The 7/11 rule: an estimate of m_rho/f_pi

TL;DR

This paper estimates the ratio of the rho meson mass to the pion decay constant using large-Nc QCD techniques, operator product expansion, and meson dominance, providing insights into chiral dynamics.

Contribution

It introduces a novel estimate of m_rho/f_pi from two-point functions and extends the analysis to scalar and pseudoscalar sectors, enabling parameter-free determination of chiral Lagrangian couplings.

Findings

Estimated m_rho/f_pi ratio consistent with experimental values.

Derived chiral Lagrangian couplings without free parameters.

Extended analysis to scalar and pseudoscalar sectors.

Abstract

We derive an estimate for the ratio of the rho mass and the pion decay constant from an analysis of vector and axial-vector two-point functions using large-Nc, lowest-meson dominance and the operator product expansion, in the chiral limit. We discuss the extension of this analysis to the scalar and pseudoscalar sector. Furthermore, this leads to a successful parameter-free determination of the L_i couplings of the chiral Lagrangian if an improved Nambu-Jona-Lasinio ansatz for Green functions is assumed at low energies.