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It has been observed in multiple lattice determinations of isovector axialand pseudoscalar nucleon form factors, that, despite the fact that the partialconservation of the axialvector current is fulfilled on the level ofcorrelation functions, the corresponding relation for form factors (sometimescalled the generalized Goldberger-Treiman relation in the literature) is brokenrather badly. In this work we trace this difference back to excited statecontributions and propose a new projection method that resolves this problem.We demonstrate the efficacy of this method by computing the axial andpseudoscalar form factors as well as related quantities on ensembles with twoflavors of improved Wilson fermions using pion masses down to 150 MeV. To thisend, we perform the $z$-expansion with analytically enforced asymptoticbehaviour and extrapolate to the physical point.

Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors