= Quartic complex-scalar mass renormalization
{title2=$\delta_{m^2}=gm^2/(8\pi^2\epsilon),\quad\gamma_m=g/(16\pi^2)+O(g^2)$}
For $\mathcal L=|\partial\phi|^2-m^2|\phi|^2-\mu^\epsilon g|\phi|^4/4$ in $d=4-\epsilon$, the directed <tadpole diagram> has <symmetry factor> one. Its divergent Feynman contribution to $i\Gamma^{(2)}$ is $igm^2/(8\pi^2\epsilon)$. A <mass> insertion $-i\delta_{m^2}$ therefore gives the displayed <minimal subtraction scheme> <counterterm>. Differentiating at fixed <bare mass> and <coupling> gives the displayed $\gamma_m=\tfrac12\mu\,d\log m^2/d\mu$. The equivalent two-real-field formulation has vertex coefficients $3g/2$ for a pure species and $g/2$ for two of each, giving total tadpole weight $(3g/2+g/2)/2=g$.
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