Isovector Charges of the Nucleon from 2+1+1-flavor Lattice QCD

We present high statistics results for the isovector charges $g_A^{u-d}$, $g_S^{u-d}$ and $g_T^{u-d}$ of the nucleon. Calculations were carried out on eleven ensembles of gauge configurations generated by the MILC collaboration using highly improved staggered quarks (HISQ) action with 2+1+1 dynamical flavors. These ensembles span four lattice spacings $a\approx$ 0.06, 0.09, 0.12 and 0.15 fm and light-quark masses corresponding to $M_{\pi }\approx$ 135, 225 and 315 MeV. Excited-state contamination in the nucleon 3-point correlation functions is controlled by including up to three-states in the spectral decomposition. Remaining systematic uncertainties associated with lattice discretization, lattice volume and light-quark masses are controlled using a simultaneous fit in these three variables. Our final estimates of the isovector charges in the $\overline{\text{MS}}$ scheme at 2 GeV are $g_A^{u-d} = 1.218(25)(30)$,$g_S^{u-d} = 1.022(80)(60) $and$g_T^{u-d} = 0.989(32)(10)$. The first error includes statistical and all systematic uncertainties except that due to the extrapolation ansatz, which is given by the second error estimate. We provide a detailed comparison with the recent result of $g_A^{u-d} = 1.271(13)$ by the CalLat collaboration and argue that our error estimate is more realistic. Combining our estimate for $g_S^{u-d}$ with the difference of light quarks masses $(m_d-m_u{)}^{\mathrm{Q}\mathrm{C}\mathrm{D}}=2.572(66)$ MeV given by the MILC/Fermilab/TUMQCD collaboration for 2+1+1-flavor theory, we obtain $(M_N-M_P{)}^{\mathrm{Q}\mathrm{C}\mathrm{D}}=2.63(27)$ MeV. We update the low-energy constraints on novel scalar and tensor interactions, ${ϵ}_S$ and ${ϵ}_T$, at the TeV scale by combining our new estimates for $g_S^{u-d}$ and $g_T^{u-d}$ with precision low-energy nuclear experiments, and find them comparable to those from the ATLAS and the CMS experiments at the LHC.