FV transitions are estimated is generically small and can be neglect for our estimates. We now study separately the FC and the FV contributions.

Flavour conserving contribution
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Starting in the LF basis at $M_{Pl}$ from $A_e =  y_{e} a_0$, the seesaw interactions generate a ${\cal I}m(A_{ii})$ in the LF basis at $M_1$. At leading order in the $t$’s and defining $y_\nu^\dagger P_a y_\nu \equiv \a$ ($a=1,2,3$) and the right-handed neutrinos projectors $P_1={\rm diag}(1,0,0)$, $P_2={\rm diag}(1,1,0) $, $P_3 = \i3$, the latter reads [^7]: m (A\_[ii]{}) = 8 a\_0 y\_[e\_i]{} ( t\_2 t\_3 [I]{}m( )\_[ii]{} + t\_1 t\_3 [I]{}m( )\_[ii]{} + t\_1 t\_2 [I]{}m( )\_[ii]{} )   , \[ss\_ae\] where the Yukawas in the r.h.s. are evaluated at $\Lambda$. A similar [^8] formula were previously presented in Refs. [@ellis-1; @ellis-2; @ellis-n], but with the various Yukawas involved defined at different scales. Then, one must be more cautious in drawing general conclusions and the authors validate theirs with specific numerical examples. Our approach offers the advantage that the corresponding results become more transparent and allow for an easier estimate of the effects once a pattern of seesaw parameters is assigned. Anyway, the crucial point [@ellis-1] is that the more right-handed neutrinos are 