the sfermion representation ${\cal R}_i$ under the corresponding gauge group labeled by $a$, which is given by $(N^2-1)/(2N)$ for SU(N) and $Y^2$ for U(1)$_Y$, $T_a$ is defined by ${\rm Tr}T^\alpha T^\beta = T_a({\cal R}_i)\delta^{\alpha \beta}$, and $f(x_i)$ is the loop function of $x_i=F/M_i^2$ which is close to one for small $x_i$. On the other hand, the 2-loop tri-linear A term is very small and can be neglected at the messenger scale.

For the second origin of soft terms, we introduce a SUSY breaking spurion $X$ which couples to the right-handed neutrinos. Majorana mass of the right-handed neutrino comes from the scalar vacuum expectation value (VEV) of the SUSY breaking spurion $X$, [$$\begin{split} W \supset \lambda X N N.\end{split}$$]{} Then $N$ acts as the messengers of supersymmetry breaking, and the neutrino Dirac Yukawa coupling, [$$\begin{split}W \supset Y_\nu N L H_u,\end{split}$$]{} is interpreted as the direct mixing term among the messengers, Higgs and matter (leptons).

The SUSY breaking effects at the See-Saw scale $M_N=\lambda \langle X \rangle$ is studied in [@Giudice:2010zn]. When right-handed neutrinos couple to the SUSY breaking sector, Majorana mass matrix is analytically continued to be $M_N \rightarrow (1+ \theta^2 B_N)M_N$, as in the case of gauge mediation[@Giudice:1997ni; @ArkaniHamed:1998kj; @Chacko:2001km]. 