Isovector Axial Charge and Form Factors of Nucleons from Lattice QCD

A survey of the calculations of the isovector axial vector form factor of the nucleon using lattice QCD is presented. Attention is paid to statistical and systematic uncertainties, in particular those due to excited state contributions. Based on a comparison of results from various collaborations, a case is made that lattice results are consistent within 10%. A similar level of uncertainty is in the axial charge g(A)(u-d), the mean squared axial charge radius < r(A)(2)>, the induced pseudoscalar charge g(P)*, and the pion-nucleon coupling g(pi NN). Even with the current methodology, a significant reduction in errors is expected over the next few years with higher statistics data on more ensembles closer to the physical point. Lattice QCD results for the form factor G(A)(Q(2)) are compatible with those obtained from the recent MINER nu A experiment but lie 2-3 sigma higher than the phenomenological extraction from the old nu-deuterium bubble chamber scattering data for Q(2) > 0.3 GeV2. Current data show that the dipole ansatz does not have enough parameters to fit the form factor over the range 0 <= Q(2) <= 1 GeV2, whereas even a z(2) truncation of the z expansion or a low order Pade are sufficient. Looking ahead, lattice QCD calculations will provide increasingly precise results over the range 0 <= Q(2) <= 1 GeV2, and MINER nu A-like experiments will extend the range to Q(2) similar to 2 GeV2 or higher. Nevertheless, improvements in lattice methods to (i) further control excited state contributions and (ii) extend the range of Q(2) are needed.