Precision determination of nucleon iso-vector scalar and tensor charges at the physical point

Abstract

We report a high precision calculation of the isospin vector charge $g_{S,T}$ of the nucleon using recently proposed ``blending" method which provides a high-precision stochastic estimate of the all-to-all fermion propagator. Through multiplying the current operator by the traditional nucleon interpolator, we create a new operator that captures the major excited state contaminations. The linear combination of this new operator and traditional nucleon interpolator reduces these excited states and improves the robustness of the multi-state fit. Using 15 $N_f=2+1$ lattice ensembles which cover 5 lattice spacing, 5 combinations with the same quark masses and lattice spacing but multiple volumes, including three at the physical pion mass, we report so far most precise lattice QCD prediction $g_T^{\rm QCD} = 1.0264[77]_{\rm tot}(53)_{\rm stat} (13)_{a} (46)_{\rm FV} (01)_\chi (28)_{\rm ex} (04)_{\rm re}$ and $g_S^{\rm QCD} = 1.106[43]_{\rm tot}(31)_{\rm stat} (03)_{a} (28)_{\rm FV} (01)_\chi (08)_{\rm ex} (08)_{\rm re}$ at $\overline{\mathrm{MS}}$ 2~GeV, with the systematic uncertainties from continuum, infinite volume, chiral extrapolations, excited state contamination and also renormalization.