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We study multi-particle state contributions to the QCD two-point functions ofthe axial-vector and pseudo-scalar quark bilinears in a finite spatial volume.For sufficiently small quark masses one expects three-meson states with twoadditional pions at rest to have the lowest total energy after the groundstate. We calculate this three-meson state contribution using chiralperturbation theory. We find it to be strongly suppressed and too small to beseen in present-day lattice simulations.

Excited-state contribution to the axial-vector and pseudo-scalar correlators with two extra pions