Figure 1: The flavor content of the neutrino mass eigenstates. The splitting between ${\nu }_3$ and ${\nu }_2$ (or ${\nu }_1$) (labelled here by 1, 2, and 3) is responsible for oscillation at $500\text{km/GeV}$ (relevant to neutrinos arriving from the Earth’s atmosphere), whereas the splitting between ${\nu }_2$ and ${\nu }_1$ leads to an oscillation at the scale of $15,000\text{km/GeV}$ (relevant to neutrinos arriving from the sun). ${\nu }_e$ appearance at the T2K experiment is primarily controlled by the size of ${\sin }^2{\theta }_{13}$, the fraction of ${\nu }_e$ in the ${\nu }_3$ mass eigenstate.