 Ultraviolet finiteness

An amplitude is ultraviolet finite if its regulated high-loop momentum contribution has a finite regulator-removal limit after whatever lower-order subtractions are specified. A zero superficial degree of divergence does not force divergence: gauge invariance can cancel the candidate local term. Conversely, superficial convergence alone does not exclude divergent subgraphs. Ultraviolet finiteness makes no claim about infrared divergences or physical threshold singularities.