Abstract
In this work, we study the analytic properties of S-matrix for unstable particles, which is defined as the residues on the unphysical sheets where unstable poles reside. We demonstrate that anomalous thresholds associated with UV physics are unavoidable for unstable particles. This is in contrast to stable particles, where the anomalous thresholds are due to IR physics, set by the scale of the external kinematics. As a result, any dispersive representation for the amplitude will involve contributions from these thresholds that are not computable from the IR theory, and thus invalidate the general positivity bound. Indeed using toy models, we explicitly demonstrate that the four-derivative couplings for unstable particles can become negative, violating positivity bounds even for non-gravitational theories. Along the way, we show that contributions from anomalous thresholds in a given channel can be captured by the double discontinuity of that channel.
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Acknowledgments
We would like to thank Holmfridur Hannesdottir and Sebastian Mizera for discussions and comments on the draft. The Feynman diagrams in this paper were drawn with the help of TikZ-FeynHand [38]. K.A. is grateful to the organizers of the workshop “14th Taiwan String Workshop” and the hospitality of NTU where part of this work was carried out. Y-t H would like to thank the hospitality and support of YITP, during which a majority of this work was completed. The work of K.A. was supported by JSPS Grants-in-Aid for Scientific Research, No. 20K14468 and No. 24K17046. The work of Y-t H is supported by NSTC grant no. 112-2811-M-002 -054 -MY2.
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Aoki, K., Huang, Yt. Anomalous thresholds for the S-matrix of unstable particles. J. High Energ. Phys. 2024, 45 (2024). https://doi.org/10.1007/JHEP09(2024)045
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DOI: https://doi.org/10.1007/JHEP09(2024)045