Positivity in Multifield Effective Field Theories

We discuss the general method for obtaining full positivity bounds on multifield effective field theories (EFTs). While the leading order forward positivity bounds are commonly derived from the elastic scattering of two (superposed) external states, we show that, for a generic EFT containing three o...

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Bibliographic Details
Published in:Physical review letters Vol. 127; no. 12; p. 121601
Main Authors: Li, Xu, Xu, Hao, Yang, Chengjie, Zhang, Cen, Zhou, Shuang-Yong
Format: Journal Article
Language:English
Published: College Park American Physical Society 17.09.2021
Subjects:
Cosmology
Elastic scattering
Fermions
Gravitons
Parameter identification
Particle physics
Scalars
Semidefinite programming
ISSN:0031-9007, 1079-7114, 1079-7114
Online Access:Get full text
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Summary:We discuss the general method for obtaining full positivity bounds on multifield effective field theories (EFTs). While the leading order forward positivity bounds are commonly derived from the elastic scattering of two (superposed) external states, we show that, for a generic EFT containing three or more low-energy modes, this approach only gives incomplete bounds. We then identify the allowed parameter space as the dual to a spectrahedron, constructed from crossing symmetries of the amplitude, and show that finding the optimal bounds for a given number of modes is equivalent to a geometric problem: finding the extremal rays of a spectrahedron. We show how this is done analytically for simple cases and numerically formulated as semidefinite programming (SDP) problems for more complicated cases. We demonstrate this approach with a number of well-motivated examples in particle physics and cosmology, including EFTs of scalars, vectors, fermions, and gravitons. In all these cases, we find that the SDP approach leads to results that either improve the previous ones or are completely new. We also find that the SDP approach is numerically much more efficient.
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ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.127.121601