NNLO Positivity Bounds on ChPT for a General Number of Flavours

Abstract

We present positivity bounds, derived from the principles of analyticity, unitarity and crossing symmetry, that constrain the low-energy constants of chiral perturbation theory. Bounds are produced for 2, 3 or more flavours with equal meson masses, up to and including next-to-next-to-leading order (NNLO), using the second and higher derivatives of the amplitude. We enhance the bounds by using the most general isospin combinations posible (or higher-flavour counterparts thereof) and by analytically integrating the low-energy range of the amplitude. In addition, we present a powerful and general mathematical framework for efficiently managing large numbers of positivity bounds.

Comments: In proceedings of the 10th International Workshop on Chiral Dynamics - CD2021, 15-19 November 2021, Beijing (online). 10 pages, 5 figures