= Monomial scalar interaction power-counting identity
{title2=$\Delta=d-(d-2)E/2-[\lambda]V$}
For a connected scalar graph with nonderivative interaction $-\lambda\phi^n$, $E$ external legs and $V$ vertices, $nV=2I+E$ and $L=I-V+1$. Since $[\phi]=(d-2)/2$ and $[\lambda]=d-n(d-2)/2$, the <superficial degree of divergence> is
$$
\Delta=dL-2I=d-\frac{d-2}{2}E-[\lambda]V.
$$
The graph contributes at order $\lambda^V$. This is simultaneous large-loop-momentum counting for an amputated graph; it does not test subdivergences or guarantee that the predicted pole coefficient is nonzero.
// Target: perturbative-quantum-field-theory.bigb
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