Two-Nucleon Bound States in Quenched Lattice QCD

TL;DR

This study uses quenched lattice QCD to investigate two-nucleon bound states, confirming their existence in both spin channels through volume dependence and energy analysis, with implications for understanding nuclear forces.

Contribution

It demonstrates the presence of two-nucleon bound states in quenched lattice QCD at heavy quark masses using volume dependence and energy spectrum analysis, a novel approach in this context.

Findings

Bound states exist in both spin channels.

Energy differences persist in infinite volume limit.

Scattering lengths are estimated using Luscher's formula.

Abstract

We address the issue of bound state in the two-nucleon system in lattice QCD. Our study is made in the quenched approximation at the lattice spacing of a = 0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the ground state and the free two-nucleon state by changing the spatial extent of the lattice from 3.1 fm to 12.3 fm. A finite energy difference left in the infinite spatial volume limit leads us to the conclusion that the measured ground states for not only spin triplet but also singlet channels are bounded. Furthermore the existence of the bound state is confirmed by investigating the properties of the energy for the first excited state obtained by 2x2 diagonalization method. The scattering lengths for both channels are evaluated by applying the finite volume formula derived by Luscher to the energy of the first excited states.