Systematic-error signal-to-noise ceiling ($Z_{\infty }$)

Let $X\sim \mathrm{Poisson}(Q+B)$ and $Y\sim \mathrm{Poisson}(fB)$ be independent. Then $X-Y$ has source-estimation bias $(1-f)B$ and variance $Q+(1+f)B$. Its accuracy ratio $Q/\sqrt{\mathbb{E}[(X-Y-Q{)}^2]}$ tends to $R_Q/(|1-f|R_B)$ when $Q=R_{Q}T$, $B=R_{B}T$ and $T$ grows. This uses mean squared error, not variance alone, and assumes a fixed uncorrected mismatch.