Abstract
The nucleon-pion-state contribution to QCD two-point 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 $G_{\rm A}(Q^2)$ is at the 5 percent level for a source-sink separation of 2 fm and shows almost no dependence on the momentum transfer $Q^2$. In contrast, for the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$ the nucleon-pion-state contribution shows a rather strong dependence on $Q^2$ and leads to a 10 to 40 percent underestimation of $\tilde{G}_{\rm P}(Q^2)$ at small momentum transfers. The ChPT 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.
Highlights
Physical point simulations, i.e., simulations with quark masses set to their physical values, eliminate the need for a chiral extrapolation
Lattice calculations typically find a large excited-state contamination in this form factor, and the momentum transfer dependence expected from the pion-pole dominance model is not reproduced by the lattice data
At the same time we find an underestimation of about 10% to 40% for G PðQ2Þ, depending strongly on the momentum transfer
Summary
I.e., simulations with quark masses set to their physical values, eliminate the need for a chiral extrapolation. Lattice calculations typically find a large excited-state contamination in this form factor, and the momentum transfer dependence expected from the pion-pole dominance (ppd) model is not reproduced by the lattice data. In this case one may suspect the source to be a low-lying Nπ state, since in ChPT there contribute tree-level diagrams where the axial vector current directly creates or annihilates a pion that is absorbed or ejected at either sink or source in the three-point (3-pt) function. This correlation function exhibits an unusual dependence on the operator insertion time: Instead of approaching a constant plateau value one observes an almost linear dependence [18] These features are qualitatively explained by the ChPT results in this paper.
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