Finite volume dependence of hadron properties and 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., mπL ≫ 4). By considering a relatively simple chiral quark model we are led to suggest that a more realistic constraint would be mπ(L − 2R) ≫ 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 modelwe 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.