...)-handed¹

The subscripts $L$ and $R$ really refer to the left and right chiral projections. In the limit of zero mass these correspond to left and right helicity states.

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... state²

Which is referred to as the particle or the antiparticle is a matter of convenience.

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... Sterile³

Sterile neutrinos are often referred to as ``right-handed'' neutrinos, but that terminology is confusing and inappropriate when Majorana masses are present.

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... singlet⁴

In principle this could also be generated by a bare mass, but this is usually forbidden by higher symmetries in extensions of the standard model.

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... quasi-degeneracy⁵

For MSW oscillations, the data implies that most likely $m_2^2 > m_1^2$ under the convention that $\theta < \pi/4$. For vacuum oscillations, the sign of $\Delta m^2_{\rm solar}$ is undetermined.

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... cosmologically⁶

There is no viable large mixing angle (LMA) or low mass (LOW) solar neutrino solution for $\nu_e \mbox{$\rightarrow$}\mbox{$\nu_s$}$. These are most likely excluded independently by the BBN data.

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