Universal Bounds for SU(3) Low Energy Constants

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.

6 pages, 1 figure. Two references added. Some minor changes. Published version

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Cited by in corpus (15)

• Softness and Amplitudes' Positivity for Spinning Particles
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Dispersion Relation Bounds for pi pi Scattering
• Bootstrapping Pions at Large $N$
• Bounding Violations of the Weak Gravity Conjecture
• Generalized positivity bounds on chiral perturbation theory
• Causality, Unitarity and Symmetry in Effective Field Theory
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Positivity bounds on Minimal Flavor Violation
• Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons
• NNLO Positivity Bounds on Chiral Perturbation Theory for a General Number of Flavours
• Positivity Bounds on Massive Vectors
• Non-Forward UV/IR Relations
• Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters
• Positivity constraints on the low-energy constants of the chiral pion-nucleon Lagrangian