Axial, scalar, and tensor charges of the nucleon from 2+1+1-flavor Lattice QCD
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 𝛽-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 lattice-QCD calculations were done using nine ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quarks 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 𝑀 𝜋 ≈ 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 $\overline{MS}$ scheme at 2 GeV, of the isovector charges are 𝑔$^{𝑢−𝑑}_{𝐴}$ = 1.195(33)(20), 𝑔$^{𝑢−𝑑}_{𝑆}$ = 0.97(12)(6), and 𝑔$^{𝑢−𝑑}_{𝑇}$ = 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$^{𝑢−𝑑}_{𝑆}$ with the difference of light quarks masses (𝑚 𝑑 − 𝑚 𝑢 ) QCD = 2.67(35) MeV given by the Flavor Lattice Average Group, we obtain (𝑀 𝑁 − 𝑀 𝑃 ) QCD = 2.59(49) MeV.