Determine the sign of Delta m^2_32 (neutrino mass ordering)

Determine the sign of the atmospheric mass-squared splitting Delta m^2_32 = m_3^2 − m_2^2, thereby establishing whether the neutrino mass ordering is normal (Delta m^2_32 > 0) or inverted (Delta m^2_32 < 0).

Background

In the three-flavor framework of neutrino oscillations, the ordering of the neutrino mass eigenstates remains unresolved. While solar neutrino experiments have determined that Delta m2_21 is positive, the sign of Delta m2_32 distinguishes between the normal mass ordering (m_3 heavier than m_2) and the inverted mass ordering (m_3 lighter than m_2).

Long-baseline experiments such as NOvA are sensitive to this sign through matter effects in neutrino propagation. However, parameter degeneracies, including those potentially introduced by nonstandard interactions, can complicate the determination of the mass ordering, motivating continued experimental efforts to resolve the sign of Delta m2_32.

References

Measurements from solar neutrino experiments determined that Δm2_{21} is positive, while the sign of Δm2_{32} is still unknown. Taking the mass state ν1 as having the largest contribution from the flavor state ν_e, if Δm2{32} > 0, neutrinos are said to have a normal mass ordering (NO), while if Δm2_{32} < 0, neutrinos would have an inverted mass ordering (IO).

— Search for $CP$-Violating Neutrino Nonstandard Interactions with the NOvA Experiment  (2403.07266 - Collaboration et al., 2024) in Introduction, paragraph beginning “The frequency of neutrino oscillations is mainly governed by the mass-squared splittings Δm^2_{ji}…”.

The neutrino mass ordering---Normal Hierarchy (NH: $m_3 \gg m_1, m_2$) or Inverted Hierarchy (IH: $m_1 \approx m_2 \gg m_3$)---remains one of the central open questions in particle physics.

— Flavor Tomography of Long-Lived Neutrino-Mass Mediators: Probing the Neutrino Mass Ordering at the HL-LHC  (2609.04761 - Wang, 4 Sep 2026) in Section 1, Introduction