Finite-Size Effects in Lattice QCD with Dynamical Wilson Fermions

TL;DR

This study investigates finite-size effects on pion and nucleon masses in lattice QCD with Wilson fermions, comparing simulation results with theoretical formulas to assess the feasibility of volume extrapolation before chiral and continuum limits.

Contribution

It provides a systematic analysis of volume dependence in unquenched Wilson fermion simulations, comparing results with Luescher's formula and Chiral Perturbation Theory.

Findings

Finite-size effects are consistent with theoretical predictions.

Volume extrapolation may reduce computational costs.

Results depend on lattice spacing and quark mass.

Abstract

As computing resources are limited, choosing the parameters for a full Lattice QCD simulation always amounts to a compromise between the competing objectives of a lattice spacing as small, quarks as light, and a volume as large as possible. Aiming to push unquenched simulations with the Wilson action towards the computationally expensive regime of small quark masses we address the question whether one can possibly save computing time by extrapolating results from small lattices to the infinite volume, prior to the usual chiral and continuum extrapolations. In the present work the systematic volume dependence of simulated pion and nucleon masses is investigated and compared with a long-standing analytic formula by Luescher and with results from Chiral Perturbation Theory. We analyze data from Hybrid Monte Carlo simulations with the standard (unimproved) two-flavor Wilson action at two different lattice spacings of a=0.08fm and 0.13fm. The quark masses considered correspond to approximately 85 and 50% (at the smaller a) and 36% (at the larger a) of the strange quark mass. At each quark mass we study at least three different lattices with L/a=10 to 24 sites in the spatial directions (L=0.85-2.08fm).