$$ \newcommand\Tr{\mathrm{Tr}} \newcommand{\braket}[2]{\langle #1 \mid #2 \rangle} \newcommand\I{\mathbb{I}} \newcommand{\avg}[1]{\left< #1 \right>} \newcommand{\RD}{D} \newcommand{\ri}{\mathrm{i}} \DeclareMathOperator{\sign}{sign} \DeclareMathOperator{\Sign}{Sign} \newcommand{\ii}{\mathrm i} \newcommand{\vv}{\mathrm v} \newcommand{\ff}{\mathrm f} \newcommand{\mm}{\mathrm m} \newcommand{\ee}{\mathrm e} \newcommand{\xx}{\mathrm x} \newcommand{\RR}{\mathrm R} \newcommand{\dd}{\mathrm d} \newcommand{\FF}{\mathrm F} \newcommand{\BB}{\mathrm B} \newcommand{\vph}{v_{\mathrm{ph}}} $$

General Principles of Neutrino Oscillations

Since the flavor eigenstates of the neutrino are not the same as its propagation eigenstates, it can change flavor while it propagates. In this chapter, I will use the two-flavor scheme to explain neutrino oscillations in some simple scenarios.1 I will first discuss neutrino oscillations in vacuum. After explaining the general principles of neutrino oscillations in matter, I will show how the solar neutrino problem can be explained by neutrino oscillations. Finally, I will demonstrate the flavor isospin picture which can be used to visualize neutrino oscillations.

  1. In most physical problems, the two-flavor scheme is a good approximation to the phenomena of neutrino oscillations. The two mass splitings between the three mass eigenstates are so different that the corresponding oscillations occur on very different length scales. On a given length scale, the two-flavor scheme captures the prominent features of the neutrino oscillation of the corresponding mass spliting. ↩︎

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