Complete next-to-leading-order calculation for pion production in nucleon-nucleon collisions at threshold

Based on a counting scheme that explicitly takes into account the large momentum √(Mmπ) characteristic for pion production in nucleon-nucleon collisions we calculate all diagrams for the reaction NN→NNπ at threshold up to next-to-leading-order. At this order there are no free parameters and the size of the next-to-leading- order contributions is in line with the expectation from power counting. The sum of loop corrections at that order vanishes for the process pp→ppπ0 at threshold. The total contribution at next-to-leading-order from loop diagrams that include the delta degree of freedom vanishes at threshold in both reaction channels pp→ppπ0,pnπ+