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

A calculation of the pion-production operator up to next-to-next-to-leading order for s-wave pions is performed within chiral effective field theory. In the previous study [Phys. Rev. C 85, 054001 (2012)] we discussed the contribution of the pion-nucleon loops at the same order. Here we extend that study to include explicit delta degrees of freedom and the 1/m(N)(2) corrections to the pion-production amplitude. Using the power counting scheme where the delta-nucleon mass difference is of the order of the characteristic momentum scale in the production process, we calculate all tree-level and loop diagrams involving delta up to next-to-next-to-leading order. The long-range part of the delta loop contributions is found to be of similar size to that from the pion-nucleon loops which supports the counting scheme. The net effect of pion-nucleon and delta loops is expected to play a crucial role in understanding of the neutral pion production data.