= One-loop stationary scale for the hadronic annihilation correction
{title2=$\mu_*^2=q^2e^{-C/b}$}
Suppose $K=1+a+a^2[C-b\ln(q^2/\mu^2)]$, with $da/d\ln\mu^2=-ba^2$. Differentiation gives $dK/d\ln\mu^2=-2ba^3[C-b\ln(q^2/\mu^2)]$. For nonzero $a,b$, the <principle of minimal sensitivity> therefore gives $\boxed{\mu_*^2=q^2e^{-C/b}}$. The derivative vanishes identically through order $a^2$: this prescription retains the residual $a^3$ term generated by one-loop running of the truncated expression. Higher-order running and coefficients can shift the stationary scale. For $b=0$ or $a=0$, no unique scale is selected.
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