= Engineering term in a dimensionally continued beta function
{title2=$\lambda_0=\mu^\epsilon F(\lambda,\epsilon)\Longrightarrow\widehat\beta(\lambda)=-\epsilon\lambda+\beta(\lambda)$}
In $d=4-\epsilon$, the quartic scalar coupling has <engineering dimension> $\epsilon$. Factoring out $\mu^\epsilon$ makes the renormalized <running coupling> dimensionless. Differentiating its bare expression at fixed bare parameters generates the linear term $-\epsilon\lambda$, even when the quantum contribution to the <renormalization-group beta function> begins quadratically. The <simple-pole formulas for minimal-subtraction renormalization group functions> determine the remaining contribution from the simple pole of $F$.
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