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Nonperturbative anomalous thresholds

Miguel Correia1

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Phys. Rev. D 110, 025012 – Published 16 July, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.025012

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 E8 integrable model.

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Phys. Rev. D 110, 025012– Published 16 July, 2024
  • Received 24 January 2024
  • Accepted 16 June 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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