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

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 $g_A^{u-d}=1.242(25{)}_{\text{stat}}(\genfrac{}{}{0px}{}{+00}{-31}{)}_{\text{sys}}$, $g_S^{u-d}=1.13(11{)}_{\text{stat}}(\genfrac{}{}{0px}{}{+07}{-06}{)}_{\text{sys}}$ and $g_T^{u-d}=0.965(38{)}_{\text{stat}}(\genfrac{}{}{0px}{}{+13}{-41}{)}_{\text{sys}}$, 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 $\langle x\rangle_{u-d}=0.180(25)$\text{stat}$(\genfrac{}{}{0pt}{2}{+14}{-06})$\text{sys}$$,$\langle x\rangle_{\Delta u-\Delta d}=0.221(25)$\text{stat}$(\genfrac{}{}{0pt}{2}{+10}{-00})$\text{sys}$$and$\langle x\rangle_{\delta u-\delta d}=0.212(32)$\text{stat}$(\genfrac{}{}{0pt}{2}{+20}{-10})$\text{sys}$$, respectively.