is separated into holomorphic and anti-holomorphic parts, respectively. Since $\theta^2\bar{\theta}^2$ term is not generated, we do not have one-loop soft masses.

Hence, as in minimal gauge mediation, soft masses are generated at two loop level. In [@Kang:2012ra], it was shown that soft scalar masses of the fields which directly couple to messengers and those which do not are different. In our model, the slepton $\tilde{L}$ and the up-type Higgs $H_u$ couple to messengers $N$ directly to give soft terms,

[$$\begin{split}&\delta m_{L}^2 = \frac{B_N^2}{(4 \pi)^4} \Big[ \Big({\rm Tr} [Y_{\nu} Y_{\nu}^\dagger]+3{\rm Tr} [Y_U Y_U^\dagger] - 3 g_2^2 - \frac{1}{5} g_1^2 \Big) Y_{\nu}^\dagger Y_{\nu} + 3 Y_{\nu}^\dagger Y_{\nu} Y_{\nu}^\dagger Y_{\nu} \Big]
  \\
  &\delta m_{H_u}^2 = \frac{B_N^2}{(4 \pi)^4} \Big[ 4{\rm Tr} [Y_{\nu} Y_{\nu}^\dagger Y_{\nu}^\dagger Y_{\nu}] -\Big( 3 g_2^2 + \frac{1}{5} g_1^2 \Big){\rm Tr} [Y_\nu Y_\nu^\dagger] \Big]. \label{eq:mlsqaure}\end{split}$$]{}

On the other hand, $\tilde{Q}$ and $\tilde{U}$ obtain two-loop soft scalar masses through the wave function renormalization of $H_u$ and the corrections are given by [$$\begin{split}&\delta m_{Q}^2=-\frac{B_N^2}{(4 \pi)^4} {\rm Tr}[Y_\nu Y_\nu^\dagger]Y_U^\dagger Y_U
  \\
  &\delta m_{U}^2=-\frac{B_N^2}{(4 \pi)^4} {\rm Tr}[Y_\nu Y_\nu^\dagger]Y_U Y_U^\dagger\end{split}$$]{} while the soft masses of $\tilde{E}$ and $H_d$ come out of the wave function renormalization of $L$ and the corrections are given by [$$\begin{split}
  &\delta m_{E}^2=-\frac{B_N^2}{(4 \pi)^4} 