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Previous lattice QCD calculations of axial vector and pseudoscalar formfactors show significant deviation from the partially conserved axial current(PCAC) relation between them. Since the original correlation functions satisfyPCAC, the observed deviations from the operator identity cast doubt on whetherall the systematics in the extraction of form factors from the correlationfunctions are under control. We identify the problematic systematic as a missedexcited state, whose energy as a function of the momentum transfer squared,$Q^2$, is determined from the analysis of the 3-point functions themselves. Itsmass is much smaller than those of the excited states previously considered andincluding it impacts the extraction of all the ground state matrix elements.The form factors extracted using these mass/energy gaps satisfy PCAC and otherconsistency conditions, and validate the pion-pole dominance hypothesis. Wealso show that the extraction of the axial charge $g_A$ is very sensitive tothe value of the mass gaps of the excited states used and current lattice datado not provide an unambiguous determination of these, unlike the $Q^2 \neq 0$case. To highlight the differences and improvement between the conventionalversus the new analysis strategy, we present a comparison of results obtainedon a physical pion mass ensemble at $a\approx 0.0871\,\mathrm{fm}$. With thenew strategy, we find $g_A = 1.30(6)$. A very significant improvement overprevious lattice results is found for the axial charge radius $r_A =0.74(6)\,\mathrm{fm}$, extracted using the $z$-expansion to parameterize the$Q^2$ behavior of $G_A(Q^2)$, and $g_P^\ast = 8.06(44)$ obtained using the pionpole-dominance ansatz to fit the $Q^2$ behavior of the induced pseudoscalarform factor $\widetilde{G}_P(Q^2)$.

Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation