  We present results for the isovector axial, scalar and tensor charges
$g^{u-d}_A$, $g^{u-d}_S$ and $g^{u-d}_T$ of the nucleon needed to probe the
Standard Model and novel physics. The axial charge is a fundamental parameter
describing the weak interactions of nucleons. The scalar and tensor charges
probe novel interactions at the TeV scale in neutron and nuclear
$\beta$-decays, and the flavor-diagonal tensor charges $g^{u}_T$, $g^{d}_T$ and
$g^{s}_T$ are needed to quantify the contribution of the quark electric dipole
moment (EDM) to the neutron EDM. The 9 ensembles, generated by the MILC
Collaboration using the HISQ action with 2+1+1 dynamical flavors, 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 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 $\overline{\text{MS}}$
scheme at 2 GeV, of the isovector charges are $g_A^{u-d} = 1.195(33)(20)$,
$g_S^{u-d} = 0.97(12)(6) $ and $g_T^{u-d} = 0.987(51)(20)$. 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 $g_S^{u-d}$ with the difference of light quarks masses
$(m_d-m_u)^{\rm QCD}=2.67(35)$ MeV given by FLAG, we obtain $(M_N-M_P)^{\rm
QCD} = 2.59(49)$ MeV. Estimates of the connected part of the flavor-diagonal
tensor charges of the proton are $g^{u}_T=0.792(42)$ and $g^{d}_T=-0.194(14)$.
Combining our new estimates with precision low-energy experiments, we update
constraints on novel scalar and tensor interactions, $\epsilon_{S,T}$, at the
TeV scale.
