Axial Vector Form Factors of the Nucleon from Lattice QCD

We present results for the form factors of the isovector axial vector current in the nucleon state using large scale simulations of lattice QCD. The calculations were done using eight ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12$ fm and light-quark masses corresponding to the pion masses $M_\pi \approx 135, 225$ and $310$ MeV. High-statistics estimates allow us to quantify systematic uncertainties in the extraction of $G_A(Q^2)$ and the induced pseudoscalar form factor $\tilde{G}_P(Q^2)$. We perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses of the axial charge radius $r_A$ data to obtain physical estimates. Using the dipole ansatz to fit the $Q^2$ behavior we obtain $r_A|_{\rm dipole} = 0.49(3)$ fm, which corresponds to ${\cal M}_A = 1.39(9)$ GeV, and is consistent with ${\cal M}_A = 1.35(17)$ GeV obtained by the miniBooNE collaboration. The estimate obtained using the $z$-expansion is $r_A|_{z-{\rm expansion}} = 0.46(6)$ fm, and the combined result is $r_A|_{\rm combined} = 0.48(4)$ fm. Analysis of the induced pseudoscalar form factor $\tilde{G}_P(Q^2)$ yields low estimates for $g_P^\ast$ and $g_{\pi {\rm NN}}$ compared to their phenomenological values. To understand these, we analyze the partially conserved axial current (PCAC) relation by also calculating the pseudoscalar form factor. We find that these low values are due to large deviations in the PCAC relation between the three form factors and from the pion-pole dominance hypothesis.