Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory

TL;DR

This paper investigates the effectiveness of chiral perturbation theory in predicting pion production in nucleon systems, highlighting challenges in reaction bridging and emphasizing the need for higher-order calculations.

Contribution

It demonstrates the limitations of current chiral operators in bridging reactions with different kinematics and explores the impact of higher-order terms on predictive accuracy.

Findings

The lowest-order operator fails to match experimental data.

Adding higher-order counter terms improves the energy dependence description.

Convergence issues in the chiral expansion are identified for the pion production reaction.

Abstract

I study an aspect of chiral perturbation theory (\chi PT) which enables one to ``bridge'' different reactions. That is, an operator fixed in one of the reactions can then be used to predict the other. For this purpose, I calculate the partial wave amplitude for the p-wave pion production (pp\to pn\pi^+) using the pion production operator from the lowest and the next nonvanishing orders. The operator includes a contact operator whose coupling has been fixed using a matrix element of a low-energy weak process (pp\to de^+\nu_e). I find that this operator does not reproduce the partial wave amplitude extracted from experimental data, showing that the bridging over the reactions with significantly different kinematics is not necessarily successful. I study the dependence of the amplitude on the various inputs such as the NN potential, the \pi N\Delta coupling, and the cutoff. I argue the importance of a higher order calculation. In order to gain an insight into a higher order calculation, I add a higher order counter term to the operator used above, and fit the couplings to both the low-energy weak process and the pion production. The energy dependence of the partial wave amplitude for the pion production is described by the operator consistently with the data. However, I find a result which tells us to be careful about the convergence of the chiral expansion for the pp\to pn\pi^+ reaction.