  Multi-particle states with additional pions are expected to be a
non-negligible source of the excited-state contamination in lattice simulations
at the physical point. It is shown that baryon chiral perturbation theory
(ChPT) can be employed to calculate the contamination due to two-particle
nucleon-pion states in various nucleon observables. Results to leading order
are presented for the nucleon axial, tensor and scalar charge and three Mellin
moments of parton distribution functions: the average quark momentum fraction,
the helicity and the transversity moment. Taking into account experimental and
phenomenological results for the charges and moments the impact of the
nucleon-pion-states on lattice estimates for these observables can be
estimated. The nucleon-pion-state contribution leads to an overestimation of
all charges and moments obtained with the plateau method. The overestimation is
at the 5-10% level for source-sink separations of about 2 fm. Existing lattice
data is not in conflict with the ChPT predictions, but the comparison suggests
that significantly larger source-sink separations are needed to compute the
charges and moments with few-percent precision.
