The Neutrino Minimal Standar Model (nuMSM or $\nu$MSM) is an extension of the Standard Model with three right-handed (or sterile) neutrinos. It aims to address within one consistent framework several problems beyond the Standard Model

• neutrino oscillations
• baryon asymmetry of the Universe
• the existence of dark matter

The Lagrangian of the $\nu$MSM is Here $F_{\alpha I}$ are new Yukawa couplings, $L_\alpha$ are left-handed leptonic doublets, the index $\alpha =e,\mu ,\tau$ labels generations, $\phi$ is a Higgs doublet with $\tilde \phi _j = i(\tau _2)_{j}^k \phi ^*_k$. The right-handed neutrinos $N_I$ have zero electric, weak and strong charges. The Majorana masses$M_I$ are consistent with the gauge symmetries of the SM This is the see-saw Lagrangian, however the Majorana masses of the right-handed neutrinos are chosen to be below electroweak scale. The smallness of the neutrino masses is achieved via small Yukawa couplings.
See references [1, 2] for the original paper and [3] for the recent review