  We employ chiral perturbation theory to calculate the nucleon-pion-state
contribution to the 3-point correlation functions measured in lattice QCD to
compute various moments of parton distribution functions (quark momentum
fraction, helicity and transversity moment). We estimate the impact of the
nucleon-pion-state contribution on the plateau method for lattice simulations
with a physical pion mass. The nucleon-pion-state contribution results in an
overestimation of all three moments. The overestimation is at the 5-20% level
for source-sink separations of about 1.5 fm.
