Power Counting in Peripheral Partial Waves: The Singlet Channels

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.

15 pages, 18 figures

References in corpus (11)

• Chiral effective field theory and nuclear forces
• Nuclear Physics from Lattice QCD
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Short-range nuclear forces in singlet channels
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Renormalization of Singular Potentials and Power Counting
• Deconstructing triplet nucleon-nucleon scattering
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Deconstructing 1S0 nucleon-nucleon scattering
• Effective short-range interaction for spin-singlet P-wave nucleon-nucleon scattering

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