Bjorken Limit and Sum Rules for theπ0Lifetime and theρωπCoupling Constant

The Bjorken limit is applied to obtain sum rules for the lifetime of ${\pi }^0$ and for the vector-meson coupling constants. In particular we obtain predictions that $\frac{{g_{\rho \omega \pi }}^2}{4\pi }=0.53\mathrm{}\pm 0.1$ and ${\tau }_{{\pi }^0}\simeq (0.84\mathrm{}\pm 0.83)\times {10}^{-16\mathrm{}}$ sec. The latter is in good agreement with the experimental value (0.89±0.18)×${10}^{-16\mathrm{}}$ sec. From our knowledge of the approximate value of $g_{\rho \omega \pi }$, we conclude that the high-energy behavior of the ${\pi }^0\gamma \gamma$ vertex function is not important to the pion lifetime. The results of this calculation constitute a consistency condition on the plausibility of the Bjorken limit.