Pion Emission in Proton-Antiproton Annihilation Processes

Using the formalism of current algebra and PCAC (partially conserved axial-vector current) we calculate the amplitudes for emission of two neutral pions in $\overline{p}p\to K^{+}{K}^{-}$ and in $\overline{p}p\to K^{+}{K}^{-}{K}^{+}{K}^{-}$, and from these the ratios of cross sections $\frac{(\overline{p}p\to K^{+}{K}^{-}{\pi }^0{\pi }^0)}{(\overline{p}p\to K^{+}{K}^{-})}$ and $\frac{(\overline{p}p\to K^{+}{K}^{-}{K}^{+}{K}^{-}{\pi }^0{\pi }^0)}{(\overline{p}p\to K^{+}{K}^{-}{K}^{+}{K}^{-})}$ at various energies.