A Partial Conservation of Axial-Vector Current Check on the Consistency among ±-Parity Meson Couplings in the Quark Model

Abstract

The supermultiplet coupling constant ${\overline{g}}_{1}$ for the transition from ${L}^{P}={1}^{+}$ meson states to those of ${L}^{P}={0}^{\ensuremath{-}}$ in a relativistically boosted $\mathrm{SU}(6)\ifmmode\times\else\texttimes\fi{}O(3)$ quark model developed previously by the author is evaluated by exploiting the connection between the ${A}_{1\ensuremath{\rho}\ensuremath{\pi}}$ and $\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}$ couplings in the model via partial conservation of axial-vector current and Weinberg sum rules. The new determination of ${\overline{g}}_{1}$ is in excellent agreement with its value obtained earlier from a direct fit to the experimental decay widths.