Nucleon axial structure from lattice QCD

Abstract

We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to 96 3 × 192 sites and Lm π = 6.4), and lattice spacings down to 0.039 fm, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the z-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz (M z-exp A = 1.02(10) GeV versus M dipole A = 1.31(8) GeV). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization (g z-exp P = 8.68(45) and g dipole P = 8.30(24)), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant g A .

Double parton distributions in the nucleon from lattice QCD

“…As already mentioned, the nucleon form factors as functions of the virtuality t can be obtained from lattice calculations. In this study we use the form factor data [83] which has been generated in the simulation described in [84]. In that work various gauge ensembles have been investigated; we take the form factor data for gauge ensemble H102, which is the same ensemble that is used in our DPD study.…”

“…We thank Thomas Wurm for providing the nucleon form factor data generated in the context of the simulation in [84]. Furthermore, we gratefully acknowledge the CLS effort (http://wiki-zeuthen.desy.de/CLS/CLS) for generating the n f = 2+1 ensembles [79], one of which we employed for the present study.…”

Investigating $\mathbf{N \to Nπ}$ axial matrix elements

“…However, it has been found that the extraction of these quantities is contaminated by excited states, in particular 𝑁 𝜋. 𝜒PT analyses have shown that the closer we go to physical pion masses, the more the 𝑁 𝜋 states cannot be neglected, especially for the pseudoscalar form factors 𝐺 𝑃 and 𝐺 P (see [1,2]). Recently, our group estimated the tree-level 𝜒PT 𝑁 𝜋 contribution to the ratio in the axial and pseudoscalar channels and was able to extract form factors that satisfy the PCAC relation (see [3]). In this work, we compute directly 𝑁 → 𝑁 𝜋 three-point functions and in the final analysis we aim to extract 𝑁 → 𝑁 𝜋 matrix elements, with the aim of validating 𝜒PT expectations, but also to explore 𝜋 production.…”

Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology

“…ChPT also allows to account for finite lattice-volume and lattice spacing corrections in a systematic way [7,8]. It has also proved helpful to deal with the contamination from excited states [5,6,9]. The interplay between ChPT and LQCD can also be used to determine poorly known LECs, which are difficult to access with experimental data.…”