BRST current in derivative-b gauge fixing ($j_B^{\mu }=F^{\mu \nu }\cdot D_{\nu }c+b\cdot D^{\mu }c+\frac{1}{2}({\partial }^{\mu }\bar{c})\cdot [c,c]$)

Use gauge-fixing term $({\partial }^{\mu }b)\cdot A_{\mu }$, ghost term $-({\partial }^{\mu }\bar{c})\cdot D_{\mu }c$, and the left-acting BRST differential with $s\bar{c}=b$. Localizing the odd parameter on the left yields $\delta S=-\int ({\partial }_{\mu }ϵ)j_B^{\mu }$. Moving it through the antighost derivative determines the last sign. Changing the overall Noether convention reverses this current; rewriting gauge fixing by integration by parts changes its improvement term. Every summand has ghost number one.