Triple crossing positivity bounds for multi-field theories

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.

Automated summary

A formalism is developed to extract triple crossing symmetric positivity bounds for effective field theories with multiple degrees of freedom. This generalizes the convex cone approach to higher orders in the coefficient space. Optimal positive bounds can be obtained using semi-definite programs and continuous decision variables. The study explicitly computes the positivity constraints for bi-scalar theories, showing that all Wilson coefficients can be constrained in a finite region.