Abstract
It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation functions, the corresponding relation for form factors (sometimes called the generalized Goldberger–Treiman relation in the literature) is broken rather badly. In this work we trace this difference back to excited state contributions and propose a new projection method that resolves this problem. We demonstrate the efficacy of this method by computing the axial and pseudoscalar form factors as well as related quantities on ensembles with two flavors of improved Wilson fermions using pion masses down to 150 MeV. To this end, we perform the z-expansion with analytically enforced asymptotic behaviour and extrapolate to the physical point.
Highlights
The axial nucleon structure is central for the description of weak interactions and plays a prominent role in long-baseline neutrino experiments, where it is important for a precise determination of the neutrino flux and the cross section for nuclear targets [1,2,3]
In this work we demonstrate that the largest part of the deviation from the PCACFF relation is due to excited states in the temporal axialvector ( A0) and pseudoscalar ( P ) channels
We have presented a method to identify excited state contributions that spoil the PCAC relation on the form factor level
Summary
The axial nucleon structure is central for the description of weak interactions and plays a prominent role in long-baseline neutrino experiments, where it is important for a precise determination of the neutrino flux and the cross section for nuclear targets [1,2,3]. Various determinations of the nucleon couplings and form factors using a wide variety of lattice actions and analysis methods can, e.g., be found in Refs. In this work we demonstrate that the largest part of the deviation from the PCACFF relation is due to excited states in the temporal axialvector ( A0) and pseudoscalar ( P ) channels These excited states are, so strongly enhanced relative to the ground state that the usual multistate fit ansatz is bound to fail for any feasible time distances between the source, the sink, and the current insertion.
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