We present results for the isovector axial, scalar and tensor charges g The lattice-QCD calculations were done using nine 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 ≈ 0.06, 0.09 and 0.12 fm and light-quark masses corresponding to the pion masses Mπ ≈ 135, 225 and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume and light-quark masses for the connected contributions. Our final estimates, in the MS scheme at 2 GeV, of the isovector charges are g (51)(20). The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for g 194(14). Combining our new estimates with precision low-energy experiments, we present updated constraints on novel scalar and tensor interactions, S,T , at the TeV scale.