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arXiv · 2212.06157

Nonperturbative Anomalous Thresholds

Miguel Correia
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Abstract

Feynman diagrams (notably the triangle diagram) involving heavy enough particles contain branch cuts on the physical sheet - anomalous thresholds - which, unlike normal thresholds and bound-state poles, do not correspond to any asymptotic $n$-particle state. ``Who ordered that?" We show that anomalous thresholds arise as a consequence of established S-matrix principles and two reasonable assumptions: unitarity below the physical region and analyticity in the mass. We find explicit nonperturbative formulas for the anomalous threshold singularity and test them against the Coleman-Thun poles of the exactly solvable $E_8$ integrable model.

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Miguel Correia. 2022-12-12. Nonperturbative Anomalous Thresholds. https://arxiv.org/abs/2212.06157

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