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 $G_{\rm P}(Q^2)$ 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 $\tilde{G}_{\rm P}(Q^2)$. 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.
Highlights
In a recent paper [1] the nucleon-pion (Nπ) contribution in the nucleon axial-vector three-point function was computed in leading order (LO) chiral perturbation theory (ChPT)
Preliminaries To LO in ChPT the Nπ contribution to the ratio Rμ and the effective form factors depends on a few low-energy coefficients (LECs) only, and these are known rather precisely from experiment
The plot reflects what we have already observed in Fig. 1: The Nπ contribution in the induced pseudoscalar form factor underestimates the true form factor, the filled blue symbols are below the open ones over the entire Q2 range
Summary
In a recent paper [1] the nucleon-pion (Nπ) contribution in the nucleon axial-vector three-point (pt) function was computed in leading order (LO) chiral perturbation theory (ChPT). We present the results for the Nπ-state contamination in the pseudoscalar three-pt function and lattice estimators for the pseudoscalar form factor GPðQ2Þ. Together with the analogous results for the axial form factors GAðQ2Þ and G PðQ2Þ we explicitly calculate the dominant violations of the gGT relation by Nπ excited states. Comparing the LO ChPT results with lattice QCD data recently obtained by the PACS Collaboration [6] we find remarkable agreement even for source-sink separations as small as t ≈ 1.3 fm This supports the conclusion that the observed violation of the generalized Goldberger-Treiman. [9] in the computation of the three-pion excited-state contribution to the QCD two-point functions of the axial-vector current and the pseudoscalar density. The general ideas behind ChPT calculations of the Nπ-state contamination in nucleon observables have been recently reviewed in [10,11] and are not repeated here
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