Soft-pion limits of the inclusive pion distributions in NN → π± + anything at rest

The PCAC hypothesis of extrapolating off mass shell is used to show that the invariant pion distributions in the reactions $\text{N}\text{N}\text{→ π}{}^{\mathrm{\pm }}\text{+}$ anything at rest must vanish as the pion momentum tends to zero, a behavior which is supported by recent data on $\text{p}\text{n}\text{→ π}{}^{\mathrm{\pm }}\text{+}$ anything.