New positivity bounds from full crossing symmetry - Tolley,AJ; Wang,Z-Y; Zhou,S-Y (Journal of High Energy Physics (JHEP), 2021)
Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry ofthe 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.