  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.
