Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ dynamical Wilson quarks

Abstract

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_{\pi }\approx 200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed non-perturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{MS}$ scheme at a scale of $\mu =2$GeV and are obtained from a combined chiral, continuum and finite-size extrapolation. For the nucleon isovector axial, scalar and tensor charges we find physical values of $g_A^{u-d}=1.242(25{)}_{\text{stat}}(\genfrac{}{}{0ex}{}{+00}{-31}{)}_{\text{sys}}$, $g_S^{u-d}=1.13(11{)}_{\text{stat}}(\genfrac{}{}{0ex}{}{+07}{-06}{)}_{\text{sys}}$ and $g_T^{u-d}=0.965(38{)}_{\text{stat}}(\genfrac{}{}{0ex}{}{+13}{-41}{)}_{\text{sys}}$, respectively, where individual systematic errors in each direction from the chiral, continuum and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $⟨x{⟩}_{u-d}=0.180(25{)}_{\text{stat}}(\genfrac{}{}{0ex}{}{+14}{-06}{)}_{\text{sys}}$, $⟨x{⟩}_{\Delta u-\Delta d}=0.221(25{)}_{\text{stat}}(\genfrac{}{}{0ex}{}{+10}{-00}{)}_{\text{sys}}$ and $⟨x{⟩}_{\delta u-\delta d}=0.212(32{)}_{\text{stat}}(\genfrac{}{}{0ex}{}{+20}{-10}{)}_{\text{sys}}$, respectively.

Comments: 35 pages, 13 figures; matching version accepted for publication in PRD