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Neutrino Oscillation Overview

When a neutrino is created it must be of a specific flavor, that is, it must be an electron neutrino (), a muon neutrino () or a tau neutrino (). When one speaks of massive neutrinos they are given the lables , and which have masses m₁, m₂ and m₃, respectively. What is interesting is that there does not need to be a one to one correspondence between each neutrino of a particular flavor and each neutrino of a particular mass. In general a neutrino of a particular flavor will be a linear superposition of three neutrinos, each of a particular mass,

$$\left(\begin{array}{c} \nu_e \\ \nu_{\mu} \\ \nu_{\tau} \end... ...t(\begin{array}{c} \nu_1 \\ \nu_2 \\ \nu_3 \end{array}\right).$$

Where U is an SU(3) matrix giving the rotation between the mass states and the flavor states. Often it is assumed that there is measureable mixing between only two states. This is usually the case taken for testing the hypothesis that oscilation explains such problems as the solar neutrino and atmospheric neutrino problems.

For two flavor oscillation and assuming either that the energy or the momentum of the two mass components are equal allows one to write down the probability that a neutrino of one flavor will be detected as a neutrino of the other flavor. This probability for neutrino of flavor a to be observed as a neutrino of flavor b is,

$$P(\nu_a \rightarrow \nu_b) = \sin^2{2\theta} \; \sin^2{\frac{\delta m^2 L}{4E}},$$

where , L is the distance between source and observer and E is the neutrino energy.