Bethe-Salpeter study of vector meson masses and decay constants

Abstract

The masses and decay constants of the light vector mesons $\ensuremath{\rho}/\ensuremath{\omega},$ $\ensuremath{\varphi},$ and ${K}^{\ensuremath{\star}}$ are studied within a ladder-rainbow truncation of the coupled Dyson-Schwinger and Bethe-Salpeter equations of QCD with a model two-point gluon function. The approach is consistent with quark and gluon confinement, reproduces the correct one-loop renormalization group behavior of QCD, generates dynamical chiral symmetry breaking, and preserves the relevant Ward identities. The one phenomenological parameter and two current quark masses are fixed by requiring that the calculated ${f}_{\ensuremath{\pi}},$ ${m}_{\ensuremath{\pi}},$ and ${m}_{K}$ are correct. The resulting ${f}_{K}$ is within 3% of the experimental value. For the vector mesons, all eight transverse covariants are included and the dominant ones are identified; the complete angle dependence of the amplitudes is also retained. The calculated values for the masses ${m}_{\ensuremath{\rho}},$ ${m}_{\ensuremath{\varphi}},$ and ${m}_{{K}^{\ensuremath{\star}}}$ are within 5%, while the decay constants ${f}_{\ensuremath{\rho}},$ ${f}_{\ensuremath{\varphi}},$ and ${f}_{{K}^{\ensuremath{\star}}}$ for electromagnetic and leptonic decays are within 10% of the experimental values.