Pionic decays ofφ(1020) andf′(1514)

The decay amplitudes $\phi \mathrm{}\left(1020\right)\mathrm{}\to 3\pi$ and $f^{\prime }\mathrm{}\left(1514\right)\mathrm{}\to \pi \pi$ are calculated using unitarity corrections to the Okubo-Zweig-Iizuka rule. We use dispersion relations for the amplitudes $\phi \to \rho \pi$ and $f^{\prime }\to \pi \pi$ and evaluate the contributions arising from intermediate states such as $K\overline{K}$, $K^{*}\overline{K}$, etc. The $K\overline{K}$ intermediate state contributes to the absorptive part of the amplitude $\phi \to \rho \pi$ a value which corresponds to a partial width $\Gamma (\phi \to 3\pi )$ of 150 keV. The contribution of the $K\overline{K}$ and $K^{*}\overline{K}+\overline{K}{K}^{*}$ to the dispersive part of the amplitude $\phi \to \rho \pi$ within the context of approximations employed by us is somewhat larger and corresponds to a partial width of 900 keV for $\phi \to 3\pi$. For the $f^{\prime }\to \pi \pi$ amplitude we have evaluated the contributions of the $K\overline{K}$, $\eta \eta$ and $K^{*}\overline{K}+{\overline{K}}^{*}K$ intermediate states using the dual model for the amplitudes $K\overline{K}\to \pi \pi$, $\eta \eta \to \pi \pi$, and $K^{*}\overline{K}\to \pi \pi$. The effective strength of the amplitude $f^{\prime }\to \pi \pi$ arising from such unitarity corrections to the Okubo-Zweig-Iizuka rule corresponds to a partial width $\Gamma (f^{\prime }\to \pi \pi )$ of 170 keV via the absorptive part and a value of 500 keV via the dispersive part.