divergence
lack of convergence of a series or integral
ultraviolet divergence
situation in which a Feynman integral diverges due to high-energy (short-distance) contributions, requiring regularization/renormalization or some ultraviolet completion
infrared divergence
situation quantum field theories with massless particles, in which Feynman integrals diverge due to low-energy (long-distance) contributions, requiring a cutoff representing detector threshold