Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
(May 28, 1999)Abstract
The masses and decay constants of the light vector mesons \$\rho/ømega\$,
\$\phi\$ and \$K^\star\$ are studied within a ladder-rainbow truncation of the
coupled Dyson-Schwinger and Bethe-Salpeter equations of QCD with a model
2-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\_\pi, m\_\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\_\rho, m\_\phi\$ and
\$m\_K^\star\$ are within 5\%, while the decay constants \$f\_\rho, f\_\phi\$ and
\$f\_K^\star\$ for electromagnetic and leptonic decays are within 10\% of the
experimental values.