New positivity bounds from full crossing symmetry

By A. Tolley, Zi-yue Wang, Shuang-Yong Zhou. Journal of High Energy Physics, 2020

157 citations recorded by the source corpus.

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{D}}^{\mathrm{stu}} $$\end{document} bounds. While the PQ bounds and Dsu bounds only make use of the s↔u dispersion relation, the Dstu and D¯stu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{D}}^{\mathrm{stu}} $$\end{document} 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 constraining 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 standard 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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/03a36d66aaae2025df13410f5d2719340c6d44dc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

Citations in the corpus

Extremal effective field theories (2020, result): “ about the potential use cases of the numerical framework presented and the further implications of the numerical results. Note added: When this manuscript was being completed, the works [7] and then [8] appeared with partial overlap in the results. The second paper in particular gave a two-sided bo”
The EFT-hedron (2020, result): “Bounds involving the combination of positivity away from the forward limit and full permutation invariance was discussed in [9] and [10], which have some overlap with the s-u polytope discussion in subsection 8.”