Power Counting of Contact-Range Currents in Effective Field Theory

TL;DR

This paper revises the power counting scheme in nuclear effective field theories, showing that contact-range currents are more significant at lower orders due to non-perturbative effects and singular potentials, affecting low-energy nuclear processes.

Contribution

It demonstrates that short-range currents enter at lower order in chiral EFT than previously thought, due to modifications in renormalization-group flow caused by non-perturbative physics.

Findings

Short-range currents are enhanced in importance at lower orders.

Non-perturbative effects modify the power counting scheme.

Impacts on low-energy processes like electron-deuteron scattering and neutron capture.

Abstract

We analyze the power counting of two-body currents in nuclear effective field theories (EFTs). We find that the existence of non-perturbative physics at low energies, which is manifest in the existence of the deuteron and the 1S0 NN virtual bound state, combined with the appearance of singular potentials in versions of nuclear EFT that incorporate chiral symmetry, modifies the renormalization-group flow of the couplings associated with contact operators that involve nucleon-nucleon pairs and external fields. The order of these couplings is thereby enhanced with respect to the naive-dimensional-analysis estimate. Consequently, short-range currents enter at a lower order in the chiral EFT than has been appreciated up until now, and their impact on low-energy observables is concomitantly larger. We illustrate the changes in the power counting with a few low-energy processes involving external probes and the few-nucleon systems, including electron-deuteron elastic scattering and radiative neutron capture by protons.