Finite Volume Dependence of Hadron Properties and Lattice QCD

TL;DR

This paper investigates how finite lattice size affects hadron properties in lattice QCD, proposing a more accurate size constraint to prevent unphysical results, demonstrated through a chiral quark model.

Contribution

It introduces a refined finite volume constraint for lattice QCD simulations based on a chiral quark model, improving upon the traditional rule of thumb.

Findings

Violating the new size constraint leads to unphysical hadron behavior.

The axial charge of the nucleon decreases rapidly near the chiral limit.

The proposed constraint better predicts finite volume effects in lattice QCD.

Abstract

Because the time needed for a simulation in lattice QCD varies at a rate exceeding the fourth power of the lattice size, it is important to understand how small one can make a lattice without altering the physics beyond recognition. It is common to use a rule of thumb that the pion mass times the lattice size should be greater than (ideally much greater than) four (i.e., $m_\pi L \gg 4$). By considering a relatively simple chiral quark model we are led to suggest that a more realistic constraint would be $m_\pi (L - 2R) \gg 4$, where $R$ is the radius of the confinement region, which for these purposes could be taken to be around 0.8-1.0 fm. Within the model we demonstrate that violating the second condition can lead to unphysical behaviour of hadronic properties as a function of pion mass. In particular, the axial charge of the nucleon is found to decrease quite rapidly as the chiral limit is approached.