Two-nucleon systems at $m_{\pi}\approx292$ MeV from lattice QCD

TL;DR

This study uses lattice QCD to analyze two-nucleon systems at a pion mass of approximately 292 MeV, revealing virtual state poles in both the deuteron and di-neutron channels with specific binding energies.

Contribution

It provides the first lattice QCD determination of nucleon-nucleon scattering amplitudes at this pion mass using multiple finite-volume ensembles and compares two analysis methods.

Findings

Both channels exhibit a virtual state pole.

Binding energies are approximately 6 MeV for deuteron and 11 MeV for di-neutron.

Results from Lüscher's method and NPHF are consistent.

Abstract

Nucleon-nucleon systems in the $^3S_1$ and the $^1S_0$ channels are studied in lattice quantum chromodynamics at a pion mass of approximately $m_{\pi}\approx292$ MeV, employing three $N_f = 2+1$ ensembles with the same pion mass and lattice spacing $a=0.10530(18)$ fm but different spatial volumes. Finite-volume energies of the nucleon-nucleon systems are determined in both the rest frame and a moving frame. The distillation quark smearing method is applied to improve the precision and to ensure the symmetric correlators by using the same interpolating operators at sink and source. The scattering amplitudes are extracted from the finite-volume spectra using the L\"uscher's finite-volume method. At the studied pion mass, both the $^3S_1$ (deuteron) and $^1S_0$(di-neutron) channels exhibit a virtual state pole, with binding energies of $6^{+5}_{-3}$ MeV and $11^{+6}_{-5}$ MeV, respectively. To investigate the effects of the left-hand cut, an alternative method -- the Non-Perturbative Hamiltonian framework (NPHF) -- is used for the scattering analysis and yields consistent results with those from the L\"uscher method.