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Inflation correlators with one-loop massive exchange encode rich informationabout the dynamics of the massive loop particles. Their nonanalytic behavior incertain soft limits leads to characteristic oscillatory pattern, which is theleading signal of many particle models of cosmological collider physics. Inthis work, we investigate systematically such nonanalyticity for arbitraryone-particle-irreducible (1PI) one-loop correlators in various soft limits.With the partial Mellin-Barnes representation, we present and prove afactorization theorem and a cutting rule for arbitrary 1PI one-loop inflationcorrelators, which is reminiscent of the on-shell cutting rule for flat-spacescattering amplitudes. We also show how to understand this factorizationtheorem from the viewpoint of operator product expansion on the futureboundary. As an application of the one-loop factorization theorem, we derivenew analytic and exact formulae for nonlocal cosmological collider signals formassive one-loop four-point inflation correlators of all possible 1PItopologies, including the bubble, the triangle, and the box graphs. Finally, weshow how to push the computation of nonlocal signals to higher orders in themomentum ratio.

Inflation Correlators at the One-Loop Order: Nonanalyticity, Factorization, Cutting Rule, and OPE