Power Counting in Peripheral Partial Waves: The Singlet Channels

TL;DR

This paper investigates the power counting of peripheral singlet partial waves in nucleon-nucleon scattering, confirming pion exchanges are perturbative and providing a systematic EFT approach to include higher partial waves.

Contribution

It quantifies the suppression of pion exchanges in peripheral singlet channels and systematizes their inclusion in effective field theory calculations.

Findings

Pion exchanges are perturbative in peripheral singlet channels.

Higher partial waves are systematically suppressed by the centrifugal barrier.

The approach clarifies how to include higher partial waves in EFT calculations.

Abstract

We analyze the power counting of the peripheral singlet partial waves in nucleon-nucleon scattering. In agreement with conventional wisdom, we find that pion exchanges are perturbative in the peripheral singlets. We quantify from the effective field theory perspective the well-known suppression induced by the centrifugal barrier in the pion-exchange interactions. By exploring perturbation theory up to fourth order, we find that the one-pion-exchange potential in these channels is demoted from leading to subleading order by a given power of the expansion parameter that grows with the orbital angular momentum. We discuss the implications of these demotions for few-body calculations: though higher partial waves have been known for a long time to be irrelevant in these calculations (and are hence ignored), here we explain how to systematize the procedure in a way that is compatible with the effective field theory expansion.