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

TL;DR

This paper derives positivity bounds on low-energy constants in chiral perturbation theory for multiple flavours, using analyticity, unitarity, and crossing symmetry up to NNLO, with a new mathematical framework for managing bounds.

Contribution

It introduces a comprehensive method to derive and manage positivity bounds for chiral perturbation theory with any number of flavours, including new bounds and analytical techniques.

Findings

Bounds applicable to 2, 3, or more flavours.

Enhanced bounds using general isospin combinations.

A new mathematical framework for large bounds management.

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 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.