We perform a precise calculation of physical quantities related to the axial structure of the nucleon using $2+1$ flavor lattice QCD gauge configuration (PACS10 configuration) generated at the physical point with lattice volume larger than $(10\mathrm{fm}{)}^4$ by the PACS Collaboration. The nucleon matrix element of the axial-vector current has two types of the nucleon form factors, the axial-vector ($F_A$) form factor and the induced pseudoscalar ($F_P$) form factor. Recently, lattice QCD simulations have succeeded in reproducing the experimental value of the axial-vector coupling, $g_A$, determined from $F_A(q^2)$ at zero momentum transfer $q^2=0$, at a percent level of statistical accuracy. However, the $F_P$ form factor so far has not reproduced the experimental values well due to strong $\pi N$ excited-state contamination. Therefore, we propose a simple subtraction method for removing the so-called leading $\pi N$-state contribution. This method succeeds in reproducing the values obtained by two experiments of muon capture on the proton and pion electroproduction for $F_P(q^2)$. The novel approach can also be applied to determine the pseudoscalar ($G_P$) form factor from the nucleon pseudoscalar matrix element with the help of the axial Ward-Takahashi identity. The resulting form factors, $F_P(q^2)$ and $G_P(q^2)$, are in good agreement with the prediction of the pion-pole dominance model. In the new analysis, the induced pseudoscalar coupling $g_P^{*}$ and the pion-nucleon coupling $g_{\pi NN}$ can be evaluated with a few percent accuracy including systematic uncertainties using existing data calculated at two lattice spacings.

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• Electroweak interaction
• Form factors
• Nucleons
• Hybrid Monte Carlo algorithm
• Lattice QCD