N π -state contamination in lattice calculations of the nucleon axial form factors

The nucleon-pion-state contribution to QCD two- and three-point functions used in lattice calculations of the nucleon axial form factors are studied in chiral perturbation theory. For small quark masses this contribution is expected to be the dominant excited-state contamination at large time separations. To leading order in chiral perturbation theory the results depend on only two experimentally known low-energy constants and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the axial form factor GA(Q2) is at the 5 percent level for a source-sink separation of 2 fm and shows almost no dependence on the momentum transfer Q2. In contrast, for the induced pseudoscalar form factor G˜P(Q2) the nucleon-pion-state contribution shows a rather strong dependence on Q2 and leads to a 10 to 40 percent underestimation of G˜P(Q2) at small momentum transfers. The chiral perturbation theory results can be used to analytically remove the nucleon-pion-state contribution from lattice data. Performing this removal for lattice data generated by the PACS collaboration we find agreement with experimental data and the predictions of the pion-pole dominance model. The removal works surprisingly well even for source-sink separations as small as 1.3 fm.