NNLO positivity bounds on chiral perturbation theory for a general number of flavours

Benjamin Alvarez (1) , Johan Bijnens , Mattias Sjö

1 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: Chiral Lagrangians; Effective Field Theories; perturbation theory: chiral; meson: mass; symmetry: crossing; meson meson: scattering; derivative: high; higher-order: 2; flavor; unitarity; analytic properties; isospin; Chiral Lagrangians

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]

Benjamin Alvarez, Johan Bijnens, Mattias Sjö. NNLO positivity bounds on chiral perturbation theory for a general number of flavours. Journal of High Energy Physics, 2022, 2022, pp.159. ⟨10.1007/JHEP03(2022)159⟩. ⟨hal-03500376⟩