$N\pi$-state contamination in lattice calculations of the nucleon axial form factors

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 $G_{\mathrm{A}}(Q^2)$ 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 ${\tilde{G}}_{\mathrm{P}}(Q^2)$ the nucleon-pion-state contribution shows a rather strong dependence on $Q^2$ and leads to a 10 to 40 percent underestimation of ${\tilde{G}}_{\mathrm{P}}(Q^2)$ 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.

30 pages, 11 figures

References in corpus (6)

• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• A local factorization of the fermion determinant in lattice QCD
• Time Dependence of Nucleon Correlation Functions in Chiral Perturbation Theory
• Chiral Corrections to Nucleon Two- and Three-Point Correlation Functions
• Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD
• Nucleon-pion-state contribution in lattice calculations of moments of parton distribution functions

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• Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle
• The pion-nucleon sigma term from lattice QCD
• Nucleon axial-vector and pseudoscalar form factors, and PCAC relations
• Toward $N$ to $N\pi$ matrix elements from lattice QCD
• $N\pi$-states and the projection method for the nucleon axial and pseudoscalar form factors
• $N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors
• Excited states in nucleon structure calculations
• Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators
• Investigation of pion-nucleon contributions to nucleon matrix elements
• Axial transition form factors of octet baryons in the perturbative chiral quark model
• Method for high-precision determination of the nucleon axial structure using lattice QCD: Removing $\pi N$-state contamination
• Application of Laplace filters to the analysis of lattice time correlators
• A Lattice Story of Proton Spin