Neutrino Oscillation

Mixing

Flavor states need not be mass eigenstates. In a two-flavor model,

$$|\nu_\alpha\rangle =\cos\theta|\nu_1\rangle+\sin\theta|\nu_2\rangle.$$

Oscillation Probability

The transition probability has the form

$$P_{\alpha\to\beta} =\sin^2(2\theta) \sin^2\left(\frac{\Delta m^2 L}{4E}\right).$$

More commonly in practical units,

$$P_{\alpha\to\beta} =\sin^2(2\theta) \sin^2\left(1.27\frac{\Delta m^2 L}{E}\right),$$

with $\Delta m^2$ in $\mathrm{eV}^2$, $L$ in km, and $E$ in GeV.