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

Abstract

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 $(m_d-m_u{)}^{\mathrm{QCD}}=2.572(66)$ MeV given by the MILC/Fermilab/TUMQCD collaboration for 2+1+1-flavor theory, we obtain $(M_N-M_P{)}^{\mathrm{QCD}}=2.63(27)$ 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.

Final published version with 35 pages and 17 figures. arXiv admin note: text overlap with arXiv:1606.07049

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