Nucleon axial charge and pion decay constant from two-flavor lattice QCD

The axial charge of the nucleon $g_A$ and the pion decay constant $f_π$ are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as $m_π=130\,MeV$. The volume dependence of $g_A$ and $f_π$ can be understood quantitatively in terms of lattice ChPT. At the physical pion mass we find $g_A=1.24(4)$ and $f_π=89± 1.1± 1.8\, MeV$, using $r_0=0.50(1)\,fm$ to set the scale, in good agreement with experiment. As a by-product we obtain the low-energy constant $\barl_4=4.2(1)$.