Progress in NN --> NNpi

TL;DR

This paper reviews recent effective field theory developments in NN to NNpi reactions, highlighting the importance of operator construction, loop cancellations, and the role of the Delta resonance at next-to-leading order.

Contribution

It introduces a refined method for constructing the production operator, demonstrating loop cancellations and the on-shell enhancement of the Weinberg-Tomozawa vertex, and clarifies the Delta resonance's minimal net effect at NLO.

Findings

Complete cancellation of loops at NLO in the production operator.

On-shell enhancement of the Weinberg-Tomozawa vertex by 4/3.

Negligible net effect of the Delta(1232) at NLO.

Abstract

We survey the recent developments in the reaction $NN \to NN\pi$ in effective field theory. We show that the proper construction of the production operator needs a careful separation of irreducible pieces from reducible ones. The result of this consideration is a complete cancellation of all loops in the production operator at NLO. Moreover, we show that this procedure brings the leading Weinberg-Tomozawa vertex on-shell, thus enhancing the corresponding contribution to the transition amplitude by a factor of 4/3 as compared to the commonly used value. We also discuss the role of the $\Delta(1232)$ for the s-wave pion production. Being relatively sizable individually the direct and rescattering mechanisms of the $\Delta$ excitation at NLO cancel each other to a large extent. Thus, we conclude that the net effect of the $\Delta$ at NLO is very small.