New positivity bounds from full crossing symmetry
File(s)
Published version
Author(s)
Tolley, Andrew J
Wang, Zi-Yue
Zhou, Shuang-Yong
Type
Journal Article
Abstract
Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of
the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, Dsu, Dstu and D¯stu bounds. While the P Q bounds and Dsu bounds only make use of the s ↔ u dispersion relation, the Dstu and D¯stu bounds are obtained by further imposing the s ↔ t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more con straining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a stan dard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.
the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, Dsu, Dstu and D¯stu bounds. While the P Q bounds and Dsu bounds only make use of the s ↔ u dispersion relation, the Dstu and D¯stu bounds are obtained by further imposing the s ↔ t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more con straining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a stan dard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.
Date Issued
2021-05-27
Date Acceptance
2021-05-17
Citation
Journal of High Energy Physics (JHEP), 2021, 2021 (5)
ISSN
1126-6708
Publisher
SpringerOpen
Journal / Book Title
Journal of High Energy Physics (JHEP)
Volume
2021
Issue
5
Copyright Statement
© The Authors. Article funded by SCOAP3. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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Subjects
AMPLITUDES
BEHAVIOR
CHIRAL PERTURBATION-THEORY
Cosmology of Theories beyond the SM
Effective Field Theories
GRAVITY
PARAMETERS
Physical Sciences
Physics
Physics, Particles & Fields
SCATTERING
Science & Technology
Publication Status
Published
Article Number
255
Date Publish Online
2021-05-27