Calculation of Helium nuclei in quenched lattice QCD

TL;DR

This study calculates the binding energies of helium nuclei (^4He and ^3He) using quenched lattice QCD, demonstrating bound states consistent with experimental magnitudes and employing volume dependence analysis to distinguish bound states from scattering states.

Contribution

The paper introduces an efficient computational method to calculate nuclear binding energies in lattice QCD and confirms the existence of bound helium nuclei at heavy quark masses.

Findings

Bound states of helium nuclei are observed in lattice QCD.

Binding energies are comparable to experimental values.

Volume dependence analysis confirms the bound nature of the states.

Abstract

We present results for the binding energies for ^4He and ^3He nuclei calculated in quenched lattice QCD at the lattice spacing of a =0.128 fm with a heavy quark mass corresponding to m_pi = 0.8 GeV. Enormous computational cost for the nucleus correlation functions is reduced by avoiding redundancy of equivalent contractions stemming from permutation symmetry of protons or neutrons in the nucleus and various other symmetries. To distinguish a bound state from an attractive scattering state, we investigate the volume dependence of the energy difference between the ground state energy of the nucleus channel and the free multi-nucleon states 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 to the conclusion that the measured ground states are bounded. It is also encouraging that the measured binding energies and the experimental ones show the same order of magnitude.