Logarithmic divergence
= Logarithmic divergence
{title2=$\int_\epsilon^1dx/x=\log(1/\epsilon)$}
A <logarithmic divergence> grows like a <logarithm> as a cutoff is removed. For example $\int_\epsilon^1dx/x=\log(1/\epsilon)\to\infty$ as $\epsilon\to0^+$. An integrand $f(x)=C/x+O(1)$ near zero gives $C\log(1/\epsilon)+O(1)$. This behavior distinguishes logarithmic sensitivity to an infrared or ultraviolet cutoff from power-law divergence.