Masses of Neutrinos

Neutrino masses are still not determined completely. However we have some possible patterns.

One of the questions we have about the masses of neutrinos is the generation of it.

Note

This figure also gives the terms: normal hierarchy (NH) and invertd hierarchy (IH).

Lepton mixing matrix, can be written as the product of three matrices which stands for a rotation in 23, 13(with a CP phase), 12 respectively. This is called the PMNS mixing matrix.

\mathbf U &= \mathbf {U_{23}} \times \mathbf {U_{13,\delta}} \times \mathbf {U_{12}} \\ & = \begin{pmatrix} 1 & 0 & 0 \\ 0 &\cos\theta_{23} & \sin\theta_{23} \\ 0 -\sin\theta_{23} & \cos\theta_{23} \end{pmatrix} \begin{pmatrix} \cos\theta_{13} & 0 & e^{i\delta} \sin\theta_{13} \\ 0 & 1 & 0 \\ -e^{i\delta}\sin\theta_{13} & 0 & \cos\theta_{13} \end{pmatrix} \begin{pmatrix} \cos\theta_{12} & \sin\theta_{12} & 0 \\ -\sin\theta_{12} & \cos \theta_{12} & 0 \\ 0 & 0 & 1 \end{pmatrix}

See-saw Mechanism

RH neutrinos term in Lagrangian breaks the symmetry.

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