I think, the gauge transformation has in its definition the superspace $y_\mu$, which is equal with $x_\mu + i \theta \sigma_\mu \bar \theta$. Thus in its Taylor expansion appears only 3 terms: $Ω(y) = Ω(x) + i \theta \sigma_\mu \bar \theta Ω(x) + \frac{1}{4} \theta \theta \bar \theta \bar \theta \Box{Ω(x)}$$Ω(y) = Ω(x) + i \theta \sigma_\mu \bar \theta \partial_\mu Ω(x) + \frac{1}{4} \theta \theta \bar \theta \bar \theta \Box{Ω(x)}$.
Mitchell
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