Three-particle Nππ state contribution to the nucleon two-point function in lattice QCD

The three-particle $N\pi\pi$-state contribution to the QCD two-point function of standard nucleon interpolating fields is computed to leading order in chiral perturbation theory. Using the experimental values for two low-energy coefficients the impact of this contribution on lattice QCD calculations of the nucleon mass is estimated. The impact is found to be at the per mille level at most and negligible in practice.