On the convergence of nuclear effective field theory with perturbative pions

Abstract

The classic paper by Fleming, Mehen and Stewart cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage and Wise to construct nuclear effective field theory around the unitary fermion limit with perturbative pion exchange. FMS identified the subclass of iterated one-pion exchange potential graphs as the cause of this poor convergence, which they showed persisted in the chiral limit. Theoretical tools are developed here to compute these Feynman graphs analytically to high order in all angular momentum channels simultaneously, examining the amplitudes computed to seven loops in the $L=J$ channels, and three loops in the coupled $L=J\pm 1$ channels. One finds that there is nothing pathological about the perturbative expansion of a $1/r^3$ potential in general, and that the expansion converges satisfactorily in all partial waves except those with the lowest angular momentum, particularly the ${}^3{P}_0$ and the coupled ${}^3{S}_1-{}^3{D}_1$ channels. The results corroborate work by Birse, which suggests possible avenues to explore for improving the range of validity of the EFT expansion.

arXiv commentThis revision aligns with the published version and includes a discussion of related work from atomic physics which has allows for a nonperturbative estimate of the radius of convergence of the KSW expansion in each partial wave, which is shown to agree well with the perturbative results computed here. 32 pages, 11 figures

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• Nuclear Currents in Chiral Effective Field Theory
• Geometry and entanglement in the scattering matrix
• Naturalness in Nuclear Effective Field Theories
• Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems
• Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Nuclear Effective Field Theories: Reverberations of the early days
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Effective field theory for shallow P-wave states
• High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook
• Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases
• Renormalization of One-Pion Exchange in Chiral Effective Field Theory for Antinucleon-Nucleon Scattering
• Nucleon-nucleon scattering with perturbative pions: The uncoupled $P$-wave channels
• Enhancement of deltaful two-pion exchange nuclear forces