Bound state of two-nucleon systems in quenched lattice QCD

TL;DR

This study uses quenched lattice QCD to demonstrate the existence of bound states in two-nucleon systems, analyzing volume dependence and excited states to distinguish bound states from scattering states.

Contribution

It provides the first lattice QCD evidence of bound two-nucleon states at heavy quark masses, using volume dependence and excited state analysis.

Findings

Bound states confirmed in both spin triplet and singlet channels.

Finite energy difference persists in infinite volume limit.

Scattering lengths estimated using Luscher's finite volume formula.

Abstract

We address the issue of bound state in the two-nucleon system in lattice QCD with the quenched approximation at the lattice spacing of a =0.128 fm using 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 the finite volume formula derived by Luscher.