6 GeV can be achieved by making the logarithmic contribution large and the stop mass should be as heavy as 5 to 10 TeV rather than 2 TeV.

Note that the plot stops at $y_\nu=0.72$. Neutrino assisted gauge mediation is classified as Higgs-messenger mixing scenario as the right-handed neutrino is the messenger and the neutrino Dirac Yukawa coupling connects Higgs, lepton doublet and the messenger (right-handed neutrino). The stop soft scalar mass squared gets smaller and becomes tachyonic as the neutrino Dirac Yukawa coupling is increased as in Fig. \[fig:stopmass\]. The logarithmic correction to the Higgs mass also rapidly drops beyond $y_\nu \sim 0.7$ as the stop mass becomes too light (and becomes tachyonic) as is shown in Fig. \[fig:Higgsmass\]. The maximal mixing is realised around this point, as shown in Fig. \[fig:XtMt\]. This also corresponds to the corner of the parameter space next to the critical point as in [@Giudice:2006sn].

![ $\tilde{A}_t \equiv A_t Y_t$ as a function of $y_\nu$ for $\tan \beta = 10$, $B_N = 5 \times 10^5$GeV. Without Yukawa mediation, one can obtain $\tilde{A}_{t} \sim -2700{\,\textrm{GeV}}$ at the weak scale by RG running effects. With help of neutrino mediation at the messenger scale, one can obtain 