Dimer Effective Field Theory

TL;DR

This paper introduces a new effective field theory approach for nucleon-nucleon scattering that accounts for nonanalytic structures and pole effects, improving data fits up to 300 MeV.

Contribution

It constructs a meromorphic $C$-matrix function to analyze the convergence and pole structure, enhancing the effective theory for nucleon interactions.

Findings

The $C$-matrix's pole structure explains the convergence obstruction.

Including dimer fields yields cut-off insensitive fits to phase shifts.

The approach is applicable to singular potentials in atomic physics.

Abstract

While chiral perturbation theory for mesons is characterized by a momentum expansion in $Q/\Lambda_\chi$ with $\Lambda_\chi \sim 1$ GeV, existing formulations of effective theory for nucleon-nucleon scattering deviate from data at $Q\sim 300$ MeV or lower. We offer heuristic evidence that unsuspected nonanalytic structure exists in the complex momentum plane obstructing the effective field theory expansion in the spin-triplet channels, associated with the peak of the angular momentum barrier whose energy in low partial waves satisfies $k=\sqrt{ME} \sim 300$ MeV. With this motivation, we construct a meromorphic function of $k^2$ we call the $C$-matrix, for which the radius of convergence of its Taylor expansion in $k^2$ is equivalent to that of the momentum expansion of the effective field theory. Thus the range of validity of the effective theory is directly related to the pole structure of the $C$-matrix. We uncover that pole structure and confirm that it is the source of the obstruction. The systematic inclusion of dimer fields as propagating degrees of freedom in the effective theory to account for those poles results in cut-off insensitive fits at order $Q^0$ to most of the lower partial wave phase shifts up to the pion production threshold, using only the one pion exchange part of the long-range nucleon-nucleon interaction. Our theory should be applicable to the singular potentials regularly found in atomic physics as well.