Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors

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.

Nπ states and the projection method for the nucleon axial and pseudoscalar form factors

“…The N π contamination in the axial and pseudoscalar form factors have a much smaller influence, in particular for small momentum transfer. These findings are apparently in contradiction with the results in [6]: How can the projection method solve the PCAC puzzle if it has essentially no impact on the N π contamination in the induced pseudoscalar form factor?…”

“…Obviously this is not the desired solution to the PCAC puzzle: Applying the projection method we are left with two form factors instead of one afflicted with a large excited state contamination. Comparing the ChPT results with the lattice data of [6] strongly supports this conclusion.…”

“…with p µ = (p µ + p µ )/2 being the mean of the initial and final nucleon momenta. By construction the projected current and density satisfy the PCAC relation (2.4) and the contraction of p µ with the SN matrix element in (2.1) vanishes [6]. Therefore, the ratios R ⊥ µ ( q, t, t ), formed with the 3-pt functions of the projected current and density, have the same constant asymptotic values as the original ratios in (2.12).…”

“…Even though the lattice techniques for the calculation of nucleon form factors are wellestablished, recent calculations of the axial form factors display an unexpected and puzzling behavior: The partially conserved axial vector current (PCAC) relation implies the so-called generalized Goldberger-Treiman (gGT) relation between the axial and pseudoscalar form factors, but the lattice results for the form factors strongly violate this relation [2][3][4][5]. As pointed out by the RQCD collaboration [6], this so-called PCAC puzzle is surprising since the PCAC relation is fulfilled rather well on the level of the correlation functions. This strongly suggests a large excited state contamination as the source for violating the gGT relation.…”

“…As a remedy RQCD proposed a simple projection method to remove the large excited state contamination from the correlation functions [6]. Numerical tests of this method show that the gGT relation is indeed satisfied if the projection method is applied.…”