 One-loop two-point divergence in six-dimensional cubic scalar theory

The two-vertex cubic bubble in $d=6-ϵ$ dimensions has the displayed amputated pole. A Feynman parameter gives mass $m^2+x(1-x)k^2$, and $\Gamma (-1+ϵ/2)$ supplies the pole. The full propagator receives $D_0^{2}I$, while its inverse receives $-I$. This sign distinguishes a two-point insertion from an inverse-propagator correction.