Renormalization group analysis of the chiral pion production operator for NN\to d\pi

TL;DR

This paper uses Wilsonian renormalization group analysis to examine the consistency of cutoff procedures with chiral symmetry and power counting in the NN→dπ pion production operator, finding that higher-order counter terms suffice to absorb cutoff effects.

Contribution

It demonstrates that cutoff regularization in chiral perturbation theory for NN→dπ does not break chiral symmetry when properly renormalized using the Wilsonian RG approach.

Findings

Renormalized operators are absorbed by higher-order chiral counter terms.

Cutoff regularization does not require chiral-symmetry-breaking counter terms.

The approach confirms consistency between cutoff, chiral symmetry, and power counting.

Abstract

We are interested in the consistency between the cutoff, chiral symmetry, and the power counting. For this purpose, we apply the Wilsonian renormalization group (RG) to an operator and then decrease the Wilsonian cutoff. As an example, we study the s-wave pion production operator for NN\to d\pi, derived in chiral perturbation theory. We find that the renormalized part of the RG effective operator is accurately absorbed by chiral counter terms of higher order with natural coefficients. Thus, the use of the (sharp) cutoff regularization does not require us to introduce chiral-symmetry-breaking counter terms, at least in the case of the NN\to d\pi reaction.