## Type I seesaw

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Type I seesaw is the specific realization of the seesaw mechanism. Here, we extend the particle spectrum of the Standard model by several sterile neutrinos $R_I$. The Lagrangian of the model is given by a sum of the Lagrangian of the Standard Model $\mathcal {L}_{SM}$ and
 (1)
The first term in the brackets describes the Yukawa coupling of sterile neutrinos to the left lepton doublet $L_\alpha$ (for example, $L_e = (\nu _e~e)$) and the Higgs doublet $\tilde H = i\sigma _2 H$. The second term is the Majorana mass term.
After the spontaneous breaking of the electroweak symmetry, $H \to (0,v)$, the Yukawa terms become quadratic in neutrino fields, as well as the other terms comprising neutrinos (except of the terms describing coupling to gauge bosons). To find the mass spectrum for this model, one has to diagonalize the terms. In case when Yukawa couplings are small, $M^D=v Y \ll M_I$, the procedure leads to the mass matrix of active neutrinos
 (2)
indicating that these neutrinos receive finite masses.
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