Single soft-pion emission in proton-antiproton annihilation

A soft-pion study using the partially conserved axial-vector current (PCAC) hypothesis is made of four proton-antiproton annihilation processes, $\overline{p}p\to K^{+}{K}^{-}{\pi }^0$, $\overline{p}p\to K^0{\overline{K}}^0{\pi }^0$, $\overline{p}p\to K^{-}{K}^0{\pi }^{+}$, and $\overline{p}p\to K^{+}{\overline{K}}^0{\pi }^{-}$. Using only the assumption of PCAC a soft-pion theorem is derived for neutral-pion emission which leads to a prediction of the cross-section ratios $\frac{\sigma (\overline{p}p\to K^{+}{K}^{-}{\pi }^0)}{\sigma (\overline{p}p\to K^{+}{K}^{-})}$ and $\frac{\sigma (\overline{p}p\to K^0{\overline{K}}^0{\pi }^0)}{\sigma (\overline{p}p\to K^0{\overline{K}}^0)}$ for annihilation at vanishing lab momentum. These predictions are then extended, using the "gentleness" assumption of PCAC, to nonzero lab momentum and directly compared with the available experimental data. A similar analysis is made for charged-pion emission resulting in a prediction of the branching ratios $\frac{\sigma (\overline{p}p\to K^{-}{K}^0{\pi }^{+})}{\sigma (\overline{p}n\to K^{-}{K}^0)}$ and $\frac{\sigma (\overline{p}p\to K^{+}{\overline{K}}^0{\pi }^{-})}{\sigma (\overline{n}p\to K^{+}{\overline{K}}^0)}$ for annihilation both at rest and at nonvanishing lab momentum. A direct comparison with existing experimental data is accomplished by making the assumption that the $I=0\mathrm{}$ and $1s$-channel $\overline{N}N$ annihilation amplitudes are comparable.