Tau single-tag and double-tag normalization

For $N$ tau-pair events and a tag mode with branching fraction $B$, the tagged-hemisphere count is $S=2NBϵ$ and the double-tag event count is $D=N{B}^2{ϵ}_{ii}$. Eliminating $B$ gives $N=S^2{ϵ}_{ii}/(4D{ϵ}^2)$. Efficiency correlations matter: ${ϵ}_{ii}$ need not equal ${ϵ}^2$. An inclusive branching-fraction fit must include unlisted decay categories.