We study multi-particle state contributions to the QCD two-point functions of
the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume.
For sufficiently small quark masses one expects three-meson states with two
additional pions at rest to have the lowest total energy after the ground
state. We calculate this three-meson state contribution using chiral
perturbation theory. We find it to be strongly suppressed and too small to be
seen in present-day lattice simulations.Comment: 17 pages, 5 figure
