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2021

Triple crossing positivity bounds for multi-field theories

Du, Zong-Zhe, Zhang, Cen, Zhou, Shuang-Yong

Understand

We develop a formalism to extract triple crossing symmetric positivity bounds for effective field theories with multiple degrees of freedom, by making use of $su$ symmetric dispersion relations supplemented with positivity of the partial waves, $st$ null constraints and the generalized optical theorem.

This generalizes the convex cone approach to constrain the $s^2$ coefficient space to higher orders.
Optimal positive bounds can be extracted by semi-definite programs with a continuous decision variable, compared with linear programs for the case of a single field.
As an example, we explicitly compute the positivity constraints on bi-scalar theories, and find all the Wilson coefficients can be constrained in a finite region, including the coefficients with odd powers of $s$, which are absent in the single scalar case.