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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 PQ,
Dsu, Dstu and D¯stu bounds. While the PQ 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 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. |
