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

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.

94 pages of which 51 in appendices, 31 figures, 2 tables. Version 2 added to reflect changes (mainly clarifications) done prior to publication in JHEP

References in corpus (11)

• Mesonic low-energy constants
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Extremal Effective Field Theories
• Crossing Symmetric Dispersion Relations in QFTs
• Falsifying Models of New Physics Via WW Scattering
• Dispersion Relation Bounds for pi pi Scattering
• Meson-meson Scattering in QCD-like Theories
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Six-pion amplitude
• Universal Bounds for SU(3) Low Energy Constants

Cited by in corpus (7)

• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Bootstrapping Pions at Large $N$
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Positivity bounds at one-loop level: the Higgs sector
• Causality constraints on nonlinear supersymmetry