NNLO positivity bounds on chiral perturbation theory for a general number of flavours

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