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 m π(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. © 2005 IOP Publishing Ltd.