NNLO Positivity Bounds on Chiral Perturbation Theory for a General Number of Flavours

Understand

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 in meson-meson scattering 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 discontinuities.
• In addition, we present a powerful and general mathematical framework for efficiently managing large numbers of positivity bounds.