# Helium Nuclei in Quenched Lattice QCD

## TL;DR

This study calculates the binding energies of helium nuclei using quenched lattice QCD, demonstrating bound states consistent with experimental magnitudes and employing symmetry-based computational optimizations.

## Contribution

First lattice QCD calculation of helium nuclei binding energies at heavy quark mass with volume dependence analysis to confirm bound states.

## Key findings

- Binding energies are consistent with experimental values.
- Finite energy difference indicates bound states in infinite volume.
- Volume dependence analysis distinguishes bound states from scattering states.

## Abstract

We present results for the binding energies for He 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 nucleus 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.