Nucleon Properties at Finite Volume: the Epsilon Prime Regime

We study the properties of the nucleon in highly asymmetric volumes where the spatial dimensions are small but the time dimension is large in comparison to the inverse pion mass. To facilitate power-counting at the level of Feynman diagrams, we introduce $\epsilon^\prime$-power-counting which is a special case of Leutwyler's $\delta$-power-counting. Pion zero-modes enter the $\epsilon^\prime$-counting perturbatively, in contrast to both the $\epsilon$- and $\delta$-power-countings, since $m_q < q\bar{q}> V$ remains large. However, these modes are enhanced over those with non-zero momenta and enter at lower orders in the $\epsilon^\prime$-expansion than they would in large volume chiral perturbation theory. We discuss an application of $\epsilon^\prime$-counting by determining the nucleon mass, magnetic moment and axial matrix element at the first nontrivial order in the $\epsilon^\prime$-expansion.