Resonance sum rules from large $N_C$ and partial wave dispersive analysis

TL;DR

This paper combines large $N_C$ methods and dispersive analysis to derive sum rules and relations in $$ scattering, linking resonance properties with low-energy constants without explicit resonance Lagrangians.

Contribution

It introduces new sum rules and relations connecting resonance couplings and low-energy constants in chiral perturbation theory.

Findings

Derived a generalized KSRF relation including scalar mesons.

Established a new relation between resonance couplings.

Expressed low energy constants in terms of resonance mass and decay width.

Abstract

Combining large $N_C$ techniques and partial wave dispersion theory to analyze the $\pi\pi$ scattering, without relying on any explicit resonance lagrangian, some interesting results are derived: (a) a general KSRF relation including the scalar meson contribution; (b) a new relation between resonance couplings, with which we have made an intensive analysis in several specific models; (c) low energy constants in chiral perturbation theory related with $\pi\pi$ scattering in terms of the mass and decay width of resonances.