Low-energy theorems for nucleon-nucleon scattering at $M_{\pi}=450$ MeV

TL;DR

This paper uses low-energy theorems to analyze lattice QCD results for nucleon-nucleon interactions at a pion mass of 450 MeV, revealing inconsistencies and providing predictions for phase shifts and scattering parameters.

Contribution

It demonstrates the application of low-energy theorems to lattice QCD data at unphysical pion mass, offering new insights into nucleon-nucleon scattering parameters.

Findings

Binding energies are inconsistent with phase shift behavior within uncertainties.

Predicted phase shifts and scattering lengths agree with EFT analyses.

Results conflict with effective-range approximation-based determinations.

Abstract

We apply the low-energy theorems to analyze the recent lattice QCD results for the two-nucleon system at a pion mass of $M_\pi\simeq 450$ MeV obtained by the NPLQCD collaboration. We find that the binding energies of the deuteron and dineutron are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the $^3S_1$ and $^1S_0$ channels. Our results for these quantities are consistent with those obtained by the NPLQCD collaboration from effective field theory analyses but are in conflict with their determination based on the effective-range approximation.