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A calculation of the pion-production operator up to next-to-next-to-leadingorder for s-wave pions is performed within chiral effective field theory. Inthe previous study [Phys. Rev. C 85, 054001 (2012)] we discussed thecontribution of the pion-nucleon loops at the same order. Here we extend thatstudy to include explicit Delta degrees of freedom and the 1/m_N^2 correctionsto the pion-production amplitude. Using the power counting scheme where theDelta-nucleon mass difference is of the order of the characteristic momentumscale in the production process, we calculate all tree-level and loop diagramsinvolving Delta up to next-to-next-to-leading order. The long-range part of theDelta loop contributions is found to be of similar size to that from thepion-nucleon loops which supports the counting scheme. The net effect ofpion-nucleon and Delta loops is expected to play a crucial role inunderstanding of the neutral pion production data.

Pion production in nucleon-nucleon collisions in chiral effective field theory with Delta(1232)-degrees of freedom