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, p̄p→K⁺K⁻π⁰, p̄p→K⁰K̄⁰π⁰, p̄p→K⁻K⁰π⁺, and p̄p→K⁺K̄⁰π⁻. 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 $\frac{\sigma (\bar{p}p\to K^{+}{K}^{-}{\pi }^0)}{\sigma (\bar{p}p\to K^{+}{K}^{-})}$ and $\frac{\sigma (\bar{p}p\to K^0{\bar{K}}^0{\pi }^0)}{\sigma (\bar{p}p\to K^0{\bar{K}}^0)}$ 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 $\frac{\sigma (\bar{p}p\to K^{-}{K}^0{\pi }^{+})}{\sigma (\bar{p}n\to K^{-}{K}^0)}$ and $\frac{\sigma (\bar{p}p\to K^{+}{\bar{K}}^0{\pi }^{-})}{\sigma (\bar{n}p\to K^{+}{\bar{K}}^0)}$ 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 and $1s-channel\overline{N}N$ annihilation amplitudes are comparable.