I have seen that people write the PMNS matrix as a multiplication of the form:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\text{PMNS}= A \cdot S_{ub} \cdot S_{ol} \cdot M[/itex]

[itex]\text{PMNS}= \begin{pmatrix} 1 & 0 & 0 \\ 0 & c_{23} & s_{23} \\ 0 & -s_{23} & c_{23} \end{pmatrix} \cdot \begin{pmatrix} c_{13} & 0 & s_{13} e^{-i \delta} \\ 0 & 1 & 0\\ -s_{13} e^{i \delta} & 0 & c_{13} \end{pmatrix} \cdot \begin{pmatrix} c_{12} & s_{12} & 0 \\ -s_{12} & c_{12} & 0 \\ 0 & 0 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 0 & 0 \\ 0 & e^{ia_1/2} & 0 \\ 0 & 0 & e^{ia_2/2} \end{pmatrix} [/itex]

where [itex]A[/itex] stands for the atmospheric, [itex]S_{ub}[/itex] is named subleading, [itex]S_{ol}[/itex] for Solar and [itex] M[/itex] stands for the Majorana phase.

My question is for example in the "atmospheric" part where we're having the creation of muons and muon-neutrinos, why do we only have the parameter [itex]\theta_{23}[/itex] (muon-tau neutrinos) and not the [itex]\theta_{12}[/itex] (muon-electron neutrinos)? Similarily for the Solar part we have only the [itex]\theta_{12}[/itex] (electron-muon neutrinos) and not the [itex]\theta_{13}[/itex] (electron-tau neutrinos)?

Thnaks.

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# Neutrino Oscillations -partition of PMNS

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