$N\pi$-state contamination in lattice calculations of the nucleon pseudoscalar form factor

Abstract

The nucleon-pion-state contribution in the QCD 3-point function of the pseudoscalar density is calculated to leading order in chiral perturbation theory. It predicts a nucleon-pion-state contamination in lattice estimates for the pseudoscalar form factor $G_{\mathrm{P}}(Q^2)$ determined with the plateau method. Depending on the momentum transfer $Q^2$ the contamination varies between -20% and +50% for a source-sink separation of 2 fm. The nucleon-pion-state contamination also causes violations in the generalized Goldberger-Treiman relation among the pseudoscalar and the axial nucleon form factors, the dominant source being the nucleon-pion-state contamination in the induced pseudoscalar form factor ${\tilde{G}}_{\mathrm{P}}(Q^2)$. Comparing the chiral perturbation theory predictions with lattice results of the PACS collaboration we find reasonable agreement even for source-sink separations as small as 1.3 fm.

22 pages, 9 figures. Revised version: Minor changes in section III and IV, typos corrected, references added, results and conclusions unchanged. Matches version published in Phys. Rev. D. arXiv admin note: text overlap with arXiv:1812.09191

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