Short-range nuclear forces in singlet channels

TL;DR

This paper refines the power counting scheme in chiral nuclear EFT for singlet channels, emphasizing the importance of subleading contact interactions and proposing a pionless-like power counting due to renormalization considerations.

Contribution

It introduces a modified power counting approach for singlet channels in chiral nuclear EFT based on renormalization group invariance and divergence analysis.

Findings

Large cutoff errors necessitate non-zero O(Q) contributions.

Ultraviolet divergences enhance 1S0 counterterms.

Proposes a pionless-like power counting scheme.

Abstract

Continuing our effort to build a consistent power counting for chiral nuclear effective field theory (EFT), we discuss the subleading contact interactions, or counterterms, in the singlet channels of nucleon-nucleon scattering, with renormalization group invariance as the constraint. We argue that the rather large cutoff error of the leading amplitude requires O(Q) of the EFT expansion to be nonvanishing, contrary to Weinberg's original power counting. This, together with the ultraviolet divergences of two-pion exchanges in the distorted-wave expansion, leads to enhancement of the 1S0 counterterms and results in a pionless-theory-like power counting for the singlet channels.