Advances in the field-theoretic understanding of pion production in   nucleon-nucleon collisions
  We study the production amplitude for the reaction $NN\to NN\pi$ up to next-to-leading order in chiral perturbation theory. We show that the irreducible chiral loops at this order exactly cancel those terms that arise from the off-shell parts of the $\pi N$ rescattering vertex. This cancellation is required for formal consistency of the whole scheme. The net effect of the inclusion of all next-to-leading order loops is to enhance the leading rescattering amplitude by a factor of 4/3 compared to phenomenological studies, bringing its contribution to the cross section for $pp\to d\pi^+$ close to the experimental value. 
V. Lensky, J. Haidenbauer, C. Hanhart, V. Baru, A. Kudryavtsev, U.-G.   Mei{\ss}ner