Failure of Soft-Pion Techniques for the Reactionpp→dπ+at Threshold

The reaction $\mathrm{pp}\to d{\pi }^{+}$ at threshold is studied using the low-energy theorem of Adler and Dothan. Predictions are found to be in serious disagreement with experimental results, both in the soft-pion limit and for physical pion mass. The inapplicability of the low-energy theorem for this process is traced to the rapid decrease of the deuteron vertex as a function of pion mass. Internal emission diagrams of the one-pion-exchange type, which vary much less rapidly with pion mass, are likely to dominate in the limit of physical pion mass. A similar analysis applies to the processes $K^{-}d\to \Lambda n, {\Sigma }^{0}n$ for kaons at rest, where the soft-kaon result disagrees with experiment even more seriously than above.