NNLO Positivity Bounds on ChPT for a General Number of Flavours

TL;DR

This paper derives NNLO positivity bounds on chiral perturbation theory constants for multiple flavours, utilizing analyticity, unitarity, and crossing symmetry, and introduces a framework for managing extensive bounds.

Contribution

It provides the first comprehensive NNLO positivity bounds for general flavour numbers in ChPT, including advanced mathematical techniques for bound management.

Findings

Bounds for 2, 3, or more flavours with equal meson masses.

Enhanced bounds using general isospin and higher-flavour combinations.

A new mathematical framework for large-scale positivity 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 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.