= Lorentz-covariant rank-two loop reduction
{c}
{title2=$\int d^dq\,q_\mu q_\nu f(q^2)=\frac{g_{\mu\nu}}d\int d^dq\,q^2f(q^2)$}
With an invariant integration measure and no external vector in $f(q^2)$, the rank-two integral must be proportional to the metric. Contracting its indices fixes the coefficient to $1/d$. In <dimensional regularization> this dimension is the continued $d$, rather than four; retaining its dependence matters when multiplying a divergent loop integral.
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