Universal Bounds for SU(3) Low Energy Constants

TL;DR

This paper derives bounds for SU(3) low energy constants in Chiral Perturbation Theory using dispersion relations and positivity conditions, testing their consistency with fundamental principles and experimental data.

Contribution

It introduces a method to establish universal bounds on L_1, L_2, and L_3 constants considering physical masses and axiomatic principles, improving previous bounds.

Findings

Bounds are tightened when physical kaon mass is used.

An overlap exists between experimental values and theoretically forbidden regions.

Large O(p^6) corrections are observed in the SU(3)_V limit.

Abstract

In this paper bounds for L_1, L_2 and L_3 are obtained in Chiral Perturbation Theory with three flavours. At the same time we test the compatibility of this theory with axiomatic principles. Following a recent paper we use dispersion relations to write positivity conditions that translate into bounds for the chiral low energy constants. As a first approach we consider the exact SU(3)_V limit and notice that if a common mass of the order of that of the kaon is adopted for the octet of pseudo-Goldstone bosons the bounds have very large O(p^6) corrections. Once the positivity conditions are adapted to account for different masses, we correct the previous bounds for a physical kaon mass and find that they tighten. We observe an overlap between the experimentally determined region and the first principles forbidden region, in the space of parameters.