Previous lattice QCD calculations of axial vector and pseudoscalar form factors show significant deviation from the partially conserved axial current (PCAC) relation between them. Since the original correlation functions satisfy PCAC, the observed deviations from the operator identity cast doubt on whether all of the systematics in the extraction of form factors from the correlation functions are under control. We identify the problematic systematic as a missed excited state, whose energy as a function of the momentum transfer squared $Q^2$ is determined from the analysis of the three-point functions themselves. Its energy is much smaller than those of the excited states previously considered, and including it impacts the extraction of all of the ground state matrix elements. The form factors extracted using these mass and energy gaps satisfy PCAC and another consistency condition, and they validate the pion-pole dominance hypothesis. We also show that the extraction of the axial charge $g_A$ is very sensitive to the value of the mass gaps of the excited states used, and current lattice data do not provide an unambiguous determination of these, unlike the $Q^2\ne 0$ case. To highlight the differences and improvement between the conventional vs the new analysis strategy, we present a comparison of results obtained on a physical pion mass ensemble at $a\approx 0.0871\mathrm{fm}$. With the new strategy, we find $g_A=1.30(6)$ and axial charge radius $r_A=0.74(6)\mathrm{fm}$, both extracted using the $z$ expansion to parametrize the $Q^2$ behavior of $G_A(Q^2)$, and $g_P^{*}=8.06(44)$, obtained using the pion-pole dominance ansatz to fit the $Q^2$ behavior of the induced pseudoscalar form factor ${\tilde{G}}_P(Q^2)$. These results are consistent with current phenomenological values.

• Received 20 October 2019
• Accepted 13 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.072002

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Published by the American Physical Society