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Neutrino Mass

The observation that neutrinos have mass, requiring extensions to the Standard Model, often through the addition of right-handed neutrinos and associated Yukawa couplings.
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The statement of the theorem

Consider the Lagrangian density L\mathcal{L} extended to include three right-handed Majorana neutrinos NR,iN_{R, i} with masses MiM_i: L=LSM+NˉR(i∂ˉγμ∂μ−12Mi)NR+Yukawa terms\mathcal{L} = \mathcal{L}_{SM} + \bar{N}_R \left( \text{i} \bar{\partial} \gamma^{\mu} \partial_\mu - \frac{1}{2} M_i \right) N_R + \text{Yukawa terms} The neutrino mass generation is governed by the effective mass matrix MνM_{\nu} derived from the seesaw mechanism. In the basis (νL,NRT)(\nu_L, N_R^T), the full mass matrix M\mathcal{M} is: M=(0MDMDTMR)\mathcal{M} = \begin{pmatrix} 0 & M_D \\ M_D^T & M_R \end{pmatrix} where MDM_D is the Dirac mass matrix (coupling νL\nu_L to NRN_R) and MRM_R is the Majorana mass matrix for NRN_R. The light neutrino mass matrix is then approximated by Mν≈−MDMR−1MDTM_{\nu} \approx -M_D M_R^{-1} M_D^T. The resulting mass eigenvalues mim_i satisfy ∑mi=0\sum m_i = 0 (if neutrinos are Majorana).
Source: Wikipedia