Yukawa couplings: = (t\_2 +t\_3)  . For realistic values, the ratio of the two loop functions is slightly smaller than one. To obtain a rule of thumb, let us take $m_0  \sim a_0 \sim m_{L,R}$ and the reference ratio $\Lambda/M_2 = 2~10^{6}$. Then, unless ad hoc fine-tunings in the structure of $N$, ${\cal I}m(\3 m_\ell^2 \2)_{ii} \sim m_\tau^2 {\cal I}m(\3 \2)_{ii}$, and one finds \~0.5              [(rule  of  thumb),]{} \[rot\] where $|\mu_{ew}|^2 \approx 0.5 m_R^2 + 20 \ti M_1^2$ is the value of $\mu$ accounting for radiative electroweak breaking in mSUGRA. Despite being of third order in the $t$’s, the FV amplitude can take over the FC one thanks to its $\tan^3 \beta$ dependence. The precise value of this ratio is displayed in figs. \[Fss\_R\] in the plane $(\ti M_1, m_R)$. Cases a) and b) are separately displayed so that the behavior for any situation in between can be easily extrapolated. The relevant generalizations are also reminded.

(-300,235)[ Theory: $\frac{ d_i^{FV_{LLRR}} } { d_i^{FC} }$ for Seesaw]{} (-335,200)[ a) $a_0^2=2 m_0^2$]{} (-120,200)[ b) $a_0^2= \ti M_{1/2}^2$]{} (-320,62)[ $ \times \frac{\tan^3 \beta}{10^3} \frac{\mu}{\mu_{ew}} \frac{t_2+t_3}{0.1}$]{} (-100,62)[ $\times \frac{\tan^3 \beta}{10^3} \frac{\mu}{\mu_{ew}} \frac{t_2+t_3}{0.1}$ ]{}

1 cm

The plots show that the rule of thumb is 