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Multipositivity bounds for scattering amplitudes

Clifford Cheung1 and Grant N. Remmen2

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Phys. Rev. D 112, 016017 – Published 15 July, 2025

DOI: https://doi.org/10.1103/wt4x-2149

Abstract

Lorentz invariance, unitarity, and causality enforce powerful constraints on the theory space of physical scattering amplitudes. However, virtually all efforts in this direction have centered on the very simplest case of four-point scattering. In this work, we derive an infinite web of “multipositivity bounds” that nonlinearly constrain all tree-level higher-point scattering amplitudes under similarly minimal assumptions. Our construction rules out several deformations of the string and implies mixed-multiplicity bounds on the Wilson coefficients of planar effective field theories. Curiously, an infinite class of multipositivity bounds is exactly saturated by the amplitudes of the open string.

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Phys. Rev. D 112, 016017– Published 15 July, 2025
  • Received 16 May 2025
  • Accepted 25 June 2025
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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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