Impulse approximation in the n p --> d pi^0 reaction reexamined

TL;DR

This paper reexamines the impulse approximation in the n p --> d pi^0 reaction, addressing issues of reducibility and recoil corrections, and finds that recoil corrections significantly affect the predicted cross section.

Contribution

It identifies and resolves an inconsistency in the impulse approximation when including one pion exchange, and quantifies the impact of recoil corrections and cutoff dependence.

Findings

Recoil corrections change the amplitude's magnitude and sign.

Including recoil corrections worsens agreement with experimental data.

Cutoff dependence significantly affects results up to 2.5 GeV.

Abstract

The impulse approximation (one-body operator) in the n p --> d pi^0 reaction is reexamined with emphasis on the issues of reducibility and recoil corrections. An inconsistency when one pion exchange is included in the production operator is demonstrated and then resolved via the introduction of "wave function corrections" which nearly vanish for static nucleon propagators. Inclusion of the recoil corrections to the nucleon propagators is found to change the magnitude and sign of the impulse production amplitude, worsening agreement with the experimental cross section by approximately 30%. A cutoff is used to account for the phenomenological nature of the external wave functions, and is found to have a significant impact up to approximately 2.5 GeV.