Two Nucleon Systems at $m_\pi\sim 450~{\rm MeV}$ from Lattice QCD

TL;DR

This study uses lattice QCD to analyze two-nucleon systems at a pion mass of about 450 MeV, determining binding energies, phase shifts, and effective field theory parameters, providing insights into nuclear interactions at unphysical quark masses.

Contribution

First lattice QCD calculation of two-nucleon systems at this pion mass, including binding energies, phase shifts, and low energy constants, with detailed analysis of the hadron sector and mass relations.

Findings

Deuteron binding energy of 14.4 MeV with uncertainties

Dineutron bound state with 12.5 MeV binding energy

Phase shifts consistent with phenomenological models

Abstract

Nucleon-nucleon systems are studied with lattice quantum chromodynamics at a pion mass of $m_\pi\sim 450~{\rm MeV}$ in three spatial volumes using $n_f=2+1$ flavors of light quarks. At the quark masses employed in this work, the deuteron binding energy is calculated to be $B_d = 14.4^{+3.2}_{-2.6} ~{\rm MeV}$, while the dineutron is bound by $B_{nn} = 12.5^{+3.0}_{-5.0}~{\rm MeV}$. Over the range of energies that are studied, the S-wave scattering phase shifts calculated in the 1S0 and 3S1-3D1 channels are found to be similar to those in nature, and indicate repulsive short-range components of the interactions, consistent with phenomenological nucleon-nucleon interactions. In both channels, the phase shifts are determined at three energies that lie within the radius of convergence of the effective range expansion, allowing for constraints to be placed on the inverse scattering lengths and effective ranges. The extracted phase shifts allow for matching to nuclear effective field theories, from which low energy counterterms are extracted and issues of convergence are investigated. As part of the analysis, a detailed investigation of the single hadron sector is performed, enabling a precise determination of the violation of the Gell-Mann--Okubo mass relation. [An Erratum to the published version is included as an appendix. It details the impact of an error discovered in 2020 and corrects typographical errors.]