# $1/N_c$ Nambu -- Jona-Lasinio model: Electrically charged and strange pseudoscalars

## TL;DR

This paper analyzes the masses and decay constants of charged and strange pseudoscalar mesons using a combined $1/N_c$ expansion and Nambu--Jona-Lasinio model, deriving sum rules that connect meson properties to light quark mass ratios.

## Contribution

It introduces new sum rules within the $1/N_c$ framework that relate meson masses and decay constants to light quark mass ratios, improving understanding of chiral symmetry breaking effects.

## Key findings

- Derived limits for quark mass ratios: 0.47<m_u/m_d<0.59 and 18.60<m_s/m_d<19.66.
- Established connections between meson phenomenology and quark mass ratios.
- Compared results with $1/N_c$ chiral perturbation theory calculations.

## Abstract

The mass formulas and decay constants of electrically charged and strange pseudoscalar mesons are analyzed within the combined framework of Nambu -- Jona-Lasinio model and the $1/N_c$ expansion up to $\mathcal O(1/N_c^2)$. The light quark masses explicitly violating $SU(3)_L\times SU(3)_R$ chiral symmetry of the strong interactions are taken to be of order $\mathcal O(1/N_c)$. The Fock-Schwinger proper-time method and the Volterra series are used to derive the effective action. A set of sum rules is obtained that relates the phenomenological values of the masses of pseudoscalar mesons to the mass ratios of light quarks. It is shown that combining the new sum rules with the experimental data on the decay width $\eta\to 3\pi$ allows to establish limits for the ratios: $0.47<m_u/m_d<0.59$ and $18.60<m_s/m_d<19.66$. A comparison with the results of similar calculations in $1/N_c$ chiral perturbation theory is made.