Extraction of the pion-nucleon coupling constant using the effective-range expansion with the left-hand cut

TL;DR

This paper uses an effective-range expansion that includes the left-hand cut to analyze low-energy neutron-proton scattering and extract the pion-nucleon coupling constant, demonstrating the method's consistency with known values despite larger uncertainties.

Contribution

It introduces a generalized effective-range expansion incorporating the left-hand cut for more accurate low-energy scattering analysis and pion-nucleon coupling extraction.

Findings

Stable low-energy parameters consistent with established values

Extraction of the pion-nucleon coupling constant with larger uncertainties

Framework effectively probes the left-hand-cut singularity

Abstract

We apply the generalized effective-range expansion of Phys. Rev. Lett. 135, 011903(2025), which incorporates the left-hand cut from one-pion exchange, to low-energy neutron-proton scattering in the $^1S_0$ and $^3S_1$ channels. The amplitude zero for the center-of-mass momentum near 0.35 GeV in the $^1S_0$ channel is naturally accommodated within this framework. We extract the pole position, scattering length, effective range, and the pseudoscalar pion-nucleon coupling constant $g_{\pi N}^2/(4\pi)$ at different expansion orders. The low-energy parameters are stable and consistent with established values, while $g_{\pi N}^2/(4\pi)$ exhibits larger uncertainties. The extraction of $g_{\pi N}^2/(4\pi)$ is data-driven, relying on the analytic constraints from the left-hand cut and phase-shift data within the one-pion-exchange approximation. Despite larger uncertainties compared to high-precision extractions, the consistency with established values demonstrates that this framework can probe the left-hand-cut singularity.