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

TL;DR

This paper extends chiral effective field theory calculations of pion production in nucleon-nucleon collisions by explicitly including Delta(1232) degrees of freedom and 1/m_N^2 corrections, providing a more comprehensive understanding of the process.

Contribution

It introduces explicit Delta degrees of freedom into the chiral EFT calculation of pion production, including loop diagrams up to next-to-next-to-leading order, enhancing the theoretical framework.

Findings

Delta loop contributions are comparable to pion-nucleon loops.

Long-range Delta loop effects support the chosen power counting scheme.

Results are relevant for interpreting neutral pion production data.

Abstract

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.