A nucleon in a tiny box

Abstract

We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ m\beta << 1) as well as in the "p-regime" (mL ~ m\beta >> 1). Based on the two leading orders, we discuss the convergence of the expansion as a function of the lattice size and quark masses. This result can be used to extrapolate lattice results obtained from lattice sizes smaller than the pion cloud, avoiding the numerical simulation of physics under theoretical control. An extraction of the low-energy coefficient c_3 of the chiral Lagrangean from lattice simulations at small volumes and a ``magic'' ratio \beta=1.22262 L might be possible.