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 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 three-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 $\overline{\mathrm{MS}}$ 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 quark masses $(m_d-m_u{)}^{\mathrm{QCD}}=2.572(66)\mathrm{MeV}$ given by the MILC/Fermilab/TUMQCD collaboration for $2+1+1$-flavor theory, we obtain $(M_N-M_P{)}^{\mathrm{QCD}}=2.63(27)\mathrm{MeV}$. We update the low-energy constraints on novel scalar and tensor interactions, ${\epsilon }_S$ and ${\epsilon }_T$, 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.

• Received 27 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.034503

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Published by the American Physical Society