Time dependence of nucleon correlation functions in chiral perturbation theory

We consider corrections to nucleon correlation functions arising from times that are far from the asymptotic limit. For such times, the single-nucleon state is contaminated by the pion-nucleon and pion-delta continuum. We use heavy baryon chiral perturbation theory to derive the spectral representation of the nucleon two-point function. Finite-time corrections to the axial-current correlation function are also derived. Pion-nucleon excited-state contributions drive the axial correlator upward, while contributions from the interference of pion-delta and pion-nucleon states drive the axial correlator downward. Our results can be compared qualitatively to optimized nucleon correlators calculated in lattice QCD, because the chiral corrections characterize only low-energy excitations above the ground state. While our computations suggest that the nucleon axial charge is subject to overestimation, we speculate as to how underestimation might arise from the use of highly improved nucleon operators.