Finite-size effects in lattice QCD with dynamical Wilson fermions

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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 L\"uscher and with results from chiral perturbation theory (ChPT). We analyze data from hybrid Monte Carlo simulations with the standard (unimproved) two-flavor Wilson action at two different lattice spacings of $a\ensuremath{\approx}0.08$ and 0.13 fm. 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 ($L=0.85--2.08\text{ }\text{ }\mathrm{fm}$). We find that an exponential ansatz fits the volume dependence of the pion masses well, but with a coefficient about an order of magnitude larger than the theoretical leading-order prediction. In the case of the nucleon we observe a remarkably good agreement between our lattice data and a recent formula from relativistic baryon ChPT.