$ for the NO(IO). Except for the top panel, all contours are $\mathrm{\Delta }{\chi }^2=2.3$ (solid) and 4.61 (dashed)—black lines indicate a joint fit of $\mathrm{T}2\mathrm{K}/\mathrm{NO}\text{v}\mathrm{A}/\mathrm{SK}18$, where blue (red) indicate a fit to NOvA (T2K) alone. Corresponding stars indicate the best-fit point of each fit. The text indicates the relative preference for mass ordering by each fit.

Figure 4

Results of our fit of the oscillation parameters ${\delta }_{CP}$ and ${\sin }^2{\theta }_{23}$. In the top panel we show $\mathrm{\Delta }{\chi }^2$ as a function of ${\delta }_{CP}$ for a fixed MO. In the middle (bottom) panel we show ${\delta }_{CP}$ versus ${\sin }^2{\theta }_{23}$ for the NO (IO). Except for the top panel, all contours are $\mathrm{\Delta }{\chi }^2=2.3$ (dashed) and 4.61 (solid)—black lines indicate a joint fit of $\mathrm{T}2\mathrm{K}/\mathrm{NO}\nu \mathrm{A}$, where blue (red) indicate a fit to $\mathrm{NO}\nu \mathrm{A}$ (T2K) alone. The corresponding stars indicate the best-fit point of each fit, and the text indicates the relative preference for mass ordering by each fit ($\mathrm{\Delta }{\chi }_{(\mathrm{NO},\mathrm{IO})}^2\equiv {\chi }_{(\min ,\mathrm{IO})}^2-{\chi }_{(\min ,\mathrm{NO})}^2$).