with Kähler correction as given via Eq.\[Kahlercorrect\]. Then the gravitino mass given by (\[gravitino\]) becomes,

$$\label{gravitino3}
m_{3/2}^2=\frac{1}{M_p^4} e^{-\frac{\alpha}{2 \tilde t_0} - 
4 \alpha_1 {{\tilde t}^2}_0}~ \frac{m^6}{16 \tilde s_0 \tilde t_0^3}\left[\frac{1}{(1+\sqrt{3})} ~
2 \tilde s_0 (\frac{k}{\tilde{s}_0} + 2\frac{\ln{\tilde{s}_0}}{\tilde{s}_0})\right]^2.$$

In (\[gravitino3\]), the derivative $f'(\tilde{s}_0) \simeq (\frac{k}{\tilde{s}_0} 
+ 2\frac{\ln{\tilde{s}_0}}{\tilde{s}_0})$ have been used ignoring terms with $k_1 \sim 10^{-17}$. The soft scalar mass (\[softmass\]) can be recast as, $$\label{massparmtr}
\begin{split}
m_{\alpha}^2= ~ &m_{3/2}^2  +\frac{1}{M_p^4} \frac{e^{- \frac{\alpha}{2 \tilde t_0} 
- 4 \alpha_1 {{\tilde t}^2}_0}}{16  \tilde s_0 \tilde t_0^3}  \frac{m^6}{\left(\frac{3}{4 \tilde t_0^2}
-\frac{\alpha}{4\tilde t_0^3}- 2\alpha_1 \right)}\\
& \left[((\ln{\tilde{s}_0})^2 + k \ln{\tilde{s}_0} + k_1 \tilde{s}_0) \left(\frac{3}{2 \tilde t_0}
- \frac{\alpha}{4 \tilde t_0^2} + 4 \alpha_1 
\tilde{t}_0 \right)\right]^2 
\left[1-\frac{1}{4 \tilde t_0^2} \frac{1}{\left(\frac{3}{4 \tilde t_0^2}
-\frac{\alpha}{4 \tilde t_0^3 } -2 \alpha_1 \right)}\right].
\end{split}$$

The trilinear and bilinear couplings can now be calculated as before. The leading contributions to the trilinear coupling (\[trilinear2\]) and bilinear couplings (\[bilinear\]) come from the gravitino mass $m_{3/2}$, which can be estimated from (\[gravitino3\]). It is worthwhile is see that whether such a scenario could actually predict a global minimum with $\tilde s_0 =1$. To investigate that, we illustrate our result with a $3D$-plot (fig \[3dminimum\]) of the hidden sector scalar potential. It clearly exhibits 