An infrared divergence arises from contributions at arbitrarily low energy or long wavelength. A massless mode can produce such a problem because many soft excitations are available at very small energy, or because a long-distance fluctuation integral fails to converge.
Its interpretation depends on the observable. In scattering, an exclusive amplitude with no additional arbitrarily soft radiation need not be separately measurable; combining appropriately inclusive real-emission and virtual contributions can remove the relevant divergence. In equilibrium field theory, an infrared-divergent order parameter fluctuation can instead diagnose failure of an assumed ordered-state approximation. A finite size or detector resolution may regulate the calculation, but the dependence on that regulator must be interpreted rather than silently discarded.
An infrared regulator suppresses the small-momentum region responsible for an infrared divergence. Examples are a small positive mass or a finite volume. It must be distinguished from an ultraviolet cutoff: setting external momenta and masses to zero to extract an ultraviolet divergence can introduce a spurious infrared divergence. Keep a positive auxiliary mass until the divergent local coefficients have been separated, then take the desired limit in infrared-safe quantities.
An observable unchanged by adding a particle with vanishing energy or replacing one massless particle by exactly collinear particles with the same total momentum. This property permits cancellation of real and virtual infrared divergences and collinear divergences in its perturbative cross-section. Fully inclusive electron-positron hadronic rates and suitably defined jet observables are examples.
A singularity of a massless scattering or radiation integral when momenta of two particles become parallel. In quantum chromodynamics, unresolved quark-gluon splittings cause such divergences. A mass regulator or dimensional regularization exposes them; they cancel between suitable inclusive real and virtual contributions or are absorbed into factorized distributions where appropriate.
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Infrared divergence refers to a type of divergence that occurs in quantum field theory (QFT) and certain fields of theoretical physics when dealing with low-energy (or long-wavelength) phenomena. Specifically, it manifests when evaluating Feynman integrals or loop diagrams that include virtual particles with very low momenta (approaching zero). In such scenarios, the contributions from these low-energy states can lead to integrals that diverge, meaning they yield infinite values.