Two-pion-exchange and other higher-order contributions to the $pp\to pp\pi^0$ reaction

TL;DR

This paper evaluates higher-order contributions, including two-pion exchange and pion-rescattering terms, to the near-threshold pp→ppπ0 reaction using a momentum counting scheme, highlighting their significance.

Contribution

It introduces a practical assessment of higher-order terms in the momentum counting scheme for the pp→ppπ0 reaction, emphasizing the importance of specific pion-rescattering and counter-term contributions.

Findings

Higher-order terms significantly affect the reaction amplitude.

Different treatments of nucleon propagators impact results.

Certain pion-rescattering and counter-term contributions are crucial.

Abstract

Much effort has been invested on effective-field-theoretical studies of the near-threshold NN \to NN\pi reactions and, in order to deal with the rather large three-momentum transfers involved, the momentum counting scheme was proposed as an alternative to the usual Weinberg counting scheme. To examine the practical utility of the momentum counting scheme, we study here the contributions of higher-order terms to the pp\to pp\pi^0 reaction. We discuss the consequences of the different treatments of the nucleon propagators in these two counting schemes. We also investigate certain higher chiral-order pion-rescattering terms and the five-point counter-term, which turn out to give important contributions.