Mass-squared difference ($\Delta m_{ij}^2=m_i^2-m_j^2$)

The difference between the squared masses of two propagation states. In vacuum its contribution to a neutrino oscillation probability has phase $\Delta m_{ij}^{2}L/(4E)$ in natural units. The exact identity $\Delta m_{13}^2=\Delta m_{12}^2+\Delta m_{23}^2$ constrains any proposed three-state numerical inputs.

The normal ordering has the third light neutrino above the solar pair in mass; the inverted ordering has it below that pair. Oscillation experiments determine differences of squared masses, not the common absolute mass scale. A pure vacuum electron-survival expression uses squared sines and does not by itself fix the signs of individual phase differences.