Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD

Abstract

We present results for the isovector axial, scalar and tensor charges $g_A^{u-d}$, $g_S^{u-d}$ and $g_T^{u-d}$ 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 $g_T^u$, $g_T^d$ and $g_T^s$ 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 $(m_d-m_u{)}^{\mathrm{QCD}}=2.67(35)$ MeV given by FLAG, we obtain $(M_N-M_P{)}^{\mathrm{QCD}}=2.59(49)$ MeV. Estimates of the connected part of the flavor-diagonal tensor charges of the proton are $g_T^u=0.792(42)$ and $g_T^d=-0.194(14)$. Combining our new estimates with precision low-energy experiments, we update constraints on novel scalar and tensor interactions, ${ϵ}_{S,T}$, at the TeV scale.

Comments: Published Version