% miko:type: atomic
% miko:title: Neutrino Oscillation
% miko:summary: Flavor change caused by the mismatch between neutrino flavor and mass eigenstates.
% miko:tags: particle
% miko:difficulty: undergrad
% miko:related: complete-particle-physics, standard-model, time-evolution-operator
% miko:keywords: neutrino, mixing, mass difference

\documentclass{article}
\usepackage{amsmath}
\title{Neutrino Oscillation}
\begin{document}
\maketitle

\section{Mixing}

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

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

\section{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.

\end{document}
