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

The supermultiplet coupling constant ${\overline{g}}_1$ for the transition from $L^P=1^{+}$ meson states to those of $L^P=0^{-}$ in a relativistically boosted $\mathrm{SU}\left(6\right)\mathrm{}\times O\left(3\right)\mathrm{}$ quark model developed previously by the author is evaluated by exploiting the connection between the $A_{1\rho \pi }$ and $\rho \pi \pi$ 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.