  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 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 3-point functions themselves. Its
mass is much smaller than those of the excited states previously considered and
including it impacts the extraction of all the ground state matrix elements.
The form factors extracted using these mass/energy gaps satisfy PCAC and other
consistency conditions, and 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 $Q^2 \neq 0$
case. To highlight the differences and improvement between the conventional
versus 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 $g_A = 1.30(6)$. A very significant improvement over
previous 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 pion
pole-dominance ansatz to fit the $Q^2$ behavior of the induced pseudoscalar
form factor $\widetilde{G}_P(Q^2)$.
